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PAGE 1 1 DETECTION OF INTRAVENTRICULAR HEMORRHAGE IN NEONATES USING ELECTRICAL IMPEDANCE TOMOGRAPHY By TE TANG 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 PAGE 2 2 2010 Te Tang PAGE 3 3 To my family in China PAGE 4 4 ACKNOWLEDGMENTS First and foremost, if there is only one person in this world that deserves all my gratitude in the past five years, this person is Dr. Rosalind Sadleir. I appreciate that she offered me this opportunity to research in the field of Electrical Impedance Tomography and her continuous support for my whole 5year Ph. D. study. I could have achieved nothing without her guidan ce, patience and instruction in the ways of the research world along the journey. Year 2005 2010 was definitely a turning point in my career. I will never forget this pleasant and valuable experience in my entire life. I want to say thank you to many oth er people, especially my committee members, Dr. Johannes van Oostrom, Dr. David Gilland and Dr. Stephen Blackband, for offering good advice at critical points along the way. I would like to give specials thanks to Dr. Peggy Borum and Dr. Michael Weiss for their help on the piglet experiments. The in vivo animal experiments would not be a possibility without their professional assistance. I hope we can continue our corporation in the following stage of this project. I would also like to thank my lab mates, S ungho Oh and Aaron Tucker. They have contributed to the completion of my work in significant ways. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...................................................................................................... 4 LIST OF TABLES ................................................................................................................ 9 LIST OF FIGURES ............................................................................................................ 10 ABSTRACT ........................................................................................................................ 14 CHAPTER 1 INTRODUCTION ........................................................................................................ 16 Electrical Impedance Tomography ............................................................................ 16 Development and Applications ............................................................................ 16 I ntraventricular Hemorrhage ....................................................................................... 17 What Is IVH .......................................................................................................... 17 Current Modalities for the Monitoring and Treatment of IVH .............................. 18 Potential of Electrical Impedance Tomography .................................................. 19 Organization of the Dissertation ................................................................................. 22 2 EIT METHODS ........................................................................................................... 25 EIT Forward Problem ................................................................................................. 25 Formulation of Forward Problem ......................................................................... 25 Formulation of the Finite Element Solution ......................................................... 26 Conjugate Gradient Method ................................................................................. 30 EIT Inverse Problem ................................................................................................... 33 Overview ............................................................................................................... 33 Formulation of Linearized Algorithm .................................................................... 35 Sensitivity Matrix .................................................................................................. 35 Lead Field Theory ................................................................................................ 37 Regularization of the Inverse Problem ....................................................................... 41 Illposed Nature of the Inverse Problem .............................................................. 41 Tikhonov Regularization ...................................................................................... 42 Truncated Singular Value Decomposition (TSVD) ............................................. 42 Singular value decomposition (SVD) ............................................................ 42 Condition number and TSVD ........................................................................ 44 L curve ........................................................................................................... 45 Weighted minimum norm method ................................................................. 46 Quantitative Measures of EIT Reconstruction ........................................................... 47 Sensitivity and Selectivity ........................................................................................... 48 EIT Hardware .............................................................................................................. 49 3 PIGLET SKULL IMPEDANCE MEASUREMENT ...................................................... 63 PAGE 6 6 Background and Significance ..................................................................................... 63 Method ........................................................................................................................ 64 Sample Preparation ............................................................................................. 64 Measurement Apparatus ..................................................................................... 64 Theory .................................................................................................................. 65 Result .......................................................................................................................... 66 Discussion ................................................................................................................... 66 Conclusion .................................................................................................................. 68 4 A ROBUST CURRENT PATTERN FOR THE DETECTION OF IVH ....................... 72 Background ................................................................................................................. 72 Method ........................................................................................................................ 72 Candidate Current Patterns ................................................................................. 72 Sensitivity Studies for the Candidate Current Patterns ...................................... 74 Data Generation ................................................................................................... 76 Finite element models ................................................................................... 76 Phantom models ............................................................................................ 77 Reconstruction Method ........................................................................................ 79 Localization of EIT Reconstructions .................................................................... 80 Image Resolution and Contrast ........................................................................... 80 Comparison between Open Skull and Closed Skull Models ........................... 82 Sensitivity analysis using a layered model ................................................... 82 Noise analysis using model B ....................................................................... 83 Results ........................................................................................................................ 84 Sensitivity and Selectivity for the Uniform Models .............................................. 84 Comparing the Three Current Patterns Using Model A ...................................... 85 Comparing RING and EEG Patterns Using Model B and Phantom Data .......... 86 Comparison between Open Skull and Closed Skull Models ........................... 87 Discussion ................................................................................................................... 88 Sensitivity and Selectivity .................................................................................... 88 Overall Evaluation with Model A .......................................................................... 89 Model B and Phantom Experiment Results ........................................................ 90 Anomaly Quantification ........................................................................................ 92 Comparison between Open Skull and Closed Skull Models ........................... 93 Comparing Localization Results with Earlier Studies ......................................... 94 Other Possib le Applications ................................................................................. 95 Conclusion .................................................................................................................. 95 5 STUDIES USING A REALISTIC HEAD SHAPED MODEL .................................... 109 Background ............................................................................................................... 109 Methods .................................................................................................................... 110 The Neonatal Head shaped Model ................................................................... 110 Sensitivity Analysis ............................................................................................. 110 Simulation of IVH ............................................................................................... 111 Investigation of Boundary Shape Mismatch ...................................................... 112 PAGE 7 7 Forward models ........................................................................................... 112 Data generation ........................................................................................... 112 Results ...................................................................................................................... 115 Sensitivity Analysis ............................................................................................. 115 Layered RG Model ............................................................................................. 116 Investigation of Boundary Geometry Effects Using H omogeneous RG Models ............................................................................................................. 117 Discussion ................................................................................................................. 118 Conclusion ................................................................................................................ 122 6 STUDIES USING PIGLET MODELS ....................................................................... 133 Introduction ............................................................................................................... 133 Methods .................................................................................................................... 133 Piglet 1 ................................................................................................................ 133 Piglet 2 and 3 ..................................................................................................... 134 Piglet 4 (the MRI Piglet) ..................................................................................... 135 Piglet 5 ................................................................................................................ 137 Piglet 6 ................................................................................................................ 137 Piglet 7 and 8 ..................................................................................................... 138 Piglet 9 and 10 ................................................................................................... 138 Results ...................................................................................................................... 139 Piglet 1 ................................................................................................................ 139 Piglet 2 and 3 ..................................................................................................... 139 Piglet 4 ................................................................................................................ 140 Piglet 5 and 6 ..................................................................................................... 140 Piglet 7 and 8 ..................................................................................................... 141 Piglet 9 and 10 ................................................................................................... 141 Summary ............................................................................................................ 142 Discussion ................................................................................................................. 143 Conclusion ................................................................................................................ 146 7 SUMMARY ................................................................................................................ 163 Conclusion ................................................................................................................ 163 Future Work .............................................................................................................. 165 Improving in vivo Animal Experiment ................................................................ 165 Improving the Measurement Strategy ............................................................... 165 APPENDIX A USEFUL C++ CODE FOR CONJUGATE GRADIENT METHOD .......................... 167 Bracket the Minimum ................................................................................................ 167 Search for the Minimum ........................................................................................... 168 Line Minimization ...................................................................................................... 170 Conjugate Gradient Method ..................................................................................... 170 PAGE 8 8 B PROCEDURES F OR IN VIVO PIGLET EXPERIMENTS ....................................... 172 LIST OF REFERENCES ................................................................................................. 177 BIOGRAPHICAL SKETCH .............................................................................................. 188 PAGE 9 9 LIST OF TABL ES Table page 1 1 Estimates of the conductivity (S/m) of body tissues below 100 Hz at body temperature (Gabriel et al. 1996) .......................................................................... 23 1 2 Grades of Intraventricular hemorrhage defined by Papile et al. (1978), with associated risks and ultrasound specificities ........................................................ 24 3 1 Measurement results for the fresh skull samples. ................................................. 70 3 2 Measurement results for the frozen skull samples. ............................................... 71 4 1 Spherical coordinates of EEG electrodes, in degrees. T7 is left t emporal and T8 right temporal. Oz is Occipital central electrode. ............................................. 96 4 2 The condition number, rank and size for the sensitivity matrix used for each current pattern and truncation point chosen for each case ................................ 101 4 3 Comparison of resolutions R calculated for each of the cases shown in Figure 414 ........................................................................................................... 106 5 1 Resolution val ues of the reconstructions for all the anomaly volumes. ............. 132 6 1 Linear Discriminant Analysis (LDA) for all the in vivo piglet QI data .................. 162 PAGE 10 10 LIST OF FIGURES Fig ure page 1 1 Intraventricular Hemorrhage (IVH). ....................................................................... 24 2 1 A domain with 4 boundaries divided into elements. .............................................. 54 2 2 A tetrahedral element ............................................................................................. 54 2 3 Demonst ration of a dipole source within a volume conductor. ............................. 55 2 4 The lead field distribution within a 2D elliptical domain. ....................................... 55 2 5 Illustration of the reciprocity theorem of Helmholtz ............................................... 56 2 6 Derivation of the equation for lead field theory. .................................................... 56 2 7 Singular values of the sensitivity matrix for the homogeneous spherical model with EEG current pattern. ............................................................................ 57 2 8 L curve examples using different regularization algorithm. .................................. 57 2 9 A comparison between unweighted and weighted 2D reconstructions. ............. 58 2 10 The first and second generation of E pack EIT systems. ...................................... 58 2 11 Comparison of aperture times in EPack1 and EPack2. ........................................ 59 2 12 Overall system design of the EPack1 system ....................................................... 59 2 13 Schematic of the EPack module. ........................................................................... 60 2 14 The EPack module, showing battery pack (top right), main acquisition board (center) and electrode connections (center) ......................................................... 61 2 15 EPack software screenshot (left). Amplified reconstructed image (top right). Phantom experiment using a full array electrode configuration (bottom right). ... 62 3 1 Skull sample preparation, showing the left frontal, left parietal, right frontal and right parietal bone samples. ............................................................................ 69 3 2 The measurement cell used to measure skull impedance. .................................. 69 3 3 Skull conductivities plotted as a function of their thickness. ................................. 71 4 1 Three electrode configurations viewing from the top and demonstrations of the current pattern applied in each case. .............................................................. 96 PAGE 11 11 4 2 Forward models with three different electrode layouts. ........................................ 97 4 3 Three dimensional EEG sph erical models showing central and lateral ventricle regions. .................................................................................................... 97 4 4 A model with an outer brain shell and a central region of CSF (Model A) viewing from the top. .............................................................................................. 98 4 5 A more complex model (Model B) with scalp, brain, ventricles and skull shells, including a structure similar to the fontanel (highlighted). ......................... 98 4 6 MRI images of a neonatal head, from which we determined the position and size of the ventricles. .............................................................................................. 99 4 7 Spherical phantoms with EEG layout (left) and RING layout (right). .................. 100 4 8 The complete phantom experiment system ........................................................ 100 4 9 Layered spherical model with EEG layout. ......................................................... 101 4 10 Average sensitivities, calculated as a fraction of maximum values observed over the domain, for EEG, Cz RING and RING patterns in the regions of int erest. ................................................................................................................. 102 4 11 Absolute selectivities observed within a relatve radius 0.8 for EEG, Cz RING and RING patterns in the regions of interest. ........................................... 103 4 12 Radial relative localization errors for simulations on model A. ........................... 104 4 13 Quantification Indices of the 37 different anomaly positions for each of the three current patterns on model A. ...................................................................... 104 4 14 Axial (relative radial position z = 0.3) and sagittal (x = 0.2) cross sections (first and second columns) and isosurfaces ( third column) of an blood like anomaly in each case. ......................................................................................... 105 4 15 Radial relative localization errors Dxy and Dz of the 6 anomaly positions for simulated (model B) and phantom data for RING and EEG patterns. ............... 106 4 16 Quantification Indices of the six anomaly positions with simulated (model B) and phantom data for the RING and EEG patterns. ........................................... 107 4 17 Comparisons between open skull and closedskull reconstructions. ............. 108 5 1 The 3D neonatal head model visualized using Pro ENGINEER (Parametric Technology Corp.). ............................................................................................... 123 5 2 The neonatal head model visualized using Comsol 3.4, showing the anatomical structures and scalp electrode configuration. ................................... 123 PAGE 12 12 5 3 Axial, saggital and coronal views of realistic geometry model, showing ventricular and central structures. ....................................................................... 124 5 4 The two ventricle structures (red dots) added within the brain, and the six anomaly positions (blue dots) within the ventricles. ............................................ 124 5 5 The three models used for data generation. ....................................................... 125 5 6 Procedures of constructing a head shaped phantom. ........................................ 125 5 7 One slice (#74) of the original Gent model MRI data, showing the five major structures in the head. .......................................................................................... 126 5 8 Dividing a rectangular brick element (12345678) into six tetrahedral elements, which are: 1245, 2456, 2346, 3678, 3468 and 4568. ........................ 126 5 9 Sensitivities and selectivities found in the regions of interest using a uniform RG sensitivity matrix. ........................................................................................... 127 5 10 Comparisons between reconstructions using SPS and RGS matrix. .................... 128 5 11 Image and conductivity profile in reconstructions of different anomaly pairs. .... 129 5 12 Quantification Indices (with the corresponding volume estimation labeled on the right) for the multi site bleeding cases using SPS and RGS .......................... 130 5 13 Comparison of average QI errors (with the corresponding errors in volume estimation labeled on the right) for the 63 cases using the two sensitivity matrices under 11 different SNR levels ranging from 60 dB to 90 dB. .............. 130 5 14 Reconstructions with the RG matrix and SP matrix using the data from the four models. .......................................................................................................... 131 5 15 Quantification indices for the images reconstructed with the RG matrix and SP matrix. ............................................................................................................. 132 6 1 The piglet head and electrode configuration used on piglet 1. ........................... 147 6 2 Electrodes and artificial brain used for piglet 1 experiment. ............................... 147 6 3 Experiment setup for piglet 2. .............................................................................. 148 6 4 Experiment setup for piglet 3. .............................................................................. 148 6 5 Piglet 4 (The MRI piglet). ..................................................................................... 149 6 6 The injection guide designed to assist introducing the canula into the ventricle. ............................................................................................................... 149 PAGE 13 13 6 7 Post mortem experiment on piglet 4. ................................................................... 150 6 8 Difference voltage measurements generated by the two 4ml saline injections on piglet 1. ............................................................................................................ 150 6 9 Isosurface plots of reconstructions of injections to the closed skull piglet (piglet 2). ............................................................................................................... 151 6 10 Quantification index as a function of injected saline volume for piglet 2. ........... 152 6 11 Isosurface plots of reconstructions of inj ections to the right open piglet skull (piglet 3). ............................................................................................................... 152 6 12 Quantification index as a function of injection time for pigle t 3. .......................... 153 6 13 Isosurface p lots of reconstructions of injections to the right side on piglet 4 (the intact MRI piglet). .......................................................................................... 153 6 14 Quantification index as a function of injection time for piglet 4. .......................... 154 6 15 Signals recorded in one of the measurements for piglet 5 and 6. ...................... 154 6 16 Coronal brain slices of piglet 6. ............................................................................ 155 6 17 QI values and reconstructed images for in vivo experiment on piglet 7. ............ 156 6 18 QI values and reconstructed images for in vivo experiment on piglet 8. ............ 157 6 19 Brain s lices taken in coronal planes for piglet 7. ................................................. 158 6 20 Brain dissection for piglet 8. ................................................................................. 159 6 21 Results for in vivo experiment on piglet 10. ........................................................ 160 6 22 Brain dissection for piglet 10. ............................................................................... 161 6 23 Linear fits between the QI values and injected volumes for all the available piglet experiment data. ......................................................................................... 162 B1 E xperiment picture showing the setups for the umbilicus catheter. ................... 175 B2 Setup for blood injection ...................................................................................... 