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Quantifying Measurement Uncertainty for Locating Hip Implant

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Title:
Quantifying Measurement Uncertainty for Locating Hip Implant
Physical Description:
1 online resource (31 p.)
Language:
english
Creator:
Zhang, Zenan
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Banks, Scott Arthur
Committee Members:
Fregly, Benjamin J

Subjects

Subjects / Keywords:
acetabularcupposition -- postoperativectmeasurement -- tha -- uncertaintyresource
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre:
Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Accurate placement of the acetabular cup during total hiparthroplasty is critical to long-term clinical success. Measurements of cupposition and orientation from postoperative CT scans are accepted as the goldstandard reference measurement, yet there have been no reports of the uncertainties associated with this method. We studied pre- and post-operativeCT scans for ten patients who received THA and measured the radiographicinclination and radiographic anteversion in an anatomic coordinate system. Toquantify measurement uncertainties, we repeated the measurements several timesand separately varied factors that might contribute to measurement error. Ourresults suggest the best measurements are achieved using full pelvis bonemodels with the acetabular area removed, and by matching the pre- andpost-operative pelvis models using 3D global registration. This standardized measurement has an accuracy, precision and bias of 0.3°, 0.7° and 0° for radiographic inclination, and 0. 2°, 0.6° and 0.1° for radiographicanteversion. We found similar results when using shorter pelvis bone segmentsfor registration. Including the periacetabular bone and/or using manuallandmark identification resulted in less accurate measurements. Post-operative CT measurements of cup position is a useful and accurate measurement referencestandard. Our results quantify the measurement uncertainty for this procedure and put previous reports of intraoperative measurement results into context.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Zenan Zhang.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: Banks, Scott Arthur.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045552:00001

MISSING IMAGE

Material Information

Title:
Quantifying Measurement Uncertainty for Locating Hip Implant
Physical Description:
1 online resource (31 p.)
Language:
english
Creator:
Zhang, Zenan
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Banks, Scott Arthur
Committee Members:
Fregly, Benjamin J

Subjects

Subjects / Keywords:
acetabularcupposition -- postoperativectmeasurement -- tha -- uncertaintyresource
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre:
Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Accurate placement of the acetabular cup during total hiparthroplasty is critical to long-term clinical success. Measurements of cupposition and orientation from postoperative CT scans are accepted as the goldstandard reference measurement, yet there have been no reports of the uncertainties associated with this method. We studied pre- and post-operativeCT scans for ten patients who received THA and measured the radiographicinclination and radiographic anteversion in an anatomic coordinate system. Toquantify measurement uncertainties, we repeated the measurements several timesand separately varied factors that might contribute to measurement error. Ourresults suggest the best measurements are achieved using full pelvis bonemodels with the acetabular area removed, and by matching the pre- andpost-operative pelvis models using 3D global registration. This standardized measurement has an accuracy, precision and bias of 0.3°, 0.7° and 0° for radiographic inclination, and 0. 2°, 0.6° and 0.1° for radiographicanteversion. We found similar results when using shorter pelvis bone segmentsfor registration. Including the periacetabular bone and/or using manuallandmark identification resulted in less accurate measurements. Post-operative CT measurements of cup position is a useful and accurate measurement referencestandard. Our results quantify the measurement uncertainty for this procedure and put previous reports of intraoperative measurement results into context.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Zenan Zhang.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: Banks, Scott Arthur.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045552:00001


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1 QUANTIFYING MEASUREMENT UNCERTAINTY FOR LOCATING HIP IMPLANT By ZENAN ZHANG A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUI REMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Zenan Z hang

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3 I dedicate this to Dr. Banks and all the other people in this study

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4 ACKNOWLEDGMENTS First, I would like to thanks my advisor, Dr. Scott A. Banks, from the bottom of my heart. He not only educates me but also guides me in daily life. I really enjoy ed his 50 th birthday party, hiking to the Pine Mountains and every conversation we have had Second, I want to thanks my lab mate, Nickolas Dunbar. I wil l always remember his patience, wisdom and creativity I am also looking forward to go hiking with him, pump water in the early morning one mile away from our camp site. Third I am grateful for the helps from all the other lab mates, surgeons and stuffs from UF, MAKO and LA. Without them, I cannot achieve that much academically and personally. At last but not the least, special thanks to my parents and my girlfriend for their support from behind.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 6 LIST OF FIGURES ................................ ................................ ................................ .......... 7 LIST OF ABBREVIATIONS ................................ ................................ ............................. 8 ABSTRACT ................................ ................................ ................................ ..................... 9 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 11 2 MATERIALS AND METHODS ................................ ................................ ................ 13 Subjects ................................ ................................ ................................ .................. 13 Measurement of Aceta bular Cup Orientation ................................ .......................... 13 Sources of Uncertainty ................................ ................................ ............................ 14 Global Registration vs. Manual Alignment ................................ .............................. 15 Impact of the Acetabulum ................................ ................................ ....................... 15 Impa ct of the Amount of Pelvis ................................ ................................ ............... 16 3 RESULTS ................................ ................................ ................................ ............... 20 Global Registration vs. Manual Alignment ................................ .............................. 20 Impact of the Acetabulum ................................ ................................ ....................... 20 Impa ct of the Amount of Pelvis ................................ ................................ ............... 20 Comparison of Factors ................................ ................................ ............................ 20 4 DISCUSSION ................................ ................................ ................................ ......... 24 APPENDIX: MATLAB CODE USED TO CALCULATE CUP ORIENTATION ................ 26 LIST OF REFERENCES ................................ ................................ ............................... 29 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 31

