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Adult Patient-specific Estimation of Active Bone Marrow Mass

Permanent Link: http://ufdc.ufl.edu/UFE0042490/00001

Material Information

Title: Adult Patient-specific Estimation of Active Bone Marrow Mass
Physical Description: 1 online resource (274 p.)
Language: english
Creator: Pichardo, Jose
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: adipocyte, bone, canine, cellularity, fat, histology, ideal, mri, separation, water
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Toxicity to the hematopoietically active bone marrow (BM) is generally dose-limiting for patients undergoing radionuclide therapy without a prior stem cell support. The goal of radionuclide therapy is thus to provide sufficient cell kill to the targeted tumor, while sparing normal tissues such as the bone marrow, lungs, and kidneys. The effectiveness of the therapy therefore depends on the accuracy of the BM dose estimate and the use of that estimate in clinical trials for developing predictive dose-response models of marrow toxicity. BM absorbed dose is estimated using the Medical Internal Radiation Dose (MIRD) schema, which requires in some cases explicit knowledge of the total mass of BM in a given patient, a parameter which cannot be readily measured. In response to this need, a regression model is developed that allows the prediction of BM mass in a given patient using only two skeletal pelvic length measurements that can be obtained from a pelvic CT or even radiograph image of the patient. However, the model is partially based on the use of standardized reference values bone marrow cellularity data from the radiation protection literature, data which is incomplete and does not provide adequate sex and age discrimination, nor the assessment of uncertainties. That cellularity changes with age and that there are differences in males and females has been well documented in the literature, and hence should be taken into account. The current gold standard for measuring marrow cellularity is BM biopsy of the iliac crest. This measure is unreliable, since cellularity is bone-site dependent and the volume sampled in a typical biopsy is very small. Magnetic resonance imaging (MRI) and localized MR spectroscopy have been demonstrated as noninvasive means for measuring BM cellularity in patients. The accuracy of these methods has been demonstrated in phantom studies and in the determination of in vivo hepatic fat fractions, but not for in vivo measurement of BM cellularity. The use of the Iterative Decomposition of water and fat with Echo Asymmetry and Least squares (IDEAL) with robust field map estimation is demonstrated on a clinical 3T scanner to measure in vivo cellularity on all bones known to contain active BM in dogs. The accuracy of the technique was validated in vivo by comparison with histology measurements taken from the same location in each bone. A Bland-Altman plot demonstrates excellent agreement between both methods with a mean difference of -0.52% cellularity and most differences falling within plus or minus2% cellularity. This technique can be used to assess patient-specific cellularity in the clinic which, when combined with the predictive equations developed in this study, results in a more accurate estimate of patient-specific BM mass, and consequently an improvement in the patient-specificity of the BM absorbed dose estimation. It is expected that the increase in patient-specificity in the calculation will result in a decrease in marrow toxicity complications that can result from the therapy.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jose Pichardo.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Bolch, Wesley E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2012-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042490:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042490/00001

Material Information

Title: Adult Patient-specific Estimation of Active Bone Marrow Mass
Physical Description: 1 online resource (274 p.)
Language: english
Creator: Pichardo, Jose
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: adipocyte, bone, canine, cellularity, fat, histology, ideal, mri, separation, water
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Toxicity to the hematopoietically active bone marrow (BM) is generally dose-limiting for patients undergoing radionuclide therapy without a prior stem cell support. The goal of radionuclide therapy is thus to provide sufficient cell kill to the targeted tumor, while sparing normal tissues such as the bone marrow, lungs, and kidneys. The effectiveness of the therapy therefore depends on the accuracy of the BM dose estimate and the use of that estimate in clinical trials for developing predictive dose-response models of marrow toxicity. BM absorbed dose is estimated using the Medical Internal Radiation Dose (MIRD) schema, which requires in some cases explicit knowledge of the total mass of BM in a given patient, a parameter which cannot be readily measured. In response to this need, a regression model is developed that allows the prediction of BM mass in a given patient using only two skeletal pelvic length measurements that can be obtained from a pelvic CT or even radiograph image of the patient. However, the model is partially based on the use of standardized reference values bone marrow cellularity data from the radiation protection literature, data which is incomplete and does not provide adequate sex and age discrimination, nor the assessment of uncertainties. That cellularity changes with age and that there are differences in males and females has been well documented in the literature, and hence should be taken into account. The current gold standard for measuring marrow cellularity is BM biopsy of the iliac crest. This measure is unreliable, since cellularity is bone-site dependent and the volume sampled in a typical biopsy is very small. Magnetic resonance imaging (MRI) and localized MR spectroscopy have been demonstrated as noninvasive means for measuring BM cellularity in patients. The accuracy of these methods has been demonstrated in phantom studies and in the determination of in vivo hepatic fat fractions, but not for in vivo measurement of BM cellularity. The use of the Iterative Decomposition of water and fat with Echo Asymmetry and Least squares (IDEAL) with robust field map estimation is demonstrated on a clinical 3T scanner to measure in vivo cellularity on all bones known to contain active BM in dogs. The accuracy of the technique was validated in vivo by comparison with histology measurements taken from the same location in each bone. A Bland-Altman plot demonstrates excellent agreement between both methods with a mean difference of -0.52% cellularity and most differences falling within plus or minus2% cellularity. This technique can be used to assess patient-specific cellularity in the clinic which, when combined with the predictive equations developed in this study, results in a more accurate estimate of patient-specific BM mass, and consequently an improvement in the patient-specificity of the BM absorbed dose estimation. It is expected that the increase in patient-specificity in the calculation will result in a decrease in marrow toxicity complications that can result from the therapy.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jose Pichardo.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Bolch, Wesley E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2012-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042490:00001


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1 ADULT PATIENT SPECIFIC ESTIMATION OF ACTIVE BONE MARROW MASS By JOSE CARLOS PICHARDO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Jose Carlos Pichardo

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3 To my wife Jennifer and daughters Olivia, Sofia, and Veronica for the sacrifices they have made and for being my source of energy and motivation during these five years.

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4 ACKNOWLEDGMENTS I wholeheartedly thank my major professor, Dr Wesley E. Bolch for his guidance and support over the five years that it has taken to complete my doctoral degree. His enthusiasm, mentoring, and guidance have made this body of work possible in spite of the multiple obstacles we have encountered along the way. I am also very grateful to my doctoral committee members : Drs. John R. Forder, David E. Hintenlang, Thomas H. Mareci, and Rowan J. Milner. I give special thanks to Dr. Alexander A. Trindade, for his invaluable support guiding my statistical analyses and to Dr. Diego Hernando, for his expert advice and providing me with the code to perform his fat water separation algorithm I am also grateful to m y colleagues and friends who have shared this journey with me : in particular, Dr. Jim Brindle, Matt Hough, Jorge Hurtado, Dr. Kayla Kie lar, Dr. Deanna Pafundi and Scott Whalen. Finally, I thank the University of Florida College of Veterinary Science for providing me with seed grant money and the National Institute of Health, in particular, the National Cancer Institute, for providing me funding under NRSA Fellowship # 1F31CA13420001 and for funding the study presented in Chapter 2 of this dissertation (gr ants RO1 CA96441 and F31 CA97522).

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 7 LIST OF FIGURES .......................................................................................................... 8 LIST OF ABBREVIATIONS ........................................................................................... 11 ABSTRACT ................................................................................................................... 13 CHAPTER 1 INTRODUCTION .................................................................................................... 15 Radionuclide Therapy Dose Calculation ................................................................. 15 Estimation of Patient Specific TAM ......................................................................... 17 2 METHOD FOR ESTIMATING SKELETAL SPONGIOSA VOLUME AND ACTIVE MARROW MASS I N THE ADULT MALE AND ADULT FEMAL E ............. 28 Materials and Methods ............................................................................................ 32 Cadaver Selection ............................................................................................ 32 Image Acquisit ion ............................................................................................. 32 Spongiosa Volume Estimation .......................................................................... 33 Anatomical Measurements ............................................................................... 35 Statistical Analysis ............................................................................................ 36 Results .................................................................................................................... 40 Discussion .............................................................................................................. 41 3 MR FAT FRACTION QUANTIFICATION METHODS ............................................. 67 Background ............................................................................................................. 68 Basic MR Physics ............................................................................................. 68 Gradient Echo (SPGR) Imaging ....................................................................... 71 Spin Echo (SE) Imaging ................................................................................... 75 Chemical S hift .................................................................................................. 77 General MR Signal Model ................................................................................ 78 MR Fat Fraction Quantification Methods ................................................................. 80 Fat/Water Suppression ..................................................................................... 80 1H NMR Spe ctroscopy ..................................................................................... 84 Chemical Shift Misregistration .......................................................................... 87 Water Fat Separation Methods ........................................................................ 91 Dixon method based on magnitude images ............................................... 95 Dixon methods based on complex images ............................................... 102

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6 Direct Phase Encoding (DPE) .................................................................. 112 Iterative Decomposition of water and fat with Echo Asymmetry and Least squares (IDEAL) ......................................................................... 114 In Vitro Accuracy and Noise Performance ............................................................ 131 Phantoms Used For In Vitro Accuracy Studies ............................................... 132 In Vitro Accuracy Studies ............................................................................... 134 Noise Performance ......................................................................................... 146 In Vivo Accuracy ................................................................................................... 151 In Vivo Accuracy of MRS ................................................................................ 152 In Vivo Accuracy of Dixon Methods ................................................................ 153 In Vivo Accuracy of IDEAL ............................................................................. 156 4 MRI ESTIMATION OF BONE MARROW CELLULARITY ..................................... 178 Materials and Methods .......................................................................................... 180 Animal Car e and Procedures ......................................................................... 180 MR Imaging .................................................................................................... 181 MR Spectroscopy ........................................................................................... 184 Dog Euthanasia and Necropsy ....................................................................... 187 Digital Image Processing ................................................................................ 188 Histology Slide Preparation ............................................................................ 188 Histology Sampling ......................................................................................... 190 Automated Adipocyte Segmentation .............................................................. 191 Results .................................................................................................................. 194 Automated Adipocyte Segmentation .............................................................. 194 MR Spectroscopy ........................................................................................... 194 IDEAL Fat Water Separation .......................................................................... 196 Agre ement Between IDEAL and Histology ..................................................... 199 Discussion ............................................................................................................ 199 Histology ......................................................................................................... 199 Spectral Analysis ............................................................................................ 201 Agreement Betw een IDEAL and Histology ..................................................... 202 5 CONCLUSIONS AND FUTURE NEEDS .............................................................. 250 Conclusions .......................................................................................................... 250 Future Needs ........................................................................................................ 253 LIST OF REFERENCES ............................................................................................. 257 BIOGRAPHICAL SKETCH .......................................................................................... 273

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7 LIST OF TABLES Table page 1 1 Anthropometric measurements used to pr oduce predictive TSSV equations ..... 24 1 2 Summary of skeletal data provided in tables 15 and 41 of ICRP Pub 70 .......... 25 1 3 Summary of adult male and female marrow volume f raction data from three studies ................................................................................................................ 26 1 4 Percent distri bution of TSSV by skeletal site ...................................................... 27 2 1 Percent distribution of active bone marrow, BVF and CF within the adult skeleton (4150 years) as given in ICRP Publication 70 ..................................... 50 2 2 Anthropometric measurements for use in the multipl e regression analysis ........ 51 2 3 Comparison of our skeletal measurements to published data. ........................... 52 2 4 Pooled, male, female, and sex specific models chosen by t he different selection criteria .................................................................................................. 53 2 5 Parameters for the recommended TSSV predictive models ............................. 54 2 6 Cadaver data us ed in the regression analysis. ................................................... 55 2 7 Percentage of cadavers for which each mode l was best at predicting TSSV. .... 57 2 8 Percentage of cadaver TSSV predictions that had absolute errors less than or equal to 5%, 10%, 15%, and 20% .................................................................. 57 2 9 Percent regional distribution of trabecular spongiosa by skeletal site ................. 58 2 10 Percent regional distribution of active bone marrow mass by skeletal site ......... 59 4 1 Spectral shifts used in this study .................................................................... 211 4 2 Normalized lipid spectral amplitudes in the canine humerus. ........................... 211 4 3 Normalized lipid spectral amplitudes in the canine femur ................................. 212 4 4 Normalized lipid spectral amplit udes in the canine upper spine ....................... 212 4 5 Normalized lipid spectral amplitudes in the canine lower spine. ....................... 213 4 6 Bone marrow CF data ...................................................................................... 214

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8 LIST OF FIGURES Figure page 2 1 Screen capture of ct con tours ............................................................................. 60 2 2 Graphical representati on of the pelvic measurements ........................................ 61 2 3 Graphical representation of the femoral measurements ..................................... 62 2 4 Cadaver height measurement ............................................................................ 63 2 5 Volume Viewer GUI screenshot .......................................................................... 64 2 6 Volu me Viewer pelvic measurements ................................................................. 65 2 7 Percent error histograms for each of the final models selected in this study. ..... 66 3 1 Distribution of proton magneti c moments ......................................................... 162 3 2 RF pulse and precession of the magnetization vector ...................................... 162 3 3 The decay of the transverse c omponent of the magnetization ......................... 163 3 4 Fanning out (dephasing) of the magnetization vector ....................................... 163 3 5 SPGR pulse sequence diagram ....................................................................... 164 3 6 The f requency e ncoding g radient ..................................................................... 164 3 7 T2* versus T2decay of the FID. ....................................................................... 165 3 8 SE pulse sequence diagram ............................................................................. 165 3 9 Rephasing of m agnetization in a SE sequence ................................................ 166 3 10 Incomplete fat suppression wit h a spectral saturation pulse ............................. 167 3 11 1H NMR spectrum of soybean oil at 3.0 T ......................................................... 167 3 12 Effect of trabeculae in the local magnetic field in bone marrow. ....................... 168 3 13 The NMR spectrum .......................................................................................... 169 3 14 Origin of chemical shift misregi stration light and dark bands. ........................... 170 3 15 Periodic oscillations in the MR signal from ti ssue containing fat and water. ..... 171 3 16 Ambiguity of the twopoint Dixon method usi ng magnitude images .................. 172

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9 3 17 Ob lique slice oil water phantom ........................................................................ 172 3 18 T2* correction of SPGR 2PD ............................................................................ 173 3 19 Phase unwrapping process .............................................................................. 173 3 20 Multiple local minima in the residual at 3.0 T. ................................................... 174 3 21 Square spiral traject ory used in 3P IDEAL with RGA ....................................... 175 3 22 Regiongrowing process with multires olution images ...................................... 176 3 23 The graph and the graph cut ............................................................................ 176 3 24 Wedge compartment phantom ......................................................................... 177 4 1 Vertebral body identification in the upper spine of a dog. ................................. 215 4 2 Vertebral body identification in the lower spine of a dog ................................... 216 4 3 Spectral fitting in the humeral head .................................................................. 217 4 4 Spectral fi tting in thoracic vertebra T2 .............................................................. 218 4 5 Necropsy photo of humerus ............................................................................. 219 4 6 Photograph of femur cut in half along its length................................................ 220 4 7 Diagram of femur for one of the dogs. .............................................................. 221 4 8 Diagram of humerus for one of the dogs .......................................................... 222 4 9 Bone marrow section with severe tearing and shredding ................................. 223 4 10 Bone marrow section with minimal tearing and shredding ................................ 224 4 11 Close up of marrow cavity showing separation between tr abecular bone and soft marrow ....................................................................................................... 225 4 12 Samplin g of digital histology slides ................................................................... 226 4 13 ROI selection in histology slides ....................................................................... 227 4 14 Semiautomated adipocyte segmentation ........................................................ 228 4 15 Determination of optimum samplesize for each histology slide ....................... 229 4 16 Linear regression plot of %CF determined from automated segmentation versus manual segmentation ............................................................................ 230

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10 4 17 Bland Altman plot comparing automated versus manual adipocyte segmentation .................................................................................................... 231 4 18 Composite plot of spectra acquired from the humerus of each dog .................. 232 4 19 Composite plot of spectra acquir ed from the femur of each dog. ..................... 233 4 20 Composite plot of spectra acquired from the upper spine of each dog ............. 234 4 21 Composite plot of spectra acquired from the lower spine of each dog ............. 235 4 22 SPIDEAL water fat separation in the femur of a dog ....................................... 236 4 23 SPIDEAL water fat separ ation in the humerus of a dog. ................................. 237 4 24 SPIDEAL water fat separat ion in the upper spine of a dog ............................. 238 4 25 SPIDEAL water fat separation in the lower spine of a dog .............................. 239 4 26 Comparison of fat distribution visually observed in the femur with fat distributio n in the calculated fat image .............................................................. 240 4 27 Comparison of fat distribution visually observed in the humerus with fat distributio n in the calculated fat image .............................................................. 241 4 28 MP IDEAL with pre calibration fat water separation in the femur of a dog. ...... 242 4 29 Side by side comparison of the fat images obtained with SP ID EAL and MP IDEAL in the femur ........................................................................................... 243 4 30 Linear regression line for CF measured by SP IDEAL versus CF measured by histology at the same loc ation on the bone in two dogs ............................... 244 4 31 Bland Altman plot of CF determined by SP IDEAL versus histology at the same loc ation on the bone in two dogs ............................................................ 245 4 32 Linear regression line for CF measured by MP IDEAL versus CF measured by histology at the same loc ation on the bone in two dogs ............................... 246 4 33 Bland Altman plot of CF determined by MP IDEAL versus histology at the same loc ation on the bone in two dogs. ........................................................... 247 4 34 Histological aspect of the femoral head and humeral head in a dog. ............... 248 4 35 Modeling of spongiosa in radiation dosi metry Monte Carlo simulations ........... 249

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11 LIST OF ABBREVIATIONS 2PD Two Point (or dual echo) Dixon Method 3PD ThreePoint Dixon Method AMARES Advanced Method for Accurate, Robust, and Efficient Spectral fitting AVF Adipocyte V olume Fraction BM Bone M arrow BW Spectral Band Width CF C ellularity Factor or B one M arrow Cellularity CRLB Cramr Rao Lower Bound CSISM Chemical Shift Imaging with Spectrum Modeling CV Coefficient of Variation DPE Direct Phase Encoding FID FreeInduction Decay FSE Fast Spin Echo GRASE Gradient Recalled echo And Spin Echo GRASS Gradient Refocused Acquisition in the Steady State IDEAL Iterative D ecomposition of water and fat with E cho A symmetry and L east squares IP In Phase LLS Linear Least Squares MP IDEAL Multi Peak IDEAL MVF Marrow V olume F raction NEX Number of EXcitations (a.k.a. number of averages) NLLS Non Linear Least Squares

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12 MIRD Medical Internal Radiation Dose NMR Nuclear Magnetic Resonance MRI Magnetic Resonance Imaging OP OpposedPhase PRESS Point R E solved SpectroS copy RF RadioFrequency Pulse SNR Signalto Noise Ratio SPGR SPoiled Gradient Recalled echo (a.k.a. gradient echo) SPIDEAL Single Peak IDEAL SSFP Steady State Free Precession STEAM STimulated Echo Acquisition Mode STIR Short Tau Inversion Recovery SV Spongiosa V olume TAM Trabecular A ctive M arrow TBVF Trabecular Bone Volume Fraction TE Echo Time TMS Tetramethylsilane: (CH3)4Si. TR Repetition Time TSSV Total S keletal S pongiosa V olume VARPRO VARiable PROjection WFR Water to Fat Ratio

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13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ADULT PATIENT SPECIFIC ESTIMATION OF ACTIVE BONE MARROW MASS By Jose Carlos Pichardo December 2010 Chair: Wesley E. Bolch Major: Nuclear Engineering Sciences Toxicity to the hematopoietically active bone marrow (BM) is generally doselimiting for patients undergoing radionuclide therapy without a prior stem cell support. The goal of radionuclide therapy is thus to provide sufficient cell kill to the targeted tumor, while sparing normal tissues such as the bone marrow, lungs, and kidneys. The effectiveness of the therapy therefore depends on the accuracy of the BM dose estimate and the use of that estimate in clinical trials for developing predictive doseresponse models of marrow toxicity. BM absorbed dose is estimated using the Medical Internal Radiation Dose ( MIRD ) schema, which requires in some cases explicit know ledge of the total mass of BM in a given patient, a parameter which cannot be readily measured. In response to this need, a regression model is developed that allows the prediction of BM mass in a given patient using only two skeletal pelvic length measurements that can be obtained from a pelvic CT or even radiograph image of the patient However, the model is partially based on the use of standardized reference values bone marrow cellularity data from the radiation protection literature, data which is inco mplete and does not provide adequate sex and age discrimination, nor the

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14 assessment of uncertainties. That cellularity changes with age and that there are differences in males and females has been well documented in the literature, and hence should be taken into account. The current gold standard for measuring marrow cellularity is BM biopsy of the iliac crest. This measure is unreliable, since cellularity is bonesite dependent and the volume sampled in a typical biopsy is very small. Magnetic resonance im aging ( MRI ) and localized MR spectroscopy have been demonstrated as noninvasive means for measuring BM cellularity in patients. The accuracy of these methods has been demonstrated in phantom studies and in the determination of in vivo hepatic fat fractions, but not for in vivo measurement of BM cellularity T he use of the Iterative Decomposition of water and fat with Echo Asymmetry and Least squares ( IDEAL ) with robust field map estimation is demonstrated on a clinical 3T scanner to measure in vivo cellularity on all bones known to contain active BM in dogs The accuracy of the technique was validated in vivo by comparison with histology measurements taken from the same location in each bone. A Bland Altman plot demonstrates excellent agreement betw een both methods with a mean difference of 0.52% cellularity and most differences falling within 2% cellularity. This technique can be used to assess patient specific cellularity in the clinic which, when combined with the predictive equations developed in this study, results in a more accurate es timate of patient specific BM mass, and consequently an improvement in the patient specific ity of the BM absorbed dose estimation. It is expected that the increase in patient specificity in the calculation will result in a decrease in marrow toxicity complications that can result from the therapy.

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15 CHAPTER 1 INTRODUCTION Radionuclide Therapy Dose Calculation A primary goal in molecular radiotherapy is to optimize various treatment parameters radionuclide, carrier molecule (peptide, antibody, pharmaceutical), administered activity, use of pretherapy drugs (cold antibody, amino acids, etc.) in o rder to maximize tumor cell kill while minimizing toxicity in nontargeted tissues. The therapeutic radiation dose is generally limited by the tolerance of the most radiosensitive tissue in the body, the bone marrow. Not surprisingly, t he dose limiting t oxicity most frequently encountered in molecular radiotherapy is myelosuppression for protocols that do not provide a prior for stem cell support ( 1 2 ) Myelosuppression refers to the condition by which bone marrow activity is severely decreased. Bone m arrow refers to the soft tissue found inside all bones. B ones consist of an outer shell of solid compact bone called cortical bone enclosing a volume filled with both bone and soft tissue called cancellous bone or spongiosa. In spongiosa, bone marrow fills the cavities the marrow cavities formed by a framework of tiny, cylindrical or flat bone plate s called trabeculae. Bone marrow cells can be separated into two types: adipocytes (fat cells) and all other marrow cells which are collectively called trabecular active (or red) marrow ( TAM ) cells TAM includes stem cells the hematopoietic cells responsible for the production of all blood cells including cells of the immune system, and also cells responsible for bone growth and repair Adipocytes are fat cel ls, smaller in size to those found in adipose tissue ( 3 ) which most likely represent a source of energy to TAM cells, since it has been observed that they decrease in size and number during periods of increased hematopoiesis ( 3 4 ) The relative proportion of active

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16 marrow and adipocytes vary primarily with bone site and age, with adipocyte concentrations increasing as we age and being larger in the shafts of long bones ( 3 5 ) Radiationinduced bone marrow toxicity occurs as a result to damage to TAM, and hence, accurate and patient specific assessments of the radiation absorbed dose to the TAM in patients under clinical trials are thus essential to the establishment of doseresponse relationships needed for prediction of these effects in future cancer patients ( 6 7 ) TAM absorbed dose is estimated using the Medical Internal Radiation Dose ( MIRD ) schema ( 8 ) using the expression D ( TAM ) = A S( TAM S ) (1 1) where ( ) is the average dose to T AM due to radiation of quality R in units of MeV/g, is the cumulated activity over 50 years, and ( ) is the S value (or S factor) for a source organ S to T AM in units of MeV/g per disintegration. The S value is defi ned by the expression ( ) = ,( ) (1 2) where is the mean energy of radiation of type R in MeV released per decay, ( ) is the absorbed fraction of the incident energy of type R from source S in T AM, and is the mass of T AM in grams. S values for different radionuclides and selected organs are tabulated in MIRD Pamphlet 11 ( 8 ) These values are derived from Monte Carlo simulations on anatomical computational phantoms known as

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17 reference phantoms that are defined with specific organ and tissue masses --reference masses --( 9 10) For radiopharmaceuticals that do not bind to marrow cells, it is possible to calculate the T A M dose in a patient without the need to determine the total T A M mass in the patient ( 11) However, for radiopharmaceuticals that bind to marrow cells, the S values based on the reference TA M mass must be scaled by the TA M mas s of the patient ( 12, 13) as ( )patient ( )reference( )reference( )patient (1 3) The dose calculated with this scaling rests on the assumption that the absorbed fractions ( ) ( Equation 1 2) do not have to be adjusted, which is will only be true if the patient is similar in size and composition to the reference phantom. Estimation of P atient S pecific TAM The main problem with the MIRD formulation is that it requires knowledge of the total TAM mass in a patient, a parameter which cannot be readily measured. Several approaches have been proposed to resolve this problem. Cristy ( 14) used the total bone marrow masses measured from 13 cadavers published by Mechani k in 1926 (later summarized by Woodward and Holodny in 1960 ( 15) ) to derive an expression that allows the calculation of TA M mass in different body parts (head and neck, chest, abdomen, pelvis, thighs, and lower legs) as a function of age. The masses were calculated from total body marrow mass by multiplication with the relative volumes of the body regions compared to total body volume and CF data. The predicted TA M masses were compared with those predicted by two 59Fe studies

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18 and show errors ranging from 3.4% to 33.4%. The predictive equation was later used in ICRP Publication 70 to calculate TA M mass reference values ( 16) A major drawback to Cristys predictive equation is that it is based on the total marrow masses of the cadavers used by Mechani k in 1926. These cadavers were victims of prolonged wasting illnesses which rendered them relatively emaciated and which might have led to changes in bone composition ( 15) Hence, the TA M masses may not be representative of patients undergoing radionuclide therapy. In addition, the process by which Mechani k measures marrow mass is not clearly explained in his original paper ( 15) More importantly, BM cellularity values used in the predictive equation are, as the authors state, very rough estimates in urgent need of improvement ( 14) Bolch et al. ( 13) tested the use of different anthropometric parameters that would scale S values in the same proportion as TAM masses. T wo skeletal site s were considered the right femoral head and the right proximal humeral epiphysis in three cadavers a 51year old male and two females of ages 82 and 86 and for nine radionuclides. Even though no single parameter was found to be consistently accurate at scaling reference S values, two were found to provide adequate scaling: lean body mass with errors ranging 127% and total skeletal spongiosa volume (TSSV) with less than 6% error S pongiosa refers to the combined tissues of the bone trabeculae and marrow (active and inactive) within cancellous bone, exclusive of cortical bone at the cortex TSSV is unknown in a patient, and there is currently no clinically feasible method for estimating this quantity. To resolve this problem, Brindle et al. ( 17, 18) used skeletal

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19 data from twenty cadavers (10 male, 10 female) to develop a multiple linear regression equation that allows the prediction of TSSV in a patient from simple pelvic measurements the os coxae width (OC.W) and os coxae height (OC.H). The predictive equation is ( cm) = 5585 5 46 3 OC. W ( cm ) + 420 6 OC. H ( cm ) (1 4) TSSV was determined from manual segmentation of spongiosa in full body CT images of the cadavers Fifteen variables were considered to develop the models: fourteen skeletal dimensions (Table 11) and age. Equation 1 4 was found to provide TS SV predictions with errors that ranged from 0.2 to 21.2% ( 18) A major limitation of Equation 1 4 is that it is not sex specific. Many skeletal dimensions are different in males and females T hese differences are used by forensic scientists to determine the sex of a victim from remains ( 19, 20) Males are usually larger than females in both height and weight ( 19, 21, 22) As a consequence of the difference in load experienced by weight bearing bones, femur length and femoral head diameter are greater in men than in women ( 21, 2325) Vertebral width is found to be gr eater in males than in females ( 22) S everal pelvic dimensions are larger in females than males partially due to the fact that females give birth ( 23) One can therefore assume that a sex specific predictive equation will be more acc urate at predicting TSSV in patients than a pooled model such as Equation 1 4. Brindle et al. ( 18) were unable to develop a sex specific model due to their small sample size. Conceptually, the value of the TAM mass in a patient may be calculated using the following expression:

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20 ( )= = (1 5) where is the volume of trabecular spongiosa, is the marrow volume fraction, and is the marrow cellularity factor, all assessed at skeletal site x, with being the mass density of active bone marrow 1.03 g/cm3 as given in ICRU Report 46 ( 26) The marrow volume fraction (MVF) is that fraction of spongiosa volume occupied by marrow tissues (i.e., not occupied by the bone trabeculae). Marrow cellularity or cellularity factor (CF) is the fraction b y volume of marrow tissue that is hematopoietically active, and for marrow tissues with normal extracellular fluid volumes, it may be considered approximately equal to the volume fraction of soft marrow tissue that is not ocuppied by adipocytes ( i.e. 1 f at fraction). Consequently, this working definition includes the presence of interstitial fluid and blood vessels ( 27) as microCT based models of skeletal dosimetry are structured at the tissue and not cellular level ( 28, 29) The skeletal regions to consider in the adult for Equation 1 5 (variable x) would be those of the axial skeleton as well as the proximal epiphyses of the humeri and femora ( 16) To apply Equation 1 5 for a given patient, one must assess, bone by bone, values of SV, MVF, and CF obviously an impractical, and in the case of MVF, virtually impossible task. MVF cannot be determined from CT images of a patient because the resolution is not fine enough to show bone marrow cavities. MicroCT imaging provides the necessary resolution, but it requires the extraction of bone cubes from the patient; clearly not an option. Until a nondestructive method for determining MVF in a patient is

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21 developed, MVF will h ave to be estimated using published data acquired for purposes of radiological protection. ICRP Publication 70 provides values of bone volume fraction (BVF = 1 MVF) and CF in Tables 15 (p. 27) and 41 (p. 68), respectively ( 16) These values are summarized in Table 12 The table of MVF values provided by ICRP Publication 70 suff ers from several limitations: (1) it is incomplete, (2) it does not provide any measure of uncertainty, and (3) it is pooled for males and females. MVF is both ageand sex dependent owing to natural processes of mineral bone loss with age, and the fact t hat osteopenia and osteoporosis are typically accelerated in older females. More thorough and accurate measurements of MVF in adult male and females are provided in studies by Shah ( 30) Kielar ( 31) and Hough ( 32) The MVF data from these studies are summarized in Table 13. The ICRP Publication CF values provided in Table 12 are very limited since in addition to being pooled for both genders, they are only provided for age 40. Several studies have demonstrated that there are gender and age differences in adult CF ( 3339) For exposures from external photons, it is common practice to ignore CF in the calculation of BM dose; i.e. BM is considered as a homogeneous mixture of hematopoietically active and inactive tissues. However, a recent study by Caracappa et al. ( 40) shows that BM doses calculated assuming a homogeneous mixture differ by as much as 40% compared to doses calculated when CF is explicitly considered. In regards to internal exposures, Watchman et al. ( 41) h as shown that differences in CF result in large differences in the absorbed fraction of energy to target tissues from

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22 internal alpha emitters, and hence calculation of BM dose requires knowledge of the patients own CF ideally within each bone site of the skeleton. A similar conclusion was reached by Bolch et al. ( 42) for low to intermediate energy beta emitters for marrow self irradiation. The current gold standard for measuring marrow CF is a painful and highly invasive BM biopsy of the iliac crest. This measure is unreliable, since the volume sampled in a typical biopsy is very small and CF in the iliac crest is unlikely to be representative of CF in other bone sites A large number of studies have used proton magnetic resonance imaging (MRI) techniques ( 33, 34, 4352) and localized MR spectroscopy (MRS) ( 3537, 5359) to measure CF noninvasively in humans and hence these noninvasive techniques provide a possible avenue for measuring CF in a patient Even though the accuracy of these methods has been well established in phantom studies ( 46, 60, 61) in vivo accuracy has not been clearly demonstrated. In addition, most studies have focused their efforts on a limited number of bone sites, mainly the lumbar vertebrae and iliac bone. As shown in the 2nd formulation of Equation 1 5 values of in a skeletal site x can alternatively be represented as the product of the total skeletal spongiosa volume (TSSV) and its fractional distribution by skeletal site x ( ). As i ndicated previously, neither of these quantities is known for a patient. However, patient specific TSSV can be estimated using Equation 1 4, and Brindle et al. ( 18) provide a table of that can be used in lieu of patient specific values (Table 14 ) Unfortunately, both the lack of sex and agespecificity, and uncertainty about the accuracy of the tabulated values greatly limits the accuracy of Equation 1 5

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23 The work presented in this dissertation addresses several very important shortcomings in the prediction of patient specific TAM with Equation 1 5 In Chapter 2 the lack of sex specificity of the TSSV predictive equation and data in Brindle et al. ( 18) is addressed by the development of a sex specific model for the prediction of TSSV and the generation of a table of sex specific data. In Chapter 3 the feasibility of the use of a magnetic resonance imaging technique called Iterative Decomposition of water and fat with Echo Asymmetry and Least squares (IDEAL) to measure CF in a patient at all bone sites known to contain TAM is demonstrated and the in vivo accuracy in bone marrow of this technique is evaluated. The data and methods described in these chapters represent major steps toward patient specific dosimetry in molecular radiotherapy which will hopefully result in a reduction in bone marrow toxicity, a major limitation to its therapeutic success.