176 PAGE 14 14 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 DETECTION OF INTRAVENTRICULAR HEMORRHAGE IN NEONATES USING ELECTRICAL IMPEDANCE TOMOGRAPHY By Te Tang Augus t 2010 Chair: Rosalind J. Sadleir Major: Biomedical Engineering Electrical impedance tomography (EIT) is a medical imaging technique in which images of conductivity within a body can be inferred from surface electrode measurements. EIT has been studied i n different clinical areas such as brain imaging, thorax imaging and breast imaging. The focus of this thesis is to investigate the feasibility of EIT on the detection of intraventricular hemorrhage in premature neonates. Cerebral intraventricular hemorrhage (IVH) in neonatal human infants is a common consequence of preterm delivery. It is currently assessed using ultrasound, MRI or CT scan. These modalities are not suitable for continuous monitoring of infants and involve large personnel or equipment cost s. Because blood has a high electrical conductivity contrast relative to other cranial tissue, its appearance can be detected and monitored using electrical impedance methods. EIT is a noninvasive, low cost monitoring alternative to these imaging modaliti es, and has the potential to measure bleeding rate and approximately localize the bleeding site. The first part of this work aimed to find a robust current pattern for the detection of IVH. We proposed three different electrode layouts and current patterns (RING, EEG and Cz RING patterns), and compared their performance using a homogeneous PAGE 15 15 spherical head model. Sensitivity analysis shows that the EEG current pattern has larger absolute selectivities than the RING and Cz RING patterns in all the regions of interest. Numerical simulation and saline phantom experiments also show that the reconstructed images using the EEG pattern have better image qualities and quantification accuracies in general. The second part of this study involved numerical simulations and phantom experiments using models with realistic boundary geometry. We investigated the advantage and disadvantage of using a sensitivity matrix calculated from a homogeneous realistic geometry model (the RG matrix). We found that the RG matrix does not always produce better image quality than the spherical matrix when there is a model mismatch in boundary geometry. In addition to that, the RG matrix does not show any advantage in terms of quantification accuracy. Therefore, we decided that using the sph erical sensitivity matrix would be a better choice for applications on real subjects. Finally, post mortem and in vivo experiments were conducted on piglets to validate our method. We were able to detect 0.2 ml saline injections in post mortem piglets and quantify the accumulative blood volumes with consistent accuracy. We successfully detected 0.5 ml blood injections in live animals. The quantification results are consistent for all the in vivo experiments. The reconstructed images of blood volumes are confirmed by the brain slices after each experiment. All the results indicate that EIT will be an effective method for monitoring intraventricular bleeding in neonates. PAGE 16 16 CHAPTER 1 INTRODUCTION Electrical Impedance Tomography Development and Applications Elec trical impedance tomography (EIT) is a noninvasive medical imaging technique in which images of conductivity within a body can be inferred from surface electrode measurements. In conventional EIT measurements, currents are injected into a volume through one pair of an electrode array, and the data consists of differential voltages measured between other array electrodes. EIT is a novel imaging method that has evolved over the past 20 years. The main goal of EIT is to reconstruct the electrical conductivity distribution as a physiologically useful image, which is possible because the voltage measurements depend on the conductivity distribution within the object. Originally, EIT was not developed for clinical applications. The first use of EIT was reported i n 1930 on geological studies (Stephanesco and Schlumberger 1930). People today are still using EIT for industrial purposes, such as detecting air bubbles in process pipes (Ljaz et al. 2008) and landmine detections (Wort et al. 1999). The fact that different human tissues have different electrical properties (Stoy et al. 1982) indicated the possibility of using EIT for clinical applications. Table 11 listed the conductivity of different human tissues at low frequency. It has been more than 20 years since th e Sheffield group produced the first clinical images using EIT in the year 1987 (Brown and Seager 1987). However, EIT has not been routinely used in daily clinical practice. People should face the difficulty that EIT does not have a good spatial resolution as other commonly used imaging modalities such as Magnetic Resonance Imaging (MRI) and Computer Tomography (CT). The spatial resolution is related to the number of PAGE 17 17 electrodes used. There are practical problems applying a large number of electrodes, due to the complexity of electronics and the computational difficulties to process a large quantity of data (Rahim et al. 2003). However, EIT is much cheaper than the conventional imaging techniques and requires no ionizing radiation. Another advantage of EIT is its temporal resolution. It is capable of producing multiple images within a second. In addition to that, the EIT system can be easily made portable using a laptop or even a PDA (Tang et al. 2006). All these advantages made EIT a promising bedside tool in clinical use for the purpose of continuous monitoring. EIT has potentials on a range of clinical applications. We can summarize the research in different clinical areas into the following categories: Pulmonary function (Holder and Temple 1993, Brown et al 1995, Cheney et al. 1999, Mueller et al. 2001) Thoracic blood volume (Eyuboglu et al. 1987, Mueller et al. 2001, Hoetink et al. 2002) Breast tumors (Cherepenin et al. 2002, Kerner et al. 2002, Glickman et al. 2002) Hyperthermia (Foster and Schwann 1989, Liu and Griffiths 1993, Moskowitz et al. 1995) Gastrointestinal function (Mangnall et al. 1987, Mangnall et al. 1991, Akkermans and Tekamp1993, Nour et al. 1995 ) Internal bleeding (Meeson et al. 1995, Sadleir and Fox 1998, Sadleir and Fox 2001, Xu et al. 2 007) Brain Imaging (Holder et al. 1996, Rao et al. 1997, Tidswell et al. 2001a, b, c ) Intraventricular Hemorrhage What Is IVH While many aspects of birth outcomes have been vastly improved worldwide in the last 50 years, preterm birth is still the major ca use of poor birth outcome (Goldenberg PAGE 18 18 and Jobe 2001) and more than 50% of infants born at 24 weeks or less gestation will die. Although survival rates of preterm infants have increased markedly, survivors of neonatal intensive care units suffer high rates of neurodevelopmental disability such as cerebral palsy and sensory impairment. Handicap rates for very low birth weight (VLBW) preterm infants are high: more than 50% of infants with a birth weight of 1kg or less are educated in special education environm ents ( Ment et al. 2002 ). A common cause of such disabilities is hemorrhage, hypoxia or ischemia in the neonatal brain. Incidence of premature births is also increasing (from 9.5% in 1980 to 11% in 1998) partly as a consequence of infertility treatment and a ssociated multiple births (Goldenberg and Jobe 2001). Intra ventricular hemorrhage (IVH) (Figure 1 1) affects 3550% of premature human infants who are born at 32 weeks gestation and below (York and DeVoe 2002), and is a major cause of death and disabil ity. Papile et al. (1978) classified intraventricular hemorrhage into four grades (Table 12 ). Grades I and II are rarely associated with morbidity or permanent incapacity. Grades III and IV are associated with increased morbidity (nearly uniform morbidit y in the case of Grade IV), conditions such as cerebral palsy (CP), periventricular leukomalacia (PVL) and post hemorrhagic hydrocephalus (PHH). Current M odalities for the M onitoring a nd T reatment o f IVH About 65% of IVH in VLBW preterm infants is detected during the first week, with most occurring in postnatal days 4 5 (Ment et al. 2002 ). While serious IVH may be de tected from a bulging fontanel or encephalopathy of the patient, at present, the conventional diagnosis method for newborns at risk of IVH is ultrasound. Additionally, MRI is increasingly recommended for patients where there is an ambiguity in bleeding status or in term neonates who have presented with suspicious clinical signs (Hintz and PAGE 19 19 O Shea 2008). Neither ultrasound, MRI nor CT are suitabl e for continuous monitoring use because of their cost, interference with normal patient management or the presence of ionizing radiation. While many localities are equipped to care for premature infants, the ability to monitor complications may be compromi sed by lack of access to more expensive imaging modalities such as MRI. Ultrasound is 76100% specific in at detection of grade I lesions of greater than 5mm width and almost 100% specific in grade III or IV hemorrhage. However, US detection of grade II hemorrhages (free blood in normal sized ventricles) is much less accurate ( Babcock et al. 1982 Mack et al. 1981) Over the last decade, results have been presented that demonstrate early testing of Optical Tomography (NIRS, OT or OCT) in monitoring IVH (Aus tin et al. 2006 ). Other workers are involved in evaluation of IVH detection methods using PET, SPECT and fMRI (Ment et al. 2002 ), all in initial stages. Serial lumbar punctures or placement of a permanent ventroperitoneal shunts may be required to relieve posthemorrhagic hydrocephalus subsequent to confirmed grade III or IV IVH ( York and DeVoe 2002). Glucocorticoid drugs may be administered to mature the tissue if patient shows abnormal s igns. Low dose indomethacin ( Ment 1994) steroids or glutamine therapy may also be used as IVH preventatives or therapies (Anon 2004 ). As treatments become available, early warning of IVH becomes crucial. Potential of Electrical Impedance Tomography EIT monitoring involves the application of an electrode array (typically 16 to 32 electrodes) over the surface of an area of interest ( Boon e et al. 1997, Cheney et al. 1999) Sequences of current patterns are applied to a subset of electrodes, and voltages produced by the applied currents are measured. The currents employed are hi gh frequency (ca. 50 kHz) and at a low enough magnitude that they are harmless. PAGE 20 20 These measurements are used to create a cross sectional map of electrical impedance. Measurements can typically be made and images reconstructed rapidly. As mentioned earlier, a lthough EIT images have relatively poor spatial resolution compared to modalities such as MRI and CT, they nevertheless contain valuable physical information, and can be collected with little cost. By comparing data collected at an earlier time to those c ollected at the current time, images of impedance change, and therefore, rates, of processes may be identified. Blood is generally easily detectable in the body because free blood has a significant impedance contrast with other tissues and fluids (Geddes a nd Baker 1967, Faes et al. 1999 ). Determining absolute conductivity values is considerably more difficult and is hindered by other problems such as unknown boundary shape, and the need to estimate electrode contact impedances. The major advantage of EIT in clinical situations is that it is non invasive and not operator dependent. It may also be used in nurseries in remote areas or as a monitoring tool during transfer to larger care faci lities. EIT may be a good alternative to ultrasound as a screening tool to monitor and alert clinicians to the presence and progress of bleeding, an increasingly important utility as therapies for IVH become available (Hansen 2006) The application of EIT to detect bleeding in the head is potentially useful because of the cond uctivity changes that occur as the result of bleeding, but suffers the disadvantage of being hindered by the poorly conductive skull and highly conductive CSF. The skull is always a big problem when using scalp electrodes because the scalp which is relativ ely more conductive tends to shunt the current away from the skull. Therefore the amount of current that actually enters the skull is very limited. Phantom PAGE 21 21 experiment s performed by the UCL group demonstrated that the presence of a skull could reduce the im pedance change to one fifth that observed without the skull (Tidswell et al. 2001 b) For the same reason, the CSF layer existing between the skull and brain also tends to shunt current away from the brain. The CSF in the ventricles also shunts current away from the blood, which makes the overall impedance change caused by bleeding relatively smaller. All these shunting effects make the detection of bleeding difficult. T he ultimate goal of this study is to develop and test a reconstruction method in a piglet head model in order to form 3D images of electrical conductivity inside the neonatal head. EIT was briefly tested to the detection of neonatal intra ventricular hemorrhage in the late 1980s ( Murphy et al. 1987, McArdle et al. 1988 ), with a result showing detection of ventricular bleeding in one neonatal patient. These data were, however, significantly affected by artifacts. Murphy et al. (1987) found that breathing movements and variations in cerebral blood flow caused the largest signal artifacts up to 1% variation in their baseline signal at a frequency of approximately 0.5 Hz. The other significant artifact was synchronous with heart electrical activity, causing a variation of about 0.1% in signals. Large artifacts due to movement of the infant were al so encountered. Nevertheless, these early studies of IVH using EIT demonstrated the potential of EIT for this application. More recently, EIT has also been applied to detection of brain activity, stroke and epilepsy (Tidswell et al. 2001a, b, c, Liston 200 4 ). Their studies have indicated the possibility of using EIT as an imaging tool in circumstances where blood volume changes occur in the brain. PAGE 22 22 Organization of the Dissertation The goal this dissertation is to detect and quantify intraventricular bleedin g in a piglet model. One future goal is to make this application available as a routine clinical procedure on neonates. The dissertation is organized as follow s In Chapter 1 we gave a literature review of EIT applications. Then, we pointed out the signifi cance of IVH, which led us to the ultimate goal of this study. In Chapter 2 we review two important aspects of EIT, mathematics and hardware and introduc e the algorithms used in this work. Piglet skull impedance measurements are discussed in Chapter 3. The measurement results were important for us to choose a proper skull parameter in the simulations for neonates. We demonstrat e in Chapter 4 the first step of this work, which was finding a robust current pattern for this application using spherical models. The advantage of the current pattern on a neonatal application was analyzed based on the results from numerical simulation and phantom experiments. In Chapter 5 we further investigate this current pattern using more complicated models with realistic boundary geometries show ing that using a homogeneous spherical forward model is consistent in term s of quantification. Chapter 6 contains the details of animal experiments on piglet models. Both post mortem and in vivo experiments were conducted. We show that w e were able to detect blood volumes as low as 0.2 ml and that t he bleeding process can be quantified consistently using a homogeneous spherical forward model. PAGE 23 23 Table 1 1. Estimates of the conductivity (S/m) of body tissues below 100 Hz at body temperature (Gabriel et al. 1996) Tissue Conductivity Bladder 0.2 Bone Cancellous 0.07 Bone Marrow 0.05 Cartilage 0.18 Cerebro Spinal Fluid 2.0 Cornea 0.4 Fat 0.04 Gall Bladder Bile 1.4 Heart 0.1 Lens 0.25 Lung Deflated 0.2 Muscle 0.35 Pancreas 0.22 Small Intestine 0.5 Stomach 0.5 Testis 0.4 Tongue 0.3 Blood 0.7 Bone Cortical 0.02 Breast 0.06 Cerebellum 0.1 Colon 0.1 Dura 0.5 White matter 0.06 Grey matter 0.1 Kidney 0.1 Liver 0.07 Lung Inflated 0.08 Nerve 0.03 Skin Wet 0.1 Spleen 0 .1 Tendon 0.3 Vitreous Humour 1.5 Thyroid 0.5 PAGE 24 24 A B Figure 1 1. Intraventricular Hemorrhage (IVH). A) A sagittal view of head anatomy, showing the ventricles B) Pictures showing the four IVH grades Table 1 2. Grades of Intraventricular hem orrhage defined by Papile et al. (1978) with associated risks and ultrasound specificities Grade Description Consequences Detection I Isolated germinal matrix hemorrhage with no extension to the ventricles Unlikely to lead to morbidity and disability 75 % of cases detectable using ultrasound II Intraventricular hemorrhage with normal ventricular size; blood occupies up to 50% of the of the ventricular volume Unlikely to lead to morbidity and disability alone 50% of cases detectable using ultrasound III Intraventricular hemorrhage with ventricular dilatation; blood occupies more than 50% of the ventricular volume Increased risk of CP, PHH and PVL. Morbidity possible 75% 100% of cases detectable using ultrasound IV Intraventricular hemorrhage with par enchymal i nvolvement; ventricles often di lated. Increased risk of CP, PHH and PVL. High risk of morbidity 75% 100% of cases detectable using ultrasound PAGE 25 25 CHAPTER 2 EIT M ETHODS EIT Forward Problem Formulation of Forward Problem The world of electromagn etic fields is governed by Maxwells equations which relate the electric and magnetic fields to their sources, charge density and current density. To formulate the EIT forward problem, we firstly need to reduce the complexity by making the assumption that EIT is an electrostatic system. That means the effect generated from changing magnetic fields can be neglected. Therefore, the equation for Faradays law of induction becomes: 0 B E t (2 1) Lets assume that is a three dimensional domain with smooth surfaces. (,,) xyz is the conductivity distribution within the domain. Equation 21 implies that, for a electrostatic system, the electric field E can be w ritten as the gradient of the potential distribution (,,) xyz within domain (Equation 2 2). E (2 2) Amperes law relates the magnetic field to its electric current source (Equation 23), where H is the magnetic field intensity, fJ is the enclosed conduction current density and D is the electric displacement field. fHJD t (2 3) JE (2 4) PAGE 26 26 In an electrostatic sy stem, the term D t is 0. The current density is related to the electric field by Ohms law (Equation 2 4). By taking the divergence on both sides of Equation 23 then combining with Equation 2 2, we have: ()0 in domain (2 5) Equation 25 is exactly the Laplace equation, with Dirichlet boundary condition v or Neumann boundary condition () j where denotes the normal derivative to the surface. The forward problem in EIT reconstruction is to solve for with a given conductivity distribution Formulation of the Finite Element Solution The forward problem c an be solved analytically when the geometry of the domain is simple (such as a circular shape in 2D and a spherical or cylindrical shape in 3D) and the conductivity distribution is homogenous or at least simple enough (Pidcock et al. 1995a, Pidcock et al. 1995b, Holder 2004). When the geometry and conductivity structure become complicated, analytical solutions are generally not available. In most situations, numerical methods are needed to solve the forward problem, such as the Finite Element Method (FEM). Before formulating the FEM solution, we need to introduce two theorems that will be useful to understand the journey of formulation later on. The first concept is the functional. The functional is the function that minimizes the energy of a system. For the system Lf where L is an operator, the functional is written as Equation 2 6. If operator L is self adjoint and positive definite, the solution of the system is unique and occurs at the minimum of [] I PAGE 27 27 [] 2RRILdxdyfdxdy (2 6) Minimization of [] I can be achieved by applying the Rayleigh Ritz method. The RayleighRitz method is a systematic method to obtain a minimum. In this method the solution 0 is approximated as a sum of n linearly independent weighted basis functions (Equation 2 7). Then the problem is equivalent to finding the value for each ic to minimize the functional. 0 1 n nii ic (2 7) Therefore, the functional for the Poisson equation ( 2f ) can be written as Equation 28. The Laplace equation is a special case of the Poisson equation when f is zer o. 22 1(,...,)()()2ii n i i ii RIccc c cfdxdy xy (2 8) So now we have related the solution to the entire domain. The next step is to divide the domain into elements. Then the solution can be discretized to the solutions on the nodes of the elem ents 1(,...,)n For the 2D domain shown in Figure 21, lets assume that the domain has 4 boundaries, C1 to C4. Boundaries C1 and C2 have Dirichlet conditions and boundaries C3 and C4 have Cauchy conditions. If we apply the Laplace equat ion ()0 k to the domain, the functional can be written as: PAGE 28 28 12 342 2 12 22 1122[] 2()2() (2())(2())R CC CCIkkdxdyhsdshsds xy gsds gsds (2 9) By applying equation 28 to 29, we can prove that the functional of the entire domain is equivalent to the sum of the functionals of the si ngle elements (Equation 210), where E is the total number of elements and eI is the functional of a individual element. 1 1[](,...,)E e n eIII (2 10) Therefore, to minimize [] I we can use equation 211: 10 1,...,e E e iiII in (2 11) If we look at a single element, the derivative of the functional eI to each i can be written as: 22 22eeeee e e iii ii RCI k k dxdy hds xy (2 12) The sol ution within a single element e can be expressed using the element shape function and the solutions on the element nodes (Equation 213). e(,) N...p e eeee jj ps je sxyN NN (2 13) eN is the shape function of th e element. The shape function is an interpolation function which interpolates the internal solution within the element using the solutions PAGE 29 29 on the nodes. Substituting Equation 213 into 212 and reorganizing the equation, we have a final form for e iI (Equation 214): 2222e eeee ijj ijjii je je iI kkff (2 14) Such that: NN NNeee ee jj e ii ij Rkk dxdy xxyy (2 15) NNeeee ij ij Ck ds (2 16) Neee ii Rffdxdy (2 17) hNeee ii Cfds (2 18) To minimize the functional of each element, the term e iI needs to be 0. Therefore, we can write the final equation for a single element as: eeeeekkff (2 19) The matrix eekk is called the element stiffness matrix. We can assemble equation 219 for all the elements. Finally, we have the equation for the system: K = F (2 20) The EIT forward problem is governed by the Laplace equation. Therefore, the term ef in equation 219 is 0. The term F in equation 220 represents the applied current density on the boundary nodes. The matrix K is called the system stiffness matrix. K is a well conditioned matrix It is symmetric and positive definite. It is totally invertible if the PAGE 30 30 solution at one node is specified Therefore, the solution can be obtained by directly inverting the matrix K However, the dimension of K depends on the number of nodes in the mesh, which is generally a large number. This results in that the direct inversion of K is very memory consuming and time consuming. K is a sparse matrix in characteristic, because the element stiffness matrix is nonzero only if the row and column indices refer to the nodes that occupy the same of adjoining elements. We can take advantage of this feature by solving equation 220 usi ng the conjugate gradient method (Press et al. 1989). Conjugate Gradient Method The conjugate gradient method is a numerical algorithm to solve a particular system of equations, when the system matrix is symmetric and positive definite. The idea here is, t o solve equation 220, we construct a new function, whose first order derivative is KF Then solving equation 220 is equivalent to finding the point that minimizes the new function. The new function is constructed as: 1 ()KF 2 f (2 21) So the gradient of the function is expressed as ()KF f We can imagine that the solution 01(,...,)n is a point in the ndimensional space. Therefore, the minimization of () f is a multidimensional problem. The minimization process is going to be iterative. To minimize equation 221, lets start with the idea of line minimization. The idea is, given an arbitrary point P and an arbitrary direction of n, we can find a scalar that minimizes () fPn Then we replace P with Pn and find a minimum along a new PAGE 31 31 direction. Doing this iteratively, eventually, we are going to find the mi nimum of function f There are different ways to choose the directions, such as Powells method (Malmivuo and Plonsey 1995) which chooses an orthogonal direction to previous directions, and the Steepest Descent method (Malmivuo an d Plonsey 1995) which chooses the direction along the gradient of each step. However, both of them have been found to be inefficient in some special situations. The conjugate gradient algorithm (Malmivuo and Plonsey 1995) involves choosing conjugate direct ions. We say that the two vectors u and v are conjugate to each other when equation 222 holds. A is the hessian matrix of the system, which corresponds to the matrix K in equation 221. When this relation holds pairwise for a set of vectors, we call them a conjugate set. The benefit of using a conjugate set is, when you do line minimizations along such a set of directions, you dont need to redo any of t hese directions, which makes this algorithm very time efficient. 0 uAv (2 22) To formulate such a set of conjugate directions, we construct two sequences of vectors from the recurrence (Equation 223). We start with an arbitrary vec tor 0g and let 00hg Then: 1 11 0,1,2,...iiii iiiiggAh hghi (2 23) The scalar i can be calculated by equation 224. 