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6 LIST OF TABLES Table page 3 1 Cup orientation measurement results of RI using global registration and manual alignment methods. ................................ ................................ ............... 21 3 2 Cup orientation measurement results of RA using global registration and manual alignment methods. ................................ ................................ ............... 21 3 3 The impact of using the periacetabular bone on the RI and RA. ........................ 21 3 4 The impact of the amount of pelvis on the RI. ................................ .................... 22 3 5 The impact of the amount of pelvis on the RA. ................................ ................... 22 3 6 Cup orientation measurement results of RI for all evaluations. ........................... 22 3 7 Cup orientation measurement results of RA for all evaluations .......................... 23 4 1 Original and refined results from other intro op measurement. .......................... 25

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7 LIST OF FIGURES Figure page 2 1 Anatomic coordinates were derived from the pre op CT orientation and aligned to the medial/lateral axis formed by ASIS points. ................................ ... 17 2 2 The post operative pelvis model (white) is registered to the pre op pelvic model (orange), preserving the pre op coronal p lane. ................................ ........ 18 2 3 Flow chart of measuring the orientation of acetabular cup and list of uncertainty sources. ................................ ................................ ........................... 19 2 4 Flow chart of measuring the orientation of acetabular cup and list of uncertainty sources. ................................ ................................ ........................... 19

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8 LIST OF ABBREVIATIONS 3 D /2 D Three dimensions and two dimensions A CETABULAR AXIS T he axis perpendicular to the rim of the cup and passing through the center of the cup C T Computed tomography T HA Total Hip Arthroplasty

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9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requi rements for the Degree of Master of Science QUANTIFYING MEASUREMENT UNCERTAINTY FOR LOCATING HIP IMPLANT By Zenan Z hang August 2013 Chair: Scott A. Banks Major: Mechanical Engineering Accurate placement of the acetabular cup during total hip arthroplasty is critical to long term clinical succes s. Measurements of cup position and orientation from postoperative CT scans are accepted as the gold standard reference measurement, yet there have been no reports of the uncertainties associated with this method. We studied pre and post operative CT scan s for ten patients who received THA and measured the radiographic inclination and radiographic anteversion in an anatomic coordinate system. To quantify measurement uncertainties, we repeated the measurements several times and separately varied factors tha t might contribute to measurement error. Our results suggest the best measurements are achieved using full pelvis bone models with the acetabular area removed, and by matching the pre and post operative pelvis models using 3D global registration. This sta ndardized measurement has an accuracy, precision and bias of 0.3, 0.7 and 0 for radiographic inclination, and 0. 2, 0.6 and 0.1 for radiographic anteversion. We found similar results when using shorter pelvis bone segments for registration. Including the periacetabular bone and/or using manual landmark identification resulted in less accurate measurements. Post operative CT measurements of cup position is a useful and accurate measurement reference

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10 standard. Our results quantify the measurement uncert ainty for this procedure and put previous reports of intraoperative measurement results into context.

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11 CHAPTER 1 INTRODUCTION Accurate placement of the acetabular cup is a critically important part of total hip arthroplasty (THA) since inaccurate cup position may cause serious complications such as dislocation [1 4], accelerated wear of the liner [4] and cup loosening [5]. Conseq uently, there have been many studies [6 9] measuring cup orientation and evaluating the accuracy, precision and bias of various surgical technologies by comparing intraoperative placement measurements with postoperative measurements from computed tomograph y (CT) scans. Several different post op CT measurements techniques have been used, and they can be separated into three categories: 2D, 2D/3D and 3D. Typical 2D methods [10] use projections of post op CT images on the coronal plane and sagittal plane to me asure the cup inclination and anteversion on 2D images. 2D/3D methods [11] generate a 3D cup model to reach the best possible match in all 2D views, then define the cup plane and cup axis to measure the inclination and anteversion. Widely used 3D methods [ 6, 7] create 3D models of both the pelvis and the implanted cup, establish an anatomic coordinate system based upon bony landmarks, and virtually translate and rotate the cup using 3D registration. Finally, the radiographic inclination and anteversion angl es are calculated based on the definitions of Murray et al. [12]. Collectively, these post reference measurements, yet none of these studies has reported the accuracy, precision or bias of the measurement We, too, have interest measuring the accuracy of cup placement and have developed techniques to perform the measurement using 3D global registration with pre and post operative CT scans. The purpose of this study is to