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24 Table 1 1. Anthropometric measurements used to produce predictive TSSV equations. Parameter Abbreviation Description Height HT Total body height. Os coxae width OC.W Maximum width of the os coxae viewed in CT scout image (projection). Os coxae height OC.H Average of the maximum height of the left and right side of the os coxae viewed in the CT scout image (projection). Os coxae length OC.L Average of the maximum length of the left and right side of the os coxae when viewed in the transverse plane of the 3 D CT data set. Bitrochantric breadth Bi.B Distance between the exterior portions of the greater trochanters viewed in the CT scout image. (projection) Anterior sacral height ASH Distance between the anterior sacral promontory to the apex of the sacrum vi ewed in the sagittal plane of the three dimensional (3 D) data set. Sacral width S.W Maximum width of the sacrum viewed in the transverse plane of the 3 D CT data set. L5 thickness L5.T Thickness of the fifth lumbar (L5) vertebrae when viewed in the sagittal plane of the 3 D CT data set. The measurements were made parallel to the anterior surface of the vertebral body and approximately 1.5 cm into the vertebral body. S1 sacral breadth S1.B Distance between the two most lateral points on the superi or surface of S1 when viewed in the transverse plane of the 3 D CT data set. Femoral head perimeter P Average of the maximum perimeter of the left and right femoral heads when viewed in the sagittal plane of the 3 D CT data set. Ferets diameter FD Measurement is based on the femoral head perimeter. This measurement is referred to as the caliper length as it represents the longest distance between any two points along a selected boundary and in this instance the perimeter measurement served as this boundary. Maximum height of femoral head Max.H Maximum height of the femoral head when viewed in the sagittal plane of the 3 D CT data set. Each measurement represented an average of the left and right femoral heads. Maximum width of femoral head Max.W Maximum width of the femoral head when viewed in the sagittal plane of the 3 D CT data set. Each measurement represented an average of the left and right femoral heads. Humeral head breadth HH Distance between the exterior portion of the right and left proximal humeral heads viewed in CT scout image (projection). Femur height FH Maximum height of the femur bones when viewed in the CT scout image. Each measurement represented an average height of the left and right femur bones (projection). Adapted f rom Brindle et al. ( 18 )

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25 Table 12 Summary of skeletal data provided in tables 15 and 41 of ICRP Publication 70 ( 16) Marrow volume fraction (MVF) was calculated fr om the tabulated bone volume fraction (BVF) data as 1 BVF. CF is the cellularity factor. MVF CF 21 30y 31 40y 41 50y 51 60y 71 80y 40y Cranium Parietal Bone 0.446 0.38 Clavicle 0.38 Sternum 0.70 Ribs 0.896 0.70 Vertebrae 0.844 0.847 0.881 0.886 0.915 0.70 Os Coxae: Ilium 0.796 0.800 0.801 0.814 0.923 0.48 Humerus, proximal 0.25 Femur, proximal Neck Head 0.700 0.852 0.25

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26 Table 13. Summary of adult male and female marrow volume fraction data from three studies. Female (1) Male (2) Male (3) 64y 64y 4 0 y Cranium Frontal 0.398 0.596 0.555 Occipital 0.107 0.541 0.088 Parietal 0.412 0.643 0.606 Mandible 0.889 0.835 0.911 Scapula 0.775 0.848 0.847 Clavicle 0.960 0.804 0.884 Sternum 0.988 0.909 0.918 Ribs Upper 0.943 0.896 0.897 Middle 0.944 0.935 0.858 Lower 0.830 0.928 0.899 Cervical Vertebra C3 0.755 0.894 0.841 C6 0.811 0.859 0.806 Thoracic Vertebra T3 0.871 0.900 0.868 T6 0.917 0.924 0.959 T11 0.915 0.762 0.889 Lumbar Vertebra L2 0.900 0.920 0.887 L4 0.916 0.771 0.909 Sacrum 0.965 0.876 0.882 Os Coxae Ilium 0.884 0.887 0.901 Ischium 0.919 0.923 Pubis 0.820 0.884 Humerus, proximal 0.951 0.837 0.904 Femur, proximal Head 0.713 0.677 0.771 Neck 0.868 0.890 0.897 (1) Kielar 2009 ( 31 ) (2) Shah 2004 ( 30 ) ; ( 3 ) Hough 2009 ( 32 )

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27 Table 14 Percent distribution of TSSV by skeletal site. Skeletal Site ( mean SD in % ) Cranium 9.3 ( 1.55) Mandible 1.0 ( 0.15) Scapulae 3.9 ( 0.38) Clavicles 1.5 ( 0.14) Sternum 2.1 ( 0.25) Ribs 9.3 ( 0.77) Cervical Vertebrae 2.5 ( 0.15) Thoracic Vertebrae 11.9 ( 0.52) Lumbar Vertebrae 10.1 ( 0.64) Sacrum 7.5 ( 0.53) Os coxae 22.5 ( 1.04) Femora (proximal) 12.8 ( 0.50) Humeri (proximal) 5.5 ( 0.24) Data f rom Brindle et al. ( 18 )

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28 CHAPTER 2 METHOD FOR ESTIMATING SKELETAL SPONGIOSA VOLUME AND ACTIVE MARROW MASS IN THE ADULT MALE AND ADULT FEMALE A primary goal in molecular radiotherapy is to optimize various treatment parameters radionuclide, carrier molecule (peptide, antibody, pharmaceutic al), administered activity, use of pretherapy drugs (cold antibody, amino acids, etc.) in order to maximize tumor cell kill while minimizing toxicity in nontargeted tissues. The doselimiting toxicity most frequently encountered in molecular radiother apy is myelosuppression for protocols that do not provide a prior for stem cell support ( 1 ) Accurate and patient specific assessments of the radiation absorbed dose to the hematopoietically active (or red) marrow ( T AM) in patients under clinical trials are thus essential to the establishment of doseresponse relationships needed for prediction of these effects in future cancer patients ( 6 7 ) For radiopharmaceuticals that bind to marrow tissues or to mineral bone, explicit knowledge of the patients total and, in some cases, regional active marrow mass is required for proper scaling of radionuclide S values ( 12) which are in turn assessed in a reference computational phantom or skeletal model ( 9 10 ) Under the assumption that no adjustments are required of the radiation absorbed fraction fraction of emitted particle energy that is absorbed in the target tissue patient specific S values to T AM from radiopharmaceuticals localized in skeletal source tissue rS m ay be estimated as: ( )patient ( )reference( )reference( )patient ( 2 1) where mT AM is the total active marrow mass in either the reference phantom or the patient. While values of mT AM may be taken from the radiation protection literature for reference patients, it remains a significant challenge to measure or even estimate

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29 values of mT AM in a live patient of vastly different or even similar body morphometry. Values of mT AM for a refer ence 35year male and female are given in ICRP Publications 70 and 89 as 1170 g and 900 g, respectively ( 16, 62) Conceptually, the value of ( mT AM)patient may be calculated using the following expression: ( )= = SV f MVFCF (2 2 ) where SVx is the volume of trabecular spongiosa, MVFx is the marrow volume fraction, and CFx is the marrow cellularity factor, all assessed at skeletal site x, with T AM being the mass density of active bone marrow [1.03 g cm3 as given in ICRU Report 46 ( 26) ]. Spongiosa refers to the combined tissues of the bone trabeculae and marrow (active and inactive) within cancellous bone, and is therefore exclusive of cortical bone at the cortex at each skeletal site. The marrow volume fraction (MVF) is that fraction of spongiosa volume occupied by marrow tissues (i.e., not occupied by the bone trabeculae). Marrow CF is then the fraction of marrow tissue volume that is hematopoietically active, and for marrow tissues with normal extracellular fluid volumes, it may be considered approximately equal to (1 fat fraction). The skeletal regions to consider in the adult for Equation 2 2 (variable x) would be those of the axial skeleton as well as the proximal epiphyses of the humeri and femora ( 16) As shown in the second formulation of Equation 2 2 values of SVx in a skeletal site x can alternatively be repres ented as the product of the total skeletal spongiosa volume (TSSV) and its fractional distribution by skeletal site x ( ). Neither of these variables are defined in reference patients used in nuclear medicine dosimetry ( 16, 62)

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30 To apply Equation 2 2 for a given patient, one must assess, bone by bone, values of SV, MVF, and CF obviously an impr actical, and in the case of MVF, virtually impossible task. Magnetic resonance techniques do exist, however, to noninvasively measure CF, but these techniques have only been applied selectively in larger skeletal regions (e.g., pelvis, lumbar vertebrae) ( 43, 44) In lieu of clinically feasible methods of assessing patient specific values of MVF and CF, clinicians may continue to rely on data acquired for purposes of radiological protection. In ICRP Publication 70, literature values of both bone volume fraction (BVF = 1 MVF) and marrow C F are given in Tables 15 (p. 27) and 41 (p. 68), respectively. While these are not officially reference values, they may be provisionally adopted as such in the application of Equation 2 2 to patient specific estimates of mT AM. These values are given i n Table 2 1 along with reference values for the percentage mass distribution of active bone marrow in the adult. As will be noted later, the coefficients of variation of provided in this chapter are noted to be very small, and thus can be applie d with confidence in current patient studies. Values of MVF are both ageand sex dependent owing to natural processes of mineral bone loss with age, and the fact that osteopenia and osteoporosis are typically accelerated in older females. Mean cadaver based estimates of BVF are given in Table 15 of ICRP 70 in decade increments for adults 2130y to 8190y for the vertebrae and iliac crest, while additional values of BVF are given for the femur, ribs, and parietal bone for only the age range 4150y. Due to limited sample sizes, data for males and females are combined. Values of CF in Table 41 of ICRP 70 give only a single set by bone site for the 40y adult, and are thus not given as a function of age or sex. Meunier et al. ( 63)

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31 however, indicates that as bone trabeculae thin, the additional marrow space is primarily occupied by adipocytes, and thus the agedependent product of MVF and CF might possibly remain constant with age in normal marrow. Consequently, the data in Table 2 1 may perhaps be used in Equation 2 2 irrespective of patient age. The most important determinant of mT AM in Equation 2 2 is the patient specific estimate of TSSV. To address this clinical need, Brindle et al. ( 17, 18) developed a predictive equation for patient specific TSSV requiring only two measurements in a pelvic CT os coxae width (OC.W) and os coxae height (OC.H). Their predictive equation is ( ) = 5585 .5 46.3 ( ) + 420.6 ( ) (2 3) The equation was constructed using multiple linear regression on data from 20 cadavers 10 males and 10 females. SV was determined from manual segmentation of full body CT images. A leaveoneout analysis showed that the above equation is able to make TSSV predictions with errors that range from 0.2 to 21.2%, wit h most errors being under 11% ( 18) Due to limitations in sample size (due in part to the tedious nature of t he data collection), the predictive model of Equation 2 3 was based on pooled data from both sexes. However, male and female skeletal dimensions are expected to be different. T hese differences are used by forensic scientists to determine the sex of a vic tim from remains ( 19, 20) Males are usually larger than females in both height and weight ( 19, 21, 22) As a consequence of the difference in load experienced by weight bearing bones, femur length and femoral head diameter are greater in men than in women ( 21, 2325) Vertebral width is found to be gr eater in males than in females ( 22) S everal

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32 pelvic dimensions are larger in females than males partially due to the fact that females give birth ( 23) One can infer from the previous discussion that a sex specific predictive equation will be more accurate at predicting TSSV in patients than a pooled model such as Equation 2 3. In the work described in this chapter the study in Brindle et al. ( 18) is expanded to construct sex specific predictive models of TSSV, along with sex specific estimates of its fractional distribution within the skeleton for cli nical applications of Equation 2 1 and 22 Materials and Methods Cadaver Selection Ten male and ten female cadavers were acquired via approved procedures from the State of Florida Anatomical Board. The same selection criteria used in Brindle et al. ( 18) were applied in this study. The targeted age range was 40 to 80 years as representative of cancer patients potentially treated with radionuclide therapy. Each candidate was screened and excluded if the cause of death or previous medical condition was indicative of excessive bone loss. Finally, a body mass index (BMI) of between 18.5 and 24.9 kg m2 was additi onally targeted as representative of average nonobese adults ( 64) Body donation records did not include the cadaver body mass either before or after the embalming process. Hence, body mass was estimated from visual inspection by the senior laboratory technician. While ethnicity was not a selection factor, all cadavers selected for this study were white. Image Acquisition Each cadaver was imaged on a Siemens Sensation 16 CT scanner in the Department of Radiology of Shands Hospital at the University of Florida. The slice

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33 thickness for each was 2 mm with an inp lane resolution of 977 m. The scan spanned from the top of the head to slightly above the middle of the femoral shaft. Given that it is difficult to discern the location of trabecular spongiosa in the skull at full body scan resolution, the head of each cadaver was imaged separately at a slice thickness of 1 mm and an inplane resolution of approximately 450 m. Spongiosa Volume Estimation Spongiosa volume ( SV) was obtained by manual segmentation using an IDLbased code (Interactive Data Language; IDL version 6.0; ITT Visual Information Solutions, Inc) written by our group called ct contours ( 65) Figure 21 shows the graphical interface of the software. Note that the CT images are shown in the three orthogonal planes. A Wacom tablet model Cintiq 18SX (WacomTechnology Corporation, Washington) connected to a PC running Windows XP was used for this purpose. The ct contours code allows the user to assign different tag values (i.e. colors) to selected voxels in each CT slice. The stylus is used to trace the edge of spongiosa regions in the CT images which the software then fills by assigning the same tag number (i.e. color) to each voxel included in the drawn contour. Contouring is possible in all three planes, but it was found to be more convenient to do in the axial or transverse plane. The cortical bone edge is clearly visible in the CT slices (external white contours around bone slices in Figure 21). Care was taken to ensure that the same window leveling was used to per form all segmentations. The bone sites segmented were those identified by the International Commission on Radiological Protection (ICRP) Publication 70 ( 16) as those containing hematopoietically active bone in the adult (Table 21) Segmentation along the long

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34 bones (e.g. humerus, femur) was stopped at the start of the shaft because it is known that in adults the shaft contains mostly fat ( 3 5 16) Fac ial bones were not segmented because they present very thin regions which appear highly fragmented and difficult to identify in the CT slices. This exclusion results in an acceptable loss in accuracy since th e combined spongiosa volume for the facial bones accounts for less than 5% of the cranial SV and less than 1% of TSSV, as determined by Brindle ( 66) Figure 21 shows how the code allows the assignment of a unique color (tag value) to each bone site. Once segmentation is completed, the SV for each bone site can be read from a table provided by the software. SV is calculated by multiplication of the total number of voxels assigned a given tag value times the volume of the CT voxels. Given the tedious and timeconsuming nature of the manual segmentation process (each cadaver consists of over nine hundred slices) not all cadavers were segmented by the same individual. In Brindle et al. ( 67) both rater accuracy and inter rater variability were assessed using CT images of a 2.54cm section of PVC pipe submerged in water To reproduce the conditions of the cadaver im ages, scans were done with 1 mm slice thickness and 977 m in plane resolution. In addition, three CT image sets were acquired with the pipe at different angles with respect to the horizontal (z axis): 0o, 45o, and 90o. A ll individuals involved in the segmentation effort were required to segment the plastic volume and the volume enclosed within the pipe in the three image sets In this simple bone model, the plastic volume is a surrogate for cortical bone and the pipe lumen for spongiosa. Since both volumes can be calculated very accurately from physical measurements of the inner and other diameters and the

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35 height of the pipe section, it was possible to determine the percent error in the segmentation performed by each individual. The mean percent error for the segmentation of the PVC plastic volume ranged from 7% to 15%, while the mean percent error for the segmentation of the enclosed volume ranged from 1% to 3 %. That the error i s larger for the segmentation of the plastic volume was to be expected since this volume is smaller and segmentation accuracy is more greatly affected by the partial volume effect. Inter ra ter variability was also determined in vivo using pelvic CT images Spongiosa was segmented at several bone sites: the os cox ae, the sacrum, the femoral heads and L5. No statistically significant differences were found between the raters. Anatomical Measurements The skeletal measurements considered in this study are summarized in Table 22. The table provides a brief description of each measurement. Graphical representations of the measurements are shown in Figures 22 and 23 Measurements have been focused primarily on the os coxae primarily because (i) a large percentage of the TSSV is located in this site ( 15, 16, 18) and (ii) measurements can be easily performed on a pelvic CT. These measurements may also be made f rom the CT portion of a SPECT/CT or PET/CT imaging sessions used to quantify skeletal uptake of the radiopharmaceutical ( 12 ) Many of the skeletal measurements described in T able 2 2 are based on the methodology of MooreJansen et al. ( 68) With the exception of body height and femoral height, all measurements were made using the plugin Volume Viewer v.1.21 ( 69) of the software ImageJ v.1.36b ( 70) Body height and femoral height were measured using DicomWorks v.1.3.5 ( 71) on the anterior posterior scout images

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36 produced during CT image acquisition. Given that no CT scout image spanned the entire length of a study cadaver, total body height was calculated as the sum of two measurements: the vertical distance from the top of the head to the top of a p roximal femoral head, and the vertical distance from the top of the same femoral head to the bottom of the heel on the same leg (Figure 24 ) Volume Viewer allows the user to rotate the CT image in three dimensions (3D) (Figure 25 ) This feature is useful as cadaver positioning cannot be changed (i.e. rigor mortis) and in many cases the pelvis was not parallel to the CT table. If one measures, for example, the width of the pelvic bone using the scout image, the measurement may be underestimated due to the tilt of the pelvis. By being able to rotate the CT image in 3D, one can take a snapshot of the pelvis when it is parallel to the screen and hence make a more accurate measurement (Figure 26 ) Even though Volume Viewer allows the user to view the pel vis in 3D, measurements are actually made on snapshots taken from the 3D rendering and are therefore twodimensional. All measurements were performed in duplicate. Measurements were made over the span of several weeks and hence are not sequential. The delay between corresponding duplicates was sporadic and of sufficient length so that the likelihood of bias from prior measurement recall was minimal. Statistical Analysis All statistical calculations required for the construction of the predictive equations were made using the statistical software JMP IN version 5.0 (SAS Institute Inc., Cary, NC, USA). Multiple linear regression analysis was used to select an optimal set of predictor variables (from Table 2 2 ) that could be used to predict TSSV. The general equation for the regression model is:

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37 = + + + + + (2 4) where is the intercept, are the coefficients for each of the predictor variables and is the error associated with the model. There are many criteria that can be used to determine the subset of independent variables that best fits the data. In general it is a good idea to use more than one criterion, since if different criteria result in the selection of the same subset of variables, this can be taken as confirmation that the optimum subset has been selected ( 72) The same criteria used in Brindle et al. ( 18) were applied in the sel ection of the best subset of variables in the present study: (i) stepwise selection, (ii) adjustedR2, (iii) Aikake Information Criterion (AIC), and (iv) Bayes Information Criterion (BIC). For information on these statistical parameters refer to the resources referenced here ( 7375) The stepwise selection method consists in either adding or subtracting vari ables to the model in iterative steps. In each step, pvalues and other values (e.g. R2, residual sum of squares) are calculated, and variables are either kept or eliminated based on these values. There are three modes of stepwise selection. The forwa rd selection mode starts by first finding the best onevariable model and then a new variable is added after each step. The v ariable that is added is the one that after inclusion in to the model, results in the largest reduction in the residual sum of squares (SSE), which also results in the largest increase in R2. This process is repeated until further addition of variables does not reduce SSE. A problem with this mode is that it does not remove variables once they have been added to a model, even if they become redundant after the addition of subsequent variables ( 72) The mixed selec tion mode begins as a forward selection, but after a variable is added any variable with a p value above a pre-

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38 selected level is dropped. The mixedmethod resolves the problem of keeping redundant variables in the model that can occur in the forward selec tion method. The backward elimination mode starts with a model that uses all the variables and eliminates the variable with the largest pvalue at each step. O nly the mixed and backward selection modes were used in the model development The procedure for selecting the best model using the adjustedR2, AIC and BIC criteria is similar. All possible models based on the available predictor variables are generated, starting from all possible models of one variable to the model that includes all variables. The value of the statistical parameter is calculated for each model and the parameter value is plotted versus the number of variables in the model. In the case of adjustedR2, the resulting curve presents a plateau. The optimal model is the one corresponding to the number of variables right before the plateau. In the case of AIC and BIC the optimal model is the one for which the curve reaches a minimum. The AIC is a leading criterion in model selection, h owever, it has been demonstrated that if the sample size is small it is more effective to use the corrected AIC (AICc) ( 7375) Accordingly, the AICc was used in this study in lieu of AIC. The model building process was started by produci ng models that did not include a sex variable these models are referred to as pooled. The first step is to examine all possible models that can be constructed using subgroups of the fifteen predictor variables. The JMP software produces a table that l ists all possible models composed of all fifteen variables, subsets of fourteen, and so on, all the way down to onevariable models. This results in thousands of possible models. JMP automatically calculates R2 and adjustedR2 for each model. AICc and B IC values were calculated by means of a

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39 script. A plot of each criterion statistic versus the number of variables was used to determine the optimal model for each criterion. The sex specific model was constructed following the procedure just described, with the difference that a dummy variable for sex was added to the set of predictor variables. The variable was defined as sex = 1 if male 0 if female (2 5) This is the preferable way to introduce sex specificity into a model, rather than constructing separate models for each sex, because the regression includes the entire data set and hence all measurements contribute to estimation of the regression parameters ( 72) In addition, the coefficient that multiplies the dummy variable may provide insights into differences between male and female subjects ( 76) The ultimate test of the success of a given model is it s use in predicting TSSV on individuals whose data were not used in the creation of the model. If one has the luxury of having a large data set, one can split the data set into two equal halves and use one half to generate the predictive model and the other half to test the models accuracy of prediction. This is not the case in our study and a leave oneout analysis was performed instead. This consists in generating the predictive model using the data from all but one of the cadavers and then using the model to predict TSSV for the cadaver that was excluded from the regression. Both percent difference and 95% prediction confidence intervals were thus calculated. The procedure was repeated by excluding a different cadaver from the regression each time.

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40 Results The cadaver data used in this study are shown in Table 23 and are inclusive of data from the Brindle et al. study (14). Values of active marrow mass given in the final column of Table 23 are estimates using Equation 2 2 and data from Table 2 1 Table 2 3 allows us to compare our skeletal measurements to similar measurements found in the literature for white males and females in the U.S ( 19, 21, 25, 7780) Values for some skeletal dimensions e.g. Bi.B, OC.H wer e not found in the literature and hence are omitted from the table. Values of TSSV were also omitted from the table since, to our knowledge, SV has not been measured by any other research group. Table 2 3 includes skeletal measurements obtained from The Forensic Data Bank (FDB) accessible via the software FORDISC 2.0 ( 80) The FDB contains skeletal data for about 1400 individuals from the United States (US), which include both sexes and different ethnicities. Data from the HamannTodd collection (3000 skeletons held at the Cleveland Museum of Natural History) is accessible via the website http://www.cmnh.org/site Table 24 shows the predictor variables selected using each criterion and the resulting R2 and adjustedR2 values for the model. Two categories of models are shown: pooled models, based on all data and do not discriminate sex; and sex specific models, based on all the data and discriminate sex by means of a dummy variable ( Equation 2 5 ). Models that included too many variables to be of practical use, variables with large p values (>0.3), or variables that were highly collinear, were not considered for further analysis. These models have been marked with an asterisk and the reason for rejection is stated in the final column.

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41 Table 25 provides the coefficients and relevant statistics for each of the predictor variables included in the two final models recommended for clinical use in this study. The models were selected based on the following criteria: (i) smal ler number of variables, (ii) higher R2 value, and (iii) model selection criterion used. Given that AICc has been shown to be superior over other model selection criteria ( 74) models selected by this criterion were given preference. A leave oneout analysis was produced to estimate the accuracy of predicti on for each model. Percent error was calculated from the difference between the predi cted and measured TSSV values. Figure 27 provides percent error histograms for each of the models. Discussion Our skeletal measurements are consistent with the expected ranges for white North Americans (Table 2 3). In spite of our small sample size for each sex (n = 20), our mean skeletal measurements are very close to those calculated from much larger sample siz es. Table 2 6 shows the data used in the multiple regression analysis. Note that there are two cadavers that fall outside our 4080 ageselection criterion: a 35year old from Brindle et al. ( 18) and an 18ye ar old in the new cadaver set. The fact that the cadaver sample only includes two cadavers younger than age 40 merely reflects the lack of younger subject s in the available cadaver pool from the State of Florida Anatomical Board. Neither of these two cadavers was identified as an outlier in our analysis. The 18year old cadaver was relatively large and matches the build of the male cadavers in the data pool. Table 2 4 provides the models selected by the different criteria. In the case of pooled models (i.e. no sex discrimination), all criteria except for adjustedR2 agree on a

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42 threevariable model that includes OC.H, Bi.B, and P. The model selected by the adjustedR2 method was rejected because it contains two variables P and FD that are highly collinear (>0.8) and because the coefficients for FD and L5.T have large pvalues 0.24 and 0.17, respectively. The fact that P and FD are highly collinear is not surprising since both measurements are proportional to the diameter of the femoral head. Removal of either one of these variables did not improve the predictive power of the model. Our recommended pooled model is provided in Table 25. Figure 2 7 A shows the percent error histogram for the pooled model calculated from the leaveoneout analysis. The highest prediction errors are obtained for cadaver 26 (45.4% error) and cadaver 29 (31.2% error). These cadavers represent e xtremes in our cadaver dat a set Cadaver 29 is one of the tallest cadavers in our data set (height = 182.0 cm) and is unusually large for a female --more than three st andard deviations from the mean compared to heights published in the literature (Table 2 3 ) This cadaver also has the largest value of OC.H (23.5 cm) in the cadaver set, and presents a relatively large (> 75% percentile) Bi.B value (31.4 cm). Cadaver 26 has the smallest TS SV value in our entire data set (1275.21 cm3). Studentized residuals identify both of these cadavers as moderate outliers (2.5 2.0). Given that the model tries to fit to the data used to create it, one can expect to find larger errors in individuals that have uncommon skeletal dimensions or TSSV. The sex specific models were constructed with t he addition of a dummy variable for sex, as defined in Equation 2 5. The model chosen by the stepwisemixed method was rejected on the basis that P and FD are highly collinear and have coefficients with large pvalues: 0.22 and 0.36, respectively. The model selected by AICc was chosen

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43 over the other two models first because it was selected by AICc and therefore given greater weight, and second because it is simpler, only requiring two skeletal measurements. Our recommended sex specific model is provided in Table 25. Figure 2 7 B presents the percent error histogram for the sex specific model. Cadaver 31 shows the worst prediction with an error of 35.2%. Even though this cadaver is not an extreme in our cadaver set, it is an extreme in the male cadaver set, with the smallest v alues in TSSV and OC.H in males. I t also presents very small values for OC.H, Bi.B, and TSSV. Cadavers 26 and 29, previously identified as extreme in the discussion of the pooled model are predicted more accurately with 22.8% and 25.4% error, respectiv ely. Table 2 7 shows the percentage of cadavers that were predicted best by each of the recommended models on the basis of the absolute magnitude of the percent error of prediction. Predictions were considered equally good when the difference in absolute value of the percent error between the predictions of the two models was less than 1%; else, the model with the smallest absolute error of prediction was considered best. T he sex specific model is superior at providing good predictions for males but b oth models are comparable in the prediction of TSSV in females. Table 2 8 shows the percentage of cadaver TSSV predictions that have absolute errors less than or equal to 5%, 10%, 15%, and 20%. The differences in performance between the models for male and female TSSV prediction are at worst 15% ( for 3 out of 20 cadavers), while differences in overall performance are at worst 7% ( for 3 out of 40 cadavers). Even though Tables 2 7 and 28 do not conclusively show which type of model should be used to predict TSSV in males and females, the sex specific model is

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44 strongly recommended for three reasons. First, the sex specific model is better at accurately predicting TSSV in males and is slightly better at predicting TSSV in both sexes (Table 2 7 ). Second, it does a better job at predicting TSSV in individuals that are unusual and therefore difficult to predict. Cadavers 26 and 29 are extremes in our cadaver data set. The sex specific model predicts these two cadavers with smaller errors than the pooled model, w ith cadaver 26 resulting in an error of 25.75% versus 45.42%, and cadaver 29 resulting in an error of 25.43% versus 31.21%. Third, the sex specific model accounts for sex differences in skeletal morphology. Several skeletal dimensions are different i n males and females. Ttests performed on the data of Table 26 reveal that, at least for the individuals in our study, males are larger in height, os coxae height, S1 breadth, femoral head perimeter, Ferets diameter, maximum height and width of the femoral head, humeral height, and femoral height (all tests with p value < 0.0005). Ttests also reveal that values of SV are larger (pvalue < 0.005) in males in all bone sites measured with the exception of the cranium and mandible. TSSV is also larger in males (pvalue < 107). These differences in SV may be a consequence of the fact that males are generally larger than females. However, when the SV data was grouped into equal height ranges, a large spread in SV values is observed in each height group, t hus suggesting that the difference in the distribution of SV in adult males and females may not be due to differences in height. The cadaver data sample size used in this work is insufficient to provide robust statistics when the data is grouped by height and even less so when further separated by sex, and hence this data can only provide insights into the sexual dimorphism of the skeleton and SV distribution of males and females.

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45 The models are unintentionally based on cadavers belonging to individuals of one racial groupwhite. It is well known that skeletal dimensions exhibit differences related to race and geographical location ( 19, 21, 25, 77, 81) Accordingly, caution must be used when using my models to predict TSSV in patients of other races. Table 2 9 provides values of the fractional distribution of TSSV by skeletal site. Two sex averaged sets of are given one from the study of Brindle et al. ( 18) on 20 cadavers, and one from the current study on 40 cadavers (inclusive of the former). Mean values of are essentially unchanged, with the additional data only evident in changes to the standard deviations. Table 2 9 also provides v alues of for males and females. Twotailed t tests show that the fractional distribution of TSSV is significantly different in males and females in the cranium (p < 0.0001), the mandible (p = 0.0054), the scapulae (p < 0.0001), the ribs (p = 0.0022), the sacrum (p < 0.0001), and the proximal humeri (p < 0.0001). The sex specific model provides an additional piece of information that would be missed in a pooled model The coefficient that multiplies the dummy sex variable (Table 2 5) is positive, thus suggesting that for male s and females of comparable skeletal dimensions males tend to have a greater TS SV than females. One must conclude from this that SV must be distributed differently in males and females, which is s upported by the statistically significant differences mentioned in the previous paragraph. Values of in Table 2 9 may be used for two clinical purposes. First, they may be used along with predictive TSSV models in the evaluation of Equation 2 2 In the assumption that values of BVF and CF in Table 2 1 are appropriate for a given patient

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46 (i.e., in lieu of patient specific data), Equation 2 2 can be evaluated for either the adult male or adult female patient as: ( in g )adult male= ( TSSV in c m3)adult male( 0 .450 g /cm) (2 6) ( in g )adult female= ( TSSV in cm3)adult female( 0 .442 g /cm3) (2 7 ) where the TSSV multiplier differs only with respect to differential sex changes in Clearly, more information is needed on both the age and sex dependences of BVF and CF as well patient specific methods for their measurement. For example, cadaveric values of BVF may be acquired via bone harvesting and microCT analysis, and then empirically tied to individual patients through quantitative CTbased assessments of volumetric bone mineral density in the lumbar vertebrae (measurements that can be performed on both the patient of interest and the cadaver of the source tissues). Similarly, MR imaging volunteer studies can be conducted to further parameterize (by age, sex, disease state, prior chemotherapy, etc.) the very limited ageand sex averaged values of marrow CF given in ICRP Publication 70 (Table 21) Second, imagebased methods of radiopharmaceutical activity concentration in the skeletal tis sues are usually performed on selected regions of interest (ROI) such as the sacrum, femoral head, or portions of the lumbar vertebrae. Once a regional estimate of marrow (or bone) activity is made via PET or SPECT, this activity may be proportionally sca led to yield a total skeletal estimate of radiopharmaceutical marrow or bone activity. Values of in Table 2 9 can be used for just this purpose. For lumbar vertebrae imaging, the ROI is typically restricted L2 to L4 due to the need to avoid ROI overlap with the pelvis or urinary bladder. As shown at the bottom of Table 2 9, these three vertebrae account for, on average, 6.08% and 6.16% of TSSV (corresponding to ~8.6%

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47 and ~8.9% of active marrow mass Table 2 10) in the adult male or females of our 40subject study, respectively. Within the sacrum, some 6.8% and 8.1% of TSSV (corresponding to ~9.6% and ~11.6% of active marrow mass Table 2 10) is found in male and female patients, respectively. Caution must be exercised, however, in the use of for regional scaling of marrow activity when the radiopharmaceutical skeletal uptake is not uniform across all skeletal sites. The data of Tables 2 1 and 2 9 may be used in combination with Equation 2 2 to establish values of the percent mass dist ribution of active bone marrow in both sexes: gender = -gender -gender (2 8) where gender is either male or female. As the patient specific value of TSSV from the predictive regression equations cancels in Equation 2 8 these male and female values of are not patient specific per se, but are more akin to reference val ues as based on mean values of in this study. S ex differences in the values of ( from Equation 2 8) shown in Table 2 10 stem only from changes in and not from changes in MVF and CF (as only sex averaged mean values are given in ICRP 70). These estimates may then be compared to the sex averaged reference values given in ICRP Publication 70. Discrepancies between the ICRP 70 model and the sex dependent distributions of this study (values greater than 2%) are noted for the cranium, lumbar vertebrae, and os coxae in the male model, and for the cranium, ribs, and lumbar vertebrae in the female model. While the male and female distribution data shown in Table 2 10 from this study are based on

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48 imagebased measurements of SV, the ICRP 70 reference distribution of mTA M were derived from an analysis by Cristy ( 14) using data originally published by Mechanik ( 82) The cadavers of this 1926 study were victims of prolonged wasting illnesses which rendered them relatively emaciated and which might have led to significant changes in the tissue components ( 15) As noted by this author, the process by which Mechanick measured marrow mass was not c learly explained in his original paper. Of particular note is the overly large assignment of active bone marrow to the cranium (7.6%), a value which is not supported by the range of SV obtained in this current 40subject study, which results in of 2. 7% in males and 4.3% in females (Table 210) Nevertheless, it is cautioned that the male and female distributional values in Table 2 10 may be further improved following the creation of more patient specific methods of assigning both MVF and CF in the evaluation of Equation 2 2 for individual patients. In this study, pooled and sex specific models are presented (Table 25 ) that can be used to predict total skeletal spongiosa volume in a given patient with an error generally expected to be within 10% to 20% (Figure 2 7 and Table 2 8 ). The models require values of only two to three skeletal dimensions that are easily measured on pelvic CT images. The study does not conclusively determine which of type of model pooled versus sex specific is best a t predicting TSSV. However, the use of the sex specific model is strongly recommended, as it generally provides the best predictions (Table 2 7 ), is more accurate in predicting TSSV in patients of atypical skeletal morphometry, and accounts for gender dif ferences. Even though the model is based on a small sample size (n = 40), the data has been shown to be representative of the white US population (Table 23) and when applied to patients that fit this category the models

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49 should provide accurate predictions. One should be cautious when applying the models to individuals from other races or geographical locations. In situations where it is necessary to know SV at a particular bone site, average values of (Table 2 9 ) may be applied to t he patient sp ecific TSSV predicted by our models (Table 25) Clearly, direct CT volumetry in the skeletal site of interest would yield a more accurate result but this is impractical in the clinic It is noted that patients of unusually small or large skeletal stature may be poorly predicted by the models. Under the further assumption that reference values for both MVF and CF are representative of a specific patient the patient specific estimate of TSSV can be used in Equation 2 6 and 2 7 to yield an estimate of total active bone marrow mass for male and female patients, respectively. Chapter 4 demonstrates the use a noninvasive technique that can be used to determine patient specific CF, thus enhancing the patient specificity of the BM mass estimation. Further research is required in the development of clinically feasible methods of assessing MVF on an individual patient thus further improving the patient specifi city of the method presented here.

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50 Table 2 1. Percentage distribution of active bone marrow, bone volume fractions, and marrow cellularity within the adult skeleton (4150 years) as given in ICRP Publication 70. Skeletal Site (no. of bones) Bone Volume Fraction* (BVF = 1 MVF) Marrow Cellularity (C F) Active Marrow (% by mass) Craniofacial Bones 0.554 0.38 7.6 Mandible (1) 0.104 0.38 0.8 Scapulae (2) 0.104 0.38 2.8 Clavicles (2) 0.104 0.33 0.8 Sternum (1) 0.104 0.70 3.1 Ribs (12) 0.104 0.70 16.1 Cervical Vertebrae (7) 0.119 0.70 3.9 Thoracic Vertebrae (12) 0.119 0.70 16.1 Lumbar Vertebrae (5) 0.119 0.70 12.3 Sacrum (1) 0.119 0.70 9.9 Os coxae (1) 0.199 0.48 17.5 Femora (proximal) (2) 0.148 0.25 6.7 Humeri (proximal) (2) 0.148 0.25 2.3 Source: Table 15 of ICRP Publication 70 ( 16 ) Data taken for ages 41 50 years. Values of BVF for the mandible, scapulae, clavicles, and sternum are approximated by those listed for the ribs. Value for the proximal humeri taken to be that listed for the proximal femora. Data are pooled for both males and females. Source: Table 41 of ICRP Publication 70 ( 16 ) Values of marrow cellularity for the sacrum taken to be that listed for t he vertebrae. Data are pooled for both males and females. Source: Table 40 of ICRP Publication 70 ( 16 ) Values taken from that listed for the 40year adult. No distinction made between males and females.

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51 Table 22. Anthropometric measurements for use in the multiple regression analysis. Parameter Abbreviation Measuremen t (cm) Height HT Total body height measured on the CT scout images. Os coxae width OC.W Maximum width of the os coxae in the coronal plane. Os coxae height OC.H Average of the maximum heights of the left and right side of the os coxae in the coronal plane. Bitrochanteric breadth Bi.B Distance between the outermost portions of the greater trochanters in the coronal plane. Anterior sacral height ASH Distance from the anterior sacral promontory to the apex of the sacrum in the sagitta l plane. Sacral width S.W Maximum width of the sacrum in the transverse plane. L5 thickness L5.T Thickness of the fifth lumbar (L5) vertebrae in the sagittal plane. The measurements were made parallel to the anterior surface of the vertebral body and approximately 1.5 cm into the vertebral body. S1 breadth S1.B Longest diameter of the S1 sacral plate in the transverse plane. Femoral head perimeter P Averag e of the maximum perimeter of the left and right femoral heads in the coronal plane. Ferets diameter FD Average of the FD for the right and left femoral heads measured in the coronal plane. This measurement, based on the femoral head perimeter, represents the longest distance between any two points along the perimeter of the femoral head. Maximum height of femoral head Max.H Maximum height of the femoral head in the coronal plane, calculated as the average of the left and right femoral heads. Maximum width of femoral head Max.W Maximum width of the femoral head in the coronal plane, calculated as the average of the left and right femoral heads. Humeral head breadth HH Distance between the outermost portions of the right and left proximal humeral heads in the CT scout image. Femoral height FH Maximum height of the femoral bones in the CT scout image, calculated as the average of the left and right femoral bones. Adapted from Brindle et al. ( 18 )

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52 Table 23. Comparison of our skeletal measurements to published data. Skeletal measurements for which no data was found in the literature are excluded from the table. All measurements correspond to white males and females in the United States. Sex Sample Size Age HT OC.H ASH S.W L5.T S1.B Femoral Head FH Source FD Max.H Range Mean Male 20 18 81 64 173.2 ( 6.7 ) 21.9 ( 1.0 ) 11.4 ( 1.2 ) 12.3 ( 0.9 ) 2.7 ( 0.3 ) 5.5 ( 0.4 ) 4.9 ( 0.4 ) 4.7 ( 0.4 ) 47.4 ( 2.5 ) Present study / Ref. ( 67 ) 1687 18 96 53 170.7 ( 7.3 ) Hamann Todd Collection 242 70 79 74 172.7 ( 6.2 ) 43.2 ( 0.1 ) Ref. ( 19 ) 141 60 97 76 173.3 ( 7.4 ) 6.2 ( 0.3 ) Ref. ( 77 ) 244 22.3 11.2 10.8 5.1 4.9 47.5 Ref. ( 25 ) 55 22 80 50 2.7 ( 0.2 ) 5.7 ( 0.5 ) Ref. ( 80 ) Female 20 49 82 68 161.6 ( 7.0 ) 20.5 ( 1.0 ) 11.1 ( 1.3 ) 12.6 ( 0.8 ) 2.6 ( 0.3 ) 4.8 ( 0.7 ) 4.3 ( 0.3 ) 4.1 ( 0.4 ) 43.9 ( 2.2 ) Present study / Ref. ( 67 ) 237 18 93 53 158.5 ( 8.4 ) Hamann Todd Collection 197 70 79 74 157.9 ( 7.0 ) 39.5 ( 0.2 ) Ref. ( 19 ) 330 60 99 74 158.4 ( 6.6 ) 5.4 ( 0.3 ) Ref. ( 77 ) 144 20.1 10.9 11.1 4.5 4.2 43.8 Ref. ( 25 ) 71 22 80 49 2.5 ( 0.2 ) 5.0 ( 0.5 ) Ref. ( 80 ) Age is given in years. All skeletal measurements are in cm. The number in parentheses is the standard deviation. Entries left blank were not provi ded by the source. Haman n Todd Collection: http://www.cmnh.org/site/ResearchandCollections_PhysicalAnthropology_Collections_HamannToddCollection.aspx

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53 Tabl e 24. Pooled, male, female, and sex specific models chosen by the different selection criteria. The criteria used to select each model are provided in parentheses next to the type of model. In the case of the stepwise method, the modei.e. backward or m ixed is only indicated when each mode selected a different set of variables Model Based on Variables R 2 adj -R 2 Reason(s) for rejection Pooled (stepwise, AICc, BIC) All data OC.H, Bi.B, P 0.76 0.74 Pooled (adj R 2 )* All data OC.H, Bi.B, P, L5.T, FD 0.78 0.74 P and FD are highly collinear. Sex Specific (AICc, BIC) All data Sex, OC.H, Bi.B 0.79 0.77 Sex Specific (adj R 2 ) All data Sex, Age, OC.H, Bi.B, Max.W 0.81 0.78 Sex Specific (stepwise mixed)* All data Sex, OC.H, Bi.B, L5.T, P, FD 0.80 0.77 P and FD are highly collinear. Sex -Specific (stepwise-backward) All data Sex, OC.H, Bi.B, P 0.79 0.77 Abbreviations are explained in Table 2 2 Models marked by an asterisk (*) were not considered for further analysis because they included too many variables, included variables with large p values, or include variables that were highly collinear.