1 iii i iiggg gg (2 24) PAGE 32 32 It is not so hard to prove th at 0ijgg and 0ijhAh So we can see that the g vectors are an orthogonal set and the h vectors are a conjugate set. The h vectors are th e directions we are going to use to minimize the function f. From equation 223 we found that the calculation of the next g vector requires the knowledge of A Here is another trick to update the vector ig. Suppose that we happened to have ()iigfP at some arbitrary point iP Then we move along the direction of ih and find the minimum at the point 1 iP We can prove that the 1 ig calculated from equation 223 is the same as 1()ifP This is actually what we do when implementing the algorithm on computers. Therefore, the algorithm is outlined as follows: Give an initial point P (for example, a zero vector). Let ()iighfP Let () fpfP Do a line minimization along the direction ih Update point P with the position where the minimum occurred. Let () fretfP If the difference between fp and fret is smaller than the tolerance, stop the iteration. Otherwise, let fpfret Calculate 1 ig using 1()igfP Calculate i using equation 224, then update ig with 1 ig Calculate 1 ih using equation 2 23, then update ih with 1 ih Iterate from the second step Another technical problem in this algorithm is how to perform line minimization along a given direction. The first task is to bracket the m inimum. In other words, we need to find a range that guarantees it contains a minimum. After that we are going to search for the minimum within this range. This can be done using Brents method, which PAGE 33 33 is a combination of the Golden Section Search method an d the Parabolic Interpolation method (Malmivuo and Plonsey 1995). For implementation of Golden Section Search method and Brents method, please refer to functions mnbrak() and brent() in Appendix A. EIT Inverse Problem Overview In the inverse problem, we aim to estimate the conductivity distribution from a known set of boundary voltage measurements. The inverse problem is a nonlinear problem in nature. A lot of work has been done in designing practical reconstruction algorithms f or 2D and 3D inverse conductivity problem s which can be categorized as follows ( Mueller and Siltanen 2003 ): N on iterative linearizationbased algorithms I terative algorithms solving the full nonlinear problem L ayer stripping algorithms (Somersalo et al. 1 991) D bar a lgorithm The linearization based algorithms are based on the assumption that the conductivity distribution is a small perturbation from a known conductivity so that the change of the potential on the boundary is linear Examples of linearizationbased algorithms include the Barber Brown backprojection method (Barber and Brown 1984) and onestep Newton methods (Cheney et al. 1990) etc. Clinical results produced using EIT so far have come from linear algorithms only (Bayford 2006). However, EIT is a non linear problem in nature. Algorithms solving the full nonlinear problem have been mostly iterative in nature. These iterative methods have been based on output least squares (Kallman and Berryman 1992), the equation PAGE 34 34 error formulation (Kohn and McK enney 1990), high contrast asymptotic theory ( Borcea et al. 1999 ), or statistical inversion (Kaipio et al. 2000 ). These algorithms tend to reconstruct more accurate absolute conductivity values. However, they may be too slow to converge a nd the reconstruc ted values will always have large oscillations. Therefore, an appropriate regularization is always necessary however, this may blur features and boundaries. These algorithms have actually produced successful results from numerical simulations and tank exp eriments. However, no success has yet been obtained from clinical subjects (Bayford 2006). There are two major reasons. The first reason is the electrode contact impedance is hard to accurately characterize, and tends to vary over time when making clinical measurments. The second reason is the subject shape can be deformed during measurement, and this may create artifacts in the reconstructed images. The layer stripping algorithm is a promising method because it is fast and addresses the full nonlinear pr oblem (Somersalo et al. 1991). The implementation of this algorithm involves first finding the impedance on the boundary by using voltage measurements that corresponds to the highest spatial frequency. The outermost layer is then mathematically stripped aw ay. This process is then repeated, layer by layer, until the full domain is solved. This algorithm would be particularly useful when the object has a layered structure. The D bar method (Siltanen et al. 2000) is a newly developed noniterative direct reconstruction algorithm It is based on the 2D global uniqueness proof of Nachman (Nachman 1996) It solves the full nonlinear problem, so it has the potential of reconstructing conductivity values with high accuracy. However, the D bar algorithm is a PAGE 35 35 2D rec onstruction algorithm in nature. Developing a D bar method for 3D still remains a challenge (Cornean et al. 2006) Formulation of Linearized Algorithm The one step linearization based algorithms a re time efficient and have proved effective in real time ima ging applications. To formulate the inverse problem as a linearized problem, we first consider the boundary voltage measurement V as a function of the conductivity distribution denoted as () V When there is a small perturbation on the original conductivity distribution 0 the boundary measurement changes from 0() V to 0() V We can expand 0() V as a Taylor series at 0 (2 25) 2 00 000() () ()()() ...... ...... 2! !nnVV VVV n (2 25 ) We can linearize the problem by neglecting the high order terms in equation (225). The linearized form of the problem is express ed by equation (226 ). 000()()() VVVV (2 26 ) Usually we solve the inverse problem using numerical approaches such as the finite element method. So we need to rewrite equation (226 ) into a discrete format. Then the problem becomes a set of li near equations (227 ). VS (2 27 ) Here we call S the sensitivity matrix. Reconstructing the conductivity change that created differential voltage change V as described by equati on (227) may be used to perform time difference imaging. Sensitivity M atrix PAGE 36 36 The dimension of the sensitivity matrix depends on the length of vector V which is the number of voltage measurements on the boundary, and the length of vector which is the number of tetrahedr ons in the finite element mesh. Each entry ijS of the matrix S can be calculated by equation (228 ) ( Murai and Kagawa 1985), where i and j are measurement index and element index respectively : 00()() ij j jS dv II (2 28 ) This equation indicates that the sensitivity of each element can be calculated by the negative integral of dot product of lead fields over the volume. This calculation involves the use of the sensitivity theorem or lead field theorem by Geselowitz (1971). 0() I and 0() I are lead fields generated by the current injection and voltage measurement electrode pairs at conductivity distribution 0 which we call input and output lead fields respectively. Details of lead field theory are explained in the next section. If the element is small enough, we can calculate the sensitivity at the center of the element instead of calculating the integral. Assuming that I and I are both 1A, we can rewrite equation (228) into a discrete form (2 29 ). 00()()ij j jjSv (2 29) where 0()j and 0()j are the voltage gradients at the center of element j, and jv is the volume of element j. Taking for example, the potentials on the four nodes of a tetrahedron ( ,,,ABCD ) (Figure 2 2 ) can be obtained from the forward solution process introduced in the first section in this chapter Therefore, the gradient at the PAGE 37 37 center O can be calculated by averaging the four gradient vectors between the four nodes and the center (2 30). The volume of a tetrahedron can be calculated by the determination in equation (2 31). ()()()() 1 [] 4AO BO CO DO OOA OB OC OD OAOAOBOBOCOCODOD (2 30 ) w here O is the potential at the center and can be approximated as 1 () 4ABCD ,,, OAOBOCOD are the vectors between the center and each of the four nodes. Since the coordinates of the each node are known, the coordinate s of the centroid and thus the four vectors can be determin ed as: 1 1 1 1 6 1AAA BBB CCC DDDxyz xyz v xyz xyz (2 31 ) Lead Field Theor y To understand the lead field theory, the first concept that needs to be explained is the lead vector. Suppose that there is a dipole source at point Q in a 3D volume conductor. The dipole moment of the source is p which can be decomposed into 3 components ,,xyzpipjpk (Figure 2 3). P is a point on the boundary. Therefore, the potential of the point P p can b e related to the dipole moment at point Q by equation 2 32. The vector c is called the lead vector. It is a threedimensional transfer coefficient which describes how a dipole source at a fixed point insi de a volume conductor influences the potential at a point within or on the surface of the volume conductor. Its value depends on the locations of PAGE 38 38 point Q and P and also the properties of the volume conductor. An example of the lead vector application is the famous Einthoven triangle used in the field of electrocardiography (ECG) (Malmivuo and Plonsey 1995) p xxyyzzcpcpcpcp (2 32) Assume that we have a fixed pair of electrodes on the conduct or surface defining a lead. If dipole sources are distributed over the volume, we can figure out the total lead voltage using the concept of superposition LkkVcp Later we can see that the dipole element kp can be mathematically replaced by impressed current source element iJdV where iJ is the current density and has the dimension of dipole moment per unit volume. The lead field has a very important property, whi ch can be derived from the reciprocity theorem of Helmholtz (Helmholtz 1853) This property tells us that, the lead field LEJ is exactly the same as the current flow field resulting from applying a unit reciprocal current rI to the lead. Figure 2 4 shows a lead field (the red arrows) within a homogeneous elliptical domain calculated using Comsol 3.4. The reciprocal theory will be explained later. Here is the form of the reciprocity theorem described by Helmholtz (Helmholtz 1853): A galvanometer is connected to the surface of the body. Now every single element of a biological electromotive surface produces such a current in the galvanometer circuit as would flow through that element itself if its electromotive force were impressed on the galvanometer wire. If one adds the effects of all the PAGE 39 39 electromotive surface elements, the effect of each of which are found in the manner described, he will have the value of the total current through the galvanometer. So Helmho ltz told us that it is possible to swap the dipole source and the detector without any change in the detected signal amplitudes. To make this clearer, we can look at the examples in Figure 2 5 In case 1, there is a differential element of double layer source, whose voltage is dV A galvanometer is connected on the surface. The galvanometer measured that the source generated a current LI in the circuit. In case 2, the voltage source is removed from the volume conductor. Then we replace the galvanometer with an electromotive force of magnitude dV This EMF will generate a reciprocal current ri through the same differential area as the voltage source in case 1 does. So the reciprocity theorem states that the current LI flowing through the galvanometer in case 1 is equal to the current ri through the differential area at the location of the removed double layer source element in case 2. The lead field theory can be derived from the reciprocity theorem. Let us reconsider the example in Figure 2 5, but express the sources and detectors in different ways (Figure 26). In case 1, we describe the source with a current dipole layer element i dJV d (2 33) where is the conductivity at the source point and d is the pole separation. Instead of measuring the current produced, we measure the voltage produced using a voltmeter. Therefore, we have: LLVRI (2 34) PAGE 40 40 where R is the resistance between the measurement points. In case 2, instead of applying an EMF, we apply a current source with value /rdIVR (2 35) T his should generate the same ri at that (removed) source location in the direction of iJ The ri can be expressed in terms of the lead field current density. Therefore we have: i rLL iJ isJsJ J (2 36) where s is the length of the double layer and LJ is the lead field current density. According to the reciprocity theorem, we can combine equation 233 through 236, we have: 1 2 i L L i i r case caseJ V sJ J R Jd IR (2 37) In equation 237, the left side describes case 1 and the right side describes case 2. Rearranging equation 2 37, we have: 11i LL rVJJsd I (2 38) Here we assume that the reciprocal current is a unit current 1rIA The term sd is exactly the volume element v If the source iJ is distributed over the entire volume, we can rewrite equation 238 in an integral for m: 1i LE LEVJJdv (2 39) PAGE 41 4 1 The term 1 can be put outside the integral if the medium is homogeneous. Equation 239 is the most important equation in the lead field theory. It relates the lead voltage to an arbitrary vol ume source. For a more detailed explanation about lead field theory, we can refer to chapter 11 of the book Bioelectromagnetism (Malmivuo and Plonsey 1995). Regularization of the Inverse Problem Illposed Nature of the Inverse Problem If we regard the li nearized EIT inverse problem ( equation 2 27) as a general linear algebra problem, we can solve the conductivity change by inverting the matrix S However, S is generally not a square matrix because the number of measurements is usually much less than the number of elements. Therefore, this is an under determined problem and S can not be directly inverted. W e can solve for usi ng the MoorePenrose generalized inverse ( equation 2 40 ): 1()TTSVSSSV (2 40 ) where 1()TTSSS is called the pseudoinverse or MoorePenrose generalized inverse of matrix S if TSS is invertible. Equa tion 2 40 is exactly known as the least squares solution which minimizes the residual norm ( argmin SV ). However, the 1()TSS may not exist either. Taking the 16 electrode adjacent ring current pattern for example, we always take 16(163)208 measurements on the boundary. However, only 104 of these measurements are independent in theory due to the fact of reciprocity (Malmivuo and Plonsey 1995). This means that all the rows in matrix S are not linearly independent, neither are the rows in TSS In addition to that, the EIT inverse problem is PAGE 42 42 generally very ill pose d A large variation of resistivity may only produce a small variation on the boundary measurements. It is also ill conditioned because a small oscillation on boundary measurements can cause a large oscillation for the solution of It has been reported that it was impossible to see object in a tank without any regularizati on (Eyuboglu 1996). Therefore, we need to regularize the problem to obtain a reasonable solution. The Tikhonov and Truncated singular value decomposition (TSVD) regularization methods are generally used to regularize the EIT inverse problem. Tikhonov R egul arization The least squares approach does not work when S is ill conditioned. The Tikhonov method is to find the that minimizes 22 2SVx T h e solution for this new problem is given by equation (24 1): 1()TTSSSIV (2 4 1) where I is the identity matrix, and is called the regularization parameter. The introduction of makes the matrix better conditioned and smoothes t he solution. However, the solution can be very sensitive to the choice of which makes choosing an optimal important in the problem of EIT. is a small number in general. Tru ncated Singular Value Decomposition (TSVD) Singular value decomposition (SVD) In linear algebra, singular value decomposition (SVD) is an important factorization of a rectangular matrix. It has been widely applied to the study of inverse problems (Bertero and Boccacci 1998). Suppose that A is a mn matrix, where mn A can be decomposed into the product of three matrices. The derivation is described below. PAGE 43 43 L et the transpose of matrix A be denoted by *A Then the matrix *AA is going to be a nn nonnegative definite Hermitian. Therefore *AA has a complete set of real eigenvalues 120 Correspondingly, there are n unit eigenvectors 1,,nvv orthogonal to each other. Putting the eigenvectors together, we have a nn matrix 12nVvvv Therefore, V is an unitary matrix and satisfies *1VV For convenience, we define ii and 1 iiiuAv for 0i Since i and iv are the eigenvalues and egenvectors of *AA we have: *2 iiiiiAAvvv (2 42) Therefore, it is not hard to obtain the following equation: *1* iiiiiAuAAvv (2 43) And *2 iiiiiAAuuu (2 44) So we can see that the vectors iu are the eigenvectors of the Hermitian matrix *AA In the beginning of this section, we assumed mn for the dimension of A Therefore, the rank of A will be less than or equal to m The eigenvalues 1 m through n and their corresponding eigenvectors, are actually zero. From the definition of iu we can easily get iiiAvu for im Let 12mVvvv by removing the null vect ors and 12mUuuu we have: AVU (2 45) PAGE 44 44 w here is the diagonal matrix of singular values i. By multiplying *V to the right on both sides of equation 245, we have the nearest thing to diagonalization for a rectangular matrix A : *AUV (2 46) Equation 246 is called the singular value decomposition (SVD) of matrix A Once we have the SVD, the MoorePenrose generalized inverse equation can be quickly calculated as equation 2 47: *AVU (2 47) where is simply calculated by replacing the nonzero i with 1 i Equation 2 47 holds regardless of the rank of A and gives the minimum normed least squares solution. Condition number and TSVD As mentioned earlier, the sensitivity matrix S in the EIT problem is very poorly conditioned. The presence of very small singular values will produce very large value s in Therefore, a small error in the measurements will generate l arge error s in the reconstructed im age. Condition number is a quantity that measures numerically how ill conditioned the matrix is. It is defined to be the ratio between the maximum and minimum singular value (Equation 2 48): max min() S (2 48) A high condition number indi cates a poorly conditioned matrix. The singular values for a sensitivity matrix used in this study were plotted in a log scale in Figure 27. The PAGE 45 45 condition number for this matrix was calculated to be 2.84e+14, which indicates that this EIT inverse problem is very ill conditioned. Therefore, to obtain a more reasonable image, we replace these small singular values by zeros in to reduce the uncertainties in the reconstruction. This procedure is called the TruncatedSVD (TSVD) (Xu 1998) Equivalently, the reconstructed image can be described by equation (249), where iu and iv are the singular vectors and id are the singular values (we use d here for singular values because is used to denote conductivity). The truncation level k can be determined by approache s such as the Lcurve criteria (Hansen 1990 ). 1 k i i i iuV v d (2 49) L curve To choose an optimal truncation level for TSVD ( or regularization parameter for Tikhonov regularization), an Lcurve criterion was suggested by Hansen ( 1992 ). In this method, the solution norm was plotted against the residual norm in a log log scale. It always appears in an L shape which is why it was called Lcurve. The corner of L corresponds to the optimal regularization point where we have both the minimum solution norm and resid ual norm (Hansen and O Leary 1993). Figure 28 A shows the L curve using the TSVD regularization. The boundary measurement was generated from an anomaly located at the center of a spherical model equipped with the EEG electrode configuration in simulation. We can see that the corner of the L curve was not sharp enough to choose a unique truncation number. However, it indicated that a truncation number within the range 54 72 would give useful PAGE 46 46 solutions Figure 28 B shows a similar Lcurve for the Tikhonov method. The regularization parameter should be chosen between 7.2388e9 and 2.0506e7. Weighted minimum norm method The sensitivity within a domain is always greater near the surface electrodes and weaker in the interior (Oh 200 9). Therefore, a deeper perturbation may be blurred or not detected in reconstructions. Clay and Ferree (2002) suggested a correction scheme which has been shown effective in the application of acute cerebral stroke. This one step algorithm was motivated b y the FOCal Underdetermined System Solver (FOCUSS) algorithm (Gorodnitsky and Rao 1997). It suggested that equation 227 can always be written as equation 250: 1()() VSWW (2 50) where W is a nonsingular matrix and has a well behaved inverse 1W To choose such a matrix, we can simply use a diagonal matrix: ()kWdiagw (2 51) In the EIT problem, we can choose kw as the norm of each column vector in S (equation 252) to normalize the total sensitivity and thus make the matrix SW less ill conditioned than S The inverse solution is written as equation 253, where () SW is the MoorePenrose pseudoinverse of SW 1 2 2 1 M kkwS (2 52) () WSWV (2 53) An example of weighted images is shown in Figure 29. A circular domain with unit radius and homogen ous conductivity distribution was equipped with an adjacent 16 PAGE 47 47 electrode ring current pattern. An anomaly was moved along a radial direction from 0.2 x to 0.7 x The reconstructed images were mapped onto 20x20 gri ds. We observed that without any weighting, the reconstructed image was more and more blurred when moving the anomaly toward the center. When the weighted algorithm was applied, the image qualities for the 6 anomaly positions tended to become even. When th e anomaly was moved toward to the boundary, more artifacts appeared in the image compared to the unweighted images. Quantitative M easures of EIT R econstruction In EIT, we can estimate the volume of the anomaly using the reconstructed image. In a real istic situation, the only information we may have is the boundary voltage measurements. Therefore we want to find a function F s uch that the volume of the anomaly can be related to the differen tial voltage measurements as () volumeFV Of course we would like this equation to hold for an anomaly of any size and at any position within the domain. However, EIT is a nonlinear and shift variant problem in general. So finding an ideal function F is n ot likely to be possible. But we can define a Quantity Index (QI) using the following approximation procedure. In the discrete format, the function F is a row vector, so that the volume is related to the voltage measurements as equation (2 54 ): volumeFV (2 54 ) where V is a column vector of boundary voltage measurements. We assume that the perturbation happens within only one single element. And we want equation (2 54 ) to hold for any s ingle element. Therefore, we are trying to find a form of F s uch that equation (255 ) holds. PAGE 48 48 11[......][......]nnvolumevolumeFVV (2 55 ) where n is the total number of elements. T he volumes can be calculated with equation (2 31 ) We kn o w f rom earlier section s that when such a small perturbation happens, the boundary measurements can be approximated by equation (227 ). Therefore, iV can be approximated by the thi column of matrix S and the rig ht side of equation (255) can be replaced by FS So F can be calculated by equation (256 ). And we can define the QI with equation (257 ): 1[......]nFvolumevolumeS (2 56 ) 1 1[......]n n ii iQIFVvolumevolumeSVvolume (2 57 ) Sensitivity and Selectivity Selectivity ( Kauppinen et al. 2005 ) denotes the contribution of a region of interest to the total measured transimpedance. The reference transimpedance for a particular four electrode configuration may be obtained from se nsitivity matrix entries by summing all entries over all pixel locations. The contribution to the thi measurement from a particular region of interest R may be extracted by summing sensitivity matrix entrie s over this volume, as expressed by the equation below: () () 11()() ()()RV ij ijj jR jR iR jTE jTE ij ijj jjdv ZS II Sel ZZ dv II (2 58 ) where denotes the entire measurement volume and R is the region of interest. PAGE 49 49 Sensitivity values were calcul ated with equation (228). To compare sensitivities for different current patterns, we express the sensitivity values as the mean sensitivity over the region of interest as a fraction of the maximum sensitivity over the entire domain, for each measurement configuration in the scheme. The sensitivity of the models reflects the interaction between current and measurement pair geometries in the model, whereas the selectivity shows the contribution from the target region to measured voltages and transimpedance s. EIT Hardware Many EIT hardware systems have been developed for different applications over the last three decades to obtain data for reconstructing EIT images. For example, the first Sheffield MK1 system was developed in the 1980s (Brown and Seagar 198 7). This was a 16 electrode EIT system with a single current source. It measured data at a single frequency of 50 kHz. The Sheffield system has been further developed to versions Mk2 (Smith et al. 1990) and Mk3.5 (Wilson et al. 2001). The latest system (M k 3.5) uses 8 electrodes and collects data using a neighboring method. This multi frequency system can operate at 30 different frequencies between 2kHz and 1.6 MHz at 25 frames per second. There are also other multi frequency EIT systems designed for diffe rent purposes in the EIT literature. For example, the UCLH Mk1b (Yerworth et al. 2002) and UCLH Mk2 (Yerworth et al. 2003) systems were developed primarily for brain imaging. The Rensselars Adaptive Current Tomographs (ACT4) system (Ross 2003, Liu et al. 2005) was mainly used to image pulmonary function. The Dartmouth group developed their own EIT system for breast imaging (Halter et al. 2004). The OXBACT system (Zhu et al. 1994, Yue and McLeod 2008) developed by the Oxford Brookes group utilized the field programmable gate array (FPGA) technique for signal PAGE 50 50 generation. It was designed particularly for thoracic imaging of patients with respiratory distress and chronic heart failure (CHF) in intensive care hospital environments. In recent years, the EIT group in Kyung Hee University, Korea have developed the KHU Mark1 (Oh et al. 2007a, 2007b, 2008) and KHU Mark2 (Hun and Woo 2009) systems for research and commercial purposes. The EPack1 EIT system (Figure 210 A) was designed and developed by Dr. Rosalind Sad leir in the 1990s. It had similar architecture with the classic Sheffield Mark1 EIT system. The EPack system was developed for the application of intraperitoneal bleeding detection. The system has been updated to the second generation (EPack2, Figure 21 0 B) with higher data acquisition rate and more advanced features such as Bluetooth transmission. We define the amount of time to capture a complete set of boundary voltage measurements as the aperture time. Figure 211 shows a comparison of aperture time between EPack1 and 2. The EPack2 system has been used in clinical studies on peritoneal dialysis patients (Sadleir et al. 2008). The third generation (EPack3) is currently under construction. It uses newer technologies than EPack 1 and 2, and will be much smaller in size (probably 50% smaller than EPack1). To understand how an EIT system works, we describe the details of the EPack1 system below. The overall system design is illustrated in Figure 212. The unique flexible electrode belt was designed with 8 electrodes. In practical use we will connect the flexible ele c trode belt to the anterior abdomen of the patient to avoid the need to lift a patient with suspected spinal injury. Commands sent by the handheld computer control the E pack module which coordinates data colle c tion, preprocesses data, and sends PAGE 51 51 this data back to the handheld computer. Images are then reconstructed and displayed on the PDA. Radio c o m munication between the PDA and E pack is provided for, but is not implemented in the EPack1 system It will be incorporated into the system in future versions. The schematic of the E pack module is illustrated in Figure 213 The E pack module is composed of a data acquisition board and a constant current source. It is powered by two 12V batteries. Figu re 2 14 demonstrates the structure of the E pack module. The prototype (with large (DIP) chip packages) fit s in a box 9 inch x 8 inch x 2 inch in size If an entirely surface mount design is used, the board footprint will be approximately 2 x 2 inches. At present, communication between the E pack and han d held computer is accomplished by a cable connecting the two serial comm ports. When the E pack receives commands from the handheld computer, the command is pro c essed by the digital signal processor (DSP) ac cording to its cus tom designed protocol. We chose an Analog Devices ADSP 2181 as our digital signal processor. This is a 16bit fixed point single chip microcomputer optimized for high speed n u meric processing applic ations The current supply for the EIT measurements was real ized using a direct digital synthesizer (DDS) waveform and a constant current source. The DSP configures the DDS, which generates a stable sinusoidal voltage signal with a pr e cise frequency and phase locked to the DSP clock. This sinus oidal signal served as the input of the Howlandtype current source, which generates a 1mA sinusoidal current input with a fr e quency of 62.5 KHz. PAGE 52 52 Drive and receive electrode pairs are selected by current multiplexer s and voltage multiplexer s We have chosen to use 4 DG408DJ multiplexers, two of which are for the drive