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54 Table 25. Parameters for the recommended TSSV predictive models. Model Type R 2 Adjusted R 2 Variable Coefficient Estimate Coefficient p value Pooled Intercept 2872.91 0.0001 OC.H 238.71 <0.0001 0.76 0.74 Bi.B 58.78 0.0027 P 97.33 0.0156 Sex -specific Intercept -2204.42 0.0029 Sex 286.51 0.0012 0.79 0.77 OC.H 233.91 <0.0001 Bi.B -36.05 0.0489

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55 Table 26. Cadaver data used in the regression analysis. All skeletal measurements are in cm and TSSV is in given in cm3. Abbreviations are explained in Table 22. The data corresponding to the first ten cadavers are from Brindle et al. ( 18) Cadaver Sex Age (y) HT OC.W OC.H Bi.B ASH S.W L5.T S1.B P FD Max.H Max.W HH FH TSSV (cm 3 ) 1 M 35 188.2 32.7 23.3 29.7 11.7 12.7 2.8 6.1 16.1 5.2 4.8 5.3 46.8 52.3 2493.20 2 M 66 172.2 28.7 21.8 26.9 12.9 13.2 2.4 5.5 14.5 4.7 4.5 4.9 35.6 47.7 2151.14 3 F 77 156.8 29.7 20.1 31.0 10.3 11.9 2.2 4.0 12.7 4.1 4.0 3.9 34.1 41.9 1265.24 4 M 68 181.2 27.6 21.6 27.4 10.7 10.8 2.4 5.1 15.3 5.0 4.7 5.1 39.9 50.2 2380.45 5 M 81 175.8 29.3 23.1 28.5 11.4 13.8 2.5 5.8 15.1 4.9 4.5 5.0 38.6 48.5 2852.19 6 M 72 165.2 27.6 21.3 29.9 10.4 11.6 2.4 5.5 14.7 4.7 4.5 4.7 38.9 47.4 2256.33 7 F 70 159.1 33.6 20.1 30.3 9.2 12.9 2.5 4.7 12.8 4.2 3.9 4.2 38.6 42.8 1364.31 8 F 62 157.5 26.3 20.0 24.6 8.5 11.7 2.4 5.0 12.4 4.1 3.7 4.0 33.3 43.0 1426.07 9 M 67 171.1 31.5 21.3 27.9 11.3 13.1 2.8 5.6 14.6 4.8 4.3 4.7 38.7 47.3 2300.99 10 M 78 175.0 33.6 22.5 28.5 12.5 12.0 2.7 5.6 14.9 4.8 4.4 4.9 41.3 49.3 2318.72 11 F 82 162.9 32.3 20.5 27.2 10.5 12.5 2.2 5.7 13.2 4.4 3.9 4.3 38.4 46.0 1410.27 12 F 78 149.9 28.3 19.7 27.1 10.1 11.4 2.6 5.4 12.7 4.1 3.9 4.1 34.7 41.4 1354.31 13 F 73 159.6 30.3 20.8 28.2 13.2 12.5 2.3 4.6 13.2 4.3 4.3 4.2 34.8 43.0 1764.06 14 M 76 165.0 23.6 20.9 24.9 10.2 10.9 2.6 4.9 13.6 4.4 4.1 4.5 34.7 42.6 2137.16 15 F 64 168.0 32.0 20.3 26.7 12.1 13.7 2.3 5.6 12.0 3.9 3.6 3.9 35.9 45.5 1585.72 16 F 68 158.4 31.2 20.3 31.1 8.7 11.9 2.5 5.1 12.4 4.0 3.8 3.9 35.9 42.6 1661.10 17 F 80 156.9 33.8 21.1 28.3 12.1 13.7 2.1 3.7 12.2 4.1 3.4 4.0 34.7 44.4 1788.23 18 F 75 165.0 30.5 20.6 31.8 11.2 12.8 2.7 4.8 12.8 4.2 4.1 4.2 35.4 43.3 1590.72 19 M 75 169.2 26.0 20.5 26.0 11.8 11.7 2.1 4.8 12.3 4.0 4.1 4.1 38.4 43.3 1716.77 20 M 40 168.6 30.3 21.2 31.2 11.8 12.5 2.3 4.6 13.5 4.4 4.2 4.1 41.1 46.7 1605.73 21 F 73 157.9 28.7 20.6 30.2 13.0 12.8 2.6 6.0 14.0 4.6 4.3 4.6 32.0 42.2 1611.88 22 M 61 176.7 27.3 22.0 29.0 11.2 12.3 2.9 5.5 14.9 4.9 4.5 4.9 37.2 49.1 1861.87 23 M 65 171.2 27.4 22.1 32.5 9.2 12.2 2.9 5.9 15.6 5.4 5.4 4.6 43.5 47.4 2205.28 24 M 18 177.5 28.1 22.4 31.7 11.8 12.6 3.1 5.8 15.0 4.9 4.6 4.9 43.2 46.9 2125.40 25 M 73 173.7 29.5 23.1 32.4 9.8 13.3 2.7 6.0 16.4 5.4 5.2 5.2 41.0 47.6 2330.17 26 F 68 164.4 28.7 20.7 30.2 10.9 13.8 2.8 4.9 15.3 5.1 4.9 4.8 35.7 45.9 1275.71 27 F 63 162.3 26.7 20.2 29.4 11.2 12.4 3.2 4.3 12.3 4.0 3.9 3.9 36.2 44.1 1294.98 28 M 56 177.6 27.0 21.0 30.2 12.4 11.3 2.7 5.6 16.1 5.3 5.1 5.2 42.9 46.9 1856.28 29 F 49 182.0 32.8 23.5 31.4 11.6 13.8 3.2 5.6 14.1 4.6 4.5 4.5 40.1 49.9 1837.11 30 F 61 152.5 26.5 18.7 25.5 11.6 11.4 2.9 4.6 13.5 4.3 4.2 4.3 34.7 40.9 1545.60 31 M 65 158.8 26.1 19.8 26.2 9.2 10.6 2.7 5.4 13.4 4.3 4.2 4.3 36.5 43.0 1372.11 32 F 60 160.3 27.0 19.8 29.7 12.5 12.8 2.6 5.2 13.3 4.4 4.1 4.4 37.1 42.8 1528.78 33 F 63 160.7 26.8 20.4 29.7 11.1 13.1 3.0 4.6 12.9 4.2 4.2 4.1 35.3 44.0 1340.00 34 F 60 172.8 28.7 21.8 28.7 12.0 12.8 3.0 4.4 14.4 4.7 4.6 4.5 37.2 47.7 1979.25 35 M 70 172.2 28.9 22.1 31.6 11.2 13.3 2.9 5.4 16.1 5.3 5.1 5.2 43.4 45.9 2058.80 36 F 69 161.0 24.6 19.4 28.1 11.8 11.6 2.8 3.5 12.5 4.1 4.0 4.0 33.5 42.9 1567.89 37 M 59 166.8 27.6 22.1 29.3 12.6 12.0 3.1 5.5 15.8 5.1 5.1 5.0 40.8 45.8 2322.50 38 F 63 164.3 26.6 21.2 30.0 10.7 12.3 2.8 5.1 14.5 4.7 4.2 4.7 34.7 43.6 1694.59 39 M 75 181.8 29.1 23.2 32.0 12.5 12.9 2.8 6.4 16.2 5.2 5.2 5.1 42.6 50.3 2414.21 40 M 74 176.6 26.9 23.0 29.3 13.6 12.4 2.7 5.4 16.4 5.5 5.0 5.5 41.9 48.9 2310.57

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57 Table 27. Percentage of cadavers for which each model was best at predicting TSSV as determined by the absolute value of the percent error of the prediction. The error of prediction was calculated as the percent difference of the pr edicted and measured TSSV. Predictions were considered equally good when the difference in absolute value of the percent error between the predictions of the two models was less than 1% Prediction of Model Best Equal Females Pooled 40% 15% Sex -specific 45% Males Pooled 25% 35% Sex -specific 40% Both Sexes Pooled 32.5% 25.0% Sex -specific 42.5% Table 28. Percentage of cadaver TSSV predictions that had absolute errors less than or equal to 5%, 10%, 15%, and 20%. Prediction of Model 15% Females Pooled 25% 50% 70% 80% Sex specific 20% 45% 70% 85% Males Pooled 55% 70% 85% 100% Sex -specific 50% 60% 80% 90% Both Sexes Pooled 40% 60% 78% 90% Sex -specific 35% 53% 75% 88%

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58 Table 29. Percent regional distribution of trabecular spongiosa by skeletal site in bones known to contain active marrow in the adult. Percentage distribution of TSSV by skeletal site x SVf (mean SD in %) Skeletal site From Brindle et al. (18) (n = 20) Present study (combined) (n = 40) Present study (males) (n = 20) Present study (females) (n = 20) Cranium 9.3 ( 1.55) 9.0 ( 2.95) 7.0 ( 1.72) 11.0 ( 2.56) Mandible 1.0 ( 0.15) 1.0 ( 0.36) 0.9 ( 0.29) 1.2 ( 0.36) Scapulae 3.9 ( 0.38) 4.0 ( 0.78) 4.6 ( 0.53) 3.4 ( 0.50) Clavicles 1.5 ( 0.14) 1.5 ( 0.28) 1.6 ( 0.28) 1.4 ( 0.25) Sternum 2.1 ( 0.25) 2.1 ( 0.44) 2.2 ( 0.55) 2.0 ( 0.25) Ribs 9.3 ( 0.77) 9.6 ( 1.76) 10.5 ( 1.50) 8.8 ( 1.65) Cervical vertebrae 2.5 ( 0.15) 2.5 ( 0.35) 2.5 ( 0.38) 2.5 ( 0.34) Thoracic vertebrae 11.9 ( 0.52) 11.8 ( 1.15) 12.0 ( 1.25) 11.5 ( 1.01) Lumbar vertebrae 10.1 ( 0.64) 10.1 ( 1.20) 10.1 ( 1.19) 10.0 ( 1.24) Sacrum 7.5 ( 0.53) 7.4 ( 1.02) 6.8 ( 0.76) 8.1 ( 0.88) Ossa coxae 22.5 ( 1.04) 22.9 ( 2.07) 22.9 ( 1.78) 22.9 ( 2.37) Femora (proximal) 12.8 ( 0.50) 12.6 ( 1.10) 13.0 ( 0.91) 12.2 ( 1.14) Humeri (proximal) 5.5 ( 0.24) 5.5 ( 0.630 5.9 ( 0.51) 5.1 ( 0.50) L2 L4 6.16 ( 0.46) 6.12 ( 0.80) 6.08 ( 0.65) 6.16 ( 0.51)

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59 Table 210. Percent regional distribution of active bone marrow mass by skeletal site. Estimates are taken using Equation 2 8 with the data of Table 2 1 (MVF and CF) and Table 2 9 (fractional spongiosa volumes). Percentage distribution of active bone marrow mass by skeletal site (mean in %) Skeletal site Present study (males) (n = 20) Present study (females) (n = 20) Present study (combined) (n = 40) ICRP Publication 70 Reference Values Cranium 2.7 4.3 3.5 7.6 Mandible 0.7 1.0 0.8 0.8 Scapulae 3.6 2.7 3.2 2.8 Clavicles 1.1 1.0 1.0 0.8 Sternum 3.2 2.9 3.0 3.1 Ribs 15.1 12.9 14.0 16.1 Cervical vertebrae 3.5 3.6 3.5 3.9 Thoracic vertebrae 16.9 16.5 16.8 16.1 Lumbar vertebrae 14.3 14.4 14.3 12.3 Sacrum 9.6 11.6 10.6 9.9 Ossa coxae 20.2 20.5 20.3 17.5 Femora (proximal) 6.3 6.1 6.2 6.7 Humeri (proximal) 2.9 2.5 2.7 2.3 L2 L4 8.6 8.9 8.7 Not Defined

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60 Figure 21. Screen capture of ct contours the IDL code used in the manual segmentation of CT images ( 65) The GUI provides three orthogonal views, window leveling, and provides a slider to modify the transparency of the tagged (colored) areas to allow anatomy to be visible through segm ented areas. Segmentation can be performed in any of the three views, but it is most accurate when performed in the transverse window.

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61 Figure 22 Graphical representation of the pelvic measurements. The key for the abbreviations is provided in Table 2 2.

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62 Figure 23 Graphical representation of the femoral measurements The key for the abbreviations is provided in Table 22.

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63 Figure 24 Cadaver height measurement. Since it is not possible to fit the entire length of the cadaver in a single CT image, the cadaver height was determined as the sum of two measurements: the vertical distance from the top of the head to the top of a proximal femoral head and the vertical distance from the top of the same femoral head to the bottom of the heel on the corresponding leg. In this example, the height of the cadaver is calculated as 80.40 + 89.70 = 170.10 cm.

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64 Figure 25 Volume Viewer GUI screenshot. The plugin allows rotation of a 3D model constructed from the CT images about different axes and allows cross sectional views on the 3D model. Two dimensional snapshots can then be extracted and used to derive measurements. In the figure, the pelvis w as rotated so that it was parallel to the screen thus allowing appropriate measurement of femoral head diameters.

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65 Figure 26 Volume Viewer pelvic measurements. A ) measurement of pelvic height and width. B) measurement of the anterior sacral length. A. B

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66 Figure 27 Percent error histograms for each of the final models select ed in this study. A) pooled; B ) sex specific.

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67 CHAPTER 3 MR FAT FRACTION QUANTIFICATION METHODS Bone marrow (BM) consists of an intricate bone scaffolding structure, trabecular bone, that results in cavities that are occupied by the soft tissue component of BM, consisting of cells --trabecular active marrow (TAM) cells and adipo cytes--, intracellular fluid, and vasculature. As discussed in Chapter 1, for the purposes of this dissertation work, bone marrow cellularity or cellularity factor (CF) is defined as the fraction by volume of soft marrow not occupied by adipocytes (i.e. one minus the fat fraction by volume). This definition is in line with the use of this quantity in radiation dosimetry and the current limitation in resolution of anthropometric computational phantoms used to calculate absorbed doses to BM. The current standard clinical method for measuring CF in a patient is by a bone marrow biopsy of the iliac crest. However, this method has two important limitations. First, it does not provide sufficient spatial resolution since it determines CF using a very small volu me of marrow, and CF is not perfectly homogeneous in a given bone site. Second, it can only be performed at the iliac crest and CF is known to vary between bone sites. Magnetic Resonance Imaging (MRI) provides a noninvasive alternative that not only all ows the determination of CF at any location in the anatomy, but allows its mapping at fine resolution. This chapter provides a review of magnetic resonance imaging (MRI) methods that can be used to quantif y CF in a patient as one minus the fat fraction or directly as the water fraction. E ach method is explai ned, discussed, and scrutinized. The in vitro accuracy (i.e. accuracy in a phantom) and in vivo accuracy (accuracy in a living subject) of the methods is discussed in separate sections of this chapter.

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68 A background section is presented first in order to provide readers who may not be familiar with MRI some fundamental MRI concepts necessary to understand the subsequent discussion of fat water separation methods. When possible, information is explained conceptually, else appropriate formulae are presented. A thorough introduction to the fundamentals of MR imaging is beyond the scope of this chapter. For a more indepth and complete description, the reader is referred to the following textbooks ( 83, 84) Background Basic MR Physics MR fat fraction quantification is based on the excitation of hydrogen nuclei. In this dissertation, the term proton is used to refer to hydrogen nuclei. Each hydrogen nucleus spins about its central axis and the spin generates a magnetic field around it which is referred t o as a magnetic moment A nonmagnetic substance in the absence of an external magnetic field presents a random distribution of orientations of proton magnetic moments (Figure 3 1A), which result in a null net magnetization (M). If the substance is placed in an external uniform magnetic field (B0), the majority of proton magnetic moments will orient in the direction of the external field (Figure 3 1B), resulting in a nonzero net magnetization parallel to B0. This orientation of the net magnetization vec tor is referred to as the equilibrium position and the axis along this direction is called the longitudinal axis. An MR image cannot be generated when the magnetization is in its equilibrium position. It is necessary to tilt the magnetization away from this orientation. Then, the magnetization will precess about B0 as it makes its way back to equilibrium at a

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69 frequency called the Larmor frequency Hydrogen nuclei in water molecules precess at the Larmor frequency of hydrogen (f0) given by = = ( 42.574 / ) (3 1 ) where is the gyromagnetic ratio for hydrogen divided by 2 and B0 is the static magnetic field strength in T eslas (T). A radiofrequency (RF) pulse is an electromagnetic wave that can be tuned to a specific frequency, just like i n a radio. The RF pulse is generated by a rotating magnetic field typically referred to as B1. RF pulses can be tuned to the Larmor frequency of hydrogen in water to tilt the magnetization by any angle. The longer the RF pulse is applied, the larger the angle by which the magnetization is tilted from the longitudinal axis. A 90o RF pulse flips the equilibrium magnetization (M0) o nto a plane orthogonal to B0the transverse plane (Figure 3 2A). Once the RF pulse is turned off, the magnetization begins a precession about B0 (Figure 3 2B) which ends when the magnetization is once again at equilibrium, i.e. parallel to B0. The magnetization can be broken down into two vector components: a longitudinal component parallel to B0 and a transverse component in the orthogonal plane. A s the magnetization returns to equilibrium, the transverse component of the magnetization the transverse magnetization (Mxy) traces a spiral on the orthogonal plane that ends at the origin ( Figure 3 3 ) The MR signal is proportional to the magnitude of the transverse magnetization, which changes as the magnetization vector traces the spiral path. T he MR signal takes the shape of a damped oscillation (projection of spiral on Figure 33). The MR signal is also referred to as the FID or free induction decay

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70 The process by which the transverse magnetization returns to equilibrium is called relaxation. Two types of relaxation are defined in terms of the two components of the magnetization: the decay of the transverse com ponent ( transverse relaxation), and the recovery of the longitudinal component to equilibrium ( longitudinal relaxation) The return to equilibrium is the result of interactions between proton magnetic moments. These interactions cause the transverse components of the magnetic moments to precess at a slower rate, which results in magnetic moments precessing out of phase. Out of phase magnetic moments reduce the net magnetization by cancellation of vector components ( Figure 3 4 ) When this happens, one says that the transverse magnetic moments fan out or that the magnetization dephases. A very useful analogy that hel ps visualize this effect is the one of runners in a circular track. At the beginning of the race all runners run together, in phase. Magnetic moments that begin to slow down due to interactions with other magnetic moments can be conceptually viewed as ru nners running slower because they become tired. Some runners tire more than others, so they begin to fall behind and now run out of phase with respect to faster runners. The runners begin to spread around the circular track ; i.e. the magnetization begins to dephase. The time needed for the transverse magnetization to decay to about 37% of its original magnitude is called T2, while the time needed for the longitudinal magnetization to increase to about 63% of its maximum is called T1. Relaxation times are different for different substances, and this is what provides contrast in MR images. In vivo, T1 increases at higher magnet strengths, while T2 remains the same or is slightly shorter

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71 ( 85) Hence, image contrast in T1 weighted images is expected to be weaker at larger field strength. The MR signal is detected by a receiving coil placed around the object. There are different types of coils used in MRI that are specifically designed and optimized for imaging different parts of the body: e.g. head coil, torso c oil, knee coil. As previously stated, only the transverse component of the magnetization contributes to the MR signal. The transverse magnetization is a timevarying magnetic field, and consequently (Faradays Law), induces a timevarying current in the coil. This time varying current is the FID. Gradient Echo ( SPGR) Imaging In the gradient echo or spoiled recalled gradient echo (SPGR) sequence, the RF pulse typically flips the magnetization at a flip angle ( ) that is less than 90o (Figure 35). This is done to shorten imaging time by reducing the repetition time (TR) i.e. the time allowed for the longitudinal magnetization to recover before it is once again flipped onto the transverse plane. By flipping the magnetization by onl y a component of the equilibrium magnetization (M0) is flipped onto the transverse plane: M0sin The smaller the flip angle, the smaller the transverse component of the magnetization and consequently the weaker the MR signal. However, since the other c omponent of the longitudinal magnetization, M0cos remain s in the z axis after the flip, it is possible to make TR very short For example, with a flip angle of 30o, half (sin30o) of the equilibrium magnetization is flipped onto the transverse plane, wh ile 87% (cos30o) of the equilibrium magnetization remains along the z axis. The advantage of a shorter TR is faster imaging.

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72 The MR signal acquired after the RF pulse is the sum of individual signals that originate from different locations on the object. Since the individual signals a re detected as a signal sum it is not possible to determine the points of origin of each signal and hence it is not possible to produce an image of the object. Position information can be included into the signal by applying a frequency encoding gradient. A gradient consists of a magnetic field that varies in strength in a linear fashion with position ( Figure 3 6) so that each point in space experiences a unique B0field strength depending on its position. Since the precessional frequency of a proton is directly proportional to the magnetic field strength at its location ( Equation 3 1), each proton will have a unique precessional frequency that can be used to determine the position from which signal originated. The Philips Achieva 3T scanner can produce gradients from 20 to 80 mT/m. Three orthogonal gradients x, y, and z are needed to define position in threedimensional space. A consequence of applying a gradient is that it forces the magnetization to fan out around the unit circle ( Figure 3 4) In order to recover the signal all dephased magnetic moments must be brought back in phase. This is achieved by establishing a gradient of opposite polarity to the initial gradient, as depicted in Figure 3 5 under Gread. The gradient is referred to as a read gradient, because it is the frequency encoding what allows the time varying signal or FID (Figure 3 3) to be read into the scanner. The negativepolarity gradient reverses the phase differences introduced by the positive polarity gradient and as the magnetic moments begin to rephase the MR signal increases from zero up to a maximum and then decreases again back to zero. The signal at the moment it reaches a maximum is referred to as an echo, since it is the

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73 ret urn of the original signal, just as an echo is the return of the original sound. Since the echo is the result of the reversal in the read gradient and is referred to as a gradient echo. The time from the flip pulse to the gradient echo is known as the ec ho time (TE). The FID used to produce the image is acquired during the time the reversepolarity read gradient is applied. Gphase and Gslice in Figure 35 depict the phaseencoding and slice selection gradients. The phaseencoding gradient also encodes s patial information into the MR signal. In contrast to the read gradient, the phaseencoding gradient is applied for a much shorter amount of time and the resultant phase is not removed by a reverse polarity gradient. The phaseencode gradient is applied perpendicular to the read gradient. A single phaseencoding step is performed during each TR and phaseencode gradients are sequentially incremented each TR. If the readgradient is applied along the x direction, phaseencoding will be applied in the y d irection to encode y spatial information into the FID. The larger the number of phaseencoding steps, the finer the image resolution in the y direction. Image resolution in the x direction, however, is provided by the sampling frequency with which the FI D is recorded. The number of frequency encode steps and the number of phaseencode steps determine the twodimensional array size that makes up the image. The sliceselection gradient defines the location and thickness of the slice through the object from which the image is generated. By a mathematical procedure called Fourier transformation it is possible to decode the information in the timevarying FIDs to produce the twodimensional image of the slice through the object. The image pi xel s

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74 originate from tiny volumes ( voxels ) with dimensions given by the number of readsampling steps, the number of phaseencode steps, and the slice thickness. As discussed previously, the MR signal experiences irreversible decay with time due to relaxation effects. Hence, the signal loses strength during the time TE. Signal loses can also occur when the B0 field is not perfectly uniform, since the strength of the B0 field determines the precessional frequency. Even though the B0 field inside the magnet can be made very uniform through a process known as shimming, the introduction of an object into the uniform field will result in warping of the magnetic field lines due to differences in magnetic susceptibility between the materials that make up the object. The warping results in local variations in the strength of the B0 field which are referred to as inhomogeneities. B0inhomogeneity results in a spread of resonant freq uencies for a given material, which causes a shortening of the decay time of the MR signal. The relaxation time in this case is referred to as T2*, defined as = 1 2 = 1 2 + ( 3 2 ) where B0 is the magnitude of the magnetic field inhomogeneity across a voxel. As can be determined from Equation 3 2 T2* is shorter than T2. Figure 3 7 shows a diagram depicting the two relaxation times. The decay is typically monoexponential, i.e. exp ( TE/T2* ). The signal to noise ratio (SNR) can be optimized by selecting the flip angle using the relation = (3 3 )

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75 where max is the flip angle (also known as the Ernst angle) that maximizes SNR for a given TR. B1 homogeneity is particularly important in SPGR since it affects the uniformity of the flip angle across the image ( 85) Spin Echo (SE) Imaging The main differences between the SPGR and the spinecho (SE) sequences (Figure 38) is that in SE, (1) the RF pulse is always set to provide a 90o flip, and (2) there is a second RF appl ied that flips the magnetization by 180o about an axis on the orthogonal plane. After the 90o pulse, the transverse magnetization begins to dephase due to transverse relaxation and B0inhomogeneity effects. The 180o pulse flips the transverse magnetic mom ents about an axis perpendicular to the longitudinal axis forcing them to rephase (Figure 39). It is for this reason that this pulse is commonly referred to as a refocusing pulse. The rephasing effect of the 180o pulse can also be visualized using the runners analogy. Recall that dephasing can be conceptually viewed as the process by which runners begin to spread around the circular circuit because some runners become more tired than others and therefore fall behind. The result is a spread of runners in the circular circuit, with faster runners farther away from the start line than slower runners. Suppose the runners are suddenly instructed to turn around (180o turn) and therefore now run toward the start line. Slower runners are closer to the start line, so even though they run slower, they will reach the start line at the same time as the faster runners who start farther away. The simultaneous arrival of all runners to the start line results in the spin echo the instant at which the image is acqui red.

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76 It is important to note that the 180o pulse does not reverse T2 decay. Just as runners lose speed irreversibly as they lose stamina, T2 decay is irreversible. Hence, just as in SPGR the signal maximum at TE is less than the original signal maximum experienced immediately after the 90o flip. An important advantage of the refocusing pulse, that motivated the development of this sequence in 1950 by Erwin Hahn, is that the pulse eliminates signal loses due to dephasing by B0 inhomogeneities. The intro duction of an object into the static magnetic field results in the warping of magnetic field lines at different locations on the object This occurs because the magnetic field strength is proportional to a quantity called magnetic susceptibility which is different for different materials. The magnetic susceptibility of air is different than the magnetic susceptibility of biological tissue, and the different materials that make up biological tissue also have different magnetic susceptibilities The warpi ng of magnetic field lines results in loss of uniformity of the magnetic field strength, which now is different at different locations in the object being images. As a result, some protons will experience lower magnetic field strengths than B0 and therefore precess at a frequency lower than the Larmor frequency T he refocusing pulse allows these protons to catch up with the rest. The effect of inhomogeneities is reversible because inhomogeneities do not change during image acquisition and do not cause energy losses In the SPGR sequence there is no 180o refocusing pulse and t he echo is only the result of the read gradient reversal. The negative gradient reverses the phase differences introduced by the positive gradient, but it does not reverse phase shifts introduced by magnetic field inhomogeneities, since the inhomogeneities continue to

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77 affect the local value of B0 during the application of the gradients and therefore continue to dephase the magnetic moments as gradient phase reversal takes place. In an SE sequence (Figure 38), both a spin echo, due to rephasing by the 180o pulse, and a gradient echo, due to the gradient reversal, occur simultaneously. This is achieved by applying the refocusing pulse at a time given by half of TE Since the refocusing pulse removes the effects from B0inhomogeneities, the signal decays as exp( TE/T2), rather than exp( TE/T2*). Since T2* is shorter than T2 this implies a faster signal decay in a SPGR sequence compared to an SE sequence. Chemical Shift Human and animal tissue may be very simplistically viewed as consisting of three basic components: water, fat, and bone. Pixel intensities in an MR image are proportional to the MR signal strengt h generated by hydrogen nuclei in tissues, which is proportional to the abundance of hydrogen nuclei commonly referred to as the proton d ensity Bone does not result in appreciable MR signal because it contains very little hydrogen and magnetic moments decay very quickly in a solid lattice. Consequently, bone appears black in MR images and pixel intensities are primarily due to water and fat protons. Protons in water precess at the Larmor frequency of hydrogen ( Equation 3 1 ). However, hydrogen nuclei in other molecules precess at slightly different frequencies due to local variations in magnetic field strength in a phenomenon known as chemical shift Electrons in motion in the electron cloud of the atoms in a molecule induce a local magnetic field that locally opposes the external magnetic field. The local net strength of the magnetic field is thus reduced and consequently the hydrogen nuclei found there

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78 precess at a lower frequency. This influence of the electron clouds on the local magnetic environment i n a molecule is referred to as shielding. The degree of shielding depends on the electron density. The difference in frequency with r espect to the water frequency, expressed as a fraction of the water frequency, is called chemical shift ( ). It is typically expressed in parts per million (ppm). = = (3 4) The chemical shift between fat and water is approximately 3.4 ppm. Even though this results in a very small difference in precessional frequency, it can be used to separate the contributions produced by water and fat protons to produce separate images as demonstrated by the methods described later in this chapter General MR Signal Model In order to discuss fat water quantification methods, it is important to consider a model for the pi xel intensi ties in the images (Sn). A general model is shown below: = + ,+ (3 5) where is the random noise associated with image n Note that the symbol i refers to 1 Hence, the pixel intensities are complex quantities, with r eal and imaginary part s. The proton densities of water and fat, and respectively, are also complex Parameters and are the T1 recovery factors and and are the T2 decay factors (T2* decay factors in the case of SPGR) for water and fat, respectively. For SE imaging, = 1 (3 6)

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79 = 1 (3 7) = e (3 8) = e (3 9) For SPGR imaging, = 1 1 ( 3 10) = 1 1 ( 3 11) where is the flip angle. Equations 3 8 and 39 still apply, but T2 must be replaced by T2*. The parameter is the phase angle difference between the water and fat magnetizations due to chemical shift, where n denotes the image acquired at echo time It can be expressed as = 2 (3 1 2 ) where f is the chemical shift in frequency, given by Equation 3 4. The phase is the additional phase introduced by magnetic field inhomogeneity resulting from quality of shim and magnetic susceptibility effects introduced by the presence of the subject in the magnetic field. It is given by ( ) = 2 (3 1 3 ) where B is the change in magnetic field strength due to local magnetic field inhomogenei t y. It is typically referred to as the field map.

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80 It is important to note that all of the variables in Equation 3 5 are pixel dependent ; that is, they are functions of position ( x, y). The position dependence is not shown to keep the expression simple. MR Fat Fraction Quantification Methods Fat /Water Suppression MR images are the result of the contribution of signal by both water and fat, and the pixel intensities are proportional to the proton densities of each. In order to measure CF one requires either the fat fraction or the water fraction. One way to determine these fractions is by acquiring two images: one that contains the signal c ontributions of both water and fat and another in which either the water or fat signal has been eliminated Then, the fat or water fraction at every pixel is calculated by dividing the singlecomponent image by the twocomponent image. The contribution of either water or fat to the image can be eliminated by adding a sequence before the imaging sequence that eliminates the unwanted signal This preimaging addon sequence consists of a 90o RF pulse of narrow bandwidth centered at the resonant frequency of the signal to be eliminated; i.e. either the fat or water resonance. This RF pulse will flip the magnetization of the unwanted signal onto the transverse plane, while the magnetization due to the desired signal remains in the longitudinal axis. A spoili ng gradient is then applied, which dephases the magnetization of the unwanted signal. If an imaging sequence follows, only the magnetization due to the desired signal will contribute to the image. Techniques that use this approach to eliminate either water or fat from the MR signal are known as spectral saturation techniques.

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81 Fat saturation is typically used to localize metastases (e.g. myeloma, lymphoma) in bone marr ow since tumor cells tend to contain more water than normal bone marrow cells ( 86) A disadvantage of spectral saturation is that the saturation pulse is long in time (narrow bandwidth) and with the spoiling gradient take up a large portion of the TR, hence either limiting the number of echoes and slices that can be acquired within each repetition or requiring the use of longer imaging times. The narrower the frequency band to be saturated, the longer the saturation pulse. In addition, complete fat suppression requires a perfectly uniform static magnetic field across the anatomy and perfect uniformity of the saturation pulse. Static field inhomogeneities inherent to the scanner can be minimized by proper shimming, but inhomogeneities introduced by local susceptibility differences along the anatomy cannot be eliminated. These inhomogeneities result in incomplete suppression at different points in the image and even suppression of the signal one does not want to eliminate ( 87, 88) Incomplete suppression is expected to be more problematic at lower field strengths, since at higher field strengths there is a greater separation in frequency between the water and fat peaks (Figure 31 0 ). Even in the absence of magnetic susceptibility effects, selective saturation methods inevitably result in incomplete fat suppression simply because fat protons do not present a single resonant frequency. The shift of 3.4 ppm corresponds only to methylene (CH2) groups, but lipids in human and animal fat contain other groups (Fig ure 3 1 1 ) with chemical shifts with respect to water ranging from 4.0 to 1.3 ppm ( 38, 8992)

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82 Spongiosa consists of a trabecular network with soft marrow embedded in its cavities. The presence of trabecula in marrow causes changes in the local value of the B0 field. Since bone has a larger magnetic susceptibility than soft marrow, the B0 field magnitude increases near trabeculae. Figure 31 2 depicts how the severit y of inhomogeneity depends on the spacing between trabeculae. The magnitude of the magnetic susceptibility effect is proportional to factors that increase bone density e.g. the number of trabeculae the size of the trabeculae, the number of trabeculasof t marrow interfaces, and the bone surface to volume ratioand increases with the magnitude of B0 ( 93) The magnetic susceptibility difference between bone and marrow is about 3. 0 ppm, very close to the 3.4 ppm chemical shift between water and fat. Hence, a fat suppression via saturation techniques will most likely result in water signal also being eliminated from the image where marrow is in close proximity to trabecular bone. Fat has a shorter T1 than water and therefore the longitudinal magnetization due to fat decays faster than the longitudinal water magnetization. Another way by which an unwanted signal can be eliminated from the image is by acquiring the image at the prec ise instant at which the longitudinal magnetization of the unwanted signal is zero. When the 90o RF pulse of the imaging sequence flips the magnetization onto the transverse plane, only the magnetization due to the desired signal is flipped and the subsequently acquired image will only be due to that signal. This approach is referred to as i nversion r ecovery (IR), and consists in applying a 180o prepulse that inverts the longitudinal magnetization (of both signals) and starting the imaging sequence at the precise instant at which the longitudinal magnetization of

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83 the unwanted signal is null. The time at which the longitudinal magnetization is zero is called the inversion time (TI), and it is given by ( ) = 1 2 0 = 1 2 = 2 (3 1 4 ) Hence, to eliminate fat from the image, the imaging sequence would have to be applied at a time given by ln(2) times the T1 value for fat. Both spectral saturation and IR are typically used to detect the presence of metastases in bone marrow ( 86) I n contrast to spectral saturation techniques, IR is not affected by B0 inhomogeneity. However, since the image is acquired after T1 decay of the magnetization during the time TI, the signal strength is reduced, which results in images with poor signal to noise ( 87) Signalto noise can be i mproved by selecting TR to be three to five times the T1 of water, but doing so results in very long imaging times. Studies that have measured water and fat T1 in bone marrow have demonstrated that it presents inter patient variability and variability with bone marrow disease state ( 57, 90, 94, 95) T1 measurements are time consuming, so it is impractical t o measure T1 in every patient. The use of published average T1 values to determine TI for a specific patient will result in incomplete nullification of the fat signal. In the case of fat suppression, IR also results in suppression of signal from tissues with T1s close to the T1 of fat, such as blood in hematomas or contrast containing tissues ( 87, 96, 97)

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84 IR consists in acquiring the signal when the fat magnetization is zero. However, this is based on a single lipid peak and therefore the resultant image will include contributions from other lipid resonances that have longer or shorter T1. 1H NMR Spectroscopy After the magnetization vector is flipped onto the transverse plane by an RF pulse, the vector begins a precession about B0 back towards its equilibrium position The FID (Figures 33 and 37) is the resulting MR signal intensity detected at the receiver coil as a function of time. It is a damped oscillation, sinc e t he signal decays as the transverse magnetizat ion dephases via T1 and T2 relaxation mechanisms. The two most commonly used pulse sequences in spectroscopy are STimulated Echo Acquisition Mode (STEAM) and Point REsolved SpectroScopy (PRESS). In spectroscopy, rather than exciting a whole slice only a specific volume (voxel) is excited, and a read gradient then acquires the FID. The excited volume is typically referred to as the VOI (voxel of interest). Since the spectrum is acquired from only that volume, this type of spectroscopy is called singlevoxel spectroscopy. Both STEAM and PRESS result in the excitation of a 3D volume (a prism or cube) by means of three orthogonal sliceselective RF pulses that are applied simultaneously In STEAM, this is accomplished by applying three 90o orthogonal slice selective pulses, while in PRESS it is accomplished by applying a 90o pulse and two 180o pulses. Since three orthogonal slices are excited in order to define the VOI, spoiler gradients are included in the sequences to eliminate signal from outside the VOI. The MR signal is recorded until it decays, providing the FID. Since the objective is just to record the FID and not to produce an image, phase and frequency encoding gradients are not required.