pairs, while the other two are for the r e ceive pairs. The DG408DJ multiplexer is an improved CMOS analog multiplexer with 8 channels Any channel could be s e lected with the control of the DSP, and only one at a time. So we used two multiplexers parallel to each other to select any of the pairs among the 8 electrodes. Voltage signals from the receive pairs were amplified through a differential a m plifier. We have chosen to use a PGA202KP which is a digitally controlled programmablegain instrumentation amplifier. The amplified signals were then converted into digi tal signals by an AD converter (ADC). We have chosen an AD9240 as our ADC. It is a 10MSPS, single supply analog to digital converter. Th e sinusoidal voltage difference signals are thus converted to a 14bit digital s e quence After being processed by the DSP, the data represen t ing the magnitude of the voltage signals is sent back to the handheld computer. In our sy s tem, to ensure accurate m easurements, current is also measured. The current is converted into voltage signals by a precision 0.1 resistor placed in the signal circuit, and its mag nitude is estimated using the procedure described above. Windows CE is the platform for our Dell Axim X50 Handheld PC. Our software was developed in Microsoft Embedded Visual C++ 4.0 which is a completely separate, standalone version of Visual Studio tools designed solely for the Windows CE development. The functions of our software include configuring the serial communication port, choosing the DDS frequency, sending and receiving data from the Epack, ch ecking the battery voltage, electrode contact quali ties selecting drive and PAGE 53 53 receive pair s and finally, reconstructing and displaying the image from the measured data. Figure 215 shows a screensh ot of the E pack software and the reconstructed image of metal bar in a saline filled phantom Communication between the handheld computer and E pack was based on protocols we defined ourselves. There were two protocols for the measurements defined in the software. One wa s called the single measurement protocol. The other wa s called the complete measurement protocol. With the former protocol, we can select any drive pair and receive pair. Then the single measurement result ing from the selected receive pair will be returned to the handheld computer and displayed in a dialog box. The socalled complete measurement protocol initiates at onetime collection for all the data we need to reconstruct the image. It was designed for the Barber Brown reconstruction algorithm (Santosa and Vogelius 1990) we used in our softw are, and therefore used adjacent current patterns and voltage measurements, however in principle there is no restriction on the measurement pattern used. We initially chose to use the Barber Brown algorithm because of its advantage for real time imaging. C ompared with several other algorithms (Yorkey et al. 1987), this ingenious onestep algorithm appeared quite exceptional in achieving a moderate accuracy at an extremely low cost. A sensitivity based reconstruction algorithm has been implemented in later v ersions of EPack. PAGE 54 54 Figure 2 1. A domain with 4 boundaries divided into elements. Figure 2 2 A tetrahedral element PAGE 55 55 Figure 23. Demonstration of a dipole source within a volume conductor. Figure 24. The lead field distribution within a 2D elliptic al domain. PAGE 56 56 Figure 25. Illustration of the reciprocity theorem of Helmholtz Figure 26. Derivat ion of the equation for lead field theory. PAGE 57 57 Figure 27. Singular values of the sensitivity matrix for the homogeneous spherical model with EEG current pattern. A B Figure 28. Lcurve examples using different regularization algorithm. A) TSVD regular ization B) Tikhonov regularization PAGE 58 58 Figure 29. A comparison between unweighted and weighted 2D reconstructions. A B Figure 210. The first and second generation of Epack EIT systems. A) EPack 1 system. B) EPack 2 system PAGE 59 59 Figure 211. Comparison of aperture times in EPack1 and EPack2. Handheld Computer (Windows CE) E pack E pack module Flexible Connector Radio Communication Flexible Electrode Belt Figure 212. Overall system design of the EPack1 system PAGE 60 60 Figure 213. Schematic of the EPack module. PAGE 61 61 Figure 214. The EPack module, showing battery pack (top right), main acquisition board ( center) and electrode connections (center) PAGE 62 62 Figure 215. EPack software screenshot (left). Amplified reconstructed image (top right). Phantom experiment using a full array electrode configuration (bottom right). PAGE 63 63 CHAPTER 3 PIG LET SKULL IMPEDANCE MEASUREMENT Background and Significance Measuring dielectric properties of human tissues has been of research interest since the 19th century (Epstein and Foster 1983) Knowledge of electrical properties of human tissues is important for researchers to model different parts of human body mathematically and investigate electrical related phenomenon. For example, it is well known that the EEG source localization problem (EEG inverse problem) is highly dependent on the knowledge of electric al resistivities of the tissues in the head (Pohlmeier et al. 1997, Awada et al. 1998). It is also well established in EIT inverse problems that incorrect skull conductivity information will bring in localization errors when reconstructing conductivity changes within the head (Ni et al. 2006, Tidswell et al. 2001c). The conductivity of the adult human skull was reported to be 0.015 S/m by Oostendorp et al. (2000). To date, little data has been reported on the conductivity for neonatal skulls. A neonatal sk ull differs from an adult skull in significant ways. The neonatal skull is much thinner than the adult skull. In addition to that, it has an open fontanel on top, which will finally fuse up as the skull develops. Sadleir and Argibay (2006) reported that th e conductivity of a neonatal piglet skull was 0.06 S/m, which was about 4 times more conductive than the adult human skull. In this study, we measured the radial conductivity of piglet skulls at different frequencies using an Electrical Impedance Spectrosc opy technique. We aim to find a relationship between skull conductivity, skull thickness and piglet age. PAGE 64 64 Method Sample P reparation Skull bone samples were extracted from nine piglet skulls. Conductivity measurements were performed on seven of the piglet sk ull samples as soon as possible after piglets were euthanized. For the other two piglet samples, the measurements were performed after the skull samples were frozen. The intact skull was removed using a bone saw. The skull bones were when separated along s uture lines into right and left parietal and frontal bones (Figure 3 1). Measurement A pparatus The impedance data was collected using a Bio impedance Spectroscope (BIS) device developed by the EIT group at KyungHee University, Korea. Using this device, i mpedance can be measured within a frequency spectrum ranging from 10 Hz to 500 kHz. To measure the radial conductivity of the skull, we constructed a measurement cell similar to the one used by Oostendorp et al. (2000). The cell (Figure 32) was designed f or a four terminal measurement strategy. It consisted of two cylindrical containers. Each container had one end sealed and the other end open. A rubber O ring was attached at both open ends. When measuring skull conductivities, we filled the two cylinders with saline, and put the skull sample between the two rubber rings. We then sealed the two parts together tightly with 4 screws on the corners. Current was applied through the two sealed end, and voltage was measured on the two voltage electrodes in betwee n. There was another electrode between the two voltage electrodes, used for grounding the BIS current source. The diameters of the O rings were 10.16 mm (0.4 PAGE 65 65 inches). The distance between the two current electrodes was about 6.5 cm. The distance between th e two voltage electrodes was about 4 cm. All the conductivity measurements reported in this thesis were carried out at the frequency of 1 kHz, since this frequency was best calibrated. A total of ten data sets were collected and then averaged for each skul l sample. All the measurements were taken at an ambient room temperature of 22C Theory Skull resistivity values were calculated using equation 31. Conductivity is calculated by taking the reciprocal of the resistivity (equation 32). A R l (3 1) 1 (3 2) In equation 31, A is the crosssectional area of the O ring, which can be calculated from its diameter. l is the thickness of th e skull sample. Generally, the skull samples were not uniform in thickness. Therefore, for each sample we measured the thickness at three points on the edge using a caliper, and then took the average value. R is the impedance of t he skull sample. This impedance can not be measured directly. We first determine the impedance of saline ( salineR ) by filling up the cell without tissue between the O rings. We then measured the impedance with the skull in place. The va lue measured here was the serial impedance for the saline and the skull sample ( salineskullR ). Therefore, the skull impedance R can be calculated as salineskullsalineRR PAGE 66 66 Result Table 3 1 lists the thicknesse s and radial conductivities calculated for skulls samples from 5 fresh piglet heads. All the piglets were no more than 3 days old. The measurements were all performed within 5 hours after the animals were killed. Measurements were also taken on skull sampl es obtained from a frozen piglet head. The thickness and conductivity values for these samples are shown in Table 3 2. The mean value of the radial conductivities was found to be about 27.8 mS/m with a standard de viation of 11.8 m S/m. A plot of the measured values of radial conductivity as a function of skull thickness is shown in Figure 33. The results obtained with both the fresh samples and the frozen samples are shown with error bars. We calculated relative errors as in equation 33, where A, l and R denote relative errors in the measurements of area, thickness and impedance. A was calculated to be around 12%, and R was alway s around 5%. Because the thickness was a small number, the error was mostly introduced by l which can be as high as 30%. The solid line represents the best fit to the data taken with fresh samples using a linear regression approac h. The equation of the best fit is also indicated near the line in the figure. The slope of the line is about 21.58 mS/m2. The value of the linear regression (R2) was 0.467. ()AlR (3 3) Discussion We report radial conductivity value s in piglet skulls much higher than those reported by Oostendorp et al. (2000) and Akhtari et al. (2002) in fresh or live adult skull. The average value of radial conductivity obtained in the present study is 27.8 mS/m. Using an apparatus similar to the on e used in this study (Figure 3 2), Oostendorp et al. PAGE 67 67 (2000) reported the conductivity of fresh and live adult skull to be 15 3 mS/m. Akhtari et al. (2002) have found the value of radial conductivity to be 9.53 0.29 mS/m in live skull. Our value is 40% and 60% higher than those obtained by Oostendorp et al. (2000) and Akhtari et al. (2002) respectively. Thus our study shows that the conductivity of neonatal skull is higher than adult skull. We also report a linear increase in the conductivity with the inc rease in thickness of the neonatal skull. The reason for this is suspected to be the cancellous bone in a thicker skull. No previous study exists that explores the relationship between the conductivity and the thickness of the neonatal skull. All the measurements in this study were performed on post mortem piglet tissue. Goncalves et al. (2003) pointed out several problems in using animal tissue samples. Firstly, it is known that death of the tissue induces changes in its electrical properties. On the other hand, the resistivity of the tissues depends on factors such as the water content, which might generate a change resistivity during the measurement. Physiological processes may also induce changes in the electrical properties of tissues. Therefore, more r esearch needs to be done to estimate the true in vivo electrical resistivity of neonatal skull. The calculation of skull resistivity also needs discussion. We used the O ring area for calculations using equation 31. The surface areas of the skull samples were all larger than the O ring area. When doing the measurements, current would flow beyond the O ring region and therefore make the equivalent cross sectional area larger. This effect may be neglected when the surface area is much larger than the thickn ess. A 3D PAGE 68 68 modeling study can be conducted to evaluate how much the result will be affected by the equivalent area. Conclusion Measurements on neonatal piglet skulls show that the mean value of radial conductivity is around 2 7.8 mS/m at a temperature of 22C and a frequency of 1 kHz. This value is about 40% to 60% higher than that reported for adult skull. Moreover, our measurements show for the first time that the conductivity increases as a function of the skull thickness. PAGE 69 69 Figure 3 1. Skull sample preparation, showing the left frontal, left parietal, right frontal and right parietal bone samples. Figure 32. The measurement cell used to measure skull impedance. PAGE 70 70 Table 3 1. Measurement results for the fresh skull samples. Age (days) Part Thickness (mm) Conductivity (mS/m) Piglet I 2 Left Frontal 0.762 10.807 Left Parietal 0.720 6.898 Right Frontal 0.974 15.015 Right Parietal 0.593 5.940 Piglet II 3 Left Frontal 1.058 27.516 Left Parietal 0.931 18.033 Right Frontal 1.016 31.223 Right Parietal 1.185 22.019 Piglet III 2 Left Frontal 1.778 22.112 Left Parietal 1.270 19.241 Right Frontal 1.693 33.784 Right Parietal 1.101 14.889 Piglet IV 2 Left Frontal 1.609 43.957 Left Parietal 1.524 31.194 Right Frontal 1.609 41.935 Right Parietal 1.693 39.375 Piglet V 2 Left Frontal 1.609 43.956 Left Parietal 1.524 31.194 Right Frontal 1.609 41.935 Right Parietal 1.693 39.375 Piglet VI 1 Left Frontal 1.600 25.13 1 Left Parietal 1.350 21.910 Right Frontal 1.743 32.837 Right Parietal 1.133 14.511 Piglet VII 1 Left Frontal 1.433 39.432 Left Parietal 0.883 38.571 Right Frontal 1.300 41.954 Right Parietal 0.683 22.589 PAGE 71 71 Table 3 2. Measurement results for the frozen skull samples. Part Thickness (mm) Conductivity (mS/m) Right Frontal 1.524 15.934 Right Parietal 1.600 14.898 Right Frontal 1.168 47.194 Right Parietal 1.016 31.170 Figure 33. Skull conductivities plotted as a function o f their thickness. The result included 28 fresh samples and 4 frozen samples. The solid line represents the best fit to the data taken with fresh samples. The equation for the linear fit is indicated near the curve. PAGE 72 72 CHAPTER 4 A ROBUST CURRENT PAT TERN FO R THE DETECTION OF I VH Background Different electrode configurations and measurement strategies may be more effective for different EIT applications. The classic RING electrode configuration has been widely adopted in the EIT literature. The measurement st rategies employed using the RING electrode layout can be classified into the following categories: the neighboring method (Brown and Segar 1987), the cross method (Hua et al. 1987), the opposite method (Hua et al. 1987, Bayford et al. 1996) and the adaptiv e method (Gisser et al. 1987, Zhu et al. 1993). There have also been studies and algorithms on optimizing current patterns (Gisser et al. 1987, Koksal and Eyuboglu 1995, Lionheart et al. 2001). However, an optimum injection pattern may not always be the correct choice, because minimizing the error on each channel would increase the hardware complexity (Bayford 2006). Other electrode configurations include using planar electrode arrays for the detection of breast cancer (Kao et al. 2006), using a 2plane electrode configuration for lung imaging (Graham and Adler 2007), and using a hemi array electrode configuration for the detection of intraperitoneal bleeding (Sadleir et al. 2008a, 2008b, 2008c). In this study, we performed simulations and phantom experim ents, aiming to find an effective current pattern for the detection of intraventricular bleeding in premature neonates. Method Candidate Current Patterns We investigated three 16electrode layout strategies and current patterns. The first one was a RING l ayout ( Figure 4 1 A ), where the 16 electrodes were placed equally PAGE 73 73 spaced in a single plane about the equator of the sphere. An adjacent current pattern was applied to this layout that is, current was applied to a pair of adjacent electrodes and resultin g voltages across other pairs of adjacent electrodes were measured The second one was a standard EEG layout, following the 1020 system of electrode placement ( Figure 4 1 B ). Locations of EEG electrodes in spherical coordinates are shown in table 4 1. The current pattern applied to the EEG layout was denoted EEG pattern, and in this strategy currents applied were returned via an electrode on the apex of the head, and voltages between adjacent electrodes (in terms of electrode numbering) were measured. Th e EEG pattern therefore involved 15 current positions and a total of 182 voltage measurements. The basis for formulating the EEG current pattern was the geometry of the infant human skull. Neonates have a fontanel located at the top of the skull. We expe ct that when currents flow via an electrode situated over the fontanel, there should be greater sensitivities to centrally located conductivity changes compared to cases where the skull forms a complete barrier. Therefore, we chose to test if the EEG curre nt pattern may be useful to locate bleeding in neonates. The third electrode layout we investigated was a Cz RING layout where one electrode was located at Cz, and the other 15 electrodes were placed equidistantly about the equator of the sphere ( Figure 4 1 C ). The current pattern applied in the Cz RING case involved all currents returning via the top electrode, and with all possible adjacent measurements made on the 15electrode ring. The Cz RING pattern is thus a modification of the RING pattern The el ectrode at Cz should lead to increased sensitivities above the equator plane. At the same time this pattern preserves the symmetry of the RING pattern. A PAGE 74 74 symmetric distribution may have an advantage in making post compensation of quantification and localiz ation errors easier. To formulate sensitivity matrices, we constructed spherical head models (Figure 42) with a unit radius and homogeneous conductivity distributions for each 16electrode layout using finite element modeling (Comsol, Burlington MA, USA) After creating tetrahedral meshes, we solved these forward models for each current pattern and calculated the sensitivity value corresponding to each mesh element. We constructed 26 126, 21 896 and 51 524 tetrahedral element models for the forward models with RING EEG, and Cz RING electrode configurations respectively. Sensitivity Studies for the Candidate Current Patterns Inspection of anatomical MRI scans of the neonatal head indicate that the ventricles are centrally located and if translated to a sph erical geometry would lie in the upper hemisphere at an elevation of around 0.30.5 of the sphere radius into the upper hemisphere, as shown in Figure 4 3. Therefore we chose to study the sensitivities and contributions total measured resistances in both r egions on the central axis and in regions having the same approximate size and location of the neonatal ventricles. The sensitivity of a particular measurement is defined by equation 228. Thus, the contribution of a particular region j to the th i impedance can be calculated by including the conductivity of the region (equation 41). ()()jjj ij j j VZ dv II (4 1) The two central regions were spheres with relative radii of 0.25 compared to the backgrou nd sphere radius and were centered at z = 0.33 and z = 0.50. We refer to the sphere at z = 0.50 as the upper sphere and the other as the lower sphere. The two PAGE 75 75 lateral ventricles, approximated as ellipses, were located in relative radial terms at ( 0.2, 0, 0.3) and (0.2, 0, 0.3) each having semiaxis lengths of 0.15, 0.44 and 0.15 in x, y and z axes, respectively. The four regions are illustrated in Figure 43. The spherical regions (about twice as large as the ventricles) were chosen to compare with the late ral ventricle region properties and to determine the uniformity of each pattern. A useful current pattern should produce both a large sensitivity and selectivity in the region of interest, and produce a consistent response in the neighborhood of the region of interest. To evaluate the three candidate current patterns, we compared the sensitivities, selectivities and maximum and half sensitivity volumes of the current patterns within both central and lateral ventricular regions. Sensitivity values were expr essed as the mean sensitivity over the region of interest as a fraction of the maximum sensitivity over the entire domain, for each measurement configuration in the scheme. The selectivity (Kauppinen et al. 2005, Yang and Patterson 2008) is the fraction of the total measured resistence contributed by the central region, and the half and negative sensitivity volumes measured over the sphere. The half sensitivity volume is defined as being the volume of the sphere that has more than half the maximum sensitivi ty for a particular pattern. The negative sensitivity volume is the volume of a particular measurement pattern occupied with negative sensitivity, i.e. the volume of elements that produce contributions to the total measured resistance in an opposite direct ion from that expected. In most four electrode measurement schemes there will be significant negative sensitivity regions (Kauppinen et al. 2005, Yang and Patterson 2008). In principle, negative sensitivity is not bad. If an appropriate model is used, it s hould be PAGE 76 76 possible to relate any observed change to the correct sign of conductivity change. However, negative and positive sensitivities will sum to form the total measured resistance, and it is possible that for some current patterns location of negative sensitivities may be a problem and produce contradictory information. This could occur if, for example, there is a mismatch between model and experimental conditions. The half sensitivity volume gives an indication of the breadth of the positive sensitivit y distribution. Data Generation We gathered simulated bleeding data using finite element models and salinefilled phantoms. Finite element models To obtain more realistic boundary measurements and evaluate the effects of other head structures on reconstruc tions, we constructed two finite element models to mimic electrically important structures in the infant skull. In order to compare the various current patterns fairly, we tested each pattern ( RING EEG and Cz RING ) using data gathered using the same bleed ing layout structure ( Figure 4 4 ). This structure (the A model) included a central region of CSF, having a relative radius of 0.5, and an outer shell of grey & white matter. We simulated a small amount of bleeding inside this model by placing a small spher e of blood with a relative radius of 0. 05 at 37 different locations within a central bolus of CSF. The volume of the CSF region in model A is much larger than the realistic ventricle size. However, using a large CSF background produces a smaller relative change in the overall measured transimpedances than with realistically sized ventricles. This model was adopted as a first step because we were interested to see the overall performance of each current pattern under this more stringent condition. PAGE 77 77 Comparis ons between different current patterns were made in reconstructed images in terms of anomaly localization, reconstruction quality and quantification stability. W e also made a more complicated model used with the EEG current pattern and RING current patter n only. In this model (the B model), we changed the CSF geometry from spherical in to two small elliptical spheroids, to simulate the two lateral ventricles The simulated ventricles were placed in the upper hemisphere. The size and position of the ventricl es were chosen from representative neonatal head MRI data (Figure 4 6 ) (Schierlitz et al. 2001) We determined that t he total lateral ventricle volume wa s about 1/ 7 0 of the head volume The minor and major axis of each ellipse was chosen to be 0.3 and 0.88 of the sphere radius respectively. A blood like anomaly with a relative radius of 0.1 was moved to 6 different locations within the ventricle regions ( Figure 4 5 ). I n addition to the CSF geometry change, we also introduced a skull shell with a fontanel on top, another thin layer of CSF between the brain and skull, and a scalp layer outside the skull. The conductivity of each structure was assigned according to values from the literature. T h e values used were: blood (0.67 S/m) (Geddes and Baker 1967), CSF ( 1.3 S/m) (Oostendorp et al. 2000) brain (0.17 S/m) (Stoy et al. 1982 ), and scalp (0.43 S/m) (Burger and van Milaan 1943). The conductivity of the neonatal skull was assigned to 0.06 S/m (4 times of that of the adult skull ) according to preliminary data obtained using piglet s kull (Sadleir and Argibay 2006) Phantom models Phantom experiments were conducted to allow testing of how each current pattern, electrode layout and reconstruction performed in the presence of realistic noise. Our spherical phantoms us ed only the RING and EEG layouts respectively ( Figure 4 7 ). PAGE 78 78 The spherical polycarbonate containers were obtained from a manufacture of lighting fixtures (Formed Plastics, NY, USA). Each phantom was equipped with 16 stainless steel electrodes (dia. 14 mm) a ccording to their electrode configuration. Both phantoms had inner diameters of 19.7 cm. We used 0.6% saline solution (the conductivity of which was approximately 1.3 S/m, the conductivity of CSF (Oostendorp et al. 2000)) as the phantom background and gel anomalies made using TX151 powder (Walker et al. 2004). TX151 is a solidifying medium that produces a stable gel like material when mixed with water, agar and saline. By carefully adjusting the percentage of each ingredient (Deionized water 80.8%, Sucrose 13.8%, Agar 2.5%, TX151 2.5% and Sodium chloride 1.3%), we made the anomaly conductivities approximately 0.67 S/m (the conductivity of blood). Further details of anomaly construction may be found in Sadleir et al. 2009. Anomalies had diameters of 2cm (a relative radius of 0.1). The size ratio between the phantom and the anomaly was therefore approximately the same as those used in simulations on model B. A single anomaly was placed accurately at the same 6 positions used in model B (Figure 4 5 ), using the 3D Positioner (Velmex Inc., NY, USA) Data was collected with a 16electrode EIT system provided by Impedance Imaging Research Center at Kyung Hee University, Korea. This is a multifrequency EIT system with a frequency range from 10 Hz to 500 kHz (Oh et a l. 2007). We chose to use a single frequency of 10 kHz and a constant current output of 1 mA. This frequency was chosen because the impedance properties of both TX 151 and saline are flat over the interval 10 Hz 50 kHz (Sadleir et al. 2009) and 10 kHz w as well calibrated in the center of this range. The reference electrode for the system was a copper wire placed at PAGE 79 79 the center of the phantom neck. Ten data sets were collected before anomalies were introduced. These were averaged and used as the referenc e data set. For each anomaly position, five data sets were collected and averaged as the perturbation data for that anomaly position. The overall experiment system is shown in Figure 4 8 Reconstruction Method All the time difference images in this study were reconstructed from the boundary measurements using a onestep sensitivity based method (equation 42), which has been discussed in detail in chapter 2. SV (4 2) In EIT, the sensitivity matrix is always severely ill condition ed and will therefore have large condition numbers. Each of the three sensitivity matrices used in this study had a full rank of 104 but involved a measurement strategy that involved making a larger number of observations, as shown in table 42. Typical co ndition numbers were of the order of 1910 for the RING strategy, 1410 for the EEG strategy and 1210 for the Cz RING strategy. The inversions of the sensitivity matrices were regularized using the TSVD method. The truncation point, k will be less than or equal to the rank of the matrix, but in general will be less depending on the noise level in the voltage measurements. We chose k values for our reconstructions by inspecting images generated using a range of truncation points and determining the maximum value that produced a coherent reconstructed image. The truncation values needed to be chose carefully since inappropriate truncation val ues would produce inaccurate solutions. The optimal truncation numbers for the problems in this study are between 50 and 70, and were evaluated with the l curved method. The bottom row of table 42 lists the PAGE 80 80 truncation points we chose for each case using t his heuristic method. Truncation points of 60 and 50 were used for simulated and experimental cases respectively. Localization of EIT Reconstructions T he location of conductivity changes can be estimated from reconstructed images. The location of a single perturbation can be determined by equation 4 3 The expression for anomaly location (x, y, z) is effectively the center of mass of the difference image. The values ,,iiixyz are the coordinates of the center of each element. i is the conductivity change reconstructed in the ith element and v is the vo l ume of each element. 