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85 However, these may be included in order to produce an image of the excited voxel to verify localization accuracy. The FID consists of a sum of signals at different frequencies (Figure 31 3 ). As previously discussed, hydrogen protons in dif ferent molecules experience slightly different frequencies due to chemical shift and hence each type of molecule contributes a signal at a unique frequency. The amplitude of each signal is proportional to the abundance of each type of molecule. Applicati on of a Fast Fourier Transform (FFT) of the FID results in the NMR spectrum (Figure 3 1 3 ). The FFT converts the FID from a function in ti me to a function in frequency i.e. the spectrum Any periodic function can be expressed as a sum of a basis of peri odic functions, such as the sine and cosine. Hence, the FID can be expressed as ( ) = + ( ) + ( 2 ) + + ( ) + ( 2 ) + (3 15) where the coefficients and are calculated using the Fourier Transform (FT) operation, defined by ( ) = { ( )} = ( ) (3 16) where = ( ) + ( ) The FT results in a function F( ) which is complex; that is, it has a real and an imaginary part. Note that the FT operation converts a function in time to a function in frequency and hence it is a mapping from the timedomain to the frequency domain. In the spectrum (frequency domain) each individual signal is represented by a peak at its corr esponding frequency (Figure 31 3 ) In the FID, the amplitude of each individual signal is proportional to the abundance of the type of molecule in the sample

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86 that produced it. In the spectrum, it is not the amplitude, but the area under the peak, what is proportional to the abundance of the molecule. The FFT is unable to resolve each frequency with infinite accuracy in a signal that is decaying, and hence each peak has a width resulting from the uncertainty in the frequency estimation. The full width at half maximum (FWHM) of each peak in the spectrum also known as the line width (LW), is equal to = = 1 ( 2) (3 1 7 ) where T2* is given by Equation 3 1. I n the absence of magnetic inhomogeneity effects, substances with short T2 will have larger line widths than substances with long T2. For example, the water peak is expected to have a larger line width than fat since T2 of water is longer than T2 of fat When multiple resonances occur close to each other, the individual peaks become confounded as they overlap their neighbors, resulting in peaks that appear to have relatively large line widths. Since chemical shift is directly proportional to the strength of B0, spectra appear a lot sharper at high field strength, with relatively little overlap of adjacent peaks. However, in bone marrow, magnetic field inhomogeneity due to the presence of trabecula results in spectral line broadening, and even at 3.0 T it is difficult to resolve most of the li pid peaks. Consequently, most studies that use clinical magnet s typically perform fat quantification by assuming that fat is represented by just the methylene peak. Fat fraction can be estimated from the spectrum as the area under the fat peak (s) divided by the area under the entire spectrum. The areas must be corrected for T2 decay prior to the calculation. T1 corrections are generally not required since

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87 spectroscopy sequences typically use long TR. MR spectrum analysis software programs include algori thms that allow the fit of multiple lipid peaks even if these are not distinguishable by looking at the spectrum The accuracy of the fat fraction estimation is likely to improve if more lipid peaks are considered. Unfortunately, there is a limitation. There is a lipid peak ( HC=CH, olefinic fats) slightly to the left of the water peak that, at clinical magnet strengths, is typically too close to the water peak to be clearly resolved. Consequently fat fraction quantification by NMR spectroscopy will i nevitably result in underestimation. Fortunately, t he contribution to the area under the lipid peaks from the olefinic fat peak is typically very small. Fat suppressed spectra can be acquired using a saturation prepulse prior to the acquisition of the F ID. However, it is possible that this process also results in some suppression of nearby lipid peaks, including the olefinic peak. Some authors calculate the fat fraction in terms of the amplitudes of the fat and water peaks ( 39, 92, 98, 99) They first calculate the fat to water peak ratio (FWR) by taking the ratio of the peak amplitude of fat by the peak amplitude of water and then calculat e fat fraction (FF) as = ( 1 + ) (3 18) Chemical Shift Misregistration Given that in MRI precession frequencies are used to encode spatial coordinates, chemical shift may result in the incorrect placement of signal intensities in the image chemical shift misregistration. The effect occurs along the frequency encoding (read out) direction in the image, which is typically right to left. The greatest misregistration occurs for fat (CH2) protons because they present a large chemical shift (3.4 ppm) with

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88 respect to water, and the effect is most noticeable at fatty tissue boundaries. Chemical shift misregistration results in the appearance of bright and dark bands at t he boundaries of certain organs The effect was first demonstrated by Soila et al. ( 100) The authors produced images of a patients abdomen in which they changed the direction of the readout gradient. Dark and bright bands were evident around the patients kidneys and the location of the bands switched with the rever sal of the readout gradient direction. To determine if the bands were due to patient motion, the authors repeated the experiment on an oil water phantom, where the same effect was observed. The dark band is the result of a signal void due to the fat signal having been shifted upstream (Figure 31 4 ) in the direction of the readout gradient (i.e. toward the lower fre quencies ) while the bright band is the result of signal addition since fat signal that originated downstream is shifted upstream adding to the water signal there. The distance that the fat signal shifts upstream x, can be calculated by = (3 1 9 ) where f is the chemically shifted frequency given by Equation 3 4 FOVx is the field of view dimension in the readout direction, and rBW is the receiver bandwidth. The shift in terms of number of pi xels can be then calculated by dividing x by the image resolution. In some MR scanners the receiver bandwidth is reported as bandwidth per pi xel In such a case, the shift in number of pi xels can be calculated as pixels = / pixel (3 20) The shift in mm can be calculated by multiplying the shift in pixels by the image resolution. For example, given a n rBW of 336.8 Hz/ pi xel in a 3T magnet

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89 pixels = (3 .5 ppm ) ( 42.574 MHz / T )( 3 T ) 336.8 Hz / pixel 1 .3 pixels Given an image resolution of 2.048 pixels per mm, the shift corresponds to a distance of ( 1 .3 pixels ) ( 2 .048 pixels / mm ) 0 .6 mm In this example, the chemical shift misregistration would not be noticeable in the images, since it is less than one pixel From Equation 3 1 9 or 3 20 it is clear that chemical shift misregistration can be minimized by increasing the receiver bandwidth. However, increasing the bandwidth also decreases signal to noise, so one may have to compromise between chemical shift misregistration and adequate SNR. Chemical shift misregistration can be corrected by shifting water pi xels in the readout direction by the amount calculated in Equation 3 20, but given that the calculation may not lead to an integer and that pi xels must be shifted by an integer amount, an error can be introduced when correcting the im ages ( 44) A more accurate method for correcting chemical shift misregistration is by introducing the shift calculated from Equation 3 1 9 into the Four ier transform using the shift property of the Fourier transform ( 44) ( ) = ( ) (3 21) where is the Fourier transform, W is the pixel intensity in the water image, s is the spatial frequency variable, and x is the chemical shift misregistration in units of distance.

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90 Ishizaka et al. ( 101) enhanced the chemical shift misregistration to allow for water fraction measurements in the lumbar spine. The read gradient was placed parallel to the main axis of the spine. In this manner, when the fat signal is shifted in the readout direction, the void regions (dark bands) in t he image are due only to water protons while the overlap regions (bright bands) correspond to the sum of the water and fat signals. By selecting equal sized regions of interest in both bands it is possible to calculate a ratio that is equivalent to the water fraction (surrogate for CF ) in the bone marrow region. The authors report a shift of the fat signal of approximately 10 mm, and claim this ensures that the shifted lipid signal from one vertebra does not overlap with the water signal of the adjacent v ertebra upstream. This is reasonable, considering an average thoracic vertebral height of 2.50 cm ( 102, 103 ) The method is straightf orward, simple to apply and only requires one image acquisition. However, I shizaka et al. ( 51, 101) point out several limitations to the method: (1) the water signal includes olefinic lipids (5% of lipids), which have a chemical shift comparable to that of water, thus resulting in an overestimation of the water fraction; (2) since fat and water experience different relaxation times, the ratio based on uncorrected signal intensities is only valid for long TR and short TE; (3) it is affected by susceptibility effects due to the presence of bone and iron in blood; and (4) it assumes that CF is the same at the upper and lower halves of the vertebra. This technique is not applicable in bones with small thickness and/or that are highly curvede.g. ribs and cranium since misregistration will sh ift some of the lipid signal outside of the bone, and in bones that are in close proximity to each other e.g. scapula and humeral head, pelvis and femoral headsince misregistration will result in

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91 signal contamination between adjacent bones. Hence, this m ethod may be limited to the spine. Water Fat Separation Methods There are several MR methods that use the fat water chemical shift difference to acquire images where the fat and water magnetizations are at specific phase angles that allow the production of separate images of water and fat protons during post processing. These methods are commonly referred to as fat water separation methods. The first fat water separation method was introduced by Dixon ( 104 ) in 1984 and it is therefore known as the Dixon method. Subsequent variations of the method are also referred to as Dixon methods. Dixon methods are based on the following observation. At the end of the 90o RF pulse the water and fat (CH2) transverse magnetizations point in the same direction i.e. the magnetizations are in phase (IP). This situation does not last, since due to chemical shift the water magnetization precesses 3.4 ppm faster than the fat magnetization. At 3T, the precession frequency difference due to chemical shift is = = ( 3 .4 ppm )( 42.57 MHz / T )( 3 .0 T ) = 434.3 Hz Since the fat magnetization lags behind the water magnetization, the total magnetization goes through periodic cycles of maxima and minima (Figure 3 1 5 ): maxima when the two magnetizations are in phase--and minima when they point in directly opposite directions i.e. when they are in opposed phase (OP). The total magnetization minima occur when the water and fat magnetizations are in OP. Hence, they occur when the phase difference ( ) between the magnetizations is an odd multiple of The times at which OP occurs can be calculated as follows.

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92 | | = ( 2 + 1 ) = 0 ,1 ,2 OP= ( 2 + 1 ) 2 OP= ( 2 + 1 ) OP=( ) =( ) = 0 ,1 ,2 (3 22) In a 3T magnet = 434.3 Hz, so minima occur every odd multiple of 1.15 ms. Maxima occur when the phase difference is an even multiple of 2 Therefore, IP= = = 0 ,1 ,2 (3 23) Consequently, in a 3T magnet maxima occur at t = 0 s and at every even multiple of 2.30 ms. In a SPGR sequence (Figure 3 5 ) one can obtain IP and OP images by shifting the read gradient by 1/ ( 2 f ) with respect to the TE used for the IP image. In a SE sequence (Figure 3 8 ), the refocusing pulse eliminates all phase shifts at echo time. Hence, the water and fat magnetizations are always in phase at TE and only IP images are produced. In order to produce an OP image using SE, the Hahn echo must occur at a time 1/ ( 2 f ) prior to the gradient echo. This is accomplished by shifting the refocusing pulse forward by 1/ (4 f ) while the read gradient is unchanged. At TE, the signal is the result of the gradient echo that includes phase shifts accumulated during 1/ ( 2 f ) In the OP ima ge, pixel intensities are determined by the difference between the water and fat magnetizations, whereas in the IP image, pixel intensities are determined by the sum of the water and fat magnetizations. The sum of an IP and an OP image therefore results i n an image that is only the result of signals from water protons i.e.

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93 the water imageand the difference of the IP and OP images results in an image that results from fat protons only i.e. the fat image. This technique was first proposed by Dixon ( 104) in 1984 and is therefore known as the Dixon method. Given that the original method is based on the acquisition of two images, but some future variations of the method require acquiring more than two images, this mode of the Dixon method is often referred to as a two point or a dual echo Dixon method (2PD) Methods that require t hree images are referred to as threepoint Dixon (3PD) and so on. Since 2PD consists i n adding or subtracting coregistered pixel s in the IP and OP images, it will only acc urately produce water only and fat only images if chemical shift misregistration is negligible. This can be ensured by selecting an appropriately large receiver bandwidt h, as discussed previously. If this approach is not feasible, the misregistration can be corrected by performing an inverse Fourier transform shift along the readout direction ( 44, 105) The accuracy of the water and fat separation depends on how close the phase angle between the water and fat magnetizations is to 180o when the OP image is acquired. If the water and fat magnetizations are not exactly antiparallel the OP image pi xel intensities will be too large, resulting in an underestimation of the fat fraction for true fat fracti ons below onehalf and an overestimation for true fat fractions above onehalf ( 60) Several factors can result in deviations from 180o in the phase angle between the water and fat magnetization at TE : (1) uncertainties in the parameters used to calculate tOP; (2) inaccuracy in the shifting of the refocusing pulse by tOP/2; (3) B0inhomogeneities. The time delay required for the water and fat magnetizations to be in

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94 opposedphase, tOP, is calculated assuming a known chemical shift between water and fat. If the chemical shift is not known accurately, the water and fat magnetizations will not be at 180o when the OP image is acquired. The same error occurs when tOP is calculated accurately but the refoc using pulse is not shifted accurately by tOP/2. The time delay required for the water and fat magnetizations to be at 180o, tOP, is determined at a fixed value of B0. Any factor that changes the local value of B0 will result in a deviation from 180o of t he angle between the water and fat magnetizations at the time the OP image is acquired. The scanner intrinsic B0 inhomogeneit y can be made negligibly small --i.e. much less than 1 ppm as reported by vendors ( 85, 106) -by careful shimming of the magnet, but local inhomogeneities introduced by magnetic susceptibility differences in the materials that make up the objects placed in the field cannot be avoided. B0inhomogeneities will result in the water and fat magnetizations not being directly opposite at multiple pixel s in the OP image. The largest magnetic susceptibility difference in bone marrow occurs between bone marrow soft tissue and trabecular bone. The difference in s usceptibility between these two tissues has been reported to be around 3.0 ppm ( 107 108) which is comparable to the chemical shift between fat and water. It is therefore not possible to distinguish pixel s where water and f at are opposed due to chemical shift from pixel s where water and fat are opposed due to susceptibility effects in the OP image, resulting in the potential for misidentification of water and fat pixel s. This misidentification results in what is referred to as fatwater switching since some fat pixel intensities end up in the water image and some water pixel intensities end up in the fat image.

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95 Dixon m ethod based on magnitude images Dixon ( 104 ) demonstrated his method using the SE technique to produce water and fat images of margarine, detergent, and an egg, and suggested removing B0 inhomogeneity effects by using magnitudeonly IP and OP images. However, as he noted, using magnitude images results in pixel s containing no fat and almost all fat to appear equally bright in the IP and OP images, and hence a pure fat pixel will appear with null intensity in the fat image (where IP and OP images are subtracted) and bright in the wat er image (where IP and OP images are added). Thus, the use of magnitude images results in fat and water switching. The effect wa s clearly demonstrated in the margarine cubes in his images, where, even though all margarine cubes we re identical in composit ion, one of the cubes is barely visible in the fat image. The same effect wa s observed in the liquid detergent container, where some fat pixel s we re missing from the fat image, and the water container, where some of the water pixel s appear ed in the fat im age. Consider the MR signal model ( Equation 3 5 ) For simplicity assume that the T1 recovery factors can be ignored. This assumption is valid if TR is large compared to T1 of water and fat. Further assume that TE is very short compared to T2 of water and fat so that T2 decay factors can also be ignored, and that the noise term is negligible. The MR signal model then simplifies to = + (3 2 4 ) If the chemical shift between water and fat (CH2) is accurately known, for the IP image, = = 1 and for the OP image, = = 1 Then, from Equation 3 2 4 = = ( + ) (3 2 5 )

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96 = = ( ) (3 2 6 ) In the case of SE imaging, the factor is unity in the IP image, due to th e refocusing pulse. Equations 3 2 5 and 32 6 become = ( + ) (3 2 7 ) = ( ) (3 2 8 ) If only magnitude images are considered, the phase term can be eliminated from the OP image and the sum and difference of the magnitude images provide the WF) images, respectively. If the water and fat magnetizations are W F are real positive quantities However, aW F having nonzero imaginary parts In such a case, the magnitude of the sum or difference of the two complex numbers will not be equal to the sum or differenc e of their W F are real and positive, from Equations 3 2 7 and 3 2 8 | | = + (3 2 9 ) | | = > (3 30) where | | denotes magnitude. Addition of the magnitude images results in (| | + | | ) = > (3 31) and subtraction of the magnitude images results in

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97 (| | | | ) = > (3 32) Equations 3 31 and 3 32 demonstrate that the assumption that the sum of the images leads to the water only image and the difference to the fat only image is only true for pi xels that contain more water than fat or equal amounts of fat and water. However, water or fat dominance cannot be unambiguously determined from magnitude images. Equation 3 32 can be rewritten as (| | | | ) | | = %fat if %water if < (3 33) Lodes et al. (111) demonstrated that SE 2PD based on magnitude images is unable to distinguish fat fractions that are greater than 50% from those that are smaller than 50% The authors prepared oil water phantoms by mixing seven different fat fractions of oil, water, gadolinium, and a surfactant ranging fr om 0 to 100%. IP and OP images were acquired and fat fractions were determined at each location of the phantoms in the images. The fat fractions measured by Lodes et al. ( 109) conformed to the upsidedown V shape predicted by Equation 3 33 (Figure 316) SPGR sequences typically result in T1weighted images due to use of flip angles that are less than 90o. The T1weighting can be used to determine fat water dominance when using 2PD with magnitude images. Hussain et al. ( 110) developed a post processing method which they call Dual Flip Algorithm, to determine fat dominance on T2* corrected SPGR Dixon images acquired at two flip angles: 20o and 70o. T2* correction was performed assuming the same T2* for fat and water, using a methodolo gy d iscussed later in this section.

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98 Hussain et al. ( 110) obtained SPGR images of an oil water phantom consisting of a 700mL bottle filled with equal volumes of water and mineral oil. The water was placed on its side in the scanner and an oblique slice was acquired along the interface between both liquids (Figure 3 17 ), providing a continuous gradient of fat fractions along the slice. Images were acquired at two flip angles: 20o and 70o. Equation 3 33 was used to calculate fat fractions assuming water dominance in all pixels. This resulted in two upsidedown V curves. However, the large flip angle data was shifted to the left due to overestimation of the fat fraction as a result of heavier T1weighting. U sing the se curve s it is possible to distinguish fat fractions smaller than 50% from fat fractions larger than 50%. The algorithm is performed at e ach pixel by comparing the fat fraction calculated at low flip angle to that calculated at large flip angle. If the small flip angle fat fraction is less than or equal to the large flip angle fat fraction, the fat fraction corresponding to the pixel is th e low flip angle fat fraction; else, it is one minus the low flip angle fat fraction. The authors provided a plot of corrected fat fractions for the phantom that fit nicely around the perfect agreement line thus demonstrating that the algorithm resolves t he ambiguity T1 and T2* decay were ignored in the development of Equations 3 31 and 332. In the case of SPGR imaging, if the flip angle is small, T1 decay is negligible. However, T2* decay cannot be ignored. Both the water and fat signals experience T2* decay and the IP and OP images will experience different amounts of T2* decay ( black curve in Figure 318 ) s ince each consecutive echo has decayed during the inter echo interval. Therefore, unless T2* decay is corrected (gray curve in Figure 318) or at least

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99 minimized, fat fractions will be grossly underestimated, especially in regions of high magnetic suscept ibility which shortens T2*. Since the decay is timesensitive, T2* decay can be minimized by acquiring the first echo with the shortest possible TE and the second echo immediately after the first ( 111) It is reco mmended that the OP echo is acquired prior to the IP echo, since in the OP echo pixel intensities are the result of the difference of the water and fat magnetizations and the T2* decay may make it difficult to differentiate when low pixel intensities are due to chemical shift differences or just T2* decay ( 111) Hussain et al. ( 110) performed T2* corrections using the IP and OP magnitude images. Their methodology can be understood using the signal model described by Equation 3 5. Ignoring T1recovery and noise terms, Equation 3 5 can be written as = + (3 34) Hussain et al. ( 110) make the following simplifying assu mption: = = = Then, Equation 3 34 is simplified to = + (3 35) When working with magnitude images, the phase information is removed and Equation 3 35 becomes | | = E + (3 36) Consider the case in which three echoes are acquired: an OP echo followed by two consecutive IP echoes. The equations for each echo are, from Equation 3 36, | | = E ( ) (3 37)

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100 | | = E ( + ) (3 38) | | = E ( + ) (3 39) Suppose the time interval between an IP and an OP image is Equations 3 38 and 339 can be rewritten as | | = E e ( + ) (3 4 0 ) | | = E e ( + ) (3 4 1 ) Then, e = | | | | = r (3 4 2 ) Equation 3 4 2 provides the T2* correction factor that can be applied to Equation 3 39. The corrected IP image is | |= | | e = E ( + ) (3 4 3 ) The T2* corrected fat fraction is calculated as (| | | | ) | | = %fat if %water if < (3 4 4 ) where | | is the magnitude of the first acquired image in the series (i.e. | | ). The Dual Flip Algorithm is simple to use, but it requires the acquisition of a minimum of six images, it depends on the assumption that water and fat have the same value of T2*, and, since flip angle is typically not uniform across MR images, the degree of T1weighting may not be consistent across a region of interest in the object being imaged. The method as described here consisted in acquiring, for each of the two flip

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101 angles, an OP, followed by two IP images, but it can also be performed by acquiring two consecutive OP i mages followed by an IP image. The assumption that the same T2* value applies to water and fat may not be accurate. Hence, other methods have been developed that allow for T2* corrections that do not make this assumption. In the literature, T2* correction methods that assume a constant T2* for both fat and water are referred to as monoexponential, while those that assume different values of T2* for fat and water are referred to as bi exponential. Equation 3 34 describes the general model for the signal acquired with SPGR. It rests on the assumption that T1 recovery can be ignored, which is a reasonable assumption if the flip angle is small. C onsidering magnitude images, Equation 3 34 can be written as | | = + (3 45) Equation 3 45 has four unknowns -the fat and water proton densities, and their respective T2* decays Each image acquisition (IP or OP) generates one set of values for Equation 3 45. In order to derive a unique solution for these parameters, a minimum of four image acquisitions is required. Then, a fitting method can be used to fit the data to the equations resulting in simultaneous extraction of fat and water proton densities and their respective T2* values at each pixel Because of the T2* decay terms, t he equations are non linear, so iterative convergent methods are needed to solve the system of equations such nonlinear least squares or the LevenbergMarquardt algorithm Several studies have investigated bi exponential T2* correction algorithms ( 112, 113) These are discussed later in the in vitro accuracy section of this chapter.

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102 Dixon methods based on complex images Clinicians typically work with magnitude images. This explains why, in spite of their limitations, Dixon met hods based on magnitude images are still in use and remain a topic of research. P hase information can be used to resolve the ambiguity in the determination of fat water dominance. However, it can only be derived from the complex images Clinical scanner s allow the reconstruction of the images into real and imaginary components. However, it is the experience of this researcher that, at least in Philips scanners, the reconstructed images are subjected to an irreversible scaling that renders the images useless for quantitative purposes The purpose of the scaling is to enhance the dynamic range of the images on the screen, but as just stated results in the modification of pixel intensities in a nonlinear fashion. A research key allows the user access to the complex k space image dataalso referred to as the raw data which has not been subjected to any modifications MR scanner software does not typically include applications for reading and processing the raw data. MATLAB code had to be written in thi s dissertation in order to extract k space data from the raw data files Consider the signal model for 2PD SE acquisitions in the case that complex image data is available ( Equations 3 27 and 328, shown again below for your convenience). R elaxation terms are ignored for simplicity. The equations form a system of two equations with three unknowns. = ( + ) = ( )

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103 At first glance, it seems that the system of equations cannot be solved without the addition of a third equation. However, Brix et al. ( 114) propose an ingenious way to get around this problem. They call their method the modified Dixon method. It consists in first identifying regions of the image where one can be certain of water dominance, such as muscle or brain tissue. For those pixels, the fat and water pixel intensities can be calculated from Equations 3 31 and 332. These pixel intensi ties can then be entered into Equation 3 28 to derive phase map values ( ) for these pixels. The derived phase map values are then used to calculate the following complex quantity = = ( ) = ( ) e (3 46) I f the real part of R is positive, this means that the pixel being evaluated has water dominance; else, it has fat dominance. This procedure is used to derive the phase map for the entire image. By imposing continuity on this phase map the authors correct all pixels where water fat switching has occurred. In the case of SPGR the phase term in the IP image cannot be neglected since there is no refocusing pulse. Hence, the model for the two complex images is = ( + ) (3 47) = ( ) ( ) (3 48) wh ere is the additional phase introduced by B0 field inhomogeneities during the inter echo interval. For simplicity, relaxation terms are ignored. The phase map component common to both IP and OP images can be calculated from the IP image using Equation 3 47 =| | (3 49)

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104 Then, this common phase factor c an be removed from the OP image via multiplication. = = ( ) (3 50) The additional phase factor acquired between the IP and OP acquisitions can then be calculated from = (3 51) where the sign depends on the difference If the pixel is water dominant, the sign is positive; else, it is negative. So once again the problem becomes determining water fat dominance. Ma et al. ( 115 ) propose that dominance can be determined based on the relative phase angle between a given pixel and its neighbors. In their method, phase angle differences between adjacent pixels are calculated both in the x and y directions to produce phasegradient maps Gx and Gy, respectively. If a calculated phase angle is greater than 90o it is replaced by its supplementary angle, i.e. 180o minus the calculated angle. This is done to ensure that pixels at water fat boundaries have phasegradient map values equal to 180o. Nine bins are defined covering a phase gradient angle range from 0o to 90o in 10o increments. An arbitrary seed pixel is selected from the image to start the regiongrowing process. The seed pixel is given a positive sign for its value. The four nearest pixels to the seed pixel are placed into the bins according to their Gx or Gy value depending on their position r elative to the seed pixel and are then visited sequentially, starting from the first bin (010o). As each pixel is visited, the sum of the values of pixels that have already been visited within a 7 x7 neighborhood of

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105 the current pixel is calculated. The calculated value is compared to the pixels S_OP^' value. If the angular difference between the two is less than 90o, the pixels is given a positive sign, else a negative sign. The process repeats until all pixels in the image h ave been visited. This regiongrowing algorithm removes phase discontinuities caused by fat water boundaries. A variant of this algorithm was later proposed by Rydell et al. ( 116) Equations 3 27 and 328 corresponds to a system of two equations with three unknowns. The system is not linear, due to the presence of the field inhomogeneity factor e An additional equation ca n be provided with the acquisition of an additional OP or IP image that allows the removal of the nonlinear factor. Lodes et al. ( 109) introduced a threepoint Dixon (3PD) method, consisting in the acquisition an IP image and two OP SE images: one in which the refocusing pulse is shifted forward in time by tOP/2 (to produce a phase difference of ) and the second in which the refocusing pulse is shifted back in time by tOP/2 ( for a phase difference of ). Applying the signal model ( Equation3 5) to the three spin echoes yields = + (3 5 2 ) = ( ) (3 5 3 ) = ( ) (3 5 4 ) where is the phase map, i.e. the phase acquired during the interval tOP/2 due to magnetic field inhomogeneity. The field map can be determined from the two OP images as = rg S /S = arg ( S S ) (3 5 5 )

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106 where arg is the function that returns the angle of a complex number measured from the positive real axis (i.e. the argument function) and denotes complex conjugation. Once the field map is calculated, the phase term e can be removed from Equation 3 5 3 and the system of equations to solve becomes = + = (3 5 6 ) which can be trivially solved as = + (3 5 7 ) = (3 5 8 ) 3PD can also be performed using two IP images and one OP image, where the second IP image is acquired for a phase angle difference of 2 This additional IP image acquires a phase factor equivalent to twice that acquired by the OP image. Hence, = ( + ) (3 5 9 ) and the phase map can be calculated from the two IP images as = arg S /S = arg ( S S ) (3 60) Once again, the reciprocal of the phase term is multiplied to Equation 3 53 to obtain the fat and water images as described by Equations 3 5 7 and 35 8 A disadvantage of this choice of phase angles is that it increases the inter echo spacing and hence it renders the technique more susceptible to T2 decay effects

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107 SPGR sequences for the application of 3PD have also been designed ( 117, 118) Each IP and OP gradient echo is acquired consecutively Applying the signal model ( Equation 3 5) to three gradient echoes, neglecting T1 recovery terms, and assuming T2W* = T2F*, = ( + ) (3 6 1 ) = ( ) ( ) (3 6 2 ) = ( + ) ( ) (3 6 3 ) The inter echo T2* decay term can be calculated from the magnitudes of the two IP images as e = | S | | S| (3 6 4 ) Equation 3 64 can then be used to remove T2* dependency in Equation 3 63. = = ( + ) ( ) (3 6 5 ) Then, the phase map ( ) term can be calculated from e= S S = S S | S| (3 6 6 ) or it can be expressed as half the difference of the angles the complex vectors of S and S make with the positive x axis (real axis). = [ ( S ) ( S)] (3 6 7 ) The phase term e is calculated from the first IP image as = | | (3 6 8 )

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108 The phases calculated via Equations 3 6 6 and 36 8 can be used to remove all phase dependencies of the OP echo ( Equation 3 62) as = ( )= ( ) (3 69) Finally, the water and fat images are calculated as = (| | + S ) ( 2 | | ) (3 7 0 ) = (| | S ) ( 2 | | ) (3 7 1 ) A similar procedure can be developed for the case in which two OP images are acquired at and The 3PD SE sequence requires shifting the refocusing pulse. A major problem with shifting the refocusing pulse is that the Hahn echo does not occur in the middle of the acquisition and hence some water and fat magnetic moments may interfere destructively reducing t he signal intensity ( 119) Hardy et al. ( 120) proposed a pulse sequence in which the read gradient, rather than the refocusing pulse, is shifted By shifting the gradient echo, the refocusing effect of the Hahn echo is preserved and signal loss is avoided. When this approach is used with fast SE imaging, however, inter echo spacing is inevitably increased, leading to a higher potential for T2 blurring ( 121) Ma et al. ( 121) designed a pulse sequence modification that allows gradient shifts without altering the inter echo spacing. The modification consists in adding two small gradient lobes of opposite polarity, one before and the other after the read gradient. In order to attain the desired phase shifts for the OP images, one changes the area, rather than the time length, of the two gradient lobes, thus not requiring any increases in timing. Ma et al. ( 122 ) further refined the fast SE 3PD acquisition by

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109 developing a pulse sequence that allows the acquisition of the three images simultaneously by reshaping the read gradient into thr ee lobes of alternating polarities with equal phase encoding but different chemical shift phase shifts. Calculation of the phase map as just described in the various 2PD and 3PD methods would be straightforward if it were not for a phase wrapping problem i nherent in the calculation. For a complex image pixel intensity S, the phase angle is calculated as = ( ) = 2 ( ) (3 72) where Re and Im are the real and imaginary component of the pixel intensity, respectively, and atan2 is a special inverse tangent function that takes into consideration the signs of the real and imaginary components in order to map the angle given by tan1( Im/Re ) into th e correct quadrant. As an example, consider the two complex numbers 1 + i and 1 i. If the angle each complex number makes with respect to the positive real axis is calculated using the standard arctangent formula the same result is obtained for both: /4. However, when the signs of the real and imaginary components are taken into account it is clear that in the case of 1 i the correct angle is 3 /4. The function atan2 outputs angles in the domain ( ], where the angle is measured from the posi tive real axis and the sign indicates the sense: positive for clockwise and negative for counterclockwise. The tangent function has a period of since ( ) = ( ) where n is any integer. This makes the tangent function a multi valued function, since multiple angles result in the same value of the tangent. As a consequence, the arctangent function is unable to determine which of the multiple angles yielded the value in its

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110 argument. In lieu of this ambiguity, the arctangent function i s defined to yield angles in the domain ( ] and the angles produced by the arctangent function are known as the principal values of the angle. Phase angles in an MR phase map are not restricted to ( ] and hence can take on values in absolute magnit ude much greater than When the phase map is generated, these phase angles are wrapped by the arctangent function by the addition of 2 so that they fall in the principal value domain ( ]. The phase angle is considered wrapped since it has been rotated one or more times in a full circle. The phase map of an MR image is expected to be continuous, since phase shifts are expected to be the result of B0inhomogeneities ( 123, 124) However, phase wrapping introduces artificial discontinuities into the phase map (black curve in Figure 319) since phase angles greater than become negative by subtraction of 2 and phase angles smaller than become positive by addition of 2 The result is a phase map that is riddled with sharp discontinuities Phase unwrapping consists in removing discontinuities in the phase map through the addition of 2 The phase unwrapping process results in a smoothing of the field map (gray curve in Figure 319) Phase unwrapping would be a relatively straight forward process if phase wrapping were the only cause for /+ phase discontinuities in the phase map. However, image noise and spatial resolution can also result in discontinuities, and the complexity of anatomical shapes in MR images makes it difficult to perform accurate phase unwrapping ( 123, 124) A discussion of the myriad of phase unwrapping methods available in the literature is beyond the scope of this dissertation, so instead the reader is directed to reviews published by Reichenbach et al. ( 125 ) Chavez et al.

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111 ( 123) and Ma ( 126) Phase unwrapping methods are unfortunately complicated and cumbersome to implement, and often require subjective decisionmaking input from the user, since the true in vivo phase s hifts due to magnetic field inhomogeneity are unknown. Yeung and Kormos ( 127 ) demonstrated the effect of phase wrappi ng in Dixon water and fat images of a transverse abdomi nal slice acquired on a healthy subject at the height of the kidneys. P hase wrapping result ed in the majority of voxels corresponding to the right kidney and the right section of the liver to be switched in the water and fat images. The phase map reveal e d the cause of the phase wrap: the liver, having high iron content result ed in a region of abrupt magnetic susceptibility differences Unwrapping of the phasemap in this region results in water and fat voxels to be correctly placed in their respective i mages. In addition to the liver, fat water switches were also observed in areas of adipose tissue near the liver. I mages of bone marrow generated via Dixon methods are expected to suffer from magnetic field inhomogeneity issues as a result of the magnetic susceptibility differences between trabecular bone and soft marrow. The strength of the magnetic field inhomogeneities will increase with the number of trabeculae soft marrow interfaces the size of the trabeculae, and the magnitude of the static field B0 ( 93, 128) Susceptibility effects can be reduced by both decreasing TE and increasing the receiver bandwidth ( 106) Even though the Dixon SE sequence minimizes some of the B0 inhomogeneity effects, GE sequences lack a refocusing pulse and are therefore even more s usceptible to this problem.