111 111,,ne ne ne iii iii iii iii ne ne ne ii ii ii iiivxvyvz xyz vvv (4 3) Errors in reconstructed locations were calculated as the absolute location errors quoted as a fraction of the model or phantom radius (relative radial error) We considered separately horizontal errors (errors with in the xy plane) and axial errors (errors in z direction) respectively for each of the three current patterns. T herefore, we define these value s a s : Dxy x 2 y 2 R (4 4 ) zDzR (4 5 ) Image R esolution and C ontrast We compared image resolution using a method based on one suggested in Adler et al. (2009), wherein we estimated the relative volume contained in the set of voxel anomalies that had reconstructed values more than half the maximum within the image PAGE 81 81 0 HMV V where 0V is the entire model volume, and then took the cube root of this value. That is, for each image we computed the value 3 0 HMV R V (4 6) The half maximum threshold was also used to construct isosurfaces for display of reconstructed anomalies. Use of this measure allowed comparison of both the extent of artifacts within images (as large art ifacts will tend to increase the apparent resolution) and the true resolution in ventricular regions. We examined the ability of our reconstruction to resolve two anomalies by examining the reconstructed profile through a line joining the two anomalies. We defined the two anomalies as resolvable if the value between the anomalies reached a value half the maximum conductivity found on the profile. We compared image contrast c for different reconstructions by first finding the averag e image value over a region having the same size as the original anomaly that was placed in the lower hemisphere ( Bc ), far away from artifacts and the anomaly reconstruction. We then took the difference between this value and the average conductivity in the region of the reconstructed anomaly, centered on the maximum reconstructed voxel value ( Mc ). Thus we have the definition of image contrast (equation 4 7). Larger contrast values corresponded to better rec onstruction qualities. MBccc (4 7) PAGE 82 82 Comparison between Open Skull and Closed Skull Models Sensitivity analysis using a layered model The effects of outer head composition may be significant (Gibson et al. 2000) We therefore evalu ated the sensitivity performance of the EEG based pattern using a partial prior spherical model that incorporated layers of skin, skull (with and without the fontanel) and CSF, the center of the head being assigned to have the same conductivity as brain. L ayer thicknesses were chosen according to data gathered from inspection of archived neonatal MRI models. The diameter of the model was chosen to be 11.9 cm (a volume of 884 ml), with a scalp thickness of 2.9 mm, skull thickness of 6.0 mm and CSF layer thic kness of 3.0 mm. The archived MRI data set used as a reference had a total volume of 921 ml. A 41626 element (62118 node s ) tetrahedral finite element model was created using the layer scalings noted above. The model outline is shown in Figure 4 9 Regions were assigned conductivities found in the literature: scalp ( 0.43 S/m Burger and van Milaan 1943 ); CSF (1.3 S/m Oostendorp et al. 2000); brain tissue (0.172 S/m Stoy et al. 1982). We chose the skull conductivity to be eithe r that of adult skull (15 mS/m, Oostendorp 2000) or piglet skull (60 mS/m Sadleir and Argibay 2006). We chose to use the conductivity for neonatal piglet skull in the absence of values for human neonatal skull in the literature, and because the neonatal piglet will be used as an animal model in future tests of this technique. The layered model was tested with the EEG layout only. In order to determine the interaction between the presence of the fontanel and the EEG measurement layout, the part of the head designated as fontanel in Figu re 4 9 was either chosen to have the conductivity of skull or skin, corresponding to either closed or open skull conditions respectively. Sensitivity matrices were calculated for each of these configurations. We found the condition numbers for closed PAGE 83 83 s kull cases were generally lower than for open skulls, with values for adult skull configurations being about 158.810 and 161.610 respectively; and for piglet skulls 153.510 and 154.210 Noise analysis using model B The spherical model shown in Figure 4 9 represents an open skull model, since we assigned the scalp conductivity (0.43 S/m) to the fontanel. We constructed another closed skull model by setting the fontanel condu ctivity to be the same as the skull conductivity (0.06 S/m). In this study, we compared the performance of the EEG current pattern on both open and closed models by comparing the reconstructed images when different levels of white Gaussian noise were introduced to the measurements. The noise levels were determined by the SNR levels of practical EIT systems. The KHU Mark1 system was reported to have an average 8090 dB for SNR (Oh et al. 2007). An SNR of 50 60 dB was observed with simple phantom experiments using the ITS P1000 system (Murrieta Lee et al. 2004). Therefore, we made comparisons with 50dB, 65dB and 75dB introduced Gaussian noise. We added noise to the model data by first measuring the signal power, and then adding noise at the specified SNR level using the MATLAB function AWGN. Noise was added first to the reference data and then to data from a case with an anomaly present. These two sets were subtracted from each other to form the voltage perturbation. For each noise level and skull composition we created 100 data sets. We compared the resulting resolution and contrast values in the reconstructed images at the same noise level for the two skull conditions a priori using t tests. PAGE 84 84 Results Sensitivity and Selectivity for the Uniform Models Sensi tivities to bleeding in the central part of the head were investigated by computing sensitivities in the regions of interest. This is similar to the approach used by Kauppinen et al. (2005) where sensitivities in the center of a disk were compared using di fferent measurement configurations. Sensitivity maps for the four regions of interest are show in Figure 4 10 for all three patterns on the uniform sphere. For a significant number of measurements sensitivity was negative. The RING pattern had the most pos itive sensitivity values. The average sensitivity of the EEG pattern was greater than either RING or Cz RING patterns for the upper sphere, and comparable to the RING pattern over the lower sphere. However, the EEG pattern had significant regions of negative sensitivity. On the basis of sensitivity alone, the RING pattern was superior to Cz RING and EEG patterns, as it demonstrated mostly positive values in the regions of interest. The Cz RING pattern had reasonable amplitude sensitivities but demonstrated an average negative sensitivity for both regions of interest. Examination of Figure 410 C and D shows that in the ventricles EEG pattern sensitivities were similar to those in the lower sphere and that there were significant negative sensitivities. The RI NG pattern sensitivity peaks were much larger than the EEG pattern peaks for both ventricle samples. The Cz RING pattern plots for simulated ventricles shifted considerably compared to the spherical region results and there are many large negative sensitiv ity values. Where as the sensitivity of the models reflects the interaction between current and measurement pair geometries in the model, the selectivity shows the contribution from the target region to measured voltages and transimpedances. Absolute sele ctivities for PAGE 85 85 the uniform spherical pattern were clearly better than either Cz RING or RING layouts, with up to 15% of total resistance contributed by the upper sphere and 710% of total resistance typically contributed by the lower sphere (Figure 411). E EG pattern selectivities in the ventricles were slightly smaller than those observed in the lower sphere, with average values being around 4%, but these values were on average larger than those observed for the RING pattern. Selectivities for the Cz RING p attern in the ventricles were also relatively high, averaging about 3% with peaks up to 6% of total resistances. Negative sensitivity volumes for all spherical background models were large, averaging around 50%. The negative sensitivity volumes of the thre e patterns were around 70%, 35% and 53% for RING, Cz RING and EEG patterns, respectively. By contrast, half sensitivity volumes were usually very small, being about 0.6% for the RING, 0.3% for Cz RING and 0.2% for the EEG pattern. The results broadly agree with sensitivity analyses performed using four electrode configurations in 2D (Kauppinen et al. 2005) and in 3D (Yang and Patterson 2008). Comparing the Three Current Patterns Using Model A The performances of the three current patterns on model A were compared in terms of localization errors and QI stabilities. Figure 4 12 A compares xyD for the three current patterns and Figure 4 12 B compares zD for the EEG and Cz RING patterns only, since the RING pattern was not able to localize in the z direction. The quantification stabilities of the three current patterns are compared in Figure 4 13 In order to compare the quantification stability between different current patterns, the 37 QIs were normalized with res pect to their average for each current pattern. The EEG PAGE 86 86 current pattern showed the best performance for anomaly positions above the equator in terms of both localization errors and quantification stability. The RING current pattern could localize anomalies very well in the xy plane a nd showed a great potential in overall quantification stability. The Cz RING current pattern could determine the axial position for the anomalies above the equator and off the central axis, but performed very poor for the anomalies on the central axis. It s overall performance was only slightly better than the r ing pattern alone. Comparing RING and EEG Patterns Using Model B and Phantom Data We compared the performance of the RING and EEG current patterns on model B. Cz RING was not used for phantom measurements due to its poor performance on model A. Results for reconstructions of simulated and phantom data using both current patterns and sensitivity matrices are shown in Figure 4 14. Figure 4 14 (a) shows an ideal image of blee ding accumulation at position 1, a relative radial position of (0.2, 0.25, 0.3), illustrated in axial and sagittal sections and as isosurfaces, with results for reconstructions of (b) simulated EEG data, (c) simulated RING data, (d) phantom EEG data and ( e) phantom RING data. Isosurfaces were calculated at a threshold set at half the maximum voxel value within the image. As expected, the RING pattern could n o t determine axial position s of anomal ies because of its two dimensional symmetry. Resolutions in r econstructions from all phantom data appeared similar to reconstructions from simulated data, but contained artifact s, as reflected in results shown in Table 4 3 In most cases, the characteristic size of reconstructions for EEG cases was smaller than th ose for the RING cases. Interestingly, although it is clear that in both comparisons of anomaly 1 reconstructions that those for the RING were more PAGE 87 87 diffuse, the R measure gave a smaller value for RING resolutions than for EEG resolutions. The EEG pattern could localize well in all thr ee dimensions. Figure 4 15 shows that the RING pattern localized anomalies as well as the EEG pattern in the xyplane, producing a maximum radial relative error of 0.035 in both cases. T h e EEG pattern localized the z coordina te well in simulat ed data, with the maximum Dz less than 0.03 of the radius over all intraventricular locations L ocalization errors were larger for reconstructions from both current patterns applied to the phantom case with the worst value of Dxy being 0 .17 for the EEG pattern and 0.1 for the RING pattern. The QI values found were comparable to the ideal QI, which can be calculated as: 324 ()()0.0026 [] 3 idealbloodCSF bloodQI r Sm (4 8) Q uantification result s for the RING pattern were similar to those for the EEG patter n for simulated data, with the largest variation no more than 5% for both cases Quantification results from phantom data were also similar, although QI errors found using the RING pattern were very large in some cases The worst QI error in reconstructions using the EEG pattern with phantom data was around 10% while the worst QI error in corresponding RING pattern phantom reconstructions was almost 30% (Figure 4 16 ). Comparison between Open Skull and Closed Skull Models Comparisons of r econstructions o f a bloodlike anomaly at position 1 using the EEG current pattern with open and closed skull models are shown in Figure 4 17 The advantage of using a fontanel focused pattern was made visible when 50 or 65 dB Gaussian white noise was added to data. At 50 dB the open skull model had resolution PAGE 88 88 0.1805 and contrast 0.5228, while the closed skull model had a resolution of 0.1959 and contrast 0.5158. At 65 dB we could still locate a peak conductivity change at a location corresponding to the anomaly position in an open skull reconstruction (resolution R = 0.187, contrast c = 0.523) while the reconstruction on the closedskull model was almost completely dominated by artifact (R = 0.205, c = 0.499). Both images were still affected at 75dB noise levels, with open skull resolution and contrast being 0.222 and 0.473 respectively and closed skull resolution and contrast being 0.235 and 0.467 respectively. In the 50 and 65 dB cases, R and c values were significantly better (p < .05) for open skull cases than for cl osed skull cases. At higher SNR levels (75 dB and above) we found that resolutions and contrasts were not significantly different. Discussion Sensitivity and Selectivity Sensitivity and selectivity parameters of the three different measurement strategies can be used to predict their ability to detect changes in the ventricular regions. A robust measurement method should have both high selectivity and high sensitivity in the region of interest. We have found that the EEG measurement pattern had similar magn itude sensitivity to the RING pattern in the two spherical regions of interest, but higher selectivities. In addition, the EEG pattern had both maximum measured transimpedances and a lower dynamic range than the RING pattern. Although the RING pattern had a stable sensitivity distribution and good selectivity, it can not be used to determine threedimensional anomaly locations because of its planar symmetry. The presence or absence of the fontanel and skull conductivity greatly affect sensitivity distributions. The Cz RING pattern had lower sensitivities than the RING pattern in all cases, with the average sensitivity being negative for both PAGE 89 89 regions of interest tested. Selectivities of the Cz RING pattern were comparable to those of the EEG pattern, but Cz RING patterns overall negative and variable sensitivity in central regions indicates it may be unsuitable for practical measurements. Because of the symmetry of the EEG layout, there were several very low values for resistance predicted (24 of the 182 us ed). In our analysis of selectivity, we chose to ignore these data. We expect that broadly similar patterns to those obtained for spherical model based matrices would be found when testing the RING or Cz RING patterns on realistic geometries. For example, the negative and low sensitivity values found for the Cz RING method would also be anticipated in a realistic geometry model as these are a consequence of measurement and current field patterns being orthogonal or opposed in central regions for many measur ements. While the EEG pattern seems promising, it is possible that there are superior measurement strategies that can be devised using the same layout, but avoiding measurement of near zero values. However, the number of independent measurements possible w ith this number of electrodes (104) will always limit the available information. Overall Evaluation with Model A Simulation results from model A confirmed part of the findings from sensitivity analysis. We found from the localization errors that the RING current pattern could identify x and y positions well, with the worst error in xy D obtained for this current pattern using simulated data being less than 0.08 of the sphere radius over all 37 locations. The EEG pattern could localiz e well in all three dimensions, especially for the anomaly positions above the equator, with the worst error being 0. 07 in the xy plane and 0.09 in the z direction The Cz RING current pattern could localize in the z direction PAGE 90 90 for some cases above the equator, but not consistently. Comparing the simulation results on model A in terms of QI stability we found the EEG pattern showed a smaller variation than the other two current patterns for the anomaly positions above the equator and therefore a better pot ential to quantify bleeding. The RING pattern showed the smallest QI variation overall in the simulation result s on model A However, in the problem of quantifying intraventricular bleeding, the EEG pattern seems a better choice because we expect that the intraventricular bleeding will occur above the midplane of the head. The Cz RING current pattern is supposed to combine the advantages of both the RING pattern and EEG pattern. We used both coarse (22093 elements) and fine (51524 elements) sensitivity matr ices to reconstruct Cz RING data, but found that although increasing the number of elements improved localization and QI results slightly, they were still not significantly better than the RING pattern alone. The Cz RING pattern did improve localization in the z direction over the RING pattern, but not consistently. One interesting finding from Cz RING pattern data was that we could localize the z positions when the anomaly was off the central z axis, the more the better. However, when the anomaly was close to or on the central z axis, it performed only as well as the RING pattern. This indicated that the Cz RING pattern was not sensitive enough for the location changes on the z axis because the current stream lines generated by the drive electrode pairs wer e almost perpendicular with the current stream lines generated by measurement electrode pairs on the central axis Model B and Phantom Experiment Results Again, both the RING and EEG patterns performed well in terms of xy plane localization and quantificat ion accuracy on reconstructions of simulated data generated PAGE 91 91 from model B with the localization results shown in Figure 4 15 confirming our observations from the reconstruct ed images of Figure 4 14. L ocalization accuracy was slightly worse for the phantom data presumably because of the presence of random and systematic experimental noise. We believe that the large localization errors for positions 4, 5 and 6 in the EEG phantom experiment shown in Figure 4 15 may have been caused by a degradation in anomaly quality after it had been immersed in the saline background for some time (each set of measurements at a single anomaly volume were performed by moving the anomaly around the tank over a period of approximately 10 minutes (Sadleir et al. 1998, Sadleir et al. 2006) ), but they may also have been caused by the slight lateral asymmetry of the sensitivity matrix combined with noise. As shown in Figure 4 16 the QI variability in the noiseless simulated data was relatively flat in both cases with the largest v ariations being no more than 5%. As with localization performance, phantom results tend ed to agree with the simulation results, but we observed larger QI variations for phantom cases Figure 4 16 also shows that the EEG pattern performed better than the RI NG pattern in phantom experiments confirming results of our sensitivity analysis The s ensitivity analysis of the two patterns show ed that the RING current pattern had a much lower selectivity than the EEG pattern in ventric u lar regions. Therefore for the same conductivity perturbation, smaller voltage changes were produced, as a consequence of which the noise played a more significant role in the RING phantom measurements. On closer inspection of data vectors, we found that the normed sum of the voltage p erturbation caused by a single blood like anomaly within a ventricle was about 1/5000 that of the normed sum of all reference measurements for the RING pattern, and about 1/1000 for the EEG pattern. PAGE 92 92 The SNR level of the KHU Mark1 system was reported to be 80 90 dB (Oh et al. 2007) This implies that noise accounted for 1750% of RING phantom data, while accounting for only 3 10% of EEG phantom data. As a result, the QI values were more severely contaminated by the noise generated artifacts in reconstructions based on the RING current pattern Anomaly Quantification Absolute QI values do n o t only depend on the size of the anomaly, but also depend on the current patterns sensitivity matrix and the truncation point used For example, the RING pattern and EEG p attern produced different sensitivities in the ventricle regions, and therefore had different QI accuracy for the same anomaly presented in this particular region. A truncation number of 50 was used for all the phantom experiments in this study. A different truncation point would shift all the absolute QI values to another level. In practice, we can determine the relationship between QI and anomaly volume with a n EIT system calibrated for a particular configuration and truncation number using a phantom and blood like anomalies (Sadleir et al. 1998, Sadleir et al. 2008) Variations of up to 3 0 % were observed in QI values for anomalies moved within ventric ular regions of the RING spherical phantom and up to 10% using the EEG pattern and phantom, an observation that was correlated with poor localization in the xyplane. This may have been related to the overall smaller selectivity found for RING pattern in ventricular regions combined with measurement noise. Even though the EEG pattern showed generally good r esults, s ome method of QI regularization that reduces its shift variance may be appropriate. We have results of implementing such a method in 2D 16 electrode reconstructions (Oh et al. 2009, Sadleir et al. 2008) This algorithm gave very promising results in 2D resulting in a reduction in PAGE 93 93 QI spatial variability to about half. The method may be straightforwardly extended to 3D. We believe that use of a similar approach with the EEG pattern would likewise make QI accuracy greater in th e present context. Com parison between Open Skull and C losed Skull M odels We chose to compare the open skull and closed skull models using three different levels of Gaussian noise (50 dB, 65 dB and 75dB), which were chosen from the range of SNR values reported for practical EIT systems (Oh et al. 2007, Murrieta Lee et al. 2004) O ur sensitivity analysis showed that the EEG pattern has on average a 7 10% larger selectivit y near the ventricle region on the open skull model than on the closed skull model (Sadleir and Tang 2009) This in conjunction with the overall larger sensitivities observed in open skull cases, indicates that perturbation s in side the lateral ventricle region should contribute larger relative voltage change s with an open skull than with a closed skull. There fore, the EEG pattern should have a greater potential to detect and localize a perturbation within the ventricle regions when the fontanel like opening is included The comparison of the reconstructed images in Figure 4 17 demonstrated that the EEG pattern produced overall better images on the open skull model than on the closed skull model, especially at low SNR levels. The implication of this is that the EEG pattern should produce superior images on neonatal skulls than (closed) adult skulls. Images produced above 75dB SNR were similar because the noise only accounted for about 6% of the voltage changes. However, this indicates that the EEG pattern may have the potential to detect smaller amounts of bleeding than the RING pattern above 75 dB. PAGE 94 94 Comparing L o calization R esults w ith Earlier Studies The UCL group performed phantom experiment s with a hemispherical tank and a modified 1020 EEG electrode configuration that involved 31 electrodes (Tidswell et al. 2001c) Their results showed that the localization e rrors were as low as 3.5% of the image diameter when the anomaly was placed at the anterior or posterior of the midline of the hemisphere (z = 0.5), which is overall better than our localization accuracy Another study on EEG dipole localization (Yvert et al. 2997) showed that using 32 electrodes instead of 19 improved the localization by 2.7mm on average in the upper hemisphere of the adult head. Localization errors can be further improved by weighting the sensitivity matrix. Liston et al. (2002) normalized the sensitivity matrix by dividing each column by the sum of this column before inverting the matrix, and localized a Perspex rod within 20% of the tank diameter. The localization error was further reduced to 5% of the tank diameter when an additional po st weighting and correct row normalization method was implemented (Liston et al. 2004) Therefore, increasing the number of electrodes and normalizing the sensitivity matrix may possibly improve localization errors in our context. However, in application of our method to infants, we believe that using a 16 electrode configuration is preferable than using 32 due to the small size of neonatal heads. In addition, the purpose of this context is to make a clear comparison of the two different layouts with the s ame approach. Therefore, we chose to use a simple, unfiltered sensitivity matrix. Although we have not used any weighting method, we still have a valid comparison between the two cases, and even with this simple approach, achievement of a 17 % relative radi al error is quite acceptable when compared to the minor diameter of a ventricle, which is about 30% of the head radius. PAGE 95 95 Other Possible Applications Based on our observations in this study, the EEG current pattern may also have potential for use in diagnosi s of other bleeding conditions such as intraparenchymal hemorrhage (IPH). In intraparenchymal bleeding, an increase in blood volume should result in a decrease in impedance, as blood (0.67 S/m) has a higher conductivity than brain tissue (0.172 S/m) (Gedd es and Baker 1967) Another possible application is the detection of acute stroke in neonates. Romsauerova et al. (2006) studied the feasibility of using Multi frequency EIT for the detection of stroke with numerical models and phantom experiments. Both applications would be expected to be easier than the application to detection of blood in the ventricles, since they involve less central locations and blood becoming present in an area where it is effectively masked by surrounding CSF. Application of EIT methods in adult humans is in general made very difficult because of the barrier formed by the adult skull. However, exploitation of the fontanel space may make it quite practical to diagnose several conditions in brains of neonates with EIT. Conclusion Three conductivity reconstruction methods (RING, EEG and Cz RING ) were compared on their ability to reconstruct, localize and quantify anomalies with simulations and phantom experiments. All the findings in this study indicated that the fontanel based EEG current pattern has a good potential to detect and quantify intraventricular hemorrhage and may possibly be applied to pathologies such as intraparenchymal hemorrhage and hemorrhagic stroke on neonates. PAGE 96 96 A B C Figure 41. Three electrode configurations vi ewing from the top and demonstrations of the current pattern applied in each case. A) RING layout and RING current pattern B) EEG layout and EEG current pattern. C) Cz RING layout and Cz RING current pattern. Table 4 1. Spherical coordinates of EEG electr odes, in degrees. T7 is left temporal and T8 right temporal. Oz is Occipital central electrode. Number Electrode Azimuth Latitude (degrees) 1 T7 92 0 2 C3 46 0 3 P3 60 51 4 F3 60 51 5 O1 92 72 6 FP1 92 72 7 Oz 92 90 8 Pz 46 90 9 Cz 0 0 10 Fz 46 90 11 O2 92 72 12 FP2 92 72 13 P4 60 51 14 F4 60 51 15 C4 46 0 16 T8 92 0 PAGE 97 97 A B C Figure 42. Forward models with three different electrode layouts. A) RING layout. B) EEG layout. C) Cz RING layout Figure 43. Threedimensional EEG sph erical models showing central and lateral ventricle regions. The spheres each have relative radii of 0.25 and are centered at z = 0.33 and z = 0.5. The elliptical lateral ventricle structures had relative radial locations of x = ( 0.2, 0, 0.3) and (0.2, 0, 0.3) and semiaxes of 0.15, 0.44 and 0.15 in x, y and z axes, respectively. PAGE 98 98 Figure 4 4 A model with an outer brain shell and a central region of CSF (Model A) viewing from the top The anomaly positions on the mid xy plane (equator plane) are demonstrated. Other anomaly positions are distributed the same way on the mid yz plane and mid zx plane. There are totally 37 anomaly positions within the central region of CSF. The anomaly has a relative radius of 0.05. This model was used with each of the three electrode layouts A B F igure 4 5 A more complex model (Model B) with scalp, brain, ventricles and skull shells, including a structure similar to the fontanel (highlighted). A) T op view, demonstrating that a blood like anomaly with a relative radius of 0.1 was moved over to the 6 positions within the ventricles. B) Side view, demonstrating that the ventricles were placed at a relative radius 0.3 above the equator. This model was used with the RING layout and EEG layout only PAGE 99 99 Figure 4 6 MRI images of a neo natal head, from which we determined the position and size of the ventricles. PAGE 100 100 Figure 47. Spherical phantoms with EEG layout (left) and RING layout (right). Figure 4 8 The complete phantom experiment system PAGE 101 101 Table 4 2. The condition number, rank and s ize for the sensitivity matrix used for each current pattern and truncation point chosen for each case Current pattern RING EEG Cz RING Condition number 1.43 x 1019 2.84 x 1014 2.90 x 1012 Number of elements 26126 21896 51524 Rank 104 104 104 Number of Measurements 208 182 182 Truncation point a 60 / 50 60 / 50 60 / NA a The numbers on the left of the / are the truncation points used for simulated data. The numbers on the right are truncation points used for phantom ex periment data Figure 49. Layered spherical model with EEG layout. Conductivities used in the layered model were CSF (1.3 S m1), scalp (0.43 S m1), skull (15 mS m1), brain (0.127 S m1). The fontanel was either chosen as skull or skin. PAGE 102 102 Figure 410. Average sensitivities, calculated as a fraction of maximum values observed over the domain, for EEG, Cz RING and RING patterns in the regions of interest. A) upper sphere; B) lower sphere; C) left ventricle; D) right ventricle. PAGE 103 103 Figure 411. Absolute selectivities observed within a relatve radius 0.8 for EEG, Cz RING and RING patterns in the regions of interest. A) upper sphere; B) lower sphere; C) left ventricle; D) right. PAGE 104 104 A B Figure 412. Radial relative localization errors for simulations on model A. A) Ra dial r elative localization errors in the xy plane ( xyD ) at 37 differ ent locations for the three current patterns on model A B) Radial r elative localization errors in the z direction ( zD ) at 37 differ ent loc ations for the EEG pattern and Cz RING pattern on model A In both plots, t he points in the left shade d area are the locations above the equator plane (1~10) The points in the central shade d area are the locations on the equator plane (11~27). The points in the right shade d are a are those below the equator plane (28~37). Figure 413. Quantification Indices of the 37 different anomaly positions for each of the three current patterns on model A. The 37 QIs for each case were normalized with respect to thei r average. P oints in the left shade d area correspond to locations above the equator plane (1~10) The points in the middle shade d area correspond to locations on the equator plane (11~27). Points in the right shade d area correspond to points below the equator plane (28~37). PAGE 105 105 Figure 414. Axial (relative radial position z = 0.3) and sagittal (x = 0.2) cross sections (first and second columns) and isosurfaces (third column) of an blood like anomaly in each case. (a) an blood anomaly at position 1 in model B and (b) reconstructions of EEG simulated data, (c) RING simulated data, (d) EEG phantom data and (e) RING phantom data, all using reconstruction matrices based on homogeneous spherical forward models. Isosurfaces were calculated at half maximum voxel val ues within each image. PAGE 106 106 Table 4 3. Comparison of resolutions R calculated for each of the cases shown in Figure 414 ANOMALY POSITION 1 2 3 4 5 6 EEG SIMULATION 0.285 0.243 0.253 0.212 0.159 0.208 RING SIMULATION 0.231 0.313 0.243 0.286 0.324 0.309 EEG PHANTOM 0.276 0.268 0.281 0.23 0.137 0.26 RING PHANTOM 0.259 0.326 0.211 0.242 0.177 0.274 Figure 415. Radial r elative localization errors Dxy and Dz of the 6 anomaly positions for simulated (model B) and phantom data for RING and EEG patterns PAGE 107 107 Figu re 416. Quantification Indice s of the six anomaly positions with simulated (model B) and phantom data for the RING and EEG patterns PAGE 108 108 Figure 417. Comparisons between openskull and closedskull reconstructions. Axial (Relative radial position of z = 0.3) and sagittal (x = 0.2) cross sections (first and second columns) and isosurface s (third column) showing (a) ideal image of bleeding at position 1 with in a spherical model, and the reconstructions using the EEG current pattern on open skull or clo sed skull model s at three different noise levels. The noise levels used were 50dB (b) open skull and (c) closed skull, 65dB (d) open skull and (e) closed skull and 75dB (f) open skull and (g) closed skull. Isosurfaces were calculated at half maximum voxel values within each image. PAGE 109 109 CHAPTER 5 STUDIES USING A REAL ISTIC HEAD SHAPED MODEL Background So far we have found a robust current pattern (the EEG pattern) using spherical neonatal head models. However, real neonatal heads differ from spherical models in many aspects, such as their external boundary shape and internal anatomical structures. Due to the ill conditioning of the EIT problem, these differences will introduce errors to the reconstructed images when applying the spherical algorithm on data colle cted from real patients. To investigate the true quality of the EEG current pattern on real subjects and our spherical reconstruction algorithm, we performed studies using neonatal head models with realistic boundary geometry and major anatomical structure s. Some previous studies demonstrated that an incorrect estimate of boundary shape will reduce the quality of the reconstructed image through the introduction of artefacts (McInerney and Terzopoulos 1996). Incorporating an accurate forward model instead o f using circular or spherical forward models has been a popular problem in brain imaging (Bagshaw et al. 2003, Liston et al. 2004) and lung imaging (Borsic et al. 2001, Fan et al. 2009). All the earlier studies showed that the image quality could be genera lly improved using such approaches, which are especially useful for absolute EIT imaging. However, realistic models need to be used carefully, because with inaccurate prior information, they may yield images worse than reconstructed with a simple forward m odel (Liston et al. 2004). In practice, head geometry varies from patient to patient, which makes it difficult to accurately specify the forward model. In addition, the neonatal head can vary in shape depending on posture. In this study, we compared the i mages reconstructed PAGE 110 110 using a spherical forward model and a head shaped forward model and evaluated the necessity of using an accurate forward model for the purpose of detecting and quantifying intraventricular bleeding in neonates. Methods The Neonatal Head shaped Model A 3D numerical neonatal head model (Figure 5 1) was provided by Dr. Richard Bayford and Dr. Andrew Tizzard from Middlesex University, UK. This model (the RG model) contain ed 4 different anatomical structures (skin, skull, CSF and brain) whic h were manually segmented from MRI images of a normal term neonate (Figure 5 2 ) (Tizzard et al. 2005) The total volume of the model was 791 ml. The RG model was meshed into 45702 tetrahedral elements with 8703 nodal points (the RG mesh) We implemented th e 16 EEG electrode layout on top of the scalp based on their spherical coordinates. Electrode locations were chosen to be as similar as possible to those used on the spherical background model while adapting to the realistic heads orientation. The Cz elec trode was shifted off the central axis to determine the effect of electrode location variation on models symmetry. The mesh data can be organized into a file with STL format or MPHTXT format, and then imported into COMSOL for the purpose of geometry visualization and numerical simulation. Sensitivity Analysis Similar to the analysis done with the spherical models in Chapter 4, sensitivity analysis was also done for a homogeneous RG model equipped with the EEG electrode configuration. This could help to determine the extent of differences that would be expected using this method in vivo In making comparable regions to those in spherical models, we averaged maximal x, y and z deviations from the model anatomic center PAGE 111 111 and used these values to calculate appro ximate elliptical semiaxes for the model. These values were then used to create elliptical regions with the same relative locations and semiaxis values to those used in spherical background models (Figure 55). These regions are illustrated in Figure 53. Volumes of 11.1 ml and 11 ml were calculated from lower and upper central regions, respectively. Both left and right ventricle volumes were about 4.2 ml, similar to those observed in vivo (Gilmore et al. 2001). The sensitivity matrix calculated using the E EG layout on a uniform realistic geometry model had 45702 elements, and had a condition number of 56.310 As for all other models, its rank was 104. Simulation of IVH To simulate intraventricular bleeding, we added two ventricles withi n the brain compartment of the RG model. Similar to the ventricle structures used in the spherical model, they were elliptical with a total size of about 1/70 of the head volume. The ventricles were placed 18 mm above the anatomical center and were spaced laterally 18 mm apart about this point. We used 6 bleeding sites at similar relative locations within the ventricle regions, as for the spherical model (Figure 5 4). Tissue conductivities used were the same as for the spherical model (blood 0.67 S/m, CSF 1 .3 S/m, brain 0.17 S/m, scalp 0.43 S/m, skull 0.06 S/m). To get a more comprehensive understanding of quantification in this RG model, we also investigated multi site bleeding. To do this we placed anomalies at combinations of the 6 locations, leading to a total of 123456 66666663 CCCCCC bleeding cases. PAGE 112 112 Investigation of Boundary Shape Mismatch In this study, we focused on investigating the effect of model boundary geometries on reconstructed images. More precisely, we compared image qualities and quant ification accuracies in the head using a spherical forward model and a realistic geometry forward model. Forward models Two forward models were used to formulate the sensitivity matrices. One was a spherical model with unit radius and homogeneous conducti vity distribution (the SP matrix), which has been used through out the studies in Chapter 4. The other was a neonatal head model with realistic head geometry and homogeneous conductivity distribution (the RG matrix), which is the same as the homogeneous RG model used earlier for sensitivity analysis. Data generation We gathered simulated bleeding data using three different headshaped finite element models and one headshaped phantom. The first one (the M model) (Figure 55 A) had a boundary geometry the s ame as the RG model we used to formulate the RG sensitivity matrix. The background conductivity was assigned to be homogeneous with the conductivity of CSF (1.3 S/m). In this study, we created two bleeding sites at positions corresponding to the centers of the left and right ventricles, respectively. Bleeding was simulated by manually setting the corresponding elements of the finite element forward model to the conductivity of blood (0.67 S/m) The centers of the ventricles were the same as used in Figure 5 4. We simulated 6 different cases on each side with total blood volume increasing linearly from 0.5 ml to 3 ml. PAGE 113 113 To test our methods in the presence of realistic noise, we constructed a plastic headshaped phantom of the M model, using a 3D printer (Dimension, Inc., MN, USA). The procedures to construct the phantom are illustrated in Figure 56. The surface mesh was first extracted from the M model, with the bottom surface removed. The mesh was therefore hollow at the neck. We then produced a copy of the mesh at 90% of its original scale, and placed it inside the original mesh. By connecting the two bottom circles at the neck with triangles, we created a closed shell like structure with a triangular surface mesh. The surface mesh information was then saved into a STL format file, and imported into the 3D printer. It took 20 hours for the 3D printer to construct the phantom. The phantom had the same boundary shape as the M model, but its total volume was 1628 ml, about twice the actual model volume. The phantom had 16 stainless steel electrodes attached as shown in Figure 55 B. A 0. 6 % saline solution ( the conductivity of which was approximately 1.3 S/m the conductivity of CSF ) was used as the phantom background. Bleeding was simulated using gel anomalies made of TX151, agar and saline. The TX 151 gel conductivity was adjusted to 0.67 S/m We made 6 cylindrically shaped anoma lies with volumes from 1 6 ml. Following the simulated data generated from model M, we placed g el anomalies at the left and right ve ntricle centers, which were determined to be 23 mm above the anatomical center and 23 mm apart from each other. Anomalies were placed accurately using a 3D positioner ( Velmex, Inc., N Y, USA ) Data was collected using the KHU Mark1 EIT system We chose to u se a single frequency of 10 kHz and a constant current output of 1 mA. Ten data sets were collected and averaged as a reference before anomalies were introduced. In each of PAGE 114 114 the 12 experiments, ten data sets were collected and averaged as the perturbation data for that volume of bleeding. The other RG model used in this study (model G) (Figure 55 C) was provided by researchers at the University of Gent in Belgium It was constructed from the MRI data from a 39 week gestational age patient who suffered from asphyxia. The original 3D image had a dimension of 256 x 256 x 129, with each pixel size 0.7 x 0.7 x 0.63 mm. Five major structures were segmented from the images, including CSF, brain tissue, skull, fat and scalp (Figure 57). Theoretically, we could use the original image as a rectangular brick mesh to obtain FEM solutions. However, the original image contains 7510 elements. Our experience told us that problems around this size would be very computational costly. To speed up the si mulation process, we reduced the image size by grouping each 5 x 5 x 5 block as one pixel. The image dimension was therefore reduced to 51 x 51 x 26. The process was performed very carefully to make sure the skull structures were preserved and closed in al l slices. To acquire more accurate FEM solutions, we decided to convert the mesh elements to tetrahedrons. Each rectangular brick was divided into 6 tetrahedrons in the manner shown in Figure 58. Of course this is not the only way to divide a brick into t etrahedrons. However, we needed to keep in mind that adjacent tetrahedrons have to share a common triangular face. So we divided the bricks such that the diagonal lines on the opposite sides of a brick had the same orientation. The mesh finally contained 23920 nodes and 126432 tetrahedrons. The purpose of using this model was to test our two sensitivity matrices on a different patient, whose geometry matched neither one of the forward models. In the PAGE 115 115 beginning of this study, we were primarily interested in the effects from boundary shape. Therefore, we removed the internal structures by setting the background homogeneous with conductivity value 1.3 S/m (uniform G model) and selected two bleeding sites at the ventricle centers. Ventricle center positions wer e determined using the original MRI data. We determined that the two ventricles were 44 mm above the base and 17 mm apart. We simulated six different cases each side with blood volumes increasing linearly from 0.5 ml to 3 ml. The 16 EEG electrodes were als o incorporated on the scalp according to their spherical positions. After that we decided to make this model more realistic. Therefore we put all the structures back into the model (layered G model), as shown in Figure 57. The positions and volumes of sim ulated bleeding were the same as used in the uniform G model. Results Sensitivity Analysis Figure 59 shows the sensitivities and selectivities for the EEG pattern in simulated ventricles and upper and lower spheres of the homogeneous RG model. These figu res may be compared directly with the EEG pattern results obtained for the uniform spherical model in Chapter 4. Both sensitivities and selectivities were very similar to those observed in the spherical model. Volumes of central regions were around twice t he ventricle volumes in the RG model and this is reflected in the absolute selectivity plots. The relatively large sensitivity and selectivity in the left ventricle likely reflects the asymmetry of Cz electrode placement. Maximum selectivities in the reali stic geometry sensitivity matrix were similar in all four regions to those found for the spherical model matrix, but fewer large selectivities were observed. PAGE 116 116 Layered RG Model We compared images reconstructed using a sensitivity matrix calculated from the h omogeneous spherical model ( SPS ) and a sensitivity matrix calculated from the homogeneous RG model ( RGS ). Data was generated from the layered RG model shown in Figure 5 2 Figure 5 10 shows the reconstructions for an individual impedance change at position 1. Images in Figure 5 10 reconstructed using the spherical matrix were similar to the second image in Figure 5 14, which shows the reconstruction from EEG data calculated from a spherical object Although r esolutions were better for RG reconstructions than for spherical (0.138 and 0.168 respectively), the contrast for the spherical case (0.467) was better than for RG reconstructions (0.454). To further investigate the resolution for images reconstructed us ing SPS we compared reconstructions of anomaly pairs 14, 25, 3 6 and 16 (refer to Figure 54 for anomaly positions). In each of the 4 cases, the two anomalies were located at different sides of the ventricles. This way we could test the ability of the spherical matrix to discriminate bleeding locations when there was bleeding in both ventricles. As a criteria for successful anomaly resolution, we required that the conductivity values reconstructed on the line joining the anomalie s should dip to less than half the maximum value observed in either anomaly. The anomaly profiles are shown in Figure 5 11. We found that anomalies 14 and 16 and 36 were resolvable but not 25. Q uantification results for multi site bleeding cases are co mpared in Figure 5 12 The correspondence between result s obtained using the spherical reconstruction matrix were similar to those obtained from the realistic geometry matrix: both of them giving QI estimations having a ma ximum error no more than 0.0025 S. cm2 over all positions, a PAGE 117 117 value that corresponds to a blood volume of 0.4 ml when considered relative to the total volume of the head. We also compared the performance of the two reconstruction matrices with respect to QI values when white Gaussian noise w as added to data (Figure 5 13 ). In this figure we compare the average and standard deviation of QI errors over all positions for both reconstruction matrices at 11 different SNR levels between 60 and 90 dB. We found that the variation in quantification err ors became almost 3 times larger for both reconstruction methods as the SNR was decreased to 60 dB. Investigation of Boundary Geometry Effects Using Homogeneous RG Models Reconstructions of anomaly 1 are shown for model M (Figure 514 A), uniform model G (Figure 514 C) and layered model G (Figure 5 14 D). Only reconstructions of anomaly 6 are shown for model M phantom data (Figure 514 B) because reconstructed images of anomaly 1 were severely contaminated by noise. Left and right reconstructions were com pared in each case to demonstrate asymmetry, and image resolutions for all the reconstructed images are shown in Table 51. As expected, the reconstructions from model M data using the RG matrix had consistently better image resolutions than reconstructions using the SP matrix. The RG matrix also showed an advantage over the SP matrix in reconstructing model M phantom data. However, the RG matrix did not show a consistent advantage in reconstructing data from the uniform model G. Instead, the SP reconstruct ions had consistently better image resolutions (average R = 0.1887) than the RG reconstructions (average R = 0.2168) for the right side, although the RG reconstructions showed better image qualities (average R = 0.1836) than the SP cases (average R = 0.2929) for the left side. RG reconstructions for the layered model G data showed better image resolutions in most cases, except for blood volume 1 on the right side. PAGE 118 118 Quantification indices for the 6 different anomaly sizes on the left side were calculated for each of the four models (Figure 5 15). The results for the anomalies on the right side were similar. The quantification performances of the two matrices were almost identical for simulated model M data. The RG matrix had a relatively better quantification accuracy for model M phantom data (average error = 0.0025 S.cm2), compared with the SP matrix (average error = 0.0034 S.cm2). The RG matrix did not show any significant advantage over the SP matrix for the data from uniform model G and layered model G. D iscussion Sensitivity analysis on the realistic geometry model showed that the sensitivity and selectivity patterns using the EEG electrode configuration on this model were similar to those obtained from the spherical model. This further indicated the potential of using the EEG method on real patient subjects. Studies using the layered realistic geometry model (Figure 52) showed the possibility of using a spherical forward model to reconstruct images using data collected from a real h ead. A number of e arli er studies showed that incorporating a more accurate forward model that matches the conductivity structures of the imaged object can improve image quality in general For example, inclusion in forward models of a bone model (Meeson et al. 1995) a four she ll head model (Bagshaw et al. 2003) or including anisotropy (Abascal et al. 2008) all demonstrated improvements in image quality, image resolution and localization errors. However, if the prior information within the realistic model is not accurate enough, they may yield images worse than those reconstructed with a simple model (Liston et al. 2004) In Bagshaw et al. (2003) it was noted that using a full shelled head model produced worse images than using the PAGE 119 119 homogeneous head model when reconstructing the head phantom data, because the resistivity ratio between the skull and brain region for the tank was too dissimilar to the value assumed in the model. Meeson et al. (1995) also concluded that using a uniform matrix seems less likely to generate artifacts when the underlying conductivity distribution is unknown. Bagshaw et al. (2003) also studied the effect of using realistic geometry in the forward model. They found that both localization accuracy and image quality was improved, but only slightly. In pract ice, head geometry varies from patient to patient which makes it difficult to find a forward model that is really accurate, unless each model is constructed individually However, constructing patient specific models may not be quite possible due to the d ifficulty of collecting high quality MR images from neonates. Exactly how accurate a model should be is a matter of discussion (von Ellenrieder et al. 2006) Therefore, it is of great interest to investigate the quality of reconstructions and quantity index accuracy using a homogeneous spherical model as a forward model. Figure 5 12 shows that the QIs calculated using the spherical matrix were similar to those calculated using the accurate RG matrix with a maximum error of 0.0025 S.cm2 (0.4 ml) in both cases. The response curve was not exactly linear, and appeared to have a zero intercept at a volume larger than 0 ml. This suggests that sensitivity is low at very small volumes. B oth spherical and RG matrix results tend ed to shift away from the expected QI w hen the