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112 Direct Phase Encoding (DPE) Xiang and An ( 119) des igned a fat water separation technique based on complex image data that does not require phase unwrapping called direct phase encoding (DPE). The method is based on the notion that if images are acquired when the fat and water magnetizations are perpendic ular, the real component of the complex image intensity provides the water image while the imaginary component provides the fat image. Again, this fat and water separation is only possible for the case in which B0 is perfectly homogeneous, which is rarely the case. Hence, the image intensities must be first phase corrected. Consider an image acquired when the water and fat magnetizations are at 90o. The pixel intensities can be modeled from our general signal model ( Equation 3 5) as = + = ( + ) (3 73) where, for simplicity, relaxation terms are not included. If the field map can be somehow determined, the water and fat images can be determined from = Re e (3 74) = Im e (3 75) In order to determine the field map at least two more image acquisitions are required. Xian and An ( 119) propose acquiring three equally spaced echoes with phase angles + and + 2 produced by performing 180o pulse shifts (SE) or read gradient shifts (GE) given by + and + 2 respectively. The complex signal intensities in each echo can be modeled as

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113 S= + e ee (3 76) = + e ( ) ee ( ) (3 77) = + e ( ) ee ( ) (3 78) where is the phase angle introduced by RF field (B1) inhomogeneity and B0 is the magnitude of the B0 field inhomogeneity. Using the following definitions, = = = = (3 79) Eqs 3 76 through 378 become = ( + ) (3 80) = ( + ) (3 81) S= ( + ) (3 82) Consider the c omplex variables, X and Y defined as X = (3 83) = (3 84) Equations 3 80 through 382 can be written in terms of these variables as = + Y (3 85) = + (3 86)

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114 = ( + ) (3 87) Multiplication of Equation 3 85 by Equation 3 86 yields = ( + )( + ) = + + + 1 (3 88) Equations 3 86 and 388 form the system of equations to solve. = + = + + + 1 The solution to the system of equations requires solving a quadratic equation, which results in two possible solutions for X and Y where fat and water are switched. The authors suggest that an unique solution is possible as long as is chosen such that CA the phase map and utilize local neighborhood information to determine which of the two solutions is to be accepted for each pixel. Once X and Y are uniquely determined, the water and fat images are obtained by simply taking the magnitude of X and Y, respectively. This methodology is unable to resolve the ambiguity for voxels that contain small amounts of water or fat, and for the case in which X and Y are parallel or a nti parallel Iterative Decomposition of water and fat with Echo Asymmetry and Least squares (IDEAL) Even if the ambiguity inherent to all Dixon methods and DPE were eliminated, these methods suffer from three major limitations. First, they can only be us ed to separate two chemical species; i.e. water and fat (CH2) Biological tissue contains

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115 many chemicals in addition to water and fat, and fat is not represented by a single type of molecule and consequently presents multiple resonances. Second, they are only applicable to single coil acquisitions, and current clinical scanners typically use phasedarray coils consisting of multiple coil elements. Third, the pulse sequences required with these methods require relatively long inter echo spacing which results in T2* blurring. In order to overcome these limitations Reeder et al. ( 129) developed a method called Iterative Decomposition of water and fat with Echo Asymmetry and Least squares (IDEAL). Consider the following signal model for a pixel q containing M chemical species, each with its particular chemical shift (Hz) acquired at echo time For simplicity, relaxation time factors are ignored. However, they will be included later in this section. ,= = 1 ( 3 89) where is the proton density of chemical species m n is the echo number, and is the frequency offset introduced by local magnetic field inhomogeneity ; i.e. the field map. In the Dixon method, the echoes are acquired when the magnetizations of fat and water are either parallel or anti parallel and consequently the water and fat proton densities are real quantities. In the formulation of Equation 3 89, phase angles can take any value and hence the proton densities are complex quantities. Hence, unlike the Dixon method, IDEAL can only be performed using complex image data. Equation 3 89 contains M + 1 unknowns: M complex proton density values, and one scalar field map value, Hence, a minimum of M + 1 echoes are required

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116 to obtain a unique solution. Since the proton densities are complex, obtaining a solution requires solving 2 M + 1 equations separated by real and imaginary parts. Unfortunately, the system of 2M + 1 equations is not linear due to the presence of the fie ld map term ,. Note that the chemical shift term does not introduce nonlinearity, since it is considered known and therefore a constant. If the field map could somehow be determined, the system of equations would be linear and simple t o solve. In IDEAL, the field map value is resolved by iteration starting from an initial guess, which can be zero. Hence, the field map value is known and constant at each iteration, so the system of equations to solve is linear. The iterative process i s explained next Given an initial guess of the field map, its dependency can be removed from Equation 3 8 9 as follows ,= = = 1 ( 3 90) Equation 3 90 is now separated into real and imaginary parts = ( 2 ) ( 2 ) ( 3 91) = ( 2 ) + ( 2 ) ( 3 92) where the superscripts R and I denote real and imaginary parts, respectively. If we define = ( 2 ) and = ( 2 ) Equations 3 91 and 392 are simplified to

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117 = , ( 3 93) = + ( 3 94) This forms a system of 2M + 1 linear equations that can be solved via standard linear least squares (LLS) LLS will determine values for and that minimize the sum of the squares of the residuals (SSR ); i.e. the sum of the squares of the differences between the measured pixel intensities from the image and the fitted model. The values for the proton densities are optimized for the specific field map guess. Hence, the field map guess must then be improved. This is accomplished by defining each variable, the proton densities and field map, as the variable plus an error term, and solving the resultant system of linear equations for the error terms using LLS. The error term for the field map thus calculated corresponds to the amount by which the initial field map guess has to be increased or decreased in order to minimize the difference between the measured pixel value and the fitted model. Hence, the field map guess is iteratively improved as the field map error term is minimized by the LLS procedure. The iteration will continue until the field map error term becomes acceptably small. The user can decide on a threshold value for this error. Naturally, the smaller the threshold value, the larger the number of iterations needed to reach it. Reeder et al. ( 129) recommend making it 1 Hz. The algorithm must perform this it erative process independently for each pixel in the image. Once optimum field map values have been calculated for the entire image, the field map is subjected to a smoothing filter to remove the artificial noise introduced

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118 by the iterative process. Reeder et al. ( 129) suggest using a low pass filter, such as a 3 x 3 boxcar filter. Final ly, the proton densities for each chemical species are calculated by solving the linear system of equations ( Equations 3 93 and 394) using the smoothed field map and LLS. Reeder et al. ( 129) demonstrated the use of IDEAL to perform fat water separation in multiple anatomical and phantom images. Since only two chemical species were calculated, water and fat (CH2), only three echoes were needed. For phased array coil acquisitions, Reeder et al. ( 129) recommend performing IDEAL separation on each coil element image separately, and then calculate a composite field map image from the calculated field maps for each coil element image using a weighted mean where the weights correspond to the square of the magnitude of pixel intensities in the corresponding coil element images ( Equation 3 95) = (3 95) where P is the number of coil elements. The composite field map is then smo othed using a low pass filter and the smoothed field map is subsequently used to calculate the proton densities for each coil element image using LLS Finally, the coil element images for each chemical species are combined into a composite image using standard phasedarray coil methods. IDEAL chemical species separation provides great versatil ity in comparison to Dixon methods, since it is not tied to a particular pulse sequence. IDEAL has been demonstrated in a variety of imaging sequences, including fast SE ( 1301 33) Steady -

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119 State Free Precession (SSFP) ( 134 136) partial k space acquisitions ( 135) fast SPGR ( 137140) GRASS ( 141) and GRASE ( 142) A major challenge in the use of IDEAL is that the residual (i.e. the magnitude of the difference between the image data and the model fit to the data) does not pres ent a single minimum. Instead, the residual presents multiple periodic local minima (Figure 32 0 ). IDEAL starts its iterative procedure with an initial guess for the field map. The LLS process will converge to the local minimum of the residual closest t o the initial field map guess. The pixel in Figure 32 0 was selected from muscle in the anatomical images, far from adipose tissue, so this pixel is expected to be water dominant. There are two minima near an initial field map guess of zero: one at approximately 483 Hz and the other at +430 Hz. If the LLS procedure converges to a field map value of 483 Hz, this pixel will be correctly assigned water dominance. However, if it converges to +430 Hz, the pixel will be incorrectly assigned fat dominance. Factors such as image noise and magnetic field inhomogeneity can result in the incorrect dominance being selected. Hence, just as in the Dixon methods, there is an inherent danger for ambiguity in the selection of water and fat dominance for each pixel in the image, which also leads to fat water switching This inherent ambiguity was first brought to attention by Yu et al. ( 143) The authors refer to the contradictory solutions as aliased solutions For a pure water or a pure fat voxel, the separation between the true solution and the closest aliased solution is equal to the chemical shift between fat and water ( 143) At 3.0 T, this corresponds to a difference of approximately 434 Hz. In Figure 32 0 the aliased solution at approximately 937.5 Hz is separated from the true solution ( 483.0 Hz) by

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120 454.5 Hz. This is close to the expected 434 Hz separation for a pure water pixel, which is reasonable for muscle tissue far from adipose fat. To ensure c onvergence to the true minimum the initial field map guess must be placed as close as possible to the location of the true minimum. Yu et al. ( 143) developed a regiongrowing algorithm (RGA) to achieve this goal. The IDEAL process as just described calculates the field map for each pixel in the image one pixel at a time. As s uch, Yu et al. ( 143) refer to this approach as pixel independent IDEAL. The main goal of RGA is to use information about neighboring pixels in order to improve the selection of the field map guess so that the method will converge to the true field map. It is reasonable to assume that if the process is started in a region of the image where there is a tendency to converge to true solutions, the field map for the entire image has better odds of converging to the true field map. Yu et al. ( 143 ) found that aliased solutions converge to the true solutions as the water to fat ratio approaches unity. The RGA process begins by downsampling the images to 32 x 32 and applying a mask to remove pixels with very low intensities. Low intensity pixels are typically background pixels that are very noisy. The pixels in the resulting low resolution images are most likely to contain water to fat fractions closer to unity and as such are more likely to converge to the true field map. The authors refer to the pixels in the low resolution images as super pixels. Pixel independent IDEAL is performed on the super pix els to compute a low resolution field map. In general, pixels that converge to very large or very small field map values are more likely to converge to aliased solutions. Hence, super pixels are sorted according to their field map value, from smallest to largest, and a neighborhood of the 14 super pixels closest to the

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121 median, including the median, is selected. These pixels form the super pixel median neighborhood. The center of mass super pixel is calculated based on pixel intensity in the low resolution images and the super pixel in the median neighborhood that is closest to the center of mass super pixel is chosen as the starting point in the regiongrowing process. The starting super pixel corresponds to a neighborhood of pixels in the original ima ges. Field map values for each pixel in this neighborhood are calculated using IDEAL using the low resolution field map value for the starting super pixel. The field map values determined for this pixel neighborhood become the seed for the RGA process. The field map for the remainder pixels in the image is now calculated, one pixel at a time, starting with the pixel to the left of the top left corner of the starting pixel neighborhood and following a square spiral, as shown in Figure 32 1 The initial field map guess for each pixel is determined from 2D linear interpolation on a 41 x 41 region centered at the pixel. This region will contain some of the field map values that have already been calculated and hence the interpolated value for the initial guess of the field map will follow the trend of neighboring pixels in the field map image. In order to avoid errors in image regions that contain pixels near different tissue boundaries, the linear interpolation is weighted by the image pixel intensities. This approach enforces local smoothing of the field map. The 41 x 41 box size was empirically determined as optimal for the images used in Yu et al. ( 143) but it may have to be opt imized depending on the anatomy imaged and the size of the images Smaller boxes will be more sensitive

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122 to local changes in the field map but may also become unstable near and on background regions of the image ( 143) Yu et al. ( 143 ) demonstrated the algorithm in coronal slices of the brachial plexus of a volunteer The interfaces between the lungs and surrounding muscle are areas of large changes in magnetic susceptibility, which result in magnetic field inhomogeneity. The sharpest gradients will occur in highly curved regions, such as the apex of each lung. The images demonstrated that pixel independent IDEAL fail ed in these regions with the algorithm misidentifying the pixels in these regions as water dominant pixels when in fact they were fat dominant pixels However, IDEAL with RGA wa s able to correctly calculate the field map values at these regions resulting in a correct water image. Yu et al. ( 143 ) performed pixel independent IDEAL and IDEAL with RGA fat water separation on 46 sets images of the brachial plexus taken from different patients. The failure rate, as indicated by the presence of fat water switching in the water images, was 37% for pixel independent IDEAL and 1.8% for IDEAL with RGA, indicating the superior quality of fat water separation using RG A. This however, also indicates that RGA is not always successful in avoiding aliased solutions. The success or failure of RGA is highly dependent on the choice of the starting super pixel, since the calculated field map values for each pixel in the corresponding neighborhood are used to calculate the initial field map guess for subsequent pixels ( 143) It is assumed that all pixels in the starting super pixel will converge to the true field map. However, if this is not the case, the error will be propagated to other areas in the image due to the spiral square trajectory.

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123 IDEAL decomposition of multiple chemical species requires a large number of images and hence it is typicall y performed on images acquired using fast multi echo sequences. Lu and Hargreaves ( 144) demonstrated that for symmetric echoes the IDEAL residual or cost function has a period given by 1/ TE, where TE is the inter echo spacing. Consequently, the longer the echo spacing, the closer the minima associated with aliased solutions are to the minima corresponding to the true solutions, making fat water switching more likely. Lu and Hargreaves ( 144) also conclude d that a robust field map calculation requires imposing field map smoothness. They develop an improved RGA that, rather than determining the initial field map guesses based on a single low resolution, it determines them from a hierarchy of low resolutions that vary in factors of two. The algorithm starts with the images at the coarsest resolution and employs a golden section search to locate all the local minima within a single period of the cost function. These minima are the only possible values the field map can take for the given pixel and become the minimizer set for the pixel, which typically includes 2 3 values. A starting super pixel is selected similarly to Yu et al. ( 143 ) and its corresponding field map value becomes the seed for regiongrowing. Regiongrowing is performed in the coarsest resolution images using a very simple and computationally efficient approach. Figure 322 depicts the regiongrowing process. The field map value of the starting super pixel (circle marked with the number 1) determines the field map values for its immediate neighbors (contour of super pixels marked with the number 2). Each super pixel in this contour has a particular minimizer set determined in the previous step. Each of these pixels is now assigned the field map

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124 value in their minimizer set that is closest to the field map value of the starting super pixel. The field map values for the next super pixel contour (contour 3) is determined by comparison with the field map value of the super pixels in contour 2. The regiongrowing process continues until all pixels in the coarsest resolution image have been evaluated. Each super pixel in the coarsest resolution field map corresponds to four super pixels in the field map at the next resolution level in the hierarchy. The field map for this resolution level is determined by bilinear interpolation. The interpolated field map values are used as initial guess in IDEAL for the super pixels at the current resolution. The cost function is then evaluated at each super pi xel. A threshold is preset to determine the minimum residual acceptable. At super pixels where the threshold is not met, golden search is performed at the current resolution to determine the minimizer set for the particular pixel. The field map value f or the failed super pixel is chosen from its minimizer set based on the field map of its closest neighbor (Figure 322). The advantage of this approach is that it is not necessary to determine minimizer sets for all super pixels in the image, which reduces computer time. This process of coarseresolution map to finer resolution map is continued along the hierarchy until the field map is finally evaluated at the original image resolution. Lu and Hargreaves ( 144) demonstrated their algorithm on transverse slice s through the upper abdomen of a volunteer. In spite of the high iron content in the liver, the algorithm was able to perform excellent fat water separation without any noticeable fat water switching, thus indicating the robustness of the algorithm. In contrast to the p reviously discussed IDEAL algorithms, the final field map image does not require any

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125 additional smoothing since smoothing is guaranteed by the multi resolution refinement of the field map. A final refinement of robust field map extraction is provided by a recent algorithm developed by Hernando et al. ( 145 ) The algorithm imposes field map smoothness by adding a penalty term to the cost function and, in contrast to pixel by pixel and regiongrowing schemes, it calculates the field map and the proton densities for each chemical species for the entire image simultaneously. The cost functi on (C) is defined as follows = + ( 3 96) where q is a pixel out of a total of Q pixels in the image, SSRq is the sum of the squares of the residual for pixel q --where the residual is the difference between the pixel intensity and the intensity calculated by the model ( Equation 3 89) --, and FMSPq is the Field Map Smoothness Penalty calculated by Equation 3 97. Note that now the cost function is the cost for the entire field map, and not just one pixel in the field map. The FMSP is given by = , ( 3 97) where is the regularization parameter, is an 8x8 pixel neighborhood centered at pixel q are spatially dependent weights, and is a parameter that penalizes depending on the roughness of the field map, given by = (3 98)

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126 Minimization of the cost function ( Equation 3 96) provides the complete phase map ( f), the water ( ) and fat ( ) images, simultaneously. This is not a straightforward task, since, for starters, Equation 3 38 is not linear, and its solution must be obtained via nonlinear least squar es (NLLS). In addition, the problem has 5Q dimensions, since each image consists of Q pixels, the water and fat images each have a dimension of 2Q (real and imaginary components), and the field map provides one more dimension (1Q). Hernando et al. ( 145) apply variable projection (VARPRO) formulation to remove the proton density dependence in the resolution of Equation 3 38 so that minimization of the cost function is performed exclusively in terms of the field map alone. An additional benefit is that this reduces the dimensionality of the problem from 5Q to Q. Given a solution for the field map the water and fat images can be computed using LLS. A detailed discussion of VARPRO formulation and the steps involved in the extraction of the field map using Graph Theory is beyond the scope of this chapter. For more detailed explanations on the use of VARPRO in this particular problem please review Hernando et al. ( 145, 146) and Hernando ( 147) For information on Graph Theory and Graph Cuts, please review Deo ( 148) or Paragios ( 149 ) Conceptually, the algorithm can be explained as follows The residual presents multiple local minim a, each representing a potential solution to the field map. Hence, the field map extraction problem can be discretized so that all the possible field map solutions are different combinations of the minimizers of the residual for each pixel in the image. Even if the residual is not periodic, the range of the field map values can be restricted to a specific range. The VARPRO formulation allows rewriting the problem so

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127 that rather than minimizing the cost function ( Equation 3 96) in terms of 5Q variables i t can be expressed exclusively in terms of the discretized field map solutions Even so, the problem is still too large to be resolved by LLS. Instead, Hernando et al. ( 145) employ graph cuts ( Graph Theory ) to minimize the cost function. Each pixel in the image is represented by a vertex (or node) in the graph and different parameter s of the cost function are applied as weights on edges (lines) that connect all vertices to each other but also to a common source and sink (Figure 323) In Graph Theory, a graph cut consists in cutting some of the edges that connect the vertices in the graph. Each graph cut is associated with a cost equal to the sum of the weights of the cut edges Hence, it is possible to determine which edges to cut so that the cost is a minimum. This minimum graph cut provides the field map that minimizes the VARPR O cost function. T he cut determines at each iteration, which pixels retain their current field map value and which are changed. In this manner the field map of the entire image is iteratively improved until it converges to an optimal solution. The large dimension of the problem is not a limitation in Graph Theory, so the problem can be resolved, and more importantly, it can be resolved efficiently in a computer. Hernando et al. ( 145) used anatomical images through the abdomen of volunteers at the level of the liver to show that t he method performs accurate fat water separation even i n situations where the pixel independent method and regiongrowing schemes fail. The high iron content of the liver results in regions of high magnetic field inhomogeneity, which results in fat water switching in pixel independent IDEAL and IDEAL with RGA. However, the algorithm provided by Hernando et al. ( 145) resolves the switches by imposing field map smoothness over the entire image.

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128 T1 of fat is shorter than T1 of water and hence, on T1weighted sequences the fat signal experiences a smaller loss than the water signal during the acquisition. Unless a corre ction is made the fat fraction will be overestimated. Liu et al. ( 138) provide several strategies for minimizing these error s. The simplest approach is to avoid having to perform T1 corrections by acquiring images with a small flip angle. However, SNR decreases with decreasing flip angle, so one must compromise between T1 effects and SNR. An alternative approach is possible w hen images are acquired with two flip angles. The fat and water images are first calculated separately for each flip angle using IDEAL, and then the T1corrected water and fat images can be calculated from corr= 1 (3 99) corr= 1 (3 100) where = = , (3 101) = = , (3 102) , and are t he water and fat images calculated from the images acquired at flip angles and Optimum flip angles for the image acquisitions can be determined following the procedure described in Deoni et al. ( 150) A major limitation of the dual flip angle correction just described is that it becomes highly erratic in low intensity pixels in the fat and water images, si nce these pixels are

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129 very noisy. Liu et al. ( 138) demonstrated that this problem ca n be corrected by restricting T1 to be real, positive, and within physiologically reasonable limits (e.g. 1 < T1 < 2000 ms). T1 values are calculated from Equations 3 101 and 3102, and in the cases for which the calculated values do not satisfy the preset constraints, T1 is corrected to 2000 ms. Corrected T1 values are then used to calculate E1w or E1F as 1 or 1 respectively, and these values are then ent ered into Equations 3 99 and 3100. T2* shortening occurs in areas of the anatomy subject to large magnetic field inhomogeneities and echoes acquired with uneven echospacing will be subject to different amounts of T2* decay. Unless these differences are accounted for, fat fractions will be in error. IDEAL allows T2* corrections to be performed simultaneously with the fat water separation. The methodology was developed by Yu et al. ( 151 152) Consider the signal model proposed for pixel independent IDEAL ( Equation 3 89), considering only two chemical species (water and fat), and with the inclusion of T2* decay, with the assumption that T2* is the same for fat and water. = + 2 2 2 (3 103) where = 1 Now, rather than considering the field map as a scalar quantity, it is defined as a complex field map, as shown below. = + 2 (3 104) The signal model can now be written as = + 2 2 (3 105)

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130 which is identical in form to Equation 3 89, and therefore the standard IDEAL algorithm can be applied to produce water and fat images. The assumption that fat and water have equal T2* is justifiable in areas of high magnetic field inhomogeneity where the magnetic field inhomogeneity factor dominates the value of T2* ( Equation 3 1). Yu et al. ( 151) refer to this extension of IDEAL as T2* IDEAL. A problem with T2* IDEAL is that while image pixels are the result of the contributions of multiple lipid resonances, the model assumes a single lipid resonance. As discussed in the MR spectroscopy section of this chapter, the linewidth of the methylene peak at clinical magnet strengths (e.g. 1.5 T, 3.0 T) is broadened by the presence of neighbor lipid peaks, and this consequently shortens T2*. Since the model used in T2* IDEAL assumes a single fat resonance, the calculated T2* results in an overestimation ( 152) Yu et al. ( 152 ) resolve this problem by considering multiple lipid resonances in the signal model in a method they call Multi peak IDEAL (MP IDEAL). In MP IDEAL, the chemical shift in fat is modeled as a s pectrum, rather than a single shift of 3.4 ppm. The updated signal model is = + = 1 ( 3 106) where p denotes a specific spectral lipid peak, and and f are the normalized amplitude and shift in resonant frequency with respect to water of peak p respectively. The spectral amplitudes and frequencies must be entered into the model prior to starting the IDEAL algorithm. These can be obtained from an NMR spectroscopy acquisition. Given that the MR spectroscopy package is not typically included in the clinical ima ging package of most clinical scanners, Yu et al. ( 152) suggest instead using

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131 multi species IDEAL separation. Each lipid spectral peak is modeled as a separate chemical species with known chemical shifts in the model and fat and water images can be derived for eac h. Regions of the image corresponding to pure fat can be determined by inspection of the fat and water images. An ROI is selected in the same fat region in the images for each lipid species and the average pixel intensities, after normalization, can be used as the spectral amplitudes. Sixteen echoes are required to fit six lipid spectral peaks plus the water peak ( 152) The authors also provide methodology for performing this calculation using six echoes to derive a spectrum restricted to a single water peak and 3 lipid peaks. A three peak lipid spectrum can also be derived from a standard 3point IDEAL, but it requires a more complex process described in their paper ( 152) The authors refer to these two latter methods as self calibrations since they are derived from the same images used to subsequently per form the fatwater separation. In V itro A ccuracy and N oise P erformance M ultiple MR methods that can be used to measure fat fraction have just been reviewed. The methods can be grouped into s pectral saturation methods, Dixon methods, and IDEAL. A ny of these methods can be used to produce images that are fat or water suppressed, but good images are not necessarily indicative of how accurately fat fraction i s quantified by the images. A determination of accuracy requires a priori knowledge of the fat fraction in the object on which the measurement is being performed. Fat fractions in biological tissue are highly variable and may present a heterogeneous and even patchy distribution. In vivo fat fraction determination by MR methods is typically complicated by patient and organ motion, tissue heterogeneity (magnetic susceptibility gradients), and physiological factors such as disease,

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132 temperature, and fluid flow. It is therefore important to determine accuracy fir st in an object a phantom that allows control over most of these variables. Once in vitro accuracy is determined, in vivo accuracy can be then better characterized. There are several types of phantoms that have been used to determine accuracy of the fat fraction measured by MRI and they are discussed next. P hantoms U sed F or I n V itro A ccuracy S tudies There are two types of oil water phantoms that are commonly used in the literature for the determination of in vitro accuracy. One type of phantom consists in either tubes or bottles that are typically filled wit h different volumes of water (typically doped with a chemical to shorten its relaxation, such as copper sulfate), fat in the form of organic or mineral oil, and a surfactant or emulsifier that enables oil and water to remain mixed, to produce phantoms in s erial fat fractions ( 60, 109, 113, 153156) The term phantom tubes will be used to refer to this type of phantom A major drawback of phantom tubes is that, while it is simple to produce stable homogenized emulsions of oil and water for fat fractions below 50%, it is very difficult to do so for larger fat fractions ( 109, 157) Rather than mixing liquid fat with water, s ome researchers have blended solid materials that contain fat already homogenized and in known fractions with materials presumed to contribute only water, such as mayonnaise and agar gel ( 60, 158) regular and fat free mayonnaise ( 101) calf liver blended with canola oil ( 61) pork lard with cow lean muscle ( 159) and cow gluteal muscle and cow perirenal fat ( 160 ) A main challenge with this appr oach is that the fat fraction present in the raw material limits the largest fat fraction that can be prepared. In most cases the fat fraction was estimated based on assumed or estimated fat content which reduces the phantoms value as a

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133 true reference. Only two of the referenced studies performed a chemical assay to confirm the accuracy of the fat fraction estimates ( 159, 160) Ideally one would like to create a phantom that provides a continuous range of fat fractions from 0% to 100%. One way to achieve this without the complications of emulsions is by taking an oblique slice along the oil water interface in a container filled half with oil and half with water ( 110 112, 161) (Figure 3 17). The term oblique slice phantom will be used to refer to this phantom Nominal fat fractions can be easily determined if the slice is selected in such a manner that the slice starts in only one of the two liquids and ends only in the other, as demonstrated in Figure 317. Then, knowledge of the length of the interface inside the slice allows the calculation of the equation of a straight line that predicts fat fraction as a function of horizontal position. If ROIs are to be selected from the MR image and average fat fractions are calculated inside each ROI, the linear equation can be used to determine the average fat fraction in each ROI by simple integration, given knowledge of the start and end position of the ROI al ong the oil water interface. A challenge with this type of phantom is that the oil water interface is slightly curved, especially near the container edges However, if the container is large enough it is possible to select the slice along the interface w here it is relatively flat One study added a surfactant to the water to minimize the formation of the meniscus ( 138) S ome researchers ( 46 162, 163) constructed a phantom by overlapping two pla stic wedge containers, one filled with oil and the other with water (Figure 324A ). A slice is acquired through the center of the phantom to produce an image of the phantom crosssection (Figure 324B ). Then, equal sized ROIs are selected at different lo cations

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134 along the length of the phantom in the image. Each ROI represents a different fat fraction of nominal value that can be determined directly from the image by calculating the ratio of the area of oil and water inside the ROI I n this work, this ty pe of phantom is referred to as a wedge compartment phantom. A problem one can expect in this type of phantom is the presence of air or air bubbles inside the compartments especially at the narrow end of the wedge. It may be possible, however, to select a slice that does not include the bubbles. None of the referenced studies that have used this type of phantom discuss this issue. A photo of the phantom used in Schuchmann et al. ( 163) shows the presence of air bubbles. If the air bubbles are included in the image slice this will introduce additional error into the calculated fat fraction from MRI. In V itro A ccuracy S tudies The accuracy of fat suppression techniques in measuring fat f raction was investigated by Matsunaga et al. ( 153) using phantom tubes containing mixtures of neutral fat (triglyceride), water, and emulsifier in fat fractions of 0, 1.0, 10.0, 20.0, 50.0, 71.4, 89.3, 90.9, and 100% The phantoms were imaged using SPIR and ProSet with water suppression (WS) and fat suppression (FS) SPIR stands for Spectral Presaturation with Inversion Recovery. In contrast with standard IR, the 180o prepulse is frequency selective at the resonance of fat so that it only inverts the fat so the water signal is not su bjected to T1 decay during TI ProSet is a spectral saturation method which does not require a prepulse because the unwanted signal is eliminated with the slice selection RF pulse, and therefore its application does not increase imaging time. The authors plotted the fat fractions determined by each method versus the nominal fat fractions on the same graph. Both spectral saturation methods overestimated all fat fractions, while SPIR underestimated low fat fractions but provided good agreement at

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135 large fat fractions ( 60%). The authors repeated the analysis in a later study using an oblique slice phantom ( 161) The phantom consisted of neutral fat (triglyceride) and a manganese chloride solution (MnCl2 4H2O). Spectral saturation methods resulted once again in a gross overestimation of all fat fractions. However, in contrast to their previous study, SPIR overestimated fat fractions greater than 60%. These resul ts confirm the notion that fat saturation methods, while excellent for improving image contrast, are not adequate for fat quantification. MRS is presumed to be very accurate. The scientific community considers MRS as a gold standard, and many studies have performed method accurac y stud ies using MRS as the reference. However, MRS pulse sequences, just as imaging pulse sequences, manipulate the magnetization through the use of RF pulses and gradients, and hence are subject to the many of the same effects and artifacts. U ser expertise plays a significant role on the quality of the acquired spectra and subsequent peak fitting analysis. Cooke et al. ( 164) found that the CSF (water) spectrum acquired with PRESS from a VOI placed within the spinal cord exhibits line broadening due to the magnetic field inhomogeneity near the spine. The linebroadening can be eliminated by reduci ng the size of the VOI and adjust its placement so that it crosses as few tissue interfaces as possible. This study indicates that, in spite of MRS expected inherent accuracy, it is wise to verify its accuracy, for something as simple as a choice in the placement of the VOI can result in a large inaccuracy. Three studies have investigated the in vitro accuracy of 1H MR spectroscopy (MRS) for the determination of fat fractions using phantom tubes ( 165167) Bernard et al. ( 165) used PRESS at 3.0T on phantom tubes prepared by homogenizing soybean

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136 oil, water, and a surfactant in 100mL tubes in eleven fat fractions from 0 to 100%. Imaging parameters : VOI = 3.7 cm3, TR/TE = 2000/32 ms, NEX = 32, BW = 5000 Hz, 4096 points. Fat fractions were calculated from the areas under the water and methylene (1.3 ppm) peaks. In spite of the excellent correlation (r2 = 0.993) and slope close to unit y, PRESS overestimates all but three of the fat fractions. Hu et al. ( 166) also acquired PRESS spectra from phantom tubes containing emulsions of corn oil, water, emulsifier, and agar gel. The authors did not provide their imaging parameters, but demonstrate very good agreement between the fat fracti ons measured with PRESS and the nominal fat fractions (slope = 0.95, intercept = 1.9, r2 = 0.99) A problem when trying to determine accuracy based on a linear fit or a correlation coefficient is that it does not allow for appropriate comparison between tw o studies Suppose we had just been given the correlation coefficient, the slope and intercept of the linear fit of the data. How much better is the agreement if the slope is 1.0 5 vs 0.95 and the correlation is 0.98 vs 0.99? Based on these numbers alone one could conclude that PRESS was just as accurate in both studies A better way to determine agreement between measuring methods is by the use of a BlandAltman plot ( 168, 169) A Bland Altman plot is a plot of the difference between paired measurements of two methods versus the mean of the paired measurements. It allows the determination of bias and systematic errors in measuring methods or instruments and allows for a better comparison between studies. Some investigations presented in this section have used Bland Altman plots and their use will be discussed in more detail then. Hamilton et al. ( 167) performed a phantom study based on a single phantom prepared by melting fat from 1 kg of lard. Their objective was to use this phantom to

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137 compare the accuracy of the most commonly used spectroscopy sequences: STEAM and PRESS. Spectra were acquired from the phantom at 1.5 T and 3.0 T with TEs varying in decades from 20 to 70 ms. The lipid spectra were resolved using the AMARES algorith m to fit Gaussian lineshapes to the lipid resonances shown: 0.9, 1.3, 2.1, 2.75, and 5.3 ppm. The natural logarithm of the peak areas at each TE were plotted in log scale and T2 was calculated from the slope of a linear fit through the data points The curves for STEAM resulted in straight lines suggesting that the decay is monoexponential. The T2 values for STEAM we re similar for most lipid resonance except for the methylene (CH2) resonance, which was significantly larger than the rest. Hence, perfor ming T2 corrections using T2 for methylene will result in an inaccurate fat fraction. The intercept of each line corresponds to the (log) relative abundance of each lipid molecule. The methylene (CH2, 1.3 ppm) peak presented the largest intercept, indica ting that methylene is the dominant lipid species. This supports the justification typically used in most studies to represent fat by only this resonance. In contrast with the STEAM curves, only two of the PRESS spectral peaks (1.3 ppm and 2.5 ppm) result ed in straight lines. Inspection of the spectra revealed that some of the lipid peaks observed in the STEAM spectra were missing or negative in the PRESS spectra, indicating that neighboring peaks are interacting destructively due to J coupling effects, w hich resulted in T2 shortening ( 167) The same effects were observed in vivo (liver). The water peak decay, however, was similar in both methods. The relative abundances of each lipid species were found to be significantly larger than those determined in STEAM. The authors conclud e that the use of PRESS result s in an overestimation of the fat fraction and recommend the use of STEAM for fat fraction

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138 quantification. The observation that PRESS overestimates fat fractions is in line with the results of Bernard et al. ( 165) previously discussed. Hamilton et al. ( 167) recommend that each lipid resonance be corrected for its particular T2 unless TE is kept very short Even though singlevoxel MRS, when performed correctly, is expected to yield more ac curate fat fractions than imaging methods, MRS requires relatively large VOIs (larger than 1 cm3) and therefore does not provide the spatial resolution achievable with imaging. Given that fat fractions are most likely distributed heterogeneously in tissue, an MR method that allows the mapping of fat fractions with high resolution in a large section of anatomy is more attractive than MRS. Fat water separation methods provide this more attractive alternative. Clinicians typically work with magnitudeonly im ages. Even though the original 2PD method based on magnitude images is unable to distinguish fat fractions greater than 50% from those lower than 50% (Figure 32 1 ), Hussain et al. ( 110) Dual Flip Algorithm uses differences in T1 weighting of SPGR images to establish fat water dominance in magnitude only images thus resolving the inherent ambiguity of 2PD Hussain et al. ( 110) determined the in vitro accurac y of their method using an oblique slice phantom and the results were presented in Figure 32 1 The plot demonstrates that the method does indeed resolve the ambiguity of the fat water dominance at each pixel and provides good agreement in comparison to t he perfect agreement line. The authors concluded that the 5% overestimation of the fat fraction in pure water was due to the fact that they did not dope the water in their phantom and it consequently presented very long T2*.

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139 The Dual Flip Algorithm was al so investigated by Doro et al. ( 160) Phantom tubes were constructed by blending cow fat and muscle into eleven fat fractions using a food processor. The true fat fractions in each tube were assessed using a chemical assay method (Sohxtec) Three SPGR echoes were acquired with TR = 140 ms, TE (OP) = 3.45 ms, TE (IP) = 4.6/6.9 ms at each flip angle (low 10o, high 70o) to al low for T2* c orrection. They found a systematic overestimation of the fat fraction which probably i ndicates a bias in the method. Given the limitations of magnitude images to provide unambiguous fat water separation, methods have been presented that allow fat water separation by including the phase information in the images. This requires working from the complex image data. The modified 2PD method by Brix et al. ( 46) uses the phase information in the OP image to produce fat water separation. The authors investigated the accuracy of the modified 2PD method on SE images acquired from an oblique slice phantom consisting of vegetable oil and water doped with gadolinium (T2 = 40 ms). The data demonstrated a systematic underestimation of fat fraction which increased with increasing fat content. The authors explain ed that since fat contains multiple resonances, the magnetization vector from each lipid species will be at a different phase angle with respect to water in the OP image, with only the methylene (CH2) magnetization being anti parallel to the water magnetization. Hence, the net fat magnetization will have a different magnitude in the IP and OP images. Since the water image is calculated from the sum of the IP and OP magnitude images ( Equation 3 27), the water image will include half of the difference between the net fat magnetizations in the images and it is therefore overestimated and the overestimation will increase with increased fat content in a pixel.

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140 Matsunaga et al. ( 153) used phantom tubes to compare two S PGR methods: Ma et al. ( 115) regiongrowing with phase gradient maps method (in this study referred to as doubleGRE) with Dual Double Gradient Echo (DDGRE) consisting in bi exponential T2* fit of two pairs of IP and OP images The doubleGRE method does not correct for T2* decay and consequently underestimated low fat fractions and overestimated high fat fractions. In Arai et al. ( 161) the same group repeat ed the study using an oblique slice phantom. In this case, 7 echoes were used for the bi exponential fit of the images (MRM GRE) and doubleGRE refers to 2PD with magnitude images. The 7echo bi ex ponential T2* fit method (MRM SPGR) provide d excellent accuracy, as indicated by the closeness of the fit to the perfect agreement line, but there wa s a systematic underestimation of the fat fraction with a mean difference of 2.1% ORegan et al. ( 112) also used bi exponential T2* fitting of seven consecutive SPGR echoes on an oblique slice phantom at 3.0 T, flip angle = 20o, TR = 17 ms, TE of first echo = 1.12 ms, TE = 1.12 ms. The measurements resulted in large underestimations at fat fractions below 50% and overestimations at fat fractions above 50% Arai et al. ( 161) obtained better accuracy than O Regan et al. ( 112) which may be due to two causes. ORegan et al. ( 112) used a larger flip angle (20o vs 12o) and therefore T1 corrections may have been needed. In addition, ORegan et al. ( 112 ) performed the study at 3.0 T, which made the measurements more susceptible to magnetic field inhomogeneity effects Based on the study by Hamilton et al. ( 167) one can expect differences in the T2 values for different lipid peaks. Even though the model fit ting approach assumes a monoexponential decay for fat, the accuracy of fat fraction determination is very good.