total blood volume bec a me large r than 1.5 ml This tendency agreed with the observations from (Sadleir et al. 1998) when using anomalies less conductive than the background. Both the se inaccuracies may be caused by the nonlinear characteristic s of the EIT problem itself (Seagar et al. 1987) As Figure 5 13 shows, use of the RG reconstruction matrix did not produce an advantage PAGE 120 120 over the spherical reconstruction matrix at all SNR levels. The largest QI variability found using the spherical matrix inc reased to 0.006 S.cm2 (corresponding to a blood volume of 0.95 ml) at 60 dB. However, this level of variability is not likely to lead to an incorrect diagnosis of type II IVH, in which the blood volume may be up to 3ml. The studies using the three homogeneous models (the M model, M phantom, uniform G model) and one layered model (layered G model) further proved the potential of using spherical model as a generalized forward model for different patients. As discussed earlier, EIT image quality is highly depe ndent on the forward model. Fan et al. (2009) found that the human lung reconstruction was improved by using a boundary model developed from 3D CT scan data. In our study, we found that better image resolutions were obtained using the RG matrix when using both simulated and phantom data from model M. This confirmed the findings from early studies, since the RG model had exactly the same boundary shape and electrode locations in model and phantom. When using data from model G, the RG matrix still produced better results for left located anomalies. This can be explained by the asymmetry of the Cz electrode in the RG model. In the RG model, the Cz electrode was placed to the left of the head apex and therefore produced relatively larger sensitivity and selectiv ity in the left ventricle region, as shown in Figure 59 C and D. However, the advantage for the RG matrix was not sustained for anomalies positioned on the right, and here the SP matrix showed consistent better image res olutions. Kolehmainen et al. (1997) and Blott et al. (1998) concluded that the locations of electrodes and the boundary shape of the forward model brought the most difficulties for the reconstructed images. The three homogeneous models used in this study also enabled us to investigate the e ffect from boundary PAGE 121 121 geometries alone. The layered model G enabled us to compare the performance of the two sensitivity matrices on a more realistic patient. An interesting finding was the relative performance of the RG matrix improved compared to its per formance on the uniform G model, although it did not show much advantage for small blood volumes. Future work should include collecting data from real patients to validate these findings. The RG matrix showed no better performance than the SP matrix in t erm of quantification. Figure 515 A shows that the SP matrix could be calibrated to quantify the anomalies as well as the RG matrix and these QIs matched the ideal QIs. The RG matrix did not show consistent advantage with model M phantom data (Figure 515 B). Another interesting observation was that the QIs calculated from the SP matrix showed smaller error bars in most cases, which indicates that the SP matrix may have an advantage over the RG matrix in a noisy environment. Both matrices quantified data f rom the uniform model G well (Figure 515 C). In this case, where the object geometry matched neither sensitivity matrix, the RG matrix did not show any advantage over the SP matrix. When looking at the quantification result from the layered model G (Figur e 515 D), we found that the QIs from RG matrix showed slightly better accuracy when the blood volume was getting large. However, this did not seem to give a significant advantage for the detection of grade II IVH. The spherical matrix reconstructions coul d of course not localize anomalies as well as the RG matrix cases. However, images reconstructed with the spherical matrix showed the anomalies coherently, and allowed us to verify their location something that could be of practical benefit in verifying diagnoses made from QI information. In considering whether it is appropriate to use RG or spherical models for diagnosis in this PAGE 122 122 application, it is important to bear in mind the hazards inherent in obtaining RG data in unstable neonates (involving transp ort to MRI or CT machine and the inherent risks during these steps, as well as the time needed to produce an RG model) and weighing them against the clinical need to confirm bleeding. It is probably true that use of a reconstruction based on an appropriat e geom etry will produce better images. H owever, we have shown here that postprocessing of images using both methods obtained similarly accurate QI values. If QI is used as a primary indication of bleeding status, images could be used as a secondary measur e to verify the presence of a coherent anomaly and to discount the possibility of QI variations being caused by electrode contact problems or other equipment errors. While images from spherical reconstructions are not quite as clear as in those based on a ccurate models of the head, sufficient information should be present in these reconstructions to allow verification of diagnoses. Conclusion We further investigated the performance of the EEG method using a head model with realistic geometry and anatomical structures. The results indicated the potential of using this method in real clinical trials. We also compared the performance of two sensitivity matrices ( SPS and RGS ) using different head models. It is evi dent that the matrix developed from a realistic shaped forward model does not guarantee image quality when the subject has mismatched boundary shape and electrode locations. Moreover, the SP matrix performed better in quantification of phantom experiment d ata. All our observations indicate that using a simple spherical matrix might be adequate for monitoring IVH in neonates. PAGE 123 123 A B Figure 51. The 3D neonatal head model visualized using Pro ENGINEER (Parametric Technology Corp.). A) the boundary shape and B) the internal structures. Figure 5 2 The neonatal head model visualized using Comsol 3.4, showing the anatomical structures and scalp electrode configuration. PAGE 124 124 Figure 5 3 Axial, saggital and coronal views of realistic geometry model, showing ventricul ar and central structures. A B Figure 5 4. The two ventricle structures (red dots) added within the brain, and the six anomaly positions (blue dots) within the ventricles. PAGE 125 125 A B C Figure 55. The three models used for data generation. A) The homogeneous R G model (M model). B) The RG phantom. C) The Gent model (G model) Figure 56. Procedures of constructing a headshaped phantom. PAGE 126 126 Figure 57. One slice (#74) of the original Gent model MRI data, showing the five major structures in the head. Figure 58. Dividing a rectangular brick element (12345678) into six tetrahedral elements, which are: 1245, 2456, 2346, 3678, 3468 and 4568. PAGE 127 127 Figure 59. Sensitivities and selectivities found in the regions of interest using a uniform RG sensitivity matrix. A) S ensitivities in the two spherical regions, C) Sensitivities in the ventricle regions B) Selectivities in the two spherical regions, D) Selectivities in the ventricle regions. PAGE 128 128 Figure 510. Comparisons between reconstructions using SPS and RGS matrix. Axial (Relative radial position of z = 0.3) and sagittal ( x = 0.2) c ross sections (first and second columns) and isosurface s (third column) for (a) ideal bleed ing at position 1 of the realistic geometry model an d reconstructions of the data collected from the realistic geometry model (b) using the SPS and (c) using RGS matrix Isosurfaces were calculated at half maximum voxel values within each image. PAGE 129 129 Figure 511 Image and conductivity profile in reconstructions of different anomaly pairs. A) 1 4, B) 2 5, C) 36 and D) 16. Anomalies are located at approximately 0.25 x The level at which the two anomalies are resolvable is indicated at right by the dotted line. By the criteria specified, A, C, D are resolvable. B is not resolvable. PAGE 130 130 Figure 512. Quantification Indices (with the corresponding volume estimation labeled on the right) for the multi site bleeding cases using SPS and RGS The bleeding could accumulate at any single or combinations of the 6 bleeding sites. T here were 123456 66666663 CCCCCC cases in total Figure 513. Comparison of average QI errors (with the corresponding er rors in volume estimation labeled on the right) for the 63 cases using the two sensitivity matrices under 11 different SNR levels ranging from 60 dB to 90 dB. Error bars show the range of QI values obtained at each noise level. PAGE 131 131 A B C D Figure 514. Recon structions with the RG matrix and SP matrix using the data from the four models. A) model M, B) model M phantom, C) uniform model G, D) layered model G. First and second row: anomaly on the right. Third and fourth row: anomaly on the left. PAGE 132 132 Table 5 1. Resol ution values of the reconstructions for all the anomaly volumes. Left Right S Matrix 1 2 3 4 5 6 1 2 3 4 5 6 M Model SP 0.257 0.258 0.259 0.260 0.259 0.257 0.228 0.251 0.248 0.245 0.255 0.252 RG 0.131 0.170 0.169 0.171 0.176 0.171 0.182 0 .200 0.199 0.198 0.198 0.199 M Phantom SP N/A 0.312 0.303 0.264 0.266 0.270 N/A 0.269 0.253 0.270 0.238 0.302 RG N/A 0.123 0.184 0.181 0.194 0.195 N/A 0.161 0.177 0.164 0.202 0.187 Uniform G Model SP 0.267 0.283 0.290 0.298 0.307 0.312 0.174 0.187 0.192 0.194 0.193 0.192 RG 0.181 0.179 0.179 0.186 0.187 0.189 0.217 0.213 0.212 0.217 0.220 0.222 Layered G Model SP 0.174 0.188 0.191 0.210 0.212 0.210 0.178 0.206 0.211 0.213 0.213 0.214 RG 0.172 0.167 0.163 0.159 0.160 0.164 0.197 0.184 0.17 6 0.173 0.176 0.184 A B C D Figure 515. Quantification indices for the images reconstructed with the RG matrix and SP matrix Data was collected from A) model M, B) model M phantom, C) uniform model G, D) layered model G. Anomalies were on the left. PAGE 133 133 CHAPTER 6 STUDIES USING PIGLET MODELS Introduction So far we have described promising results in numerical simulations and phantom experiments. To validate the true quality of our method, we also performed experiments on animal models. An appropriate animal model is essential for research on human applications since ethical considerations prohibit many investigations in humans (Baltzell et al. 1987). Piglets have been chosen as animal models in many neonatal studies (Aquilina et al. 2007, Puiman and Stoll 2 008, Jones et al. 2008), because of the anatomical, physiological, immunological and metabolic similarities between piglets and human neonates. Piglets have also been used in EIT applications in the study of hemorrhage (Xu et al. 2007, You et al. 2008). Th erefore, we also chose to use a piglet model in our research to study intraventricular hemorrhage in neonates. Methods Piglet 1 The experiment on piglet1 was mostly a feasibility test for our EEG method. The purpose of this experiment was to observe if we could see a correlation between the signal change and saline injections. The head of the piglet was cut off after sacrifice and the brain was removed for another study. We used the head cavity for our experiment (Figure 6 1). As a consequence, this head w as incomplete in terms of surface geometry and anatomical structures. We used 50 mm ECG electrodes (Figure 6 2 A) and cut them to smaller size, then applied 16 of them to the scalp at their approximate locations in the EEG configuration. Because the electr odes did not stick PAGE 134 134 well to the skin, we had to tape many down when adding the extra strain of the EIT system cables. We made an artificial gel brain using TX151 and agar (Figure 62 B). The conductivity of the gel was measured to be 0.6 S/m. The shape wa s modified carefully so it could just fit into the brain cavity. A hole was made in the center of the brain to create a cavity for saline injections. The head construction was first monitored to obtain a reference data set that contained 20 measurements. A 4 ml bolus of saline (conductivity 1.3 S/m) was injected into the cavity inside the brain. Another 4 ml was injected 3 minutes later through the same location. Each injection was also measured 20 times. Piglet 2 and 3 Two female piglets were sacrificed by exsanguination at approximately 1 week of age under a protocol approved by the University of Florida Institutional Animal Care and Use Committee (IACUC). The sacrificed animals were decapitated and moved to our laboratory. In contrast to piglet 1, these two piglet heads were intact. We first removed hair from the skin, and then marked the 16 electrode locations on the scalp using a permanent marker. Markings for locations were made using scaled distance measurements from nasion to the mid point between t he ears and left to right jaw distances. Sixteen 4 mm neonate EEG electrodes (Biopac Systems Inc. www.biopac.com ) were filled with electrode gel and fastened to the scalp with adhesive rings (Biopac Systems Inc.) (Fig ure 63 A). Use of neonatespecific EEG electrodes produced much better results in terms of adhesion compared to the ECG electrodes used on piglet 1. Saline solution with conductivity 1.3 S/m was made by dissolving salt at a concentration of approximately 6 g/L in water, which was the same as the saline we used for phantom experiments in the earlier chapters. An artificial fontanel was then PAGE 135 135 created on the skull of piglet 3 (Figure 6 4 A). The procedure used for this was as follows. The head was fixed in place using a table vise. The scalp was cut open in a T shape, avoiding electrode markings. The skin underneath the T shape was detached from the skull carefully with a scalpel. We then held the scalp open with two hemostats, taking care to detach the scalp from the skull as little as possible. However, we did need enough skull area exposed to make an opening. A diamondshaped hole was then created with a bone saw at the intersection of saggital and coronal sutures. The scalp flap was then replaced and sewn in place (Figure 6 4 B). Bloodequivalent saline was injected near the ventricles on left and right sides. We added 5 drops of blue dye into the 1 liter of saline used for piglet 3, so that we could dissect the brain after the experiment and determi ne where the saline had been injected. In the case of piglet 2, injections were made through the brain stem, and a total volume of 6 ml was injected to the left side and 7.5 ml was injected to the right side. For piglet 3, injections were made via the arti ficial fontanel, with i njections made in increments of 0.5 ml every 30 seconds. A total volume of 3.5 ml was injected to the right side and then 4 ml was injected to the left side of piglet 3. Piglet 4 (the MRI Piglet) In vivo experiments are important be cause this is the only way we can assess how our electrical measurements would be affected by physiological changes such as breathing and heart beats. Another reason is that the fluid injected into the ventricles would probably circulate differently in a l ive animal than in the post mortem experiments. One problem we were facing was how to make the injections into the ventricles. The ventricles in the piglet brain are tiny and it would have been hard to locate the ventricles without any external assistance. We therefore constructed a 3D PAGE 136 136 guide to match the neonatal piglet head geometry. The direction and depth of blood injections could then be accurately controlled. The procedures we used in making the guide are described below. These procedures, together w ith the post mortem experiment followed, were approved by the IACUC. The piglet (Figure 65 A) was euthanized by administration of IV Sodium Pentobarbital (100 mg/kg). It was then immediately delivered to the MRI room, and scanned with a 3T MRI machine (Fi gure 65 B). A 3D piglet head model was then reconstructed, and a mold that perfectly matched the head geometry was constructed with a guide attachment opening on top (Figure 66 A). The direction of the guide opening pointed to one of the ventricles. We constructed two guides using a ZPrinter310 3D printer (Z Corp., Burlington, MA, USA), one for the left ventricle (Figure 66 B), and the other for the right ventricle. Each guide was similar in geometry, only slightly differing in the orientation of the cy lindrical opening. The ventricle depths were also determined from the 3D model. We measured that the distance from ventricle to the entry point on the scalp was 17 mm and the distance from ventricle to entry point on the attachment was 66 mm in each case. A range of metal attachments could be connected with the opening, each having a diameter matched to a different catheter size to allow accurate placement. We chose an 18 gauge attachment to facilitate guidance of the catheter guide wire. The scanned pigl et was then transported to our lab, where we performed another post mortem experiment (Figure 67). The experimental procedures were very similar to piglet 3, except that we did not make an artificial fontanel for piglet 4. The guide was not used in this experiment. The needle was pushed directly through the scalp and skull and we first injected 0.5 ml every 10 seconds to the right side of the brain. To estimate PAGE 137 137 the minimum amount of bleeding we could detect, we then injected saline at a rate of 0.1 ml ever y 10 seconds to the left side of the brain. The saline used in this experiment had the conductivity of 0.67S/m. Piglet 5 This was our first in vivo piglet experiment. All in procedures for this and the following in vivo experiments were approved by IACUC. The piglet was first anesthetized using isoflurane by mask. Body temperature and heart beat were monitored throughout the experiment. Blood was removed from the piglets umbilicus using an umbilical artery/vein catheter (UAC/UVC). A catheter with 0.05 inch inner diameter and 0.08 inch outer diameter was then guided into the brain using a guideware insertion technique (Appendix B), with the assistance from the 3D guide we made earlier. The detailed experiment procedures are described in Appendix B. However, in this first in vivo experiment we failed to obtain blood from the umbilicus. We actually found the vein in the umbilicus successfully in the first place. We then decided to leave it there and draw the blood right before making injections. However, blood clotted in the UVC during the ventricular catheter insertion procedure and we were not able to draw any blood into the syringe. Therefore, we ended up injecting saline in this experiment. The saline was injected at the rate of 0.1 ml every 10 seconds. Pigl et 6 In this experiment we removed blood from the umbilicus immediately after it was catheterized, and following placement of the ventricular catheter we successfully injected blood into the ventricles. The head of the piglet was dissected and preserved in 10% formaldehyde for several weeks. The brain was dissected after its preservation so we could verify where the blood was injected and clotted. PAGE 138 138 Piglet 7 and 8 These two experiments were performed on the same day. There were a few improvements from the piglet 6 experiment. Bleeding was observed in piglet 6 experiment when inserting the first dilator into the brain. More bleeding was observed when introducing the second dilator. The cause of bleeding was suspected to be the entry path and the size of the dil ators. Therefore, we made a new guide for introducing the ventricular injection catheter. Using this new guide, the cannula entry point on the skin was 14 mm away from the ventricles, comparing to 17 mm using the old guide. Also we used a new type of catheter (ColeParmer, Illinois, USA) made of polyimide for blood injection. This catheter also had an inner diameter of 0.05 inches, but a much smaller wall thickness (0.002 inches) compared to the old one. Because of its smaller outer diameter, we did not hav e to use the dilator any more. These improvements largely reduced the extent of bleeding. Another improvement was that we drilled a hole in the skull using a bone drill before introducing the cannula. This made it much easier to insert the cannula into the brain. Therefore, we could control the entry point and depth with more accuracy. Blood was injected at the rate of 0.2 ml per 10 seconds for piglet 7 and 0.5 ml per 20 seconds for piglet 8. Piglet 9 and 10 These two experiments were performed on the same day. The procedures were very similar to the experiment on piglet 8, except that we used vetbond tissue adhesive (3M Global Headquarters, MN, USA) on these two piglets. Vetbond was applied at the brain entry point after the catheter was inserted in place. The reason for doing this was to prevent blood from flowing back through the entry point when making injections. It also helped to fix the catheter in place. Vetbond was also applied on the scalp along the PAGE 139 139 incisions to prevent any blood or CSF from flowing out of the skin. Blood was injected at the rate of 0.5ml per 20 seconds for both piglets. Results Piglet 1 Due to the simple experiment setup and the incomplete skull structure for piglet 1, we had electrode contact problems which caused voltage overflows in the measurements. Therefore, we were not able to reconstruct images for the saline injected. However, we did observe doubled voltage changes for the second 4 ml injection comparing to the first one. Figure 68 shows the 182 voltage changes for the tw o saline injections. Piglet 2 and 3 The reconstructed isosurface images shown in Figure 69 show the progression of reconstructed data in the head as bloodlike saline was injected into the head of piglet 2. The reconstructions clearly show an anomaly grow s in size as more saline is added. Plots of the quantity index derived from the image sequence as a function of added saline volume showed a linear dependence of QI on volume (Figure 610). The reconstructed isosurface images for Piglet 3 were shown in Figure 611 and the QI values were plotted against injection time in Figure 6 12. Only reconstructions for saline injections on the right were displayed for piglet 3. We first injected 3.5 ml on the right. When we injected on the left, saline started to leak from the sutured scalp. Therefore, we were not able to reconstruct images for the left side injections. However, the leakage was reflected clearly in the QI plot (Figure 612). PAGE 140 140 Piglet 4 The reconstructed isosurface images for the total 2.5 ml injections t o the right side were shown in Figure 613. The QI values were plotted against injection time in Figure 6 14 A. We can see that the QI was always trying to return to the baseline after each injection. The absolute QI values were on a different scale from t he results for piglet 2 and 3. The trend was more clearly reflected in the QI curve for the 0.1 ml/ 10 s injection on the left side (Figure 614 B). In this experiment, we were able to detect each 0.1ml injection. However, the QIs returned to baseline quic kly right after each injection. In the end, the accumulated QI stopped going up after the second injection. Piglet 5 and 6 We administered injections of blood or saline at the rate of 0.1 ml every 10 seconds for both piglet 5 and piglet 6. However, in both experiments we were not able to obtain a stable reference measurement. The signal changes caused by the injections were found to be completely dominated by noise. Figure 615 shows a particular measurement (measurement 79 of the 182 measurements in EEG cu rrent pattern, for which current was injected between electrode Cz and Oz, and voltage was measured between electrode FP2 and O2) changing with time. We could not observe clear signal changes during the injection period from the figures. Piglet 5 woke up d uring the injection period. Its movement caused a big spike in the measurements (Figure 615 A). The brain of piglet 6 was preserved in 10% formaldehyde solution for 4 weeks, and then sliced into 2 mm thick slices. We could see that blood existed in both v entricles (Figure 6 16). PAGE 141 141 Piglet 7 and 8 With the higher injection rates of 0.2 ml per 10 seconds and 0.5ml per 20 seconds used on piglet 7 and piglet 8, we were able to detect changes in the signal and reconstruct images. The images were reconstructed usin g a weighted TSVD method. Truncation point was chosen at 50. Figure 6 17 shows the correlation between the QI values and injected blood volume. Reconstructed images at each injection point were also displayed on the side. In piglet 8, due to the fast injec tions, blood was observed leaking out of the skin at the third injection. This can be observed in the QI curve in Figure 618. Using the same procedure as for piglet 6, we preserved the brains in separate jars containing 10% formaldehyde solution and sliced them after preservation was complete. In the brain slices for piglet 7 (Figure 619), we could see blood clotted in both ventricles. The catheter path was very close to the middle line. However, the left ventricle was more dilated and contained more clot ted blood. In the brain slices for piglet 8 (Figure 620), we saw that the catheter path went directly into the left ventricle. We could see a big clot of blood in the left ventricle and nearly no blood in the right ventricle. Piglet 9 and 10 We experienced electrode contact problems on piglet 9. Voltage overflow was observed when we made the measurements. We were unable to see any voltage changes corresponding to the blood injections. Therefore, the result for piglet 9 is not presented here. Results for pi glet 10 are shown in figure 621. We observed a good correlation between the QI values and injected blood volumes. The reconstructed images showed conductivity changes on the right hand side. The brain of piglet 10 was PAGE 142 142 also preserved in formaldehyde. The brain slices (figure 6 22) showed blood clotted in the right ventricle. Summary From all the experimental data we have available, we can determine a relationship between the QIs and injected volumes when measuring using the IIRC system. Theoretically, the r elationship should be linear. That is, we should be able to find a relation of the form QIpvolume (6 1) where p is The purpose of this study is to find a reasonable factor p that we can use to estimate the volume of bleeding in the vent ricles. In Figure 623, the QIs obtained in each experiment are plotted against the injected volumes (saline or blood). We made a linear fit of QIs against known injected volume. The relationships we established were: For the three in vivo piglets (piglet 7, 8, 10), we found 6 71.510 p 6 81.710 p and 6 102.410 p respectively. By averaging the 3 values, we have 61.910invivop with a standard deviation of 54.610 (equation 6 2). All the in vivo piglets were injected with blood. 651.9104.610invivop (6 2) For the post mortem piglet (piglet 4), we found 6 41.510 p This was our only post mortem experiment on an intact piglet (equation 63). The piglet was injected with 0.67 S/m saline. 61.510postmortemp (6 3) PAGE 143 143 For the piglet heads (piglet 2 and 3), we found 6 2_4.810rightp 6 2_6.410leftp and 6 36.910 p respectively. By averaging the 3 values, we have 66.110headp with a standard deviation of 61.110 (equation 6 4). All the piglet heads were injected with 1.3 S/m saline. 666.1101.110headp (6 4) Discussion The experiment on piglet 1 gave us encouraging results and indicated the potential of using EIT on head applications, although we were not able to do a detailed quantitative analysis using the measurements. The reconstructions for piglet 2 clearly showed an anomaly that grew in size as more saline was injected in to the brain. The spherical reconstructions could not provide accurate information about the locations where the saline was injected. However, we could at least differentiate between the left and right injections in Figure 69 Plots of the quantity index derived from the image sequence as a function of injected saline volume showed a linear dependence of QI on volume. The sensitivities (QI/ml) of injections on the left and right sides were somewhat different, which can be most likely explained by differenc es in the relative locations of left hand and right hand side injections. The open skull piglet (piglet 3) experiment showed similar QI sensitivities between the left hand and right hand side injections, although we could observe only 1 injection for the l eft hand side due to leaking. If we compare Figure 610 and Figure 612 carefully, we can find that the QI sensitivity for the openskull piglet is slightly higher than the closedskull one. This result was actually expected from our earlier modeling studi es. However, since we could not determine the relative injection locations in these two experiments, this QI sensitivity difference might PAGE 144 144 be also cause by the spatial variance of QI. The saline used in both Piglet 2 and 3 experiments was 1.3 S/m, which is about twice more conductivity than blood (0.67 S/m). Therefore, we observed stronger signal than that was supposed to be caused by bleeding. To establish a relationship between QI and blood volume, we needed to use blood like saline or real blood in the following experiments. Piglet 4 was our first animal experiment using an intact piglet. An interesting finding in this experiment was that the injected saline was always trying to flow away instead of staying in a fixed location, which was not observed in piglet 2 and 3. A possible explanation is that an intact piglet is nevertheless a closed system, even though it is post mortem. Therefore, fluid circulation might be expected in such a system. As a result, the QI sensitivity was in a much lower scale compa red to the QI sensitivities for piglet 2 and piglet 3. An encouraging result was that we could easily detect the 0.1 ml saline injections in this post mortem experiment, although they returned to baseline right afterward. Unfortunately, we were not able t o detect 0.1 ml injects in the in vivo experiments on piglet 5 and piglet 6. Analysis on the voltage measurements showed that the signal to noise ratio (SNR) in the post mortem experiments (piglet 2, 3 and 4) was around 70 dB. But the SNR for the in vivo e xperiments (piglet 5 and 6) was only around 50 dB, which means noise accounts for 0.3% of the signal magnitude. An estimation from the post mortem experiment showed that the signal change caused by a 0.5 ml saline injection was approximately 0.8% of the si gnal. Therefore, the signal change caused by a 0.1 ml injection is not likely to be detected in in vivo experiments. Improved SNR in EIT hardware system would be desirable for more accurate detections. PAGE 145 145 In experiments for piglet 7, piglet 8 and piglet 10, w e increased the injection rate. And we were able to observe the slight signal changes caused by the injections. More importantly, we could locate the ventricles with more accuracy due to the use of an improved guide and injection catheter. Before we started the injections, we could see CSF coming up through the injection catheter, which indicated that we might have located the ventricle correctly. With the measured voltage data, we could reconstruct negative conductivity changes at the corresponding locations, which further indicated that we have successfully injected blood into a more conductive CSF environment. This was double confirmed by the coronal brain slices in Figure 619, 620 and 6 22. To substantiate this, we performed a Linear Discriminant Analy sis (LDA) on the QI data for the 3 in vivo piglets. The analysis showed that the diagnosis of bleeding had a 100% true negative rate, 24% false negative rate, 76% true positive rate and 0% false positive rate (Table 6 1). In Figure 623, we found that the QI factors p were very different between the in vivo and post mortem experiments. In the in vivo experiments, we successfully injected blood into the ventricles. So the conductivity contrast was 0.671.30.63 SmSmSm In th e post mortem experiment on piglet 4, the saline ( 0.67 Sm ) was actually injected into the brain. So the conductivity contrast was 0.670.170.5 SmSmSm Therefore, the ratio between invivop and postmortemp should be around 1.26 while our result showed a ratio of 1.2439 In the experiments for piglet head 2 and 3, we actually injected saline with conductivity 1.3 S/m into the brain. So the conductivity contrast was 1.30.171.13 SmSmSm Therefore the ratio between invivop and headp should be around 0.55 while our result showed a ratio of 0.31 We did observe in in vivo PAGE 146 1 46 experiments that the QI did not increase linearly, and instead always tended to return to the baseline. This probably indicated that the injected volume did not all stay in the ventricles and can explain why the ratio between invivop and headp was lower than the expected value. Conclusion We have successfully introduced bleeding into the ventricles of piglet models using a guide wire insertion technique. Images reconstructed using a spherical sensitivity matrix and a weighted TSVD algorithm showed negative changes at the approximate corresponding location where the blood was injected. These images also produced a consistent correlation between the quantification indices and the injected blood volumes. We successfully detected and quantified 0.5ml blood injections in two piglets and 0.2ml blood injections in one piglet, but failed to detect 0.1 ml saline or blood injections. The detection of smaller volumes would become possible if the hardware SNR improves All these promising results indicated the possibility of using such an EIT method to detect and quantify intraventricular hemorrhage in neonates. PAGE 147 147 Figure 61 The piglet head and electrode configuration used on piglet 1. A B Figure 62. Electrodes and artificial brain used for piglet 1 experiment. A) The ECG electrodes. B) The artificial brain made using TX151 and agar. PAGE 148 148 A B Figure 63. Experiment setup for piglet 2. A) The EEG electrode layout. B) The saline was injected through the neck with 16g needle A Figure 64. Experiment setup for piglet 3. A) The artificial fontanel made using a bone saw. B) Saline was injected through the scalp and fontanel. PAGE 149 149 A B Figure 65. Piglet 4 (The MRI piglet). A) The piglet used for MRI scan. B) A coronal slic e of the piglet MRI head images showing the two lateral ventricles. A B Figure 66. The injection guide designed to assist introducing the canula into the ventricle. A) The numerical guide model constructed from the piglet head model, displayed in ProE. B) The plastic guide made using a 3D printer. Both images shown are for the left ventricle. PAGE 150 150 Figure 67. Post mortem experiment on piglet 4. The EIT system was shown on the back. EEG electrode layout was applied on the piglet scalp using 4mm EEG electrodes. Saline was injected through the top. Figure 68. Difference voltage measurements generated by the two 4ml saline injections on piglet 1. PAGE 151 151 A B Figure 69. Isosurface plots of reconstructions of injections to the closed skull piglet (piglet 2). A) Injec tions to the left hand side. B) Injections to the right hand side. The three electrodes located together on the equator of the sphere at foreground right of each image are (left to right) electrodes O1, Oz and O2. PAGE 152 152 Figure 610. Quantification index as a f unction of injected saline volume for piglet 2. Saline was injected at 0.5 ml per 30 seconds for both left hand and right hand side. A total of 6ml was injected on the left and 7.5 ml on the right. Figure 611. Isosurface plots of reconstructions of inj ections to the right open piglet skull (piglet 3). PAGE 153 153 Figure 612. Quantification index as a function of injection time for piglet 3. Saline was injected at the rate of 0.5ml per 30 seconds for both left hand and right hand side. Figure 613. Isosurface plots of reconstructions of injections to the right side on piglet 4 (the intact MRI piglet). PAGE 154 154 A B Figure 614. Quantification index as a function of injection time for piglet 4. A) 0.5 ml injection every 10 seconds on the right side. B) 0.1 ml injection every 10 seconds on the left side. A B Figure 615. Signals recorded in one of the measurements for piglet 5 and 6. A) Signal changing with time in measurement 79 for piglet 5. B) Signal changing with time in measurement 79 for piglet 6. PAGE 155 155 Figure 616. Coronal brain slices of piglet 6. Slice number and thickness are indicated near each slice. The orientations (Superior, Inferior, Left and Right) of all the slices are marked in the figure. The anterior of each slice is facing inside. Blood (indicated with red arrows) can be observed clotted in both ventricles. PAGE 156 156 Figure 617. QI values and reconstructed images for in vivo experiment on piglet 7. PAGE 157 157 Figure 618. QI values and reconstructed images for in vivo experiment on piglet 8. PAGE 158 158 Figure 619. Brain s lices taken in coronal planes for piglet 7. The orientations (Superior, Inferior, Left and Right) are marked on each individual slice. The anterior of each slice is facing inside. Blood (indicated with red arrows) can be observed clotted in the left ventri cle on slice 9 and 10. PAGE 159 159 A B Figure 620. Brain dissection for piglet 8. A) Brain slices taken in coronal planes for piglet 8. The orientations (Superior, Inferior, Left and Right) are marked on each individual slice. The anterior of each slice is facing inside. Blood (indicated with red arrows) can be observed clotted in the left ventricle on slice 6 11. B) A cross sectional coronal plane picture (looking from front) showing the catheter path and blood clotted in the left ventricle. Blood is indicated w ith a red arrow. PAGE 160 160 A B Figure 621. Results for in vivo experiment on piglet 10. A) QI values changing with time during the injection period. B) Isosurface plots at the time points indicated in the QI plot. PAGE 161 161 A B Figure 622. Brain dissection for piglet 10. A) Brain slices taken in coronal planes for piglet 10. The orientations (Superior, Inferior, Left and Right) are marked on each individual slice. The anterior of each slice is facing inside. Blood (indicated with red arrows) can be observed clotted in the right ventricle on slice 7 12. B) A cross sectional coronal plane picture (looking from front) showing blood clotted in the right ventricle. Blood is indicated with a red arrow. The catheter was preserved in the brain to demonstrate the injection ent ry point. PAGE 162 162 Figure 623. Linear fits between the QI values and injected volumes for all the available piglet experiment data. Table 6 1. Linear Discriminant Analysis (LDA) for all the in vivo piglet QI data Number of observations and percent classified i nto bleed From bleed 0 1 total 0 154 100% 0 0% 154 54.8% 1 30 23.62% 97 76.38% 127 45.2% total 184 65.48% 97 34.52% 281 PAGE 163 163 CHAPTER 7 SUMMARY Conclusion This work aimed to develop an effective method to detect and quantify intraventricular hemorrhage i n premature neonates using Electrical Impedance Tomography. We started with numerical simulations on a homogeneous spherical head model, then on a spherical model with important anatomical structures added. Three candidate current patterns (RING, EEG and C z RING patterns) were proposed in the beginning. After conducting sensitivity analysis, we found that the EEG pattern had the best sensitivities and selectivities in general in our regions of interest. Reconstructed images with the EEG pattern using data g enerated from simulations and saline phantoms also showed the best image qualities and quantification accuracies. The EEG pattern could also take advantage of the unique characteristics of a neonatal skull, which include its higher conductivity and the opening fontanel on top. This was proved in the sensitivity analysis and the comparison between the openskull model and closed skull model. The findings from spherical models were then applied on models with realistic boundary geometries. We studied the effe ct from model geometry mismatch by comparing the reconstructions from two sensitivity matrices, one calculated from a homogeneous spherical model ( SPS ), the other calculated from a realistic geometry model ( RGS ). The results indicated that the RGS reconstructions guaranteed the best image qualities only when the subject geometry is perfectly matched with the forward model. In addition to that, RGS did not show an y advantage over S_SP for the purpose of quantification. Therefore, we concluded that using the spherical sensitivity matrix PAGE 164 164 would be more appropriate for neonate applications, since the head shape varies from patient to patient. Piglet animal experiments both post mortem and in vivo were conducted to investigate the true quality of the EEG method. Skull impedances were measured after each experiment to estimate the radial conductivity for neonatal piglet skulls. We found that the average conductivity of the fresh skull samples was 27.8 mS/m, which was about twice higher than the conductivity for adult human skull reported in the literature (15 mS/m). In post mortem experiments, we injected saline into the piglet brains. We were able to detect as low as 0.2 ml injections. The QIs showed a stable linear relationship along with the injections. In the in vivo experiments, we obtained blood from the piglets umbilicus instead of using saline. We successfully injected blood into the ventricles with the aid of a n injection guide. Negative conductivity changes were observed in the reconstructed images. We also observed a linear relationship between the QIs and injected blood volumes. The data was more affected by noise compared to the post mortem experiments data. However, we were able to detect 0.5 ml blood volumes in two piglets and 0.2 ml blood volumes in one piglet successfully. The QI scale levels in all the 3 in vivo experiments were consistent. We preserved the piglet brains for the in vivo experiments and s liced them afterwards. We could observe blood clotted in the correct side of the ventricles which double confirmed the reconstructed images. All the promising results indicated that we can use EIT to detect and monitor intraventricular bleeding in piglets and probably extend this application to premature neonates. PAGE 165 165 Future Work Improving in vivo A nimal Experiment We have so far conducted 6 in vivo piglet experiments. More experiments are needed to validate the reconstruction and quantification standards. With in these 6 experiments, we were able to detect the blood volume in 3 of them, but failed in the other 3. The failures were presumably caused by bad electrode contacts. It could be one or multiple of the 16 measurement electrodes or the ground electrode. It would be very helpful to have a function in the software, so we can check the electrode connections in real time. The electrodes can also be improved. We have been using 4mm EEG electrodes in the experiments. To attach the electrodes to the scalp, we need to first put on 16 electrode stickers, and then inject conducting gel into each electrode carefully and attach them to the stickers. The amount of gel injected into each electrode needs to be controlled very carefully. Too much or too little will both cause electrode contact problem. Moreover, this whole process normally took more than half an hour. However, we should keep in mind that the catheter was already inserted into the brain when we were working on the electrodes (refer to Appendix B for details). This could cause physiological changes during a half an hour period and consequently affect our measurement accuracy. Therefore, new types of electrodes will be appreciated if we can make this process faster. Improving the M easurement Strategy The 16elec trode EEG current pattern has produced promising results in numerical simulations, phantom experiments and animal experiments. However, this pattern was not an optimized one. Due to the limitation in hardware design, the measurements were all taken from ad jacent pairs of electrodes. Although it contained all the independent PAGE 166 166 measurements, a number of these measurements were very low in magnitude and were likely to introduce errors when noise was presented. Our new EPack3 system is an 8electrode EIT system. It has more flexibility in selection of current and voltage electrode pairs. Therefore, we are going to reduce the number of electrodes to 8, and use an optimized current pattern. Base on our experience from the current work, using 8 electrodes should be enough for the purpose of quantification, although we may have a compromise in reconstructed image quality. However, using a small number of electrodes is always desirable in clinical applications since the scalp area of a neonate is limited. It may also sp eed up the electrode setup process in the in vivo piglet experiments PAGE 167 167 APPENDIX A USEFUL C++ CODE FOR CONJUGATE GRADIENT M ETHOD An important subprocess in conjugate gradient optimization is performing line minimization along each given direction. This i nvolves two procedures, bracketing the minimum and searching for the minimum within the range. They are implemented in the following C++ functions: mnbrak() and brent(). The function linmin() calls mnbrak() and brent(), and accomplish line minimization. Th e conjugate gradient method is implemented in frprmn(). For more details, please refer to Press et al. 1989. Bracket the Minimum void mnbrak(double *ax,double *bx,double *cx,double *fa,double *fb, double *fc, int n, double *pcom, double *xicom, double *F, double *outarr, double *xt) { double ulim,u,r,q,fu,dum; *fa=f1dim(*ax, n, pcom, xicom, F, outarr, xt); *fb=f1dim(*bx, n, pcom, xicom, F, outarr, xt); if (*fb > *fa) { SHFT(dum,*ax,*bx,dum) SHFT(dum,*fb,*fa,du m) } *cx=(*bx)+GOLD*(*bx *ax); *fc=f1dim(*cx, n, pcom, xicom, F, outarr, xt); while (*fb > *fc) { r=(*bx *ax)*(*fb *fc); q=(*bx *cx)*(*fb *fa); u=(*bx) ((*bx *cx)*q (*bx *ax)*r)/ (2.0*SIGN(MAX(fabs(qr),TINY),q r)); ulim=(*bx)+GLIMIT*(*cx *bx); if ((*bx u)*(u*cx) > 0.0) { fu=f1dim(u, n, pcom, xicom, F, outarr, xt); if (fu < *fc) { ax=(*bx); *bx=u; *fa=(*fb); *fb=fu; return; } else if (fu > *fb) { *cx=u; *fc=fu; return; PAGE 168 168 } u=(*cx)+GOLD*(*cx *bx); fu=f1dim(u, n, pcom, xicom, F, outarr, xt); } else if ((*cx u)*(uulim) > 0.0) { fu=f1dim(u, n, pcom, xicom, F, outarr, xt); if (fu < *fc) { SHFT(*bx,*cx,u,*cx+GOLD*(*cx *bx)) SHFT(*fb,*fc,fu,f1dim(u, n, pcom, xicom, F, outarr, xt)) } } else if ((u ulim)*(ulim *cx) >= 0.0) { u=ulim; fu=f1dim(u, n, pcom, xicom, F, outarr, xt); } else { u=(*cx)+GOLD*(*cx *bx); fu=f1dim(u, n, pcom, xicom, F, outarr, xt); } SHFT(*ax,*bx,*cx,u) SHFT(*fa,*fb,*fc,fu) } } Search for t he Minimum double brent(double ax, double bx, double cx, double tol, double *xmin, int n, double *pcom, double *xicom, dou ble *F, double *outarr, double *xt) { int iter; double a,b,d,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm; double e=0.0; void nrerror(); double b_tang = 0; double a_tang = 0; double x_tang = 0; a=((ax < cx) ? ax : cx); b=((ax > cx) ? ax : cx); x=w=v=bx; fw=fv=fx=f1dim(x, n, pcom, xicom, F, outarr, xt); for (iter=1;iter<=BRITMAX;iter++) { xm=0.5*(a+b); tol2=2.0*(tol1=tol*fabs(x )+ZEPS); if(b == b_tang && a==a_tang && x==x_tang) int jjj = 1; b_tang = b; a_tang = a; x_tang = x; PAGE 169 169 if (fabs(x xm) <= (tol2 0.5*(ba))) { *xmin=x; return fx ; } if (fabs(e) > tol1) { r=(x w)*(fx fv); q=(x v)*(fx fw); p=(x v)*q (x w)*r; q=2.0*(qr); if ( q > 0.0) p = p; q=fabs(q); etemp=e; e=d; if (fabs(p) >= fabs(0.5*q*etemp)  p <= q*(ax)  p >= q*(bx)) { d=CGOLD*(e=(x >= xm ? a x : b x)); } else { d=p/q; u=x+d; if (u a < tol2  bu < tol2) d=SIGN(tol1,xm x); } } else { d=CGOLD*(e=(x >= xm ? a x : b x)); } u=((fabs(d) >= tol1) ? (x+d) : (x+SIGN(tol1,d))); if(u x == 0) { u = x+0.0001; if(u x==0) int kkk = 1; } fu=f1dim(u, n, pcom, xicom, F, outarr, xt); if (fu <= fx) { if (u >= x) a=x; else b=x; SHFT(v,w,x,u) SHFT(fv,fw,fx,fu) } else { if (u < x) a=u; else b=u; PAGE 170 170 if (fu <= fw  w == x) { v=w; w=u; fv=fw; fw=fu; } else if (fu <= fv  v == x  v == w) { v=u; fv=fu; } } } fprintf(stderr,"Too many iterations in BRENT \ n"); *xmin=x; return fx; } Line Minimization void linmin(double *p,double *xi, int n, double *fret, double *F, double *outarr, double *xt) { int j; double xx,xmin,fx,fb,fa,bx,ax; ax=0.0; xx=1.0; bx=2.0; mnbrak(&ax,&xx,&bx,&fa,&fx,&fb, n, p, xi, F, outarr, xt); *fret=brent(ax,xx,bx, LTOL,&xmin, n, p, xi, F, outarr, x t); for (j=0;j PAGE 171 171 fp=fnc(p, n, F, outarr); dfnc(p,xi, n, F, doutarr); for (j=0;j PAGE 172 172 APPENDIX B PROCEDURES FOR IN VI VO PIGLET EXPERIMENT S Before experiment starts, use 10U/ml heparin to heparinize all the items that will be in contact with blood, including syringes, needles, catheters and the guide wire. Set up the 5% dextrose solution bag (D5 drip) and the administration set with the intravenous pump. Stop the pump at this stage. Place the piglet prone on a heated pad. Commence isoflurane/O2 administration to the piglet. One person is needed to control the device (watching the reaction from the piglet and adjusting gas pressure). Another person is needed to hold the mask tightly over the piglet snout at all times. Remove hair from scalp area using a razor blade. Wetting the hair can make the shaving process easier. Also remove some hair from regions below both ears, where we are going to attach electrodes T7 and T8. Clean the skin with abrasive wipes if necessary. Then dry the skin with paper towel. Mark the 16 electrode positions using a permanent (Sharpie) marker. Move the piglet into the surgery room and transfer it to the surgery bed. Insert the temperature probe into the piglet rectum. Tape the wire onto the piglet tail to hold it firmly. Attach oximeter to one rear trotter, and validate readings against heart rate. A person is needed to record the temperature and heart rate every 2 minutes. Carefully turn the piglet supine. Before doing surgery on the umbilicus, the UVC/UAC needs to be prepared. One end of the catheter has two branches. Connect each of the branches with a 3way stop cock. One 3way stop cock is connected with one syringe, which will be used to draw blood from the umbilicus later. The other 3way stop cock is connected with a syringe and t he catheter of the administration set. Both syringes should be filled with some heparin before connecting to the 3 way stop cock. (Figure B 1). The surgeon starts working on the umbilicus. A magnifier lamp will be needed to assist finding the blood vessel within the umbilicus. Insert the other end of the UVC/UAC into the vessel. Blood should be seen flowing into the catheter immediately. Suture on the UAC/UVC using Addison forceps. Tape down part of the catheter around the umbilicus to make it steady. PAGE 173 173 Turn the piglet prone carefully. Make sure the UAC/UVC, the temperature probe and the oximeter sensor do not fall off. Put the guide (either left or right) on the piglet head. The position can be determined by the eye mark and ear mark on the guide. Premark the cannula at 17 mm and 66mm with a permanent Sharpie. Introduce the cannula into the guide. Pierce the skull and keep going slowly until the 66mm mark matches the metal attachment in the guide. Hold the cannula and take the central needle out slowly. T hen raise the guide a little bit and hold the bottom of the cannula, as close to the skin as possible, to make sure the cannula does not move around while taking away the guide. Then remove the guide slowly. Introduce the dilator on top of the cannula, slowly. Once the dilator is close to the skin, switch to hold the top of the cannula as quick as possible. Then twist the dilator into the skull nice and easy. Remove the dilator slowly. Once the tip of the dilator is out of skin, switch to hold the bottom of the cannula. Always try your best to hold the cannula in place during this procedure. Bleeding may occur in this process. We may need a person to dip off the bleeding from time to time. The hole made by the dilator in the previous step is not big enough t o introduce in the 0.08 od catheter. Therefore, we need to use a bigger dilator and repeat the previous procedure. Pre mark the blood injection catheter (0.05 inner diameter, 0.08 outer diameter) at 17 mm. Send in the catheter on top of the cannula the sam e way we put in the dilators. Twist the catheter into the brain until the mark matches the skin. Once the catheter is in place, remove the cannula slowly. (The last 4 procedures have been modified since the experiment on piglet 7 and 8. We first determined the approximate entry point on the skin using the guide. We then cut the skin open and made a hole (diameter approximately 5mm) on the skull using a bone drill. We inserted the cannula following the same procedures After that, we introduce in the cathete r immediately, rather than using the dilator This new type of polyimide catheter had a much smaller wall thickness and could be inserted without dilating the entry point. We then sutured the skin back in place. ) Connect a 3 way stop cock with a blunted 16G needle and insert the needle into the other end of the catheter (the needle has to be blunted, otherwise it would pierce the wall when the catheter is bended). Another two ends of the 3 way stop cock are connected with two syringes. One is filled with bl ood for the blood injection later. The other is empty and haprinized for drawing CSF. Put the stop switch to the blood injection syringe, and hold this syringe with a clamp on a stand (Figure B 2). PAGE 174 174 Put the electrode stickers on the corresponding 16 posit ions. Then put on the 16 4mm EEG electrode. Electrode gel needs to be injected before putting on each electrode. The amount of gel injected needs to be controlled carefully. If you inject too much, the gel will flow out when pressing the electrode against the sticker. Then you will need to remove that sticker and put a new one there. According to the authors experience, it will be easier to put on the electrodes on the posterior first, then do the anterior ones. Finally, put an ECG electrode on one of the ears for ground connection. This whole procedure will take approximately 20 minutes. Try to remove some CSF using the empty syringe. At least remove the air in the catheter. Then close this branch. Turn on the EIT system and start the measurements. First d o a complete measurement using their default adjacent ring configuration and make sure there is no voltage over flow. If voltage overflow is observed, we can check the overflow log file and determine which electrode caused the problem, then reconnect that electrode to the skin. Start the EEG measurements. Set the scan interval to 2 seconds. Do a baseline measurement for 10 minutes. Administrator 0.1 ml blood every 10 seconds, until all the blood is injected. Continue recording for another 5 minutes. Turn the piglet supine and perform euthanasia. PAGE 175 175 Figure B 1. Experiment picture showing the setups for the umbilicus catheter. PAGE 176 176 Figure B 2. 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He graduated from the Daqing high school and entered the Tsinghua University in the year 1999. He earned his bachelors degree in 2003 in Biomedical Engineering. In the same year, he started to work in the Tsinghua Tongfang Co. Ltd. in Beijing as a fulltime programmer, expertise in Visual C++. In the year 2005, he moved to the USA and began his PhD study in biomedical engineering at the University of Florida. 