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141 Multi point Dixon methods attempt to remov e the ambiguity in the determination of fat and water dominance by using the phase information encoded in pairs of IP or OP images. As previously discussed, the phase map derived from these methods is affected by phase wrapping and multiple phase unwrappi ng strategies have been proposed. Accuracy of Dixon methods is typically demonstrated based on correct fat water separation in anatomical images as demonstrated by lack of artifacts. Two studies have investigated in vitro accuracy for multi point Dixon. Lodes et al. ( 109) used phantom tubes to compare 2PD and 3PD. The study show ed superior agreement with 3PD compared to 2PD, but the agreement seems to break down at fat fractions above 60. The authors indicated that it was difficult to maintain the emulsions stable at fat fractions above 70%. Kovanlikaya et al. ( 156 ) performed a 3PD phantom tube accuracy study, but unfortunately only fat fractions up to 50% w ere produced, which severely limit s the usefulness of the study. IDEAL is similar to T2* model fitting strategies in that the objective is to fit a model to the image data. However, while T2* model fitting methods are sometimes based on magnitude and/or r eal image data, IDEAL is always performed on complex image data. In addition, the main objective in IDEAL is the determination of the field map. Once the field map is determined, the water and fat images are easily calculated by simple LLS. Bernard et al ( 165) used phantom tubes to determine the accuracy of MRS and then compared pixel independent IDEAL, Dual Flip Algorithm, and fast SE with and without water suppression using MRS as the s tandard. In this study the methods were compared by presenting both a scatter plot and a Bland Altman plot Ideally there should have been a BlandAltman plot for each MRI method, but the authors chose to

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142 combine all the data into one plot The plots indicated that both IDEAL and WS provided the best agreement with MRS. However, the slopes for WS and IDEAL were not very close to unity, suggesting that the agreement is limited: 0.68 and 0.79, respectively The intercept is an indication of the accuracy of the method at very low fat fractions. The intercepts were 7.24% for IDEAL and 9.89% for WS. A Bland Altman plot is a graph of the difference between the two measuring methods (in this case MRI and MRS) versus the average of the two at each point of measurement. If the errors in the measurements are random (i.e. there is no bias), the mean difference should be zero or very close to zero. Bernard et al. ( 165) report the mean differences as: 3.7% (IDEAL), 7.4% (IOP), 7.1% (WS), and +1.2% (FS). This indicates that all methods present a bias, with most methods systematically underestimating the fat fraction, and one (FS) overestimating it The data points for the Dual Flip Algoritm (IOP ) presented a systematic error that was symmetrical about the 50% fat fraction. 2PD based on magnitude images is unable to resolve fat water dominance in each pixel and fat fractions measured with this method follow a bell shape curve. The Dual Flip Algorithm simply flips the part of the curve beyond 50% by 180 degrees. In addition, it is unable to measure fat fractions at or near 50%, since fat and water cancel out at these pixels and the estimation becomes very noisy. Since the method simply flips the rest of the curve, this behavior is mirrored for fat fractions 50% to 100%. Clearly this is a highly unreliable method f or fat fraction determination. The rest of the methods also present ed a consistent overestimation at fat fractions below 50% and underestimation above 50%. These differences are far from being random, hence indicating a serious bias in the measurements. The reference method,

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143 MRS, is not bias free, since MRS systematically overestimat ed all fat fractions The apparent behavior of the MRI methods in this study is simply a reflection of the bias in MRS, since MRS tends to increasingly overestimate with increasing fat fraction. Consequently, all methods seem to overestimate at low fat fractions and underestimate at large fat fractio ns. Bernard et al. ( 165) concluded that IDEAL provided the best accuracy and that the underestimation of the method at high fat fractions was most likely due to the inclusion of the olefinic fat signal with the water signal. The inclusion of the olefinic fat signal with the water signal results in an underestimation of the water fraction by all the methods, which is exacerbated by the fact that this peak is included in the spectrum used to derive MRS fat fractions. As fat content increases, so does the contribution by the olefinic fat, systematically increasing the denominator in the fat fraction. Consequently, fat fractions become increasingly underestimated as fat fractions become larger Unfortunately the cause of the overestimation bias in the MRS fat fractions remains unclear, although it is most likely due to peak broadening by magnetic field inhomogeneity or poor peak fitting. Hu and Nayak ( 159) produced tube phantoms by blending lard with lean cow muscle. As in Doro et al. ( 160) a chemical assay ( So h xtec method) was used to determine the true fat mass in each phantom. Fat fraction was calculated using pixel independent IDEAL based on three SPGR echoes (TR = 6.5 ms; TE = 2.0, 2.8, 3.5 ms; flip angle = 5o). MRI fat fractions were converted into fat mass by multiplication with the density of fat (0.91 g/mL) which was determined empirically. The authors were also interested in investigating the influence of pixel resolution so they down sampled the images from 1.5 mm pixel resolution to 3.0 mm and 4.0 mm. Accuracy wa s

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144 demonstrated by linear fitting. IDEAL result ed in a consistent overestimation of fat mass, which on the average, wa s about 7%. This example of overestimation based on a single lipid peak seems to conflict with the notion that exclusion of the olefinic lipid resonance near water results in underestimation of fat fractions. The agreement only improved slightly with reduced pixel resolution and the authors interpret thi s as an indication of the robustness of IDEAL. In a later study, Hu et al. ( 166) used phantom tubes to compare the accuracies of MRS (PRESS) and MPIDEAL in the determination of fat fractions. Assuming the nominal fat fractions to be exact, MRS underestimated fat fractions by 5% while MP IDEAL overestimated them by 1%, on the average. Based on the intercept, MP IDEAL outperform ed MRS in the determination of low fat fractions (0.09% vs 1.9% respectively ). The PRESS results contradict the conclusion from the study by Hamilton et al. ( 167) that PRESS overestimate s fat fractions. B1 inh omogeneity results in flip angle variation with location within the coil volume, which results in uneven T1weighting in the images. Hu and Nayak ( 159) investigated this effect by measuring the B1 map and calculating the flip angle at all pixels in the images for images acquired with a prescribed flip angle of 60o. The authors used a bird cage head coi l, which, due to its cylindrical geometry, is presumed to provide very good B1 homogeneity. Indeed, most pixels experienced flip angles very close to the prescribed flip angle with tight distributions around the prescribed flip angle. The mean flip angle and standard deviation (in parentheses) were 61.7o (5.9o) in the coronal plane and 59.9o (5.9o) in the sagittal plane. Given the tight distributions of flip angle, pixel

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145 intensities also result ed in a tight distribution, with most pixels presenting relat ively uniform intensities. In most studies, T1effects are handled by selecting a small flip angle. Liu et al. ( 138) performed a noise performance study using Monte Carlo in which the true fat fraction was fixed to 0.5 and fat fractions were calculated from fat and water signals after the addition of zeromean Gaussian noise. The standard deviation (SD) of the fat fraction for different SNR levels was calculated at the Ernst angle ( Equation 3 2) from 3000 trials. The Ernst angle was calculated assuming T1 of water and fat as 586 ms and 343 ms, respectively, and a TR of 10 ms. The results demonstrated that al though a flip angl e of 12o provides minimum noise in the fat fraction calculation at the multiple SNR levels, the T1 bias, expressed as the percent difference between the calculated fat fraction in the noisy images and the true fat fraction (0.5), is relatively high at this flip angle (bias = 4.5%). The authors recommend a flip angle of 5o as a good compromise between noise performance and bias (3%) in the fat fraction calculation. Since water has a longer T1 than fat, water and fat images do not reach optimum SNR at the s ame flip angle. Liu et al. ( 138 ) demonstrated that with a flip angle of 5o SNR is relatively the same for water and fat. Better accuracy is achieved by performing T1 corrections using the dual flip angle method, but this requires the acquisition of two sets of images, which may not always be convenient. T2* corrections are also important in SPGR acquisitions. The effect of T2* losses can be minimized by keeping T2 short, but at the cost of reduced accuracy. MP IDEAL ( 152) provides simultaneous T2* correction and Ifat water separation. The method is labor intensive, so the researcher must make the choice of keeping T2* short and

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146 accepting the loss in accuracy or taking the longer path to improve accuracy. This choice naturally depends on the application and the amount of error that the researchers are willing to accept. Hines et al. ( 170) used phantom tubes loaded with different amounts of iron in order to investigate the performance of MP IDEAL in the presence of magnetic field inhomogeneity. T2* correction improved the accuracy of the fat fraction determination in both SP IDEAL and MP IDEAL MP IDEAL accounts for six lipid resonances and hence is more representative of true fat fraction. The results in Hines et al. ( 170) demonstrated that MP IDEAL provides accurate fat fraction quantification, even in the presence of large magnetic field inhomogeneities. T he gain in accuracy from T2* corrections is more evident at lower fat fractions. Noise P erformance In fat water separation methods, multiple images are acquired to calculate a water image and a fat image. In Dixon methods magnitude images are added and subtracted, and this process could result in calculated images with larger noise than the acquired images. Noisy estimates of the water and fat images are undesirable since they impair the accuracy of the fat fraction, especially at low fat fractions. A quantity that relates noise in the calculated and acquired images is the effective number of signal averages (NSA). It is calculated as NSA = (3 107) where and are the variances in pixel intensity in the acquired and calculated images, respectively. The variances can be calculated from images produced by each fat water separation method, but the variances will vary depending on the specific

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147 conditions under which the measurements were made. R ather than specific variances, one would prefer to know a lower bound for these variances, representing measurements under the best possible conditions (i.e. noise free). This is accomplished by the Cramr Rao Lower Bound (CR L B) formulation, which is a st atistical methodology by which one can calculate the lower bound for the variance of any unbiased estimator ( 171) In the presence of noise, any unbiased estimator cannot have a variance lower than its CR L B. The CR L B can be used to optimize parameter settings in fat fraction quantification, since one can investigate how modifications in these parameters move the NSA c loser or farther than the CR L B for NSA. The NSA for the water or the fat image using 3PD (neglecting relaxation term losses) was determined by Glover ( 172) as = 1 + 2 2 ( 1 ) ( 3 108) where is the phase angle increment between successive echoes For example, for the standard SE 3PD acquisition, the echoes are acquired at (OP), then 0 (IP) and finally + (OP), so the phase angle increment is The maximum NSA achievable for the calculated images using 3PD is 3.0. From Equation 3 107 = NSA (3 109) Therefore, f or NSA = 3, = 3 which means that the calculated image has the noise equivalent of the average of the three acquired images. The standard phase difference used in Dixon methods ( = ) is not optimal, but it still provides excellent NSA ( 8/3 2.67). The optimum NSA occurs at = 120o, which corresponds to a uniform spacing of the phase encoding in the unit circle. Since the phase angle spacing

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148 is directly proportional to the inter echo spacing, this means that uniform inter echo spacing results in optimum noise performance. Glover ( 172) determined that the NSA for 4PD with a phase angle increment of i s equal to 8/7 = 1.14. Hence, 4PD with this phase angle spacing does not improve the quality of the fat water separation, in spite of the acquisition of an additional image. As previously stated, the RCLB can be used to optimize parameters in image sequences. Pineda et al. ( 171) used RCLB to determine the optimum echo spacing for threepoint fat water separation that maximizes the NSA for the fat and water images (magnitude), phase map, and field map. In order to optimize NSA for one parameter, the other two are assumed known. NSA will vary depending on the fat fraction. Rather than producing separate plots for each fat fraction, the authors plot the maximum smallest NSA of all fat fractions. Since it is advantageous to keep imaging time as short as possible, these NSA values are plotted versus the largest phase separation between the water and fat magnetizations ( max (| | ) ) that results in that NSA. Then, the phase difference at which the NSA curve stops increasing corresponds to the shortest possible echo time that achieves maximum NSA. Pineda et al. ( 171) demonstrate that for SSFP and fast SE sequences, the smallest phase angle between the water and fat magnetizations that provides optimum NSA for the calculation of water and fat images is 7 /6. Hence, the optimum echo shifts to achieve maximum NSA in the calculated fat and water images using three SSFP or FSE echoes are /6, /2, and 7 /6. This echo distribution rotated by +n also results in optimum NSA. Hence, the optimum echo phase shifts can be generalized as 6 + 2 + 7 6 + = 0 ,1 ,2 = 1 ,2 (3 110)

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149 SPGR sequences can only provide positive phase shifts, so the echo shifts for n = 0 are not possible for this type of pulse sequence. An important implication of this result is that the standard phase angles used for 3PD ( 0, ) and (0, 2 ) are not optimal for the calculation of fat fractions. 3P IDEAL acquisitions are based on the requirement that the fat and water magnetizations are perpendicular in the middle echo. Consequently, 3P IDEAL is performed using the optimum phaseshifts for the determination of fat fractions ( Equation 3 110), which explains why IDEAL tends to outperform Dixon methods. The CRLB provides only provides a lower bound in variance, i.e. the case in which the images are noise free. Pineda et al. ( 171 ) used Monte Carlo t o determine the expected NSA at each fat to water ratio (FWR) when noise is present in the images. A single pixel was modeled with the phase shifts determined as optimal by CRLB and assuming a fixed FWR at a time, SNR of 200, and a phase map value of /20. Zeromean Gaussian noise was added to the pixel and non linear least squares (NLLS) was then used to solve for the unknown parameters in the signal model. This was repeated 500 times for each FWR. The Monte Carlo simulations demonstrated that while the standard echo shifts of ( 0, provide suboptimal yet good noise performance in the determination of fat and water images, it result s in very noisy estimates of fat fraction at pixels where the water and fat content is approximately equal. In contrast, the echo shifts used in 3P IDEAL ( /6, /2, 7 /6) result in optimal and uniform NSA for fat water separation for any fat fraction. These theoretical and simulated results were confirmed experimentally in Reeder et al. ( 130) and Reeder et al. ( 139) using oblique slice p hantoms.

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150 Hernando et al. ( 157) compared the noise performance of several models --Dixon using magnitude images, Dixon using complex images, single peak and multi peak IDEAL, with and without R2* corrections using phantom tubes. CRLB were also calculated for each model type. The phanto ms were imaged at 1.5 T using SPGR, acquiring 8 echoes with TE1 = 1.43 ms and TE = 2.23 ms with flip angle = 25o (TR = 2000 ms SNR 90). Long TR was used to minimize T1 bias (< 1%). Oil and water T1 and T2 were measured using IR and MSE, respectively. Calculations were repeated 128 times. Magnitude fitting models consistently result ed in lower NSA than complex fitting and resulted in very low NSA at pixels with similar water and fat content (FWR near unity). T2* corrections help ed stabilize the nois e performance in magnitudefitting models, but result ed in a loss in NSA in complex fitting models. The authors hypothesized that the loss in SNR may be due to the fact that lipid peaks are not all at the same phase simultaneously, so spectral fitting res ults in added variability. NSA only indicates noise sensitivity of the models, but is not indicative of accuracy or bias (i.e. difference between measured and true fat fractions). Hernando et al. ( 157) also plotted the estimated fat fractions versus the true fat fractions for each model. Multi peak complex fitting provide d superior accuracy regardless of T2* modeling. Even though NSA for complex fitting is not optimal, it affects both the water and the fat images equally, and the increased variability is balanced out in the fat fraction calculation. Using a common T2* for water and fat is less computationally demanding than fitting different T2* for water and fat and the results in H ernando et al. ( 157 ) demonstrate that multi peak models perform equally well under either assumptions.

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151 In V ivo A ccuracy Phantoms are generally homogeneous in composition and magnetic field inhomogeneity is relatively low in the phantom material. Living tissues are generally heterogeneous and magnetic susceptibility differences between different tissue components (e.g. bone, air, fat, water) result in highly inhomogenous local magnetic field. In addition, living tissues contain fluids in motion which lead to signal loss, and are typically in motion (e.g. breathing, heart beat). All of these factors will affect the accuracy of fat fraction quantification and hence once expects in vivo accur acy to be inferior to in vitro accuracy. A major challenge to the determination of in vivo accuracy is the identification of a standard for comparison. The exact fat fraction of a tissue is typically unknown, and consequently in vivo accuracy is determined by comparison of two measurement methods, where the reference method is presumed to be very accurate. Not surprisingly, most in vivo accuracy studies employ MRS as the reference method ( 39, 112, 113, 155, 166, 173178) However, as discussed in previous sections, MRS accuracy is highly dependent on operator expertise, since something as simple as VOI size selection and placement can greatl y affect the accuracy of the spectroscopy measurement ( 164) In addition, most studies quantify fat based on a single lipid peak (methylene peak, 1.3 ppm), which results in an underestimation of the fat fraction. Even when multiple peaks are used, few lipid peaks are resolvable at clinical magnet strengths and it is always challenging to resolve the olefinic proton peak due to its proximity to the water peak. Magnetic field inhomogeneity and peak overlap result in linewidth broadening, which affects the accuracy of the fat fraction calculation. MRS typically uses long TR, so T1 corrections are generally not needed. How ever, T2*

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152 corrections are required, and the accuracy of the fat fraction will depend on whether a common correction is applied to all lipid peaks or each peak is corrected independently. The choice of the MRS method is also critical, as demonstrated by the comparison of the accuracy of STEAM and PRESS by Hamilton et al. ( 167) Most in vivo accuracy studies suffer from the same defect pointed out in the in vitro accuracy section of this chapter: accuracy is demonstrated with linear regression lines, rather than with BlandAltman plots. This severely impairs the analysis, since it makes it difficult to compare the results from different studies, and makes it very difficult to determine bias or systematic errors in the measurements. In V ivo A ccuracy of MRS Two studies investigated the in vivo accuracy of MRS by comparison with biopsy ( 53, 173) Ballon et al. ( 53) compared MRS (STEAM) bone marrow water fraction (one minus the fat fraction) measurements with CF determined from biopsy at the iliac crest in diseased patients. Both measurements were performed at the iliac crest at approximately the same location. MRS cellularity was determined from the water fraction calculated using only the methylene peak. Biopsy CF was determined by grading. The slope of the regression line fitted to the data was almost unity (0.94 0.04) with an intercept of 8.1 2.9 and r = 0.94. However, all water fractions we re overestimated by approximately 8.1% Given that t he MRS water fraction wa s calculated using a single lipid peak it is not surprising that all water fractions we re systematically overestimated. In addition, T2* corrections were not performed. T2* of water and fat at 1.5 T in the bone marrow of the ilium bone have been reported as 36 ms and 61 ms, respectively ( 57) Consequently, fat experiences a greater signal loss than water, which also contributes to the overes timation.

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153 DAssignies et al. ( 173) performed liver biopsies to compare MRS (PRESS) to histological fat fractions. Liver biopsies were acquired using a 16 gauge needle from the right hepatic lobe. Fat fractions were determined by segmentation of the fat vacuoles in the digitized histology images. A plot of MRS fat fractions versus histology demonstrated a severe disagreement. This is not surprising, since the needle biopsy measurements we re performed at a single location in the liver, while the MRS measurements were performed at 3 different locations in the liver. In addition, these measurements have different spatial resolutions, since the ROIs used in MRS are at least one order of magnitude larger than that covered by a 16gauge needle (9.6 mm2). The disagreement suggests that the fat fraction distribution in the liver is not homogeneous and therefor e a needle biopsy measurement is not representative of the average fat fraction in the liver. Needle biopsy is known to suffer from high sampling variability due to its small sampling volume ( 179) In V ivo A ccuracy of Dixon Methods Most clinical MR scanner produce only magnitude images and hence a fat water separation method that operates on magnitude images is of great interest The 2PD method with magnitude im ages is very simple to use and is insensitive to magneti c field inhomogeneity. Since it can be used with SPGR, TE and inter echo spacing can be kept very short, which is convenient to reduce organ motion during breathing and to minimize T2* signal losses. However, it is unable to unambiguously determine fat f ractions larger than 50%. The human liver typically presents fat fractions much inferior to 50% ( 179) and therefore provides a perfect tissue for the use of 2PD with magnitude images. Non Alcoholic Fatty Liver Diseas e (NAFLD) is the most common form of chronic liver

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154 disease in adults and children in the US that results from the accumulation of fat in hepatocytes in the liver ( 178, 180 ) It is typically diagnosed by needle biopsy, a procedure that is invasive, painful, and suffers from high sampling error ( 179181) Consequently there is a lot of interest in the use of MR as a noninvasive alternative in the diagnosis of this disease. Several studies have investigated the in vivo accuracy of 2PD in the measurement of fat fraction in the liv er by comparison to MRS ( 113, 173177) With the exception of two studies only linear regression plots were produced. All studies indicate that 2PD fat fractions are highly correlated (> 0.95) with MRS. Most show excellent agreement wit h MRS ( 113, 173, 176, 177) but two studies ( 174, 175) present grossly overestimated fat fractions. The main difference between these studies is that the studies that found excellent agreement had applied T2* corrections to both the spectrum and the 2PD images, while the other studies had assumed that the selection of a short TE of 30 ms would suffice to eliminate T2* bias, which clearly did not. DAssignies et al. ( 173) produced a BlandAltman plot comparing the measurement of liver fat fraction with SPGR 2PD to PRESS. PRESS fat fractions were calculated using the water peak and three lipid peaks (0.9, 1.3, and 2.0 ppm). The authors report ed the mean difference (PRESS 2PD) as + 0.57% and the 95% limits of agreement (i.e. mean difference 1.96 ) as 6.11% and 7.26%. All measurements except for one we re within the limits of agreement, indicating that it is an outlier. There wa s no discernable pattern to the distribution of the measurements, which is consistent with a mean difference close to zero. Most differences we re within 3%, indicating

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155 excellent agreement between PRESS and 2PD. T he positive bias may reflect the tendency by PRESS to overestimate fat fractions Guiu et al. ( 176) compared SPGR with T2* model fitting to PRESS using a Bland Altman plot. PRESS fat fractions were calculated using the water peak and a single lipid peak (1.3 ppm), and the measurements were performed at 3.0 T. The authors do not report the mean difference (MRS SPGR) but it can be estimated from the plot as + 0.3%, about half of the bias experienced in DAssignies et al. ( 173) The 95% acceptance limits are also about half as narrow in this study. The difference between the studies is most likely due to biological variability, since most fat fractions in DAssignies et al. ( 173) were found to be within 3%, which is in line with the limits of agreement observed in Guiu et al. ( 176) These limits demonstrate excellent agreement between 2PD and MRS. The authors found very large patient variability in the values of T2* for water and fat, and caution that the use of theoretical or averaged T2* to perform corrections will lead to inaccuracies. Bone marrow CF is not restricted below 50%, and its measure consequently requires Dixon methods that account for the phase information in the images. CF is measured as the water fraction, i.e. one minus the fat fraction. The in vivo accuracy of multipoint Dixon CF was investigated by Ballon et al. ( 155) They acquired FSE images of BM in the ilium bone of healthy and diseased individuals at 1.5 T and TR/TE = 1000/34 ms. Images were acquired with phase shifts of (0, 2 ) and, for purposes of comparison, fat and water suppressed FSE images were also acquired. Water fractions were calculated at the left iliac crest fr om the resulting fat and water images. Spectroscopy was performed at the same anatomical location using STEAM with the

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156 same TE and TR used in imaging and a VOI = (1 cm)3. The water and one lipid peak (CH2, 1.3 ppm) were used to calculate MRS water fracti ons. S uppression methods result ed in very poor agreement (slope = 0.58, R = 0.91), while 3PD provided excellent agreement ( slope = 1.11, R = 0.97) with STEAM In V ivo A ccuracy of IDEAL Kim et al. ( 177) investigated the in vivo accuracy of fat fraction determination by 3P IDEAL in the liver in comparison with STEAM. SPGR images were acquired with flip angle = 55o, TR = 5.38 ms, and TE = 1.49, 2.69, 3.89 ms, corresponding to phase shifts of (5 /6, 3 /2, 13 /6). Pixel independent IDEAL was performed to produce fat and water images. Fat suppressed (FS) and water suppressed (WS) STEAM spectra were acquired with VOI = (1.5 cm)3, TR =3000 ms (WS), 5000 ms (FS), TE = 20 ms, BW = 2500 Hz. MRS fat fractions were calculated using the water peak and a single lipid peak (1.3 ppm). Imaging was performed at 1.5 T, while spectroscopy was performed at 4.0 T. The linear regression plot for the measured fat fractions showed that 3P IDEAL overestimated all fat fractions by approximately 10%. The authors hypothesized that the overestimation may be due to T1and T2* weighting by the SPGR sequence used in the study. This is supported by their results for 2PD which used a standard SPGR sequence and did not result in the gross overestimation observed in the IDEAL results. Reeder et al. ( 178) obtained SPGR images of the liver with TR = 7.4 ms and TE = 2.0, 3.6, and 5.2 ms, corresponding to phase shifts of (5 /6, 3 /2, 13 /6). S P IDEAL was performed to calculate the water and fat images PRESS spectra were acquired with VOI = (2.5 cm)3, TR = 2500 ms, TE = 25 ms, BW = 2500 Hz, NEX = 4, 2048 points. Five lipid peaks were used in the fat fraction calculations. The linear plot demonstrated

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157 an underestimati on of all fat fractions by IDEAL, which increased with increasing fat fraction. This result is reasonable since IDEAL fat fractions we re calculated using a single lipid resonance while MRS fat fractions included 5 lipid resonances Reeder et al. ( 178) also investigated the in v ivo accuracy of MP IDEAL with self calibration and precalibration using PRESS as the reference method. The agreement wa s excellent for precalibration ( slope = 0.96 0.04, intercept = 1.52% 0.71% ) and adequate for self calibration ( slope = 0.83 0.05, intercept = 1.76% 0.76% ). Better agreement was expected, compared to SP IDEAL, since MP IDEAL accounts for multiple lipid peaks and includes T2* corrections. The difference in performance between the precalibrated and self calibrated approaches may be explained by the fact that self calibration is based on only three lipid peaks, while precalibration includes six. Hu et al. ( 166 ) also obtained very good agreement between M P IDEAL and PRESS at 3.0 T. Six SPGR echoes were acquired with TR = 10 ms, TE = 1.5 ms, TE = 0.8 ms, flip angle = 5o. PRESS spectra were acquired with VOI = (2.0 cm)3, TR = 4000 ms, TE = 23 ms, NEX = 8, BW = 2500 Hz. Only the water and methylene peaks were used for MRS fat fraction calculations. The mean difference (PRESS MP IDEAL) in the BlandAlt man plot was reported as 0.38% and most fat fractions we re within 3%, suggesting a comparable performance to 2PD T2* model fitting methods. The s tudy was also repeated in the pancreas, but agreement was impaired due to inaccurate placement of the spectroscopy voxel on the pancreas. The quantification of fat fraction via MR is of clinical interest since it allows the noninvasive evaluation of bone marrow CF and hepatic fat fraction. The measurement of fat fractions by MR requires the spectral separation of the signal contributions by

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158 water and fat protons. Based on the results from the studies presented in this chapter, spectral suppression methods result in poor fat fraction measurements, most likely due to incomplete suppression in regions of magnetic field inhomogeneity Inversionrecovery (IR) methods are insensitive to magnetic field inhomogeneity but require very accurate assessment of the T1 value of the tissue to be eliminated. In general, T1 is not measured in every MR exam, since it is very time consuming. The use of average T1 values will inevitably fail in eliminating the unwanted signal since T1 exhibits very large biological variabi lity. IR typically results in the nullification of the signal from other tissues that have T1 close to the T1 of the tissue whose signal is to be eliminated. In addition, T1decay during the inversion time results in images with low SNR. SNR can be impr oved by selecting long TR, but this increases the imaging time which make this technique impractical in anatomical regions subject to motion. IR techniques have also been shown to result in poor fat fraction quantification accuracy ( 153 161) MRS is generally viewed as a very accurate method for quantification. However, it is also subject to T1 and T2* decay and magnetic field inhomogeneity effects (spectral line broadening) and its accuracy is strongly dependent on the choice of spectroscopic method ( 167) and operator experience, as demonstrated by the inconsistency in the accuracy reported by different in vitro and in vivo studies. Spectral fitting is not straightforward since lipid resonances tend to be close together and result in additional line broadening. Fitting algorithms will do their best to find a solution based on i nformation provided by the user. Something as simple as the choice of line shape to fit (e.g. Lorentzian or Gaussian) can have a severe impact on the number of peaks resolved by the algorithm, their respective line widths, and amplitudes which makes the

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159 fit a complicated and highly subjective process T1 corrections are typically not needed, since TR in spectroscopy acquisitions is typically very long. However, T2* corrections are very important, as has been demonstrated by multiple studies ( 167) A major drawback of MRS is its coarse spatial resolution, and in general one is more interested in spatial mapping of fat fraction, since fat fractions typically exhibit high heterogeneity in tissues, particularly in bone marrow. Fat fraction quantification via water fat imaging methods is therefore more attractive. Fat water separation imaging methods can be separated into chemical shift misregistration, D ixon, and IDEAL. Chemical shift misregistration is very straightforward and simple to apply, but it may be limited to the spine, since it is not applicable to bones that are thin, curved, or in very close proximity to adipose fat or muscle. Both 2PD and dual echo T2* model fitting methods are attractive in that they allow the use of magnitude images, since most clinical scanners only produce magnitude images. However, 2PD is generally unable to unambiguously resolve fat fractions greater than 50%. This i s not a problem in liver studies, since hepatic fat fractions are typically smaller than 50%. Multiple studies have shown excellent agreement ( 3% fat fraction) between 2PD and MRS in the liver ( 113, 173, 176, 177) The Dual Flip Algorithm ( 110) provides methodology for determining fat water dominance in every pixel, but requires the acquisition of two sets of three images at different flip angles and it has been shown to perform poorly i n vitro ( 160, 165) The ambiguity of 2PD can be eliminated by the use of the phase information available in the complex images. Extracting the phase map from the images is problematic due to phase wrapping. The in vitro and in vivo accuracy of multi point

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160 Dixon methods has not been properly investigated. The modified 2PD method has been shown to underestimate fat fractions in vitro ( 46) and 3PD shows excellent agreement with MRS in iliac crest bone marrow ( 155) However, the standard echo shifts used in 3PD, ( 0, ) and (0, 2 ) have been shown to have suboptimal noise performance ( 171) being particular sensitive to noise in pixels that have approximately equal proportions of water and fat. In addition, noi se performance of Dixon with SPGR has been shown to be very poor. In contrast, the phase shifts typically used in IDEAL, ( /6 + n /2 + n 7 /6 + n ) have been shown to provide maximum NSA in the calculation of the fat and water images ( 171) Consequently, IDEAL typically outperforms Dixon methods in fat fraction quantification ( 157) Both in vitro ( 170 ) and in vivo ( 177, 178) studies have demonstrated that MP IDEAL provides very accurate fat fraction quantification compared to other methods. The accuracy of fat quantification is affected by long inter echo s pacing, since this increases T2* blurring and lengthens acquisition times, which is problematic when imaging in anatomical areas subject to motion. Dixon echo shifts only provide adequate noise performance when used with FSE imaging sequences, and this li mits the smallest inter echo spacing that can be used. IDEAL echo shifts are optimal in SSFP, FSE, and SPGR sequences, allowing for a greater flexibility in inter echo spacing. The use of SSFP also allows minimization of T1 effects by selection of small flip angle (e.g. 5o). In addition, MP IDEAL fat water separation allows simultaneous T2* correction and fat water separation based on multiple lipid resonances which has been shown to be necessary for accurate fat fraction determination by multiple studi es. The accuracy and

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161 versatility of IDEAL fat water separation makes it the ideal method for fat fraction quantification.

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162 Figure 3 1. Distribution of proton magnetic moments in A ) the absence of an external magnetic field and B ) the presence of an external magnetic field, B0. Circles represent protons and arrows their magnetic moments. Figure 3 2. RF pulse and precession of the magnetization vector. A ) the RF pulse pushes the magnetization vector from the equilibrium position along the z axis onto the transverse plane (x y); B ) the moment the RF pulse is turned off, the magnetization vector precesses about B0 on its way back to the equilibrium position. B 0 A. B M = 0 M 0 Z X Y B 0 M 0 A. M Z X Y B 0 B M

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163 Figure 3 3. The decay of the transverse component of the magnetization. The spiral cor responds to the trajectory of the tip of the transverse magnetization vector in its precession back to equilibrium. The projected trajectory is known as the free induction decay (FID). Figure 3 4. Fanning out (dephasing) of the magnetization vector. Interactions between some magnetic moments cause them to slow down and precess out of phase, thus fanning out over the transverse plane. X Y t M xy Z Y X

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164 Figure 3 5. SPGR pulse sequence diagram. RF = radiofrequency pulse, = flip angle, Gslice = slice selective gradient, Gphase = phase encoding gradient, Gread = frequency enc oding gradient or read gradient, Signal = MR signal that can be detected at the receiver coil, TE = echo time, TR = repetition time. The three dots after each line indicate that the sequence is repeated for each phase encode step, represented by the steps in the gradient symbol for Gphase. Figure 3 6. The f requency e ncoding g radient. G(z) is the magnetic field linear gradient established along, in this case, the z axis. Gradients can also be applied along the x and y axes. B0 is the static uniform magnetic field established in the MR magnet. The magnetic field strength experienced along the z axis is the sum of the static field and the field due to the gradient and hence it has a unique value at each point along z. 0 z Field strength B 0 B 0 + G (z) z ... RF ... G slice ... G phase ... G read ... Signal TE TR

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165 Figure 3 7. T2* versus T2decay of the FID. Figure 3 8. SE pulse sequence diagram. RF = radiofrequency pulse, Gslice = slice selective gradient, Gphase = phase encoding gradient, Gread = frequency encoding gradient or read gradient, Signal = MR signal that can be detected at the receiver coil, TE = echo time, TR = repetition time. The three dots after each line indicate that the sequence is repeated for each phase encode step, represented by the steps in the gradient symbol for Gphase. ... RF ... G slice ... G phase ... Gread ... Signal TE TR 90 o 180 o t (ms) T2 decay T2 decay

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166 Figure 3 9. Rephasing of magnetization in a SE sequence. A. relaxation causes the dephasing ( i.e. spread) of magnetic moments; B. after the 180o pulse, the magnetic moments retrace their movement i n the opposite sense and rephase. Z Y X Z Y X 180 o A. B

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167 Figure 31 0 Incomplete fat suppression with a spectral saturation pulse. The shift in frequency between water and fat is greater at 3.0 T ( B ) than at 1.5 T ( A ) A saturation pulse (shaded area) centered at the resonance of fat (CH2) may result in saturating part of the water peak at 1.5 T ( A ) but it is less likely to do it at 3.0T ( B ). Figure 31 1 1H NMR spectrum of soybean oil at 3.0 T. The spectrum was acquired by imaging a bottle containing soybeam oil using STEAM using a head TR coil. Lipid chemical shifts (ppm) are in reference to the resonant frequency of water (chemical shift = 0). (CH 2 ) n CH 3 HC=CHCH=C=CHA. water fat B. water fat

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168 Figure 31 2 Effect of trabeculae in the local magnetic field in bone marrow. The gray rectangles represent trabeculae and the solid horizontal line s represent the field lines of the static magnetic field B0 inside the magnet bore. When the bore is empty (A) the magnetic field are parallel and equally spaced; i.e. the magnetic field is uniform or homogeneous However, when bone marrow is placed inside the bore, the presence of the trabecula cause a distortion of the m agnetic field lines (B and C), resulting in an inhomogeneous magnetic field. When the trabecula are widely spaced, regions between the trabeculae (dashed rectangle) may still experience uniform B0. A. B C

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169 Figure 31 3 The NMR spectrum. Consider a biological tissue containing three different molecular types. If the tissue is imaged, the MR signal will contain signals from each of the three types of molecule (1, 2, and 3), each at a unique frequency and an amplitude proportional to its abundance in the tissue. If these signals are added, the result is the FID. A Fast Fourier Transform (FFT) is a mathematical operation by which the signal is transformed from amplitude vs time (time domain) to amplitude vs frequency (frequency domain). The resulting function is called the NMR spectrum. Note that the spectrum presents three peaks, each at a unique location (f1, f2, f3) on the horizontal (frequency) axis. 1 2 3 1 + 2 + 3 Individual signals FID (sum) NMR Spectrum f 1 f 2 f 3 FFT

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170 Figure 31 4 Origin of chemical shift misregistration light and dark bands. Since the fat magnetization lags behind the water magnetization, when the read gradient is established, the fat signal is misregistered as hav ing originated from a location farther upstream (i.e. at lower frequency along the gradient). The result is a signal void behind the fat region (dark band) and signal superposition where fat and water overlap (light band). [ Adapted from Figure 2 in page 233 of Cassidy et al. 2009, Fatty liver disease: MR imaging techniques for the detection and quantification of liver steatosis. Radiographics 29: 231260.] Fat Water Physical position Read gradient Fat Water Fat Water Encoded position Signal intensity Signal void Signal superposition

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171 Figure 3 1 5 P eriodic oscillations in the MR s ignal from tissue containing fat and water. Chemicalshift induced oscillations occur in subcutaneous fat ( A ) but not in muscle ( B ) since muscle contains little fat. TE (ms) TE (ms) Signal Signal A. B

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172 Fi gure 3 16 Ambiguity of the twopoint Dixon method using magnitude images Plot of true fat fraction versus fat fraction calculated using 2PD, as predicted by Equation 3 33. Figure 3 17 Oblique slice oil water p hantom The dashed line indicates how the oblique slice is selected at the oil water interface. This results in an image that includes a continuous range of fat fractions. 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Measured fat fraction True fat fraction

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173 Figure 318 T2* correction of SPGR 2PD. The bottom curve (black) depicts the signal decay due to T2* and the top curve shows (gray) the signal after T2* correction. After T2* correction, the signal amplitudes are the same for all IP (maxima) and OP (minima) echoes. Figure 319 Phase unwrapping process. The figure depicts the phase calculated from the Dixon image data near a water lipid boundary. As the oil lipid boundary is approached, the phase (black solid line) increases eventually reaching a value of near the boundary. The true phases of pixels beyond this point are much larger than but since the arctangent function maps phases to the domain ( ], the phases for these pixels are wrapped to a negative angle by subtr action of 2 This results in sharp discontinuities in the calculated phase map, which leads to fat water switches. The discontinuities can be eliminated by unwrapping the phases of adjacent pixels that have opposite phases through the addition of 2n The dashed line shows the corrected (unwrapped) phases P hase position or pixel number Signal TE

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174 Figure 32 0 Multiple local minima in the residual at 3.0 T. Residual (black line) for a single pixel from images processed by IDEAL for field map values (phi 0) in the range 1500 Hz. The pixel corresponds to muscle in the images (i.e. water). The residual is the difference between the measured pixel intensities from the image and the fitted model. The calculated water (blue line) and fat (red line) are also shown. The residual presents multiple and periodic local minima and the linear least squares (LLS) procedure will converge to the minimum closest to the initial guess used for the field map. Given an initial field map guess of zero, LLS may either converge to 4 83 Hz or +4 3 0 Hz. Not e that these local minima result in contradictory results: water dominance and fat dominance, respectively.

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175 Figure 32 1 Square spiral trajectory used in 3P IDEAL with RGA. The blocks depict the pixels in the image. Blocks in gray represent the starting pixel neighborhood. The field map for these pixels is determined using pixel independent IDEAL with a starting guess of zero. The field map for t he remaining pixels in the image is calculated, one pixel at a time, using an initial field map guess determined from a 2D linear fit of the field map values that have already been calculated. Pixels are evaluated in sequence, f ollowing a square spiral trajectory ( dashed line; arrows indicate direction) that starts at the pixel to the left of the top left corner of the starting pixel neighborhood ( block in black ). This process is continued until all image pixels have been evaluated.

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176 Figure 322 Regiongrowing process with multi resolution images. 1 is the starting super pixel. The immediate neighbors of the starting super pixel (2) are assigned the field map value in their particular minimizer sets that is closest to that of the starting super pixel. The next layer of neighbors (3) are assigned the field map value in their minimizer sets that is closest to the field map value assigned to layer 2. This region growing process continues until a ll image pixels have been evaluated. Figure 323 The graph and the graph cut. Each pixel in the field map is assigned a vertex ( vq) with q = 1 to Q In addition, there are two special vertices: a source (s) and a sink (t). There are edges ( dqj) that connect all pixels to each other and to the source ( dsq) and sink ( dqt) Weights are assigned to each of the edges based on parameters of the cost function. A cut consists in literally cutting some of the edges. The cost of the cut is the sum of the wei ghts of the cut edges. [ Adapted from Figure A1 in page 89 of Hernando et al. 2010, Robust water/fat separation in the presence of large field inhomogeneities using a graph cut algorithm. Magnetic Resonance in Medicine 63:79 90]. t v 1 v 2 v 3 v Q s ... graph cut d sQ d 1t d s1 d s2 d 2t d 3t d Q t d s3 d 12 d 23 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2

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177 Figure 324 Wedge compartment phantom. The phantom consists of two wedge containers that fit one over the other (A). One container is filled with water and the other with oil. I mages of a slice through the phantom are acquired (B), and rectangular ROIs (dotted rectangle) can be selected that correspond to fat fractions that vary from 0 to 100%, depending on the location of the ROI along the length of the phantom. A. B ROI

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178 CHAPTER 4 MRI ESTIMATION OF BO NE MARROW CELLULARIT Y In Chapter 1 an equation ( Equation 1 5) is described that allows the estimation of the mass of TA M in a given patient. Three of the quantities required in the calculation TSSV, fSV x, and MVF-cannot be determined i n a given patient. To overcome this limitation, i n Chapter 2 data acquired from 40 cadavers (20 male, 20 female) is used to develop a predictive equation that allows estimation of patient specific TSSV (Table 25) and to produce a table of average fSV x data (Table 29) The predictive equation is expected to provide TSSV in a patient with an error typically better than 20%. The development of a similar predictive equation for MVF was not possible at this time so instead the reader is directed to adul t average values of MVF determined in other studies ( Tables 1 2 and 13 ) In contrast to the three aforementioned quantities CF can be measured noninvasively directly on a patient. The current goldstandard method for the measurement of CF is histological analysis of a BM biopsy from the iliac crest. Problems with this method are that it is painful and invasive which limits its use for repeated measurements it is based on a very small sample volume, and CF measured at the iliac crest is not necessarily representative of CF elsewhere in the skeleton. Hence, this method is not appropriate for the determination of patient specific CF to be used with Equation 1 5 Chapter 3 contrasted multiple MR methods that can be used for the quantificati on of fat fractions in vivo. It was concluded that multi peak IDEAL (MP IDEAL) is the method of choice for the estimation of fat fractions, since it has been shown to provide the greatest accuracy and best noise performance both in vitro and in vivo. How ever, the application and in vivo accuracy of MP IDEAL has only been determined for the

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179 measurement of hepatic fat fractions. The main goal s of the work in this chapter are (1) to determine the feasibility of MP IDEAL in the measurement of bone marrow cel lularity (CF) and (2) to characterize its in vivo accuracy by comparison with the current gold standard, bone marrow histology, performed at the same location on the bone. Given that measuring CF from histology requires the extraction of cubes from multiple bone sites, this study cannot be performed in live humans. Large dogs have marrow cavities and trabeculae of size similar to those found in humans (personal observation based on preliminary studies with dog cadavers). Hence, large dogs represent an adequate in vivo phantom in which to perform the comparison. MR scans can be performed in vivo followed by bone extraction post euthanasia. MP IDEAL fat water separation requires the use of a lipid spectrum and it would be convenient to be able to characterize the multiple bones included in an MR image by a single lipid spectrum This approach requires that the lipid spectrum remain relatively constant throughout each bone. A large body of studies has perform ed bone mar row cell counts in dogs but the majority has focused exclusively on hematopoietic cell counts and CF is rarely measured. To my knowledge, there are no canine bone marrow MR spectroscopy published studies and hence the variability of lipid spectral amplitudes in canine bone marrow is currently unknown. Human bone marrow MR spectroscopy studies typically report fat fractions, but not the spectral amplitudes. One study ( 92) demonstrated high variability between two lipid peaks in the fifth lumbar vertebra in humans, where the standard deviation of the spectral amplitudes exceeded the means by a factor of three. If this result is an indication of a general trend, it is unlikely that a single spectrum will be adequate to characterize every section of a long bone or every

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180 vertebra in a section of the spine. However, if the variability within each skeletal site is found to be small enough, the error in the CF calculation resulting from the application of a common spectrum may fall within clinically acceptable levels. The use of a common spectrum would speed up and greatly simplify the CF calculations via MPIDEAL Given that it i s uncertain if the use of a common spectrum is feasible and that, in general, it may not be convenient to acquire spectroscopy data in addition to the patient images, the use of singlepeak IDEAL is also investigated. Materials and Methods Animal Care and Procedures The study was conducted with IACUC a pproval. T wo mongrels, male, 1.5 yrs old and approximately 25 kg in weight, were pur chased from an authorized provider. The dogs were housed at the University of Florida Ani mal Care Services (ACS) kennels, where ACS personnel cared for the dogs. After the required oneweek quarantine period, dogs were prepared for MR scanning by fasting for 24 hours. A nesthesia was performed the day of the scan by ACS personnel. The animals were premedicated with an intramuscular (IM) injection of 0.010.02 mg/kg of b uprenorphine and 0.030.07 mg/kg of a cepromazine. T he right or left front leg was clipped and cleaned with chlorhexidine scrub, and an IV catheter was placed aseptically in the cephalic vein. Once the IV catheter was secured, the animal was induced with p ropofol 4 mg/kg given intravenously (IV) slowly to effect. The dog was then intubated and anesthesia was maintained with 12.5% isoflurane inhalant carried in 100% oxygen. Ventilation was assisted using intermittent positivepressure ventilation. Heart rate, oxygen saturation, temperature and expired carbon dioxide were continually m onitored

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181 during the procedure. Fluids were administered at a rate of 510 mg/kg IV to maintain hydration. MR Imaging Scans were performed with a 3T Philips Achieva MR scanner using a six element torso phasedarray coil The anatomy of interest was aligne d with or near the center of the coil to obtain approximately uniform sensitivity across the target bone. Dogs were placed in left or right lateral decubitus, feet first, to make it easier for ACS staff to monitor vitals and keep the animal hydrated during the MRI session. Breathhold was not employed under the assumption that motion due to breathing would not be a problem when imaging the upper third and lower third of the spine or long bones. The long bone that was imaged was the one in contact with the table below the dogs body Hence, the limb is not expected to move as a consequence of breathing during imaging. Multi echo SPGR imaging was performed at two flip angles 5o and 34oto allow for T1 corrections and six echoes were acquired with TE1 = 5.95 ms, TE = 0.38 ms, and TR = 40 ms SENSE was not used in these scans to simplify the manual image reconstruction from the raw data. Image resolution was maintained at or below 1.0 mm and chemical shift misregistration was below 1 pixel. Receiver bandwidth (rBW) varied from 428 to 434 Hz/pixel. Each image acquisition required approximately 30 to 55s. The raw image data was saved for each acquisition. Coronal slices, 7 mm thick, were acquired as parallel to the central axis of the bone as possibl e. Given that both the spine and long bones are slightly curved, two or three slices were acquired to ensure adequate coverage of the bone volume. The

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182 following bones were imaged: humerus, femur, upper spine (C4T3), and lower spine (T10C7). Slice loca lization and placement was performed using 3D SPGR scans of the upper and lower third sections of the body of the dog. Imaging parameters: TR = 18.3 ms; TE = 1.93 ms; flip angle = 20o, NSA = 2, SENSE factor = 4.0. Each 3D SPGR localization scan took appr oximately 1016 minutes. MRI sessions lasted for approximately 4 hours for each dog. MATLAB code was written to read and process the raw image data files ( .list and .data files in a Philips scanner) The code also reconstructed the complex images fro m the complex k space data extracted from the raw data files using FFT, and then calculated the composite image from the individual coil images using a spatial matched filter using the procedure described in Walsh et al. ( 182) The noise covariance matrix was assumed to be the identity matrix and coil sensitivities were estimated from the coil images as described in Erdogmus et al. ( 183) Both single peak IDEAL (SP IDEAL) and multi peak IDEAL ( MP IDEAL ) with pre calibration were performed on the six echoes f ollowing the method in Yu et al. ( 152) and using the graph cut algorithm developed by Hernando et al. ( 145) All fat water separation s were performed using MATLAB code provided by Diego Hernando. The spectrum used in the precalibration of MP IDEAL was derived for each bone site using MR spectroscopy, as described next. Lipid s pectral amplitudes were normalized prior to implementation into MP IDEAL. T1correction of the water and fat images was performed as described in Liu et al. ( 138) T2* correction was not possible, given the short inter echo spacing used in the acquisition of the images. T2* for fat and water in human bone marrow at 3 T has been reported in the lumbar vertebra as 73 ms and 40

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183 ms respectively ( 39) Assuming that similar relaxation parameters apply in do g bone marrow, even for the largest TE used, 7.9 ms, the T2* decay s in water and fat are comparable, so it is expected to result in negligible error in the calculated fat fraction. ROIs were defined at the locations where bone cubes were extracted during n ecropsy The location and size of the cubes excised from the long bones were determined from digital photographs taken during necropsy as described in the Digital Image Processing section. Since the resolution of the MR images is known it is strai ghtforward to convert distances in pixels to distances in cm (and vice versa) in the MR images Vertebrae can be accurately identified in the MR images based on their physical appearance, so no distance measurements were required. Figure 41 shows a coronal slice through the upper spine of one of our dogs taken with the dog in right lateral decubitus head first. Note that the dorsal processes in the thoracic vertebrae are much longer than those in the cervical vertebrae and that the dorsal processes in both types of vertebrae are angled differently. Once the location of C7 and T1 is determined (dashed rectangle) it is simple to locate the rest of the vertebrae by counting. The ROI that would be selected to measure CF at C5 is shown by the white contour line. Figure 41 also shows that the spinal cord is clearly visible at the locations where the slice cuts the vertebrae perfectly through the middle. However, the spine is curved and not all the vertebrae are sliced through the middle. Given that the complete vertebral body was extracted for histology, it is important that the MR slice includes as large a volume of the vertebral bodies of interest as possible. Since this is generally not possible in a single slice, multiple slices were acquired, and CF at different vertebral

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184 bodies in the upper and lower spine was determined from the slice that cut it through its center Figure 42 shows a coronal slice through the lower spine of one of our dogs taken also with the dog in right lateral decubitus head first. Once the pelvic bone (os coxae) is located, it is simple to identify all lumbar vertebrae by counting backwards from L7. The os coxae cannot be mistaken by a lumbar vertebra since its does not have the same cross section and lacks a dorsal spine. Once again, the spinal cord is clearly visible only when the slice cuts the vertebra through the middle. CF at each ROI was determined from the calculated water and fat magnitude images as the sum of the pixel intensities inside the ROI in the water image divided by the sum of the pixel intensities inside the ROI in the water and fat images. CF can also be calculated as the average CF value inside the ROI but it was found that this calculation results in highly unstable estimates This is reasonable, since the average CF calculation consists in averaging fractions of individual pixel intensities, which are more variable than the sum of intensities inside an ROI. MR Spectroscopy Single voxel spectroscopy was performed using STEAM at selected VOIs p laced at the head, neck and shaft of the long bones (i.e. humerus and femur) and in the body of selected cervical, thoracic, and lumbar vertebrae. In the case of the femoral and humeral heads, the VOI was made as large as possible inside the head without including cortical bone or adjacent bone (e.g. scapula, pelvis). VOIs in the necks and shafts of the long bones were adjusted to the thickness/diameter of the bone but the length was fixed at 1.5 cm to mimic the size of the bone cube that would subsequently be excised to perform histology. The VOI in the vertebral bodies was made as large as

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185 possible inside the vertebral body without inclusion of the cortical bone shell. VOIs varied from 1.5 to 7.5 cm3. Acquisition parameters: N EX = 16, TR = 2000 ms, 1024 points, bandwidth 2000 Hz. TE was set to minimum, which resulted in TEs ranging from 9.2 to 13. 6 ms Water peak line widths after shimming ranged from 4 8 Hz. Spectral analysis and fitting was performed using jMRUI v.4.0 ( 184) using the Advanced Method for Accurate, Robus t, and Efficient Spectral fitting (AMARES) ( 185) Spectra were manually phasecorrected and this phase correction was fixed during the fitting process The expected resonances of the lipid peaks (Table 41) were determined from published human bone marrow spectra ( 38, 92, 186 188) and soybean oil spectrum ( 189) The spectra acquired by the Philips scanner sets all resonances with respect to water (i.e. water resonance is at 0 ppm ) Hence, chemical shifts for the lipid resonances were calculated with respect to water. It is important to note that not all of the lipid resonances shown in Table 41 are always found by the AMARES algorithm Soft constraints of 0. 05 ppm were imposed around the resonances to allow some flexibility to the fitting algorithm Amplitudes were not allowed to be complex (i.e. phases were forced to be zero). The selection of line shape (Lorentzian or Gaussian) was made based on the observed shape of the spectral peaks and the understanding that the presence of trabecular bone will result in line shapes that are typically broad ened. Hence, Gaussian line shapes were typically selected for the fit Figures 43 and 44 provide two examples of AMARES spectral fitting with jMRUI. The software produces the plots shown once the fit has converged, providing the original spectrum, the fitted spectrum, the individual peaks fitted, and the residual the difference between the acquired spectrum and the fitted spectrum. The software also

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186 provides the peak amplitudes at each fitted resonance. The peak amplitudes, according to the jMRUI user manual, correspond to twice the area under the peak. A single MR image may include multiple vertebrae or a complete long bone. MP IDEAL with pre calibration is based on a single spectrum. It would be convenient if the spectral information obtained from multiple vertebrae or multiple locations on a long bone could be integrated into a single common spectrum that represent s the entire skeletal site being imaged. T he frequency shifts for each lipid species will be within 0. 05 ppm of the expected frequencies since this was imposed as a constraint in the fit. However, the spectral amplitudes can take on any value Spectra acquired in the head, neck, and shaft of each long bone were plotted on the same graph. In order to visualize the constancy of the lipid amplitudes relative to each other each spectrum was normalized by the maximum at the CH2 peak. This process was also completed for the upper spine by plotting the spectra of cervical and upper thoracic vertebrae on the same graph and for the lower spine by plotting the spectra of lower thoracic and lumbar vertebrae on the same graph. Even if the normalized spectra show similar appearance in the composite spectral plots this does not guarantee that the normalized amplitudes fitted for the l ipid resonances will follow the same trend. Hence, the fitted spectral amplitudes for each bone site and dog were also compared. Due to time constraints it was only possible to acquire a single spectrum from different regions in each bone; e.g. head, nec k, and shaft in the long bones This only results in three to four spectral measurements at each of the four anatomical regions that were imaged. Consequently it does not

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187 provide enough measurements for a rigorous statistical analysis, but a comparison was still possible through the use of the mean and the coefficient of variation. Dog Euthanasia a nd Necropsy Euthanasia was performed by authorized ACS personnel at their facilities. The dogs were humanely euthanized using an intravenous injection of P entobarbital S odium and P henytoin S odium (BeuthanasiaD Special) at a dose of 390 mg P entobarbital and 50 mg Phenytoin per 10 lbs of body weight (1 ml per 4.5 kg of body weight). The animals were monitored by cardiac and respiratory auscultation as well as pupillary light reflex to ensure euthanasia was achieved. Immediately after euthanasia, the dog cadaver s were transported to the Small Animal Hospital of the University of Florida, where necropsy was performed to extract bone cubes from each bone of in terest Both the right and left fem o r a and humer i were excised whole and their total lengths were measured. Bone cubes were then extracted from th e head, neck, and shaft of the long bone that had been imaged with MR Digital photos were taken, with a ru ler for scale in side the FOV (Figure 45 ), to show the location of the cuts One end of the bone is always visible in the photos to allow a reference point from which to measure distance. The bodies of two cervical vertebrae (chosen from C4C7), two thoracic vertebra (T12 and one chosen from T1T4), and two lumbar vertebrae (chosen from L5L7) were also extracted. These vertebrae were chosen based on the fact that only part of the spine is visible in each MR image acquisition (upper spine, lower spine). Photos of the spine were not taken since the enti re vertebral body was extracted and it is easy to identify vertebrae in the MR images.

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188 The long bones on the opposite side of the ones that were MR imaged were cut in half along their main axis, and photographed (Figure 46 ) These photographs were used to compare the fat distribution that can be seen in the photos with the fat distribution observed i n the calculated fat images Cortical bone and excess soft ti ssue were removed from each bone cube using a band saw. Finished b one cubes were immediately placed in separate labeled jars containing 10% neutral buffered formalin in a ratio of bone to fluid by volume of 1:10. Digital Image Processing The digital necropsy photos were opened with ImageJ ( 70) which enables their calibration for distance using the ruler in the photo. The process consisted in drawing a line along the scale in the ruler and setting this length to be 15 cm. Once the image is calibrated, distances on the bone with respect to one end can be determined. The measurements derived from the photos are depicted for one of the dogs in Figures 4 7 and 48 These measurements were used to place the ROI in the calculated water and fat images at the approximate location from which the bone cubes were extracted for histology to ensure that CF is measured at the same region on t he bone. Histology Slide Preparation Bone cubes with thickness greater than 5 mm were cut in half to ensure that the formalin would be able to penetrate the bone completely. Each bone section was placed in a separate labeled glass jar filled with 10% buff ered neutral formalin solution (bone: fluid = 1:10) for 32 to 36 hours. The formalin solution was refreshed after the first hour and around the 12 h mark. To ensure fresh chemical was in contact with the bone surfaces at all times the jars were placed on their sides on a rocking platform (Cole-

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189 Parmer EW 5182020). The jars roll gently to and fro, ensuring circulation of the fluid in each jar Once the fixation period was completed the bone cubes were decalcified by submersion in DecalStat ( 3% HCl, Dec al Company, Congers, NY) for 23 hours while on the rocking platform. The solution was refreshed every hour. Appropriate decalcification was determined by cutting the edge of each cube with a scalpel: if the tissue was soft the scalpel would cut easily w ith little crunching. Post decalcification, the bone cubes were submerged into Cal Arrest (Decal Company, Congers, NY) to stop the decalcification process Each bone cube was then rinsed in running water for about 3 minutes and then placed into a Tissue Tek Megacassette (Sakura Fineteek USA Inc., Torrance, CA) submerged in 70% ethanol. The processed bone samples were then transported to the University of Florida Molecular Pathology Lab, where lab staff mounted them on paraffin blocks to produce microscope slides. Each slide consisted of a f ive micron section. For most blocks, a section was obtained from four different levels spaced by 200 to 500 microns depending on the size of the block The sections were placed on microscope slides and stained wit h hematoxylin and eosin (H&E) using standard protocols The microtome blade can get caught in trabecular bone resulting in tearing of the very thin tissue section. This tearing results in separation of soft tissue from trabeculae (gaps) and regions of mis sing tissue (shredding), which unfortunately cannot be avoided. Obtaining an acceptable section required multiple attempts. In general, all sections included some degree of tearing and shredding. Figure 49 shows a slide with severe tearing and shreddin g and Figure 410 shows a slide with minimal tearing and

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190 shredding. Even in slides such as the one shown in Figure 410, gaps between soft marrow and trabeculae are common as the result of tissue shrinkage during chemical processing and shear from the bla de during microtoming (Figure 411). Histology Sampling The UF Molecular Pathology Lab scanned each histology slide at high resolution using an Aperio Slide Scanner ( http://www.aperio.com ). The Aperio software allows visualization of the entire slide and the selection of rectangular ROIs (Figure 41 2 ) that can be saved as separate images. Square ROIs with a side of 500 m were placed inside viable marrow cavities in such a manner that they did not incl ude trabecular bone or regions of missing soft tissue (Figure 41 3 ). Most ROIs were squares, but given the variability in the shape of marrow cavities, in some cases rectangular ROIs of area equal to (500 m)2 were defined. The 500 m size was determined empirically based on the observed size of marrow cavities in the bone sites considered in this study. It was the largest square side that adequately fits inside most marrow cavities and therefore allows acceptable sampling coverage in each slide. An exc eption occurs in some slides of the femoral and humeral head, which peripherally present unusually small marrow cavities (Figure 434A) Even though these cavities are too small to be sampled with our square ROI, it is still possible to achieve adequate s ampling coverage in these slides. Sampling c overage was optimized by careful planning of the positioning of ROIs within each marrow cavity. Each ROI image was extracted and saved as a separate file ROI files were numbered sequentially as shown in Figur e 4 1 3

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191 The appropriateness of the characterization of CF in a 1cm thick bone marrow cube using a limited number of 5 micron sections is founded on the Delesse principle ( 190) which, in the context of cell studies, states that t he vol ume fraction of a component in a tissue can be estimated by measuring the area fraction of a random section occupied by transections of the component This principle is trivially valid if the tissue is homogeneous, but it is also valid in heterogeneous ti ssue as long as the sections are isotropic and uniform random (IUR) ( 190) A section is IUR when it is chosen randomly and its orientation cannot be determined by simply observing its histological appearance. Our histology slides satisfy both requirements. Once a bone marrow cube is excised, it is impossible to determine how it was oriented inside the bone. Consequently, it is impossible to determine at what angle the section occurs. In addition, the cubes were cut in half prior to histological processing, which increases the randomness by which the section is acquired, since it is then also uncertain from which depth in the original bone it originates. Therefore, even though sections are acquired at diff erent depths within each half, the true depth of each section is unknown and consequently the depth selection of each section is random. Even though the area fraction, i.e. the area of occupied by a tissue component divided by the sampled area, will vary between sections, just as the mean is an unbiased measure of central tendency, the area fraction is an unbiased estimator of the volume fraction ( 190 ) Automated Adipocyte Segmentation MATLAB code was written to randomly select one ROI at a time from the ROI set for a given slide and then process each image in turn to calculate CF Images were processed using MATLABs Image Processing Toolkit functions The ROI image is first transformed into gray scale. Next a threshold is calculat ed automatically with a

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192 function that uses a gradient sensitive filter; e.g. Canny Binarization consists in transforming the histology image, consisting of large elliptical adipocytes (white) in a background of stained cells (purple) (Figure 41 4 A), into an image where adipocyte pixels are white and the background pixels are black (Figure 41 4 D ). Histological CF for each bone site was calculated as the ratio of the recorded number of water pixels to the total number of pixels examined ( i.e. one minus the fat fraction). Since all ROIs have equal size and therefore contain equal number of pixels, the calculation is equivalent to taking the average of the water fractions calculated in each ROI, and this is how CF for each slide was actually cal culated. Adipocytes can be segmented manually, but this is very time consuming when several hundreds of ROIs need to be processed. Automated segmentation can be started with the selection of a threshold, but this typically results in peppered images. N ote that the background of Figure 41 4 A is not solid purple. A simple threshold based on separation of white from the rest of gray levels in the image will result in a background full of scattered white pixels (Figure 41 4 B) A dilation erosion algorithm cleans up the thresholded image improving the quality of the segmentation (Figure 41 4 C) Erosion eliminates all objects smaller than a user preset radius. Hence, this eliminates the pepper in the background, but unfortunately also erodes the edges of l arger objects in the image (i.e. adipocytes). Dilation following erosion restores the eroded edges of the larger objects (adipocytes). At the end of this process, all pixels inside the adipocytes have a value of one (white), while all the pixels outside of the adipocytes have a value of zero (black) (Figure 41 4 C ). The resulting image is said to be binary (or logical) because it consists of only 1s and 0s. The dilationerosion

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193 algorithm results in very clean segmentation, as can be appreciated from the comparison of Figures 41 4 A through C Segmented images were visually inspected sideby side with the original images to ensure the accuracy of the automated segmentation process. Errors in the automated process were corrected manually. Most errors a re minor and even if uncorrected typically result in negligible differences in the calculated CF (much less than 1%) Adipocyte nuclei are typically peripheral to the cell. However, depending on the slicing through the cell it may appear farther from the edge of the cell. These black dots (white arrows in Figure 41 4 A) result in dimples at the periphery of adipocytes and, when located deeper into the cell, loss of part of the cell. Dimples result in negligible changes in the calculated CF but loss of adipocyte surface does not. Hence, these losses were corrected manually (Figure 41 4 D). To ensure that t he automated segmentation performance is comparable to that of manual segmentation the two methods were contrasted using a sample of 37 ROIs The ROIs in the sample were handpicked to ensure that the full range of CF values was represented. Consequently, this is not a random sampling and ROIs had to be selected from different bone sites. The ROIs were segmented both manually and using the MATLAB code with visual inspection, as explained previously. Both a linear regression line and a Bland Altman plot were produced to characterize the agreement between both methods Adequate sampling of each histology slide was determined by plotting the cumulati ve mean CF after the evaluation of each ROI (Figure 41 5 ) Additional ROIs were randomly selected and processed until the plot converged to a steady state value;

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194 that is, when fluctuations in the cumulative mean CF were less than 1 % cellularity A 95% c onfidence interval was also calculated for each slide to test that most of the measurements were within this interval. Results Automated Adipocyte Segmentation The results for the calculation of CF on a sample of 37 histological images using manual and aut omated segmentation are shown in Figures 4 1 6 and 41 7 Figure 41 6 provides the linear regression fit line for the data, which is barely indistinguishable from the perfect agreement line. T he BlandAltman plot is provided in Figure 41 7 The bias (mean difference) is + 0. 06% cellularity and the standard deviation of the differences is 1.35% cellularity The spread of the differences is relatively even for cellularities above 30%, but the differences below 30% cellularity are only negative, suggesti ng that the automated method overestimates CF in bone marrow exhibiting large density of adipocytes. All differences lie within 2.59% and +2.71% cellularity. The CF data determined from the histology slides using the automated segmentation method is summ arized in Table 46. MR Spectroscopy Figures 41 8 through 4 21 present the composite plots of the spectra for each anatomical region. All spectra were normalized to the maximum at the CH2 peak. Tables 4 2 through 4 5 contain the amplitudes that resulted from the AMARES spectral fitting performed using jMRUI. In jMRUI the spectral amplitudes correspond to twice the area under the peak. The resonance with a shift of 2.5 ppm (Table 41) was not found in any of the spectra and wa s omitted from the tables.

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195 Figure 41 8 shows the composite spectral plot for the humerus. The spectra for both dogs are very similar. The plot demonstrates the effect of the local magnetic inhomogeneity that results from the presence of trabeculae in bone marrow. The shaft does not contain any trabeculae and results in a spectrum with multiple lipid peaks of narrow line width The presence of trabecular bone in the head and neck result in linewidth broadening, blurring the individual lipid resonances as nearby peaks overlap. This effect results in increased uncertainty in the spectral fit, as demonstrated by the fitted amplitudes in Table 42. Figure 41 8 shows that the spectra for the neck and shaft are almost identical However, only two of the lipid resonances present similar amplitudes in the head and neck: the two majority lipids CH2 and CH3C=CH. The minority lipids experience large variability as the fitting algorithm attempts to fit the resonances to a spectral shape that is distorted. C onsequently, there is a large disagreement between the shaft amplitudes and the head and neck amplitudes in the lipid minority components, as indicated by the CV. Only the majority lipid, CH2, is relatively uniform throughout the humerus, with CV of 4.2% and 6.9%. The olefinic peak presents the largest variability, but this is a consequence of its proximity to the water resonance. Figure 419 shows the composite plot for the femur. The spectrum acquired from the femoral neck and shaft is similar in both dogs. However, the spectrum acquired at the femoral head presents severe linebroadening in only one of the dogs. In both spectra the lipid peaks are shifted upstream from their expected shifts with respect to water. The spectral amplitudes (Table 43) display similar characteristics to those observed in the humerus. The majority lipid, CH2, is relatively uniform throughout the

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196 bone. CH3C=CHis relatively uniform in the head and neck, and is uniform throughout the bone in only one of the dogs. In contrast with the humerus, this lipid species is not always a majority component: CH3 results in comparable or higher contribution. The CV values indicate that all lipid components are less variable in the femur than in the humerus, which is surprising, considering the poorer quality of the femur spectra. Figure 420 presents the composite spectral plot for the bones in the upper spine. The lipid portion of the spectra is almost identical for the selected upper vertebra, but line width broadening varies significantly in one of the dogs. Interestingly, the water fraction is highly variable in one of the dogs, but relatively constant in the other. The fitted spectral amplitudes are provided in Table 44. As usual, the majority lipid species, CH2, is rela tively uniform across all vertebrae, while the remainder lipid species show large variability. CH3 is uniform in only one of the dogs. The olefinic peak ( CH=CH) was not found in any of the vertebra for one of the dogs. Figure 421 presents the composit e spectra for the lower spine. This plot would have included spectra for the lower thoracic vertebrae, but unfortunately, the spectral data for these vertebrae were lost. The lipid spectra are virtually identical for the two vertebrae in one of the dogs (lower ) but not for the other (top), which shows both differences in amplitude and spectral broadening. Table 45 provides the spectral fitting results. Both majority lipids are relatively uniform in both vertebrae. The olefinic lipid presents the largest variability, which again is a consequence of its proximity to the water peak. IDEAL Fat Water Separation Figures 4 22 through 42 5 present some of the results of SP IDEAL fat water separation performed on the images acquired in the femur, humerus, and t he upper and

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197 lower spine of the dogs. In most cases, the fat water separation appears accurate and images seem free of fat water switches T he regions inside bone are typically noisier than the surrounding soft tissues. This is more clearly appreciated in the field map images. For example, note that in Figure 422C the field map outside of the bone is relatively uniform, while the field map inside the bone shows a range of field map values. This is to be expected, since the magnetic field inhomogeneity will be more severe inside the bone than in muscle. The images were acquired without a breathhold under the assumption that breathing motion would not affect the images of the spine and long bones. The long bone that is pinned between the body of the dog and the table is not expected to experience any motion. Figures 422 and 423 do not show any artifacts from breathing motion at the humerus or femur. However, the breathing motion artifacts are clearly observed in the upper part of the images in Figure 423 in the area of the rib cage. In the case of the upper spine (Figure 424), the motion artifacts are clearly observed in the thoracic and abdominal cavities, but the artifacts are not perceptible in the upper vertebrae. The whit e arrows in the image point to locations where fat water switches occurred. Note that these regions appear with different intensity than the surrounding areas in the field map image (Figure 424C). In contrast, the images for the lower spine (Figure 425) do not show any obvious motion artifacts. As expected, the fat and water images derived from images acquired with low flip angle (Figures 422 and 424) are have lower SNR than those derived from images acquired at a larger flip angle (Figures 423 and 425). However, image quality is

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198 excellent even in the low flip angle images. This is a consequence of the use of phase shifts that maximize NSA. During necropsy, photos were taken of the long bones cut in half along their main axis. The photographed bone was the opposite bone that was imaged during MR scanning. Figure 426 shows the necropsy photo and the SP IDEAL calculated fat image for the femur in one of the dogs. Even though there is no reason to expect that fat distributions are the same on the r ight and left femur, the calculated fat image matches very closely the fat distribution in the photo. The match is particularly clear at the distal end of the femur, where the fat distribution tapers. Excellent matching is also observed in the humerus (Figure 427). The red marrow region that separates the fat at the humeral head from the fat in the shaft matches the dark pattern in the fat image. Figure 42 8 shows the fat and water separated images of the dog femur obtained using MP IDEAL with the normalized lipid spectrum provided in Table 43. The differences between the singlepeak images (Figure 422) and the multi peak images are indistinguishable by eye. Figure 42 9 shows the fat images produced by both methods side by side with their respective gray scale bars. The bars indicate that bright white pixels in the multi peak image correspond to a larger fat proton density than those in the singlepeak. Consequently, more lipid information was extracted with the multi peak approach than with singlepeak. Given that the images obtained via MP IDEAL for the remainder bone regions are indistinguishable from those obtained via SP IDEAL when viewed by eye, they are not shown.

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199 Agreement Between IDEAL and Histology Table 46 summarizes the CF values measured using both SP IDEAL and MP IDEAL. Figure 430 presents the linear regression plot of CF measured with SP IDEAL versus CF measured from histology performed at the same location in bone. Excellent agreement (slope = 0.98 ) and correl ation (r2 = 0.98 ) are demonstrated. Figure 431 presents the BlandAltman plot produced with the same data. Bias is small ( 0.52% ) with all differences within 3.76% and 4 80% cellularity and most differences within 2 .0 % cellularity. One outlier is identified, corresponding to a measurement performed in L4 in one of the dogs. Figure 43 2 presents the linear regression for the results obtained with MP IDEAL. In this case the agreement is not as good as in the case of SP IDEAL as demonstrated by a slope of 0.86 and r2 = 0. 81. The BlandAltman plot (Figure 43 3 ) indicates a bias of 7.37% with all differences within 5.08% and 19.81% cellularity, except for one outlier. The outlier corresponds to the measurement made in C6 in one of the dogs. Discussi on Histology Figure 41 6 presents the linear regression plot for the CF values determined by automated segmentation versus those determined by manual segmentation. The deviation from perfect agreement is barely perceptible by eye being very small, as indicated by a slope that is very close to unity The intercept indicates a small disagreement at low CF, i.e. high fat content, of approximately 1.2% cellularity The BlandAltman plot ( Figure 41 7 ) also indicates excellent agreement between the automated and manual segmentation methods. There is a negligible negative bias of 0.06% cellularity and all differences are within 2.7% cellularity, with most

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200 differences being within 2% cellularity. The plot reveals that the automated method se ems to overestimate CF in bone marrow regions that contain a high concentration of adipocytes (CF < 30%) This, however, is a consequence of how manual segmentation wa s performed in regions of high fat content. During manual segmentation it is impractic al to trace every adipocyte in regions of high adipocyte concentration since they contain a very large number of adipocytes in contact with each other. Although narrow, the intercellular space is visible in the images and these pixels should be assigned t o water A utomated segmentation segments every adipocyte and the intercellular spaces are correctly assigned to water, resulting in water fractions consistently larger than those obtained by manual segmentation. It is important to note that neither one of the methods is free of subjectivity but automated segmentation is expected to be more consistent Adipocytes are typically large cells, but their cross section in a slide result s in fragments of different diameters and shapes depending on the angle and the location at which the adipocyte is cut by the section. When performing manual segmentation, one subjectively decides whether to assign small fragments to water or fat. Figure 41 4 A shows that not everything that is white in the image is part of an adipocyte. The H&E stain only stains the nuclei of the hematopoietic cells, and hence the cytoplasm is transparent and shows up white in the histology images. Bone marrow slides also include cross sections of sinuses, which contain red blood cells and plas ma. Red blood cells appear opaque, but the plasma is transparent. Sinus fragments can only be distinguished from adipocyte fragments when they contain red blood cells or when their cross section is elongated, but this is not always the case. Consequentl y, one does not typically segment fragments smaller than

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201 a certain size. When manually segmenting adipocytes, t he size is not determined by measurement, but by eye, which means that the size of fragments that are not segmented will vary depending on the r elati ve size of the adipocytes in the image. The automated segmentation method also only segment s closed shapes larger than a user preset diameter. However, the diameter of the fragments is always measured and therefore the segmentation is consistent, r egardless of the relative sizes of the adipocytes in the image. The large benefit in effort and time savings obtained with the automated segmentation method far outweighs differences within 2% cellularity. Consequently, all histology CF values used in this study were obtained using the automated method. Spectral Analysis In spite of the similarity of lipid spectra in each skeletal regionhumerus, femur, upper spine, lower spinethe spectral amplitudes fitted by the AMARES algorithm resulted in large variability, particularly in the minority lipid species. Tables 42 through 4 5 indicate that the proportion of CH2 in all bone sites is, on the average, 76% ( 10%) of all fat, which is in line with the proportion observed in human bone marrow spectroscopy studies ( 92) The proportion of CH2 in all bones is relatively uniform, as demonstrated by a low CV. The approximate constancy of the fractional abundance of CH2 in all bones explains why singlepeak fa t water separation methods typically provide accurate fat fractions. The spectral component exhibiting the largest variability is the olefinic fat ( CH=CH). This is not surprising, since its resonance is very close to the water resonance and the spectral fitting algorithm will have more difficulty fitting a small peak next to a much larger water peak, especially when the peaks are subject to broadening as a result of magnetic field inhomogeneity. In retrospective, the spectra

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202 should have been acquired w ith water suppression to provide a more accurate fit of this peak. The spectra acquired from the femoral heads presented severe lineshape and frequency distortions (Figure 419). The spectrum for the humeral heads (Figure 418) did not experience the problems exhibited by the femoral heads. The humeral heads are much larger and have a smaller trabecular bone fraction than the femoral heads (Figure 43 4 ). Due to the smaller size of the femoral heads, the spectroscopic VOI had to be defined below 1 cm3, w hich typically results in noisy spectra. In addition, shimming was performed using the same VOI. The larger bone fraction in the femoral head may result in stronger magnetic inhomogeneity in that volume. The combination of these two factors is hypothesi zed to have resulted in the observed distortion of the spectrum Due to the small sample size of the spectral amplitude measurements, it is not possible to determine if the variability observed is due to the actual composition of fat at each location in each skeletal region, biological variability, the inherent variability of the spectral fit, or a combination of these factors. Based exclusively on our spectral data, it is therefore not possible to determine if a common spectrum will accurately represent each skeletal region for the purposes of fat water separation. Agreement between IDEAL and Histology Figure 430 shows the linear regression plot of CF calculated from the calculated fat and water images produced with SP IDEAL versus CF calculated from the automated segmentation of the digital histology images. Good agreement is demonstrated by a slope and correlation coeffi cient close to unity. Even though most

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203 points line up close to the perfect agreement line, there are clearly some measurements that did not agree as closely. Figure 431 shows the BlandAltman plot produced for the same data. This plot shows excellent agreement between SP IDEAL and histology, with a very small bias of 0.52% cellularity and most differences lying within 2% cellularity. The plot indicates the location of one outlier, corresponding to a measurement made in L4 in one of the dogs. Based on the observed shape and area of the vertebral body in comparison to other vertebra in the image, it is clear that the slice cut the L4 vertebrae obliquely and hence only a fraction of the vertebral body is included in the slice. This occurs because the s pine is typically curved and a slice that cuts perfectly through the center of some vertebrae will not do so for vertebrae located farther away. The effect can be appreciated in the images of the upper spine (Figure 424D ). Note that the cross sections of the vertebrae become increasingly reduced toward the bottom of the image. Oblique slicing of the lumbar vertebrae did not occur in the other dog. Figure 425 shows the lumbar vertebrae with similar shape and cross sectional area for the images taken fr om this dog. The agreement is not surprising, since the spectroscopy results suggest that CH2 was relatively uniform in all the bones considered in this study. However, considering that CH2 only accounts for approximately 76% of all lipid content, the closeness of the agreement is quite surprising. The adipocyte segmentation method, as performed in this study, will inevitably underestimate fat content, since adipocyte fragments smaller than a preselected diameter are assigned to water, and consequently r esults in an overestimation in CF. SP IDEAL also overestimates CF since it only accounts for fat

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204 originating from methylene (CH2) molecules. According to the BlandAltman plot (Figure 4 31), histology CF is typically larger than SP IDEAL CF (bias is negative). Since SPIDEAL CF measurements are already overestimations, t his suggests that histology also overestimates CF. Hence, the very close agreement is most likely a consequence of the underestimation of fat fraction by histology. So how bad is CF calc ulated using only 76% of all fat? The worst error occurs when the water and fat contents are equal, i.e. CF = 50%. If only 76% of fat is accounted for and assuming no error in the water estimation, the measured CF would be 50/(50 + 0.76 x 50) = 56.8%. H ence, the worst error would be 6.8% cellularity. For CF ranging from 20% to 80%, the error ranges from 4% cellularity at low and high CF to 6.8% cellularity at CF = 50%. Based on this simple calculation, there is a clear gain in accuracy in the use of method that accounts for as high a percentage of fat as possible. Given that histology is the current gold standard for in vivo CF determination, the close agreement between both methods indicates that SP IDEAL can be used in lieu of histology. This is great news, since SP IDEAL is non invasive and can be performed at any bone on the body, while in vivo histology can only be performed at the iliac crest. In addition, SP IDEAL provides fat and water images of the complete bone, so CF changes can be assessed at multiple locations in the anatomy providing a true anatomical mapping of CF. These results also indicate that CF measured by SPIDEAL is accurate enough to be used with the BM mass predictive equation developed in Chapter 2. The error in TSSV prediction, as it currently stands, dominates the error in the BM mass calculation.

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205 A CF error within 4% cellularity in BM cellularity will result in a negligible loss in accuracy in most cases. An advantage of using SP IDEAL versus MPIDEAL is that it does not require the acquisition and analysis of MR spectroscopy data. However, MP IDEAL is expected to provide a more accurate measurem ent of fat fraction since it takes into account multiple lipid resonances. Figure 43 2 presents the linear regression for MP IDEAL and Figure 43 3 provides the associated BlandAltman plot. The agreement is not as good as that of SP IDEAL with MPIDEAL u nderestimating CF in most measurements (bias = 7.37% cellularity) This means that MP IDEAL is consistently measuring a larger fat fraction than histology. All differences, except for an outlier, are within 5.0% and 20.0% cellularity. The disagreement is not necessarily an indication of failure by MP IDEAL The accuracy of MP IDEAL has been well established by other studies, in vitro ( 152, 157, 166, 170) and in vivo in the measurement of hepatic fat fraction ( 166 178) T he very close agreement between SP IDEAL and histology suggests that histology overestimates CF. Adipocyte segmentation of histology images will yield the same fat fraction regardless of the lipid composition of adipocytes. However, the fat fraction derived from MP IDEAL will always be larger than that derived from SP IDEAL, since the latter only accounts for one lipid species The Bland Altman plot (Figure 433) shows that almost all MP IDEAL CF measurements are smaller than those derived from histology. Based on the previous calculation of the error in the calculated CF when only 76% of fat is considered, and assuming no error in the determination of water content, the ability of MP IDEAL to detect higher lipid fractions in adipocytes explains some of

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2 06 the disagreement, approximately 4% cellularity at low and high CF and increasing to 6.8% cellularity as CF approaches 50%. Figure 433 shows that most differences are smaller than 15%. My experience with MR spectroscopy is limited, so the variability observed in the sp ectral amplitudes may partly be a consequence of my inexperience with spectral fitting In addition, if s pectra had been acquired with water suppression, the accuracy in the determination of the olefinic peak would have been greatly improved. Due to time limitations only one spectroscopy acquisition could be performed at three locations on the long bones and in selected vertebrae. It would have been advantageous to have acquired multiple spectra at the same bone sites and at more locations on the long bones and all vertebrae, in order to perform a robust statistical analysis of the fitted amplitudes. Such an analysis would determine if the variability observed is due to biological factors or simply uncertainty in the fit. H istology is a very goo d indicator of adipocyte density or adipocyte volume fraction since the calculation of the fat fraction is based on the segmentation of adipocytes from the images and is clearly independent of the relative abundance of different lipid chemical species The very close agreement between SP IDEAL and histology indicates that histology cannot be an accurate estimator of fat fraction. Given that SP IDEAL only accounts for around 76% of all fat, histology must also account for a fat fraction close to this percentage. Consequently, histological CF is probably not the best method to use to determine in vivo accuracy of MP IDEAL. The pixel intensities in the fat image calculated with MP IDEAL are proportional to the proton densities of each lipid chemical species included in the fat water separation.

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207 These intensities will vary depending on how many lipid resonances are included in the separation. However, the fat fraction calculated from histology is invariant to the chemical composition of lipids in adipoc ytes. Hence, accuracy of fat fractions determined by MP IDEAL in bone marrow may be more accurately determined by comparison with accurate HMRS measurements or measurements performed with a lipid chemical assay technique that accounts for the multiple lip id chemical species. From this point on such a fat fraction is referred to as a chemical fat fraction, in contrast to a volumetric fat fraction, such as the adipocyte volume fraction. Even though HMRS data was acquired in this study, spectra were not ac quired for the purpose of a comparison between HMRS and MP IDEAL, and were only acquired for a single TR and TE Consequently, it is not possible to perform the necessary T1 and T2* corrections for the calculation of accur ate fat fractions. One could use published values for the relaxation parameters in human bone marrow water and fat to perform the corrections but this negates the validity of the comparison since it would not be possible to determine if differences between both methods are due to the in accuracies in the standard resulting from the introduction of human data into measurements performed in canines. For the purposes of radiation dosimetry, adipocyte volume fraction is more relevant than chemical fat fraction. Anthropometric computational voxel phantoms used to calculate S values ( Equation 1 1) do not presently have the resolution to allow the differentiation of most marrow cellular components. In Monte Carlo simulations, when a particle arrives at a spongiosa voxel, particle transport is continued in a voxelized model of spongiosa produced from micro CT images. The voxels in this spongiosa voxel

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208 model are either assigned to soft marrow or trabecular bone. Soft marrow voxels are then randomly assigned to adipocytes to match the fat volume fraction given by the CF for the given bone site (Figure 435) ( 191) The microCT res olution typically used in the micro CT images of spongiosa is 60 m, which corresponds to the average diameter of adipocytes in human bone marrow ( 192, 193) Adipocyte distribution in human bone marrow does not appear to follow any specific pattern ( 194) and hence for the purposes of radiation transport they are ass umed to be randomly distributed. The adipocyte volume fraction will be the same regardless of the specific chemical composition of the lipids that make up the adipocytes. Consequently, the results from this study suggest that, t he use of SP IDEAL is more appropriate than MP IDEAL for the measurement of CF in radiation dosimetry Monte Carlo simulations In pat hology studies, marrow cellularity typically represents the volume fraction occupied by hematopoietic cells. Point counting methods typically only tally hits to hematopoietic cells and exclude counts to venous sinuses, extracellular fluid, and blood vess els. However, marrow cellularity determined from grading, where multiple experienced pathologists rate the percentage of marrow not occupied by adipocytes by comparing the adipocyte distribution observed under the microscope to photographs with nominal ce llularities on a reference card, does not conform to the same definition. Studies that have compared both methods have found that the differences in measured cellularity are statistically significant, but this difference is mainly due to inter observer va riability ( 195, 196) Hence, for practical purposes, including or not including extracellular fluid, venous sinuses, and marrow vasculature may not result in a significant differ ence in the measurement of adipocyte volume fractions

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209 The terminology used in radiation dosimetry of bone marrow must be more carefully defined. It is clearly important to make a distinction between the measurement of a chemical fat fraction, such as that performed in hepatic fat fraction histology or that obtained using an MRI multi peak technique such as MP IDEAL and an adipocyte volume fraction measurement, as typically performed in most bone marrow studies. The use of the term cellularity in CF may result in misinterpretation of this quantity as defined in radiation dosimetry, since cellularity is typically used to refer to the volume of marrow occupied by hematopoietic cells. It is therefore proposed to discontinue the use of cellularity factor and that CF be replaced more accurately by the term one minus the adipocyte volume fraction (AVF). Then, Equation 1 5 may be written as ( )= ( 1 ) ( 4 1 ) When bone marrow cellularity is measured vi a histology, it is important that the terminology used indicates whether the volume fraction measured correspond to only that of hematopoietic cells or includes all soft marrow tissues that are not adipocytes. This is particularly important if noninvasiv e methods such as those provided by MRI are to be used in place of histology. The point counting method typically only accounts for hematopoietic cells, but grading and adipocyte segmentation methods include extracellular fluid, venous sinuses, and blood vessels. Adipocyte segmentation methods, even when automated, can be designed to exclude components other than hematopoietic cells. It is therefore important to define appropriate terminology that will prevent the misinterpretation of the measurements. SPIDEAL provides excellent agreement in the measurement of bone marrow AVF provided by the current gold st andard, bone marrow histology. The excellent

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210 agreement between the methods indicates that SP IDEAL can be used to derive the AVF data necessary for the estimation of patient specific active bone marrow mass using the predictive equations developed in Chapter 2. The agreement between SP IDEAL and histology may be further improved by acquiring MR images with a breathhold and with unequally spaced TEs to allow for T2* corrections. IDEAL methods are already part of the software in General Electric (GE) MR scanners and will be available in other clinical scanners in the near future (personal communication by a Philips representative).

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211 Table 41. Spect ral shifts used in this study. Shifts in Hz are calculated at 3T. Chemical Species Shift w/r TMS (ppm) Shift w/r Water (ppm) Shift w/r Water (Hz) CH 3 0.9 3.8 485.3 (CH 2 )n 1.3 3.4 434.3 CH 2 C=CH 2.2 2.5 319.3 =HC CH 2 CH= 2.7 2.0 255.4 CH=CH 5.6 0.9 115.0 H 2 O 4.7 0.0 0.0 Table 42. Normalized lipid spectral amplitudes in the canine humerus. The table presents the normalized amplitudes from the spectral fitting performed using AMARES in jMRUI. In jMRUI the amplitudes are equal to twice the area under the peak. The peak for CH2C=CHwas not resolved in any of the spectra and is therefore omitted from the table. NR = not resolved; CV = coefficient of variation = standard deviation/mean. Normalized amplitudes Dog 1 Dog 2 Lipid species Head Neck Shaft Mean CV Head Neck Shaft Mean CV CH 3 0.035 0.072 0.050 0.052 48.8% NR NR 0.166 0.150 (CH 2 ) n 0.757 0.733 0.662 0.717 6.9% 0.759 0.718 0.707 0.655 4.2% CH 3 C=CH 0.201 0.192 0.103 0.166 32.7% 0.236 0.223 0.080 0.162 53.3% CH=CH 0.006 0.003 0.185 0.065 161.5% 0.005 0.059 0.047 0.033 84.0%

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212 Table 43 Normalized lipid spectral amplitudes in the canine femur The table presents the normalized amplitudes from the spectral fitting performed using AMARES in jMRUI. In jMRUI the amplitudes are equal to twice the area under the peak. The peak for CH2C=CHwas not resolved in any of the spectra and is therefore omitted from the table. CV = coefficient of variation = standard deviation/mean. Femur Normalized amplitudes Dog 1 Dog 2 Lipid species Head Neck Shaft Mean CV Head Neck Shaft Mean CV CH 3 0.125 0.177 0.126 0.143 25.9% 0.177 0.077 0.080 0.111 51.4% (CH 2 ) n 0.717 0.686 0.758 0.720 5.0% 0.721 0.808 0.774 0.768 5.7% CH 3 C=CH 0.108 0.110 0.067 0.095 25.3% 0.082 0.093 0.092 0.089 6.5% CH=CH 0.049 0.026 0.048 0.041 31.3% 0.019 0.023 0.054 0.032 60.7% Table 44 Normalized lipid spectral amplitudes in the canine upper spine. The table presents the normalized amplitudes from the spectral fitting performed using AMARES in jMRUI. In jMRUI the amplitudes are equal to twice the area under the peak. The peak for CH2C=CHwas not resolved in any of the spectra and is therefore omitted from the table. NR = not resolved; CV = coefficient of variation = standard deviation/mean. Normalized amplitudes Dog 1 Dog 2 Lipid species C6 T1 T2 Mean CV C6 T1 C7 Mean CV CH 3 0.052 0.039 0.147 0.079 12.1% 0.109 0.128 0.003 0.080 84.6% (CH 2 ) n 0.910 0.957 0.799 0.888 9.1% 0.745 0.629 0.708 0.694 8.6% CH 3 C=CH 0.038 0.005 0.054 0.033 77.8% 0.126 0.106 0.235 0.156 44.8% CH=CH NR NR NR 0.020 0.138 0.055 0.071 86.0%

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213 Table 45 Normalized lipid spectral amplitudes in the canine lower spine. The table presents the normalized amplitudes from the spectral fitting performed using AMARES in jMRUI. In jMRUI the amplitudes are equal to twice the area under the peak. The peak for CH2C=CHwas not resolved in any of the spectra and is therefore omitted from the table. CV = coefficient of variation = standard deviation/mean. Normalized amplitudes Dog 1 Dog 2 Lipid species L1 L6 Mean CV L5 L7 Mean CV CH 3 0.069 0.036 0.052 44.7% 0.036 0.040 0.038 8.5% (CH 2 ) n 0.756 0.774 0.765 1.6% 0.774 0.834 0.804 5.3% CH 3 C=CH 0.114 0.110 0.112 2.8% 0.110 0.123 0.116 7.6% CH=CH 0.061 0.080 0.071 19.6% 0.080 0.003 0.042 131.3%

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214 Table 46. Bone marrow CF data. This table presents all CF values determined from each dog at the indicated bone sites determined from histology, SP IDEAL, and MP IDEAL with pre calibration. All CF data is expressed as % cellularity. CF (%) Bone Site Histology SPIDEAL MP IDEAL Dog 1 Femoral head 69.39 72.46 65.82 Femoral neck 42.39 42.91 30.75 Femoral shaft 23.14 22.74 17.82 Humeral head 31.26 34.63 36.47 Humeral neck 40.29 40.74 42.19 Humeral shaft 25.62 25.59 18.34 C7 65.89 64.99 57.28 T1 68.57 68.00 56.51 T4 61.72 61.21 57.64 L4 65.19 58.41 53.54 L7 63.80 61.97 55.22 Dog 2 Femoral head 50.54 52.04 41.31 Femoral neck 46.83 46.35 35.97 Femoral shaft 32.38 30.37 20.64 Humeral head 50.90 50.09 47.00 Humeral neck 38.63 37.86 29.38 Humeral shaft 38.16 37.56 26.00 C5 59.83 57.97 56.02 C6 44.25 43.12 54.28 C7 56.64 57.38 50.51 T1 70.13 68.60 51.77 T2 58.60 54.94 44.60 L6 59.93 58.19 46.51 L7 48.36 51.80 40.11

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215 Figure 41. Vertebral body identification in the upper spine of a dog. The image corresponds to a coronal slice of the upper spine of one of our dogs while it lied on its right side, head first. The dorsal processes of thoracic vertebrae are much longer and angled differently than the dorsal processes in cervical vertebrae. One the location where C7 and T1 meet is determined (dashed rectangle) the remainder of the vertebrae can be easily identified by counting from this location. The outline of the body of C5 is shown as an example of how the ROI for this vertebra was selected. C3 C 7 T1 C 6 C 5 C 4 T2 T3 T4 T5 spinal cord

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216 Figure 42. Vertebral body identification in the lower spine of a dog. The image corresponds to a coronal slice of the lower spine of one of our dogs while it lied on its right side, head first. The cross section of th e os coxae (pelvic bone) is easily distinguished from the cuboidal shape of the bodies of the lumbar vertebrae and the os coxae does not have a dorsal spine. Once this bone is located, it is simple to identify the lumbar vertebrae by counting backwards fr om L7. os coxae L7 L6 L5 L4 L3 spinal cord

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217 Figure 43. Spectral fitting in the humeral head. From bottom to top figures --original: original spectrum after manual phase correction; estimate: fit to original spectrum; individual components: individually fitted peaks (resonances); residue: difference between the original spectrum and the fi tted spectrum (estimate). This plot is produced automatically by jMRUI once the fit is completed.

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218 Figure 44. Spectral fitting in thoracic vertebra T2 From bottom to top figures -- original: original spectrum after manual phase correction; estimat e: fit to original spectrum; individual components: individually fitted peaks (resonances); residue: difference between the original spectrum and the fitted spectrum (estimate). This plot is produced automatically by jMRUI once the fit is completed.

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219 Figure 45 Necropsy photo of humerus. A ruler is photographed with one end of the bone in the field of view as reference so that the location of the extracted bone cube, in this case a cube from the humeral neck, can be determined from that reference. These distances are used to determine where to place the ROIs in the MR images so that CF is measured from the same location in the bone both with histology and MRI.

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220 Figure 46 Photograph of femur cut in half along its length. The photo allows a visual inspection of the fat distribution along the long bone that can be compared to the fat distribution observed in the calculated fat image Note that there are fat ty areas at the distal end of the femur (white arrows) and fat is predominant in the shaft (dashed rectangle).

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221 Figure 47 Diagram of femur for one of the dogs. The diagram provides the length of the femur, measured directly from the bone during necropsy, and the relative distances to each of the locations were cuts were made to excise bone cubes from the head, neck, and shaft, determined from the necropsy photographs. These measurements are used to place ROIs in the calculated water and fat images at the approximate locations where histology was performed on the bone. Diagram is not to scale. All measurements are in cm. 19 6 head 18.2 1 6 1 neck 1 2 7 shaft 6. 9 3. 5 1.4

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222 Figure 48 Diagram of humerus for one of the dogs. The diagram provides the length of the humerus measured directly from the bone during necropsy, and the relative distances to each of the locations were cuts were made to excise bone cubes from the head, neck, and shaft, determined from the necropsy photographs. These measurements are used to place ROIs in the calculated w ater and fat images at the approximate locations where histology was performed on the bone. Diagram is not to scale. All measurements are in cm. 18 .6 head 15.2 1 3 .7 neck 1 0 .7 shaft 7 .9 4 9 2 1 4.8 1.9 3.4 16.5

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223 Figure 49 Bone marrow section with severe tearing and shredding. White areas correspond to missing tissue that was lost during the cutting process. This typically occurs in bone marrow blocks with large trabecular bone content. This section was taken from the femoral neck.

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224 Figure 410 Bone marrow section with minimal tearing and shredding. The white arrows point to some of the areas of missing tissue. The large white band along the right side of the section is not due to missing tissue, but to high fat content: marrow cavities in this area are occupied by a large number of adipocytes. The image corresponds to a section from the humeral neck.

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225 Figure 411 Close up of marrow cavity showing separation between trabecular bone and soft marrow. These gaps between trabecular bone and soft marrow are due to both shrinkage of soft tissue by chemical processing and shear from the cutting process. In this case, the most severe gaps are caused by the cutting process, while the smaller separations (black arrows) are most likely due to tissue shrinkage alone.

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226 Figure 41 2 Sampling of digital histology slides. Section taken from the humeral neck. The Aperio software allows the extraction of 500m square ROIs. Each ROI was marked on the slide image by drawing the outline of the ROI and writing the number (blue boxes)

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227 Figure 41 3 ROI selection in histology slides. Five hundred micron square ROIs were selected inside marrow cavities ensuring not to include any trabecular bone. Proper coverage of the slide was insured by carefully distributing t he ROIs to maximize coverage inside each marrow cavity.

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228 Figure 41 4 Semiautomated adipocyte segmentation. A ) ROI image taken from a marrow cavity in L 4. White arrows point to the location of adipocyte nuclei Black circle marks the location of a blood vessel B ) Thresholded image. Note that the thresholding does not result in a solid black background. C ) I mage produced by thresholding followed by dilationerosion, where adipocyte pixels have a value of 1 (white) and the backgro und pixels have a value of 0 (black) Note how the dilationerosion process results in dimples and loss of adipocyte pixels (black arrows) Dimple losses are minor and typically result in a negligible effect on the value of CF Loss of adipocyte regions were manually corrected when discovered during the visual inspection of the segmented images. D ) Manually corrected image. A. B C D

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229 Figure 41 5 Determination of optimum samplesize for each histology slide. Additional ROIs were processed until the cumulative mean CF (black diamonds) converged to a steady state value (within +/ 1 % cellularity). The stars mark the CF value of each individual ROI.

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230 Figure 41 6 Linear regression plot of % CF determined from automated segmentation versus manual segmentation. y = 0.9733x + 1.1758 R = 0.9945 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 CF (automated segmentation) CF (manual segmentation)

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231 Figure 41 7 Bland Altman plot comparing automated versus manual adipocyte segmentation. CF was measured on a sample of 37 ROIs using both manual and automated adipocyte segmentation. The middle horizontal line is the mean of the differences, + 0. 06% cellularity The top and bottom horizontal lines correspond to the 95% confidence interval --i.e. mean difference 1.96 standard deviation--corresponding to 2.59 % to 2.71% cellularity.

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232 Figure 41 8 Composite plot of spectra acquired from the humerus of each dog. The horizontal axis presents shifts (in ppm) with respect to the water resonance. As is customary, the spectrum is reversed for display purposes (i.e. shifts have the opposite sign). S pectra were normalized by the maximum at the CH2 peak (3.4 ppm).

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233 Figure 419. Composite plot of spectra acquired from the femur of each dog. The horizontal axis presents shifts (in ppm) with respect to the water resonance. As is customary, the spectrum is reversed for display purposes (i.e. shifts have the opposite sign). Spectra were normalized by the maximum at the CH2 peak (3.4 ppm).

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234 Figure 420. Composite plot of spectra acquired from the upper spine of each dog. The horizontal axis presents shifts (in ppm) with respect to the water resonance. As is customary, the spectrum is reversed for display purposes (i.e. shifts have the opposite sign). Spectra were normalized by the maximum at the CH2 peak (3.4 ppm).

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235 Figure 421. Composite plot of spectra acquired from the lower spine of each dog. The horizontal axis presents shifts (in ppm) with respect to the water resonance. As is customary, the spectrum is reversed for display purposes (i.e. shifts have the opposite sign). Spectra were normalized by the maximum at the CH2 peak (3.4 ppm).

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236 Figure 422. SPIDEAL water fat separation in the femur of a dog. SP IDEAL was performed on six SPGR echoes acquired with flip angle of 5o, TR = 40 ms, and TE1 = 5.95 ms, TE = 0.38 ms. A ) water image; B ) fat image; C ) field map; D ) composite image (sum of water and fat images). A. B C D

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237 Figure 423. SPIDEAL water fat separation in the humerus of a dog. SP IDEAL was performed on six SPGR echoes acquired with flip angle of 34o, TR = 40 ms, and TE1 = 5.95 ms, TE = 0.38 ms. A ) water image; B ) fat image; C ) field map; D ) composite image (sum of water and fat images). The white arrow points to a region where fat water switching occurred. A. B C D

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238 Figure 424. SPIDEAL water fat separation in the upper spine of a dog. SP IDEAL was performed on six SPGR echoes acquired with flip angle of 5o, TR = 40 ms, and TE1 = 5.95 ms, TE = 0.38 ms. A ) water image; B ) fat image; C ) field map; D ) composite image (sum of water and fat images). White arrows indicate regions experiencing fat water switching. A. B C D

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239 Figure 425. SPIDEAL water fat separation in the lower spine of a dog. SP IDEAL was performed on six SPGR echoes acquired with flip angle of 34o, TR = 40 ms, and TE1 = 5.95 ms, TE = 0.38 ms. A ) water image; B ) fat i mage; C ) field map; D ) composite image (sum of water and fat images). A. B C D

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240 Figure 426. Comparison of fat distribution visually observed in the femur with fat distribution in the calculated fat image. Top: photo of left femur from necropsy. Bottom: SP IDEAL fat image of right femur. Image has been cropped and rotated to match the orientation of the femur on the necropsy photo.

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241 Figure 427. Comparison of fat distribution visually observed in the humerus with fat distributio n in the calculated fat image. Top: photo of left humerus from necropsy. Bottom: SP IDEAL fat image of right humerus. Image has been cropped and rotated to match the orientation of the humerus on the necropsy photo.

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242 Figure 42 8 MP IDEAL with pre calibration fat water separation in the femur of a dog. M P IDEAL was performed on six SPGR echoes acquired with flip angle of 5o, TR = 40 ms, and TE1 = 5.95 ms TE = 0.38 ms. The spectrum for precalibration was developed by averaging the amplitudes obtained from spectral fitting of the lipid species indicated in Table 41 in spectra acquired at the femoral head, neck and shaft. Spectral fitting was performed using the AMARES algorithm in jMRUI. A ) water image; B ) fat image; C ) field map; D ) composite image (sum of water and fat images). A. B C D

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243 Figure 42 9 Side by side comparison of the fat images obtained with SP IDEAL and MP IDEAL in the femur. Differences are indistinguishable by eye, but the gray scale bar by each image indicates that bright white pixels in the multi peak fat image correspond to a larger pixel intensity value and consequently a larger fat proton density. Single peak Multi peak

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244 Figure 430 Linear regression line for CF measured by SP IDEAL versus CF measured by histology at the same location on the bone in two dogs The outlier identified in Figure 42 9 was not included in the regression. y = 0.9784x + 0.8285 R = 0.9846 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00%CF measured by SP IDEAL% CF measured by Histology

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245 Figure 431 Bland Altman plot of CF determined by SP IDEAL to histology at the same location on the bone in two dogs The middle solid horizontal line is the mean difference (bias) and it is equal to 0. 52% cellularity. The top and bottom horizontal lines correspond to the 95% confidence interval of the differences equal to 3.76% and 4.80% cellularity) The plot identifies an outlier, corresponding to a measurement in L4 in one of the dogs. The large error is most likely due to the fact the spine is curved and a slice does not capture the same cross section for each vertebra. The results for L1 are in excellent agreement (difference = 1.83%) using the same slic e. L4 is further down the spine and the cross section of L4 in the image does not correspond to the full extent of the vertebral body.

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246 Figure 43 2 Linear regression line for CF measured by MP IDEAL versus CF measured by histology at the same location on the bone in two dogs. The dashed line is the perfect agreement line. y = 0.8609x 0.3378 R = 0.8059 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00%CF measured by MP IDEAL%CF measured by Histology

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247 Figure 43 3 Bland Altman plot of CF determined by MP IDEAL to histology at the same location on the bone in two dogs. The middle solid horizontal line is the mean diff erence (bias) and it is equal to 7 37% cellularity. The top and bottom horizontal lines correspond to the 95% confidence interval of the differences equal to 5.08% to 19.81% cellularity The plot identifies an outlier, corresponding to a measurement i n cervical vertebra C6 in one of the dogs.

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248 Figure 43 4 Histological aspect of the femoral head and humeral head in a dog. The femoral head (A) is smaller and contains a larger bone fraction than the humeral head (B) in a dog. A. B

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249 Figure 435. Modeling of spongiosa in radiation dosimetry Monte Carlo simulations. The images present a single binarized microCT slice at 60 m resolution taken from a human femoral head. In the images, black voxels correspond to trabecular bone, white voxels correspond to adipocytes, and gray voxels correspond to the remainder soft marrow tissue, which includes hematopoietic cells, extracellu lar fluid, and marrow vasculature. Four values of CF are simulated: A) 10%, B) 50%, C) 80%, and D) 100%. A binarized micro CT image provides only soft marrow and trabecular bone voxels. Soft marrow voxels are randomly assigned to adipocytes according to the ratio provided by the CF.

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250 CHAPTER 5 CONCLUSIONS AND FUTU RE NEEDS Conclusions The therapeutic dose in radioimmunotherapy is limited by bone marrow toxicity. In order to avoid post therapeutic complications, it is necessary to accurately determine the absorbed dose in the bone marrow of the patient. This dose can be calculated using the MIRD schema ( Equation 1 1), but the calculation requires knowledge of the total active bone marrow mass in the patient, which cannot be measured directly as would be done for other organs and tissues based on CT volumetry In the absence of this knowledge, the dose to marrow can be estimated by scaling the dose calculated in a reference individual by the ratio of lean body masses of the patient to the reference individual. In this dissertation methodology is provided to allow the estimation of patient specific active bone marrow mass. The methodology requires the determination of several quantities ( Equation 1 5) that typically cannot be measured on a patient, such as TSSV, fSV x, and MVF. TSSV and fSV x can be determined from full body CT images of the patient. However, a full body CT is not part of the typical imaging performed on a patient, since the high radiation dose that the patient will receive is unwarranted. The measurement of MVF on a patient is not possible since it requires extraction of bone cubes from multiple bone sites and invivo imaging methods have insufficient resolution to discern the marrow cavities and bone trabeculae. However, it is possible to predict these quantities on a pat ient through the development of appropriate predictive models based on cadaver data.

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251 A TSSV predictive model (Table 25) is developed in this work that allows the estimation of TSSV in a patient based on the patients sex, and two pelvic measurements that can be easily performed in the clinic, either measured directly on the patient or on pelvic CT images from the patient, which are typically part of the standard imaging performed on patients undergoing radioimmunotherapy. A table of average fSV x values based on the same cadaver population is provided in Table 29. Due to budgetary constraints it was not possible to develop a predictive equation for MVF. However, a model can be produced using the same process employed in the development of the TSSV predic tive equation described in this work. In lieu of better data, one can use average MVF values provided in other studies (Tables 1 2 and 13 ). In Chapter 4, the use of SPIDEAL with the robust field map extraction algorithm developed by Hernando et al. ( 145 ) is used to determine patient specific CF All measurements were found to be wit hin 4% cellularity of the same quantity determined by the gold standard, bone marrow histology, performed at the same locations in bone. Most measurements agreed within 2% cellularity, indicating that this method can be used in lieu of the gold standard in the measurement of bone marrow CF. This provides an enormous advantage, since SP IDEAL is non invasive, it can be performed at any location in the anatomy and allows the mapping of CF in any bone. Image acquisition is fast, especially if the images are acquired with SPGR. Accuracy of the CF determination can be improved by acquiring unequally spaced echoes to allow for T2* correction, which can be performed simultaneously within the fat water separation algorithm.

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252 In histopathology studies of bone m arrow the term cellularity refers to the fraction by volume of marrow occupied by hematopoietic cells. Anthropometric computational phantoms currently used in radiation dosimetry do not have the sufficient resolution to distinguish marrow cellular components. Spongiosa is modeled using micro CT images of spongiosa typically acquired with resolution of 60 m. These images are binarized so that voxels correspond to either soft marrow or trabecular bone. In order to simulate the presence of adipocytes i n bone marrow, soft marrow voxels are randomly assigned to adipocytes to match the adipocyte volume fraction of each bone site. Consequently, the radiation transport modeling can only provide absorbed dose to soft marrow voxels that are not adipocytes, but does not differentiate between soft marrow components such as hematopoietic cells, extracellular fluid, and marrow vasculature. Marrow cellularity calculated from the segmentation of adipocytes in histology images corresponds to the volume fraction of s oft marrow not occupied by adipocytes, and, as such it is not equivalent to one minus the chemical fat fraction, as is calculated in hepatic fat fraction studies, derived from multi peak MRI methods such as MP IDEAL or to marrow cellularity determined by point counting. It is proposed that the term CF be no longer used in the context of bone marrow radiation dosimetry studies, and propose the use of the term adipocyte volume fraction (AVF) instead. This terminology will not only prevent misinterpretation of this quantity, but will also make it easier to convert radiation absorbed fractions when cellular level dosimetry becomes a reality in the future.

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253 The in vivo accuracy of MP IDEAL in the determination of bone marrow fat fractions could not be determined from the data acquired in this study, since the standard for comparison was bone marrow histology, which determines fat fraction from the segmentation of adipocytes in histology slides. Accuracy could have been determined by fat fractions calculated fr om HMRS. Even though HMRS data was acquired, it was not acquired with such a purpose in mind, and the data is insufficient to perform the relaxation time corrections required for accurate fat fraction calculations. Future Needs The methodology proposed in this dissertation, as it currently stands, is subject to several limitations. The TSSV predictive equation and the average fSV x values are based on a specific human population: white male and female residents of Gainesville, FL. The human skeleton is subject to morphological differences based on geographical location and race. Depending on the severity of the differences, the model and average fSV x table provided in this dissertation work may not be appropriate for a patient belonging to a different population. Hence, it is necessary to develop similar predictive models that are specific to individuals from different each geographical location and race. These models must include individuals covering an appropriate age range, as the one used in this work. Full body CTs of healthy volunteers are not appropriate since the volunteers will be subjected to an unwarranted elevated radiation dose. These models must therefore be developed using cadavers. The accuracy of prediction of these models will be greatly improved if they are based on a large and representative sample of the target population. The model provided in this work is based on a sample size of 40 individuals, which is adequate, but not ideal. The sample size limitation in this work was a direct consequence of the

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254 tedious and timeconsuming nature of the manual segmentation of TSSV from cadav er CT images. Development of accurate automated or semi automated spongiosa se gmentation methods are therefore needed to make this a reality. Due to budgetary constraints, a predictive equation for MVF could not be developed. Tables 1 2 and 13 provide average MVFs that can be used in the absence of populationspecific data. MVF i s also expected to exhibit differences for different human populations and is expected to vary with age and gender MVF can be easily determined from microCT images of bone cubes extracted from cadavers. Hence, this process can be included in the proces sing of cadavers for the determination of TSSV and fSV x. Given that MVF is expected to vary significantly with age due to normal bone loss with aging and osteoporosis, it is very important that MVF data be acquired for a wide range of age groups and for both males and females S ome disease states are known or likely to affect TSSV, fSV x, MVF and CF. Hence, it is important to investigate this by repeating the described procedures in diseased individuals and comparing the results with those from healthy individuals. A better understanding of the physiological relationships between all of these quantities will aid the development of more accurate predictive models. The variables included in the models provided in this work were selected by mathematical c riteria. More robust models can be generated when variables are selected based on biological significance. AVF changes are indicative of the existence and progression of a disease and recovery during treatment. The current gold standard used to diagnose cancer associated with bone and bone marrow (e.g. leukemia) is a bone marrow biopsy taken from the iliac crest. This measurement is highly invasive, which limits its repeated use,

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255 and can only be performed at the iliac crest. As demonstrated by this study, AVF is different, not only in different bones, but in different parts of the same bone. Hence, a biopsy performed at the iliac crest is not indicative of AVF elsewhere in the skeleton. SPIDEAL provide s a noninvasive alternative that can be used to m ap AVF during the progression of disease and to determine the efficacy of treatment. Given that increases in adipocyte concentrations correlate with decreased cancellous bone volume ( 197) it is quite possible that the measurement of AVF may be used to diagnose the onset of osteoporosis. The use of IDEAL allows the measurement to be performed directly at the sites of interest, the pelvic bone and femoral heads, and AVF mapping may allow t he determination of problem regions within the skeleton. It has been demonstrated that differences in AVF result in large differences in the absorbed fraction of energy to target tissues from internal alpha emitters, and hence calculation of TAM dose requi res knowledge of patient specific AVF ideally within each bone site of the skeleton ( 41) SPIDEAL has been shown in this study to provide accurate measurements of AVF, and therefore provides a simple noninvasive method by which the patient specificity of radiation dosimetry of alpha emitters can be greatly improved. The in vivo accuracy of MP IDEAL in bone marrow remains unknown. The use of bone marrow cellularity (or fat fraction) derived from histological methods is not adequate to determine the accuracy of MP IDEAL, since fat fraction determined from adipocyte segmentation or point counting is invariant to the chemical composition of lipids in the adipocytes. Hence, either accurate HMRS or a chemical assay method that quantifies multiple lipid chemical species is required. The fat fraction measurement

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256 derived from MP IDEAL may be important in studies of adipocyte metabolism, since it will be sensitive to changes not only in the quantity of lipid in the adipocytes, but the relative fractions of lipid components. The advantage of the use of MP IDEAL versus HMRS is that it is much simpler to perform. IDEAL methods are already part of the software in General Electric (GE) MR scanners and will be available in other clinical scanners in the near future (personal communication by a Philips represent ative).

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BIOGRAPHICAL SKETCH Jose Carlos Pichardo was born i n 1966 in Malaga, Spain. He is one of five siblings, three boys and two girls. His father Jose was the chef and owner of a very successful restaurant Casa Jose --in Benalmadena, located in the south coast of Spain. His mother was Esther, a Dutch national. Both are deceased. The family moved to Madrid, Spain, for business reasons, when he was seven years old. After completing 7th grade, he was sent to a boarding school in England (St. Johns Beaumont in Berkshire, near London) to learn English. The f ollowing year the family moved to Amsterdam, the Netherlands, where Carlos completed 8th and 9th grades at the European School in Bergen, Holland. The following year the family returned to Madrid, where Carlos completed High School, earning an International Baccalaureate (IB) diploma in 1985. Inspired by Carl Sagans Cosmos TV series, he decided to pursue a degree in p hysics at the Universidad Aut noma de Madrid. During his 2nd year of college Thorpe E. Thomas (Ted), a friend of the family, offered to pay for his studies in the U S. A. In 1987 Carlos moved to Philadelphia, Pennsylvania, to complete his B.S. degree in Physics at Dr exel University. He graduated Cum Laude with his B.S. degree in 1991 and he continued on to earn a M.S. degree in p hysics. Carlos worked as a teaching assistant in order to receive free tuition and a modest stipend. He became very excited about teaching and after graduati ng with his M.S. i n June 1993, he moved to South Florida to pursue a career as a p hysics teacher He started teaching m iddle school in a public school in Pembroke Pines, FL. It did not take more than a few months before he realized that m iddle school was not for him, so he took a position at the adjacent h igh school, Charles Flanagan HS, where he taught p hysics, p hysics h onors, and AP p hysics for several years. During this time Carlos met and married his

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wife, Jennifer, and after the birth of their first child, Olivia, he realized that he could not properly provide for his family if he remained a teacher. While at the 2003 American Association of Physics Teachers (AAPT) meeting in Miami, FL, Carlos was drawn to a booth advertising careers in m edical p hysics. The job market and salaries for m edical p hysicists were outstanding, and the discipline would allow Carlos to combine the two disciplines he loves the most: p hysics and b iology. Carlos moved with his wife and two daughters to Gainesville, FL, in 2004, and was accepted into the m edical p hysics PhD program (CAMPEP) at the University of Florida in 2005. Upon completion of his PhD degree, Carlos plans to work as a junior medical physicist in a radiation therapy clinic