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12 assess the accuracy, precision and bias of acetabular cup orientation measurements and to consider the contributions of various factors to measurement uncertainties. Our goal is to provide an assessment of the quality of these measurements and to put the results of previous related studies into a quantitative context.

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13 CHAPTER 2 MATERIALS AND METHODS Subjects Ten anonymous patients were involved in this study to determine the cup position and quantify the measurement uncertainty. All patients had THA surgeries assisted by the RIO robot system (MAKO Surgical, Davie, FL) which is a haptically guided robotic arm s ystem. Each patient was pre operative and post operative scanned with CT to create pre operative pelvis model, post operative pelvis model and post operative cup model. Measurement of Acetabular Cup Orientation The measurement procedure for quantifying ace tabular cup orientation uses CT derived pre and post operative pelvic bone models, with the periacetabular region removed, and global registration to spatially align the pelvises and cups in a well defined anatomic coordinate reference frame. There are si x steps to measure the orientation of the acetabular cup of each patient: 1. The pre and post operative pelvic bone models, and post operative cup model were constructed from pre and post operative CT scans by segmentation with open source software (ITK SNA P, Penn Image Computing and Science Laboratory, [13]). Stereolithography (STL) format models of acetabular cups in all sizes were provided by the manufacturer (MAKO Surgical, Davie, FL). 2. A common reference frame was established for the measurement (Fig. 2 1). This anatomic coordinate system was based on the pre operative alignment of the pelvis anatomy and adjusted according to several anatomical landmarks. The origin of the coordinates was placed at the acetabular cup center. Then the medial/lateral axis was aligned parallel to a line passing through the right and left anterior superior iliac spines (ASIS). Finally, the anterior/posterior axis was unchanged from the pre op CT table orientation to the anatomic coordinate system, which means that each patien t has a specific pelvis tilt. 3. After the anatomic coordinate system was defined, the post operative pelvis and cup were imported into software with the pre operative pelvis model. Global registration was used to align the pre op and post op pelvises based on an iterative closet point

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14 registration algorithm (Geomagic Studio, Geomagic Corp., Morrisville, NC). To retain the relative position between post operative pelvis and cup, the post operative cup was moved using the same coordinate transformation (4x4) u sed to align the post operative pelvis (Fig. 2 2). 4. The implant cup model was imported into software, the origin of the cup was moved to the origin of the anatomic coordinate system, and the cup acetabular axis was aligned with the proximal/distal axis of the pelvis (z axis of anatomic coordinate system). The acetabular axis was defined as the axis perpendicular to the rim of the cup and passing through the center of the cup. 5. Global registration was used to align the implant cup model to match the post op cup model. The coordinates of the acetabular axis were obtained in this step. 6. (radiographic an teversion) were calculated. Sources of Uncertainty There are two categories for sources of uncertainty, systematic uncertainties and controllable uncertainties (Fig. 2 3). Systematic uncertainties arise from steps 3 and 5 in the measurement process and ca nnot be avoided. When matching the post operative pelvis to the pre operative pelvis, and implant cup model to the CT derived post operative cup model, either global registration or manual alignment can be used to align the pelvises and cups based on views Controllable uncertainties include the quality of pelvis bone models and post operative cups, whether the acetabulum of the pelvis was used, and the amount of pelvis used for registration. Each of these factors was explored to determine their effects on registration accuracy. The quality of pelvis bone models and post operative cups will not be discussed in this paper since the resolution of CT images was fixed for all patients. A series of evaluations were conducted to assess measurement uncertaint ies for cup orientation measurements. First, the repeatability of the standard method, as outlined above, was determined by performing a repeated measurements experiment.

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15 This experiment was conducted using both automated global registration, and alignment based upon manual identification of anatomic landmarks. Second, the impact of geometric changes in the periacetabular region on cup measurements was assessed by performing measurements with pre operative intact and removed periacetabular bone in the pelvi s models. (The theory is that this area will change as a result of surgery, and so should not be used for alignment.) Finally, an experiment was conducted to determine how much pelvis is required to provide accurate registration results. If less pelvis can be used, then the patient can receive a less extensive CT scan, and much less time is consumed creating the pre and post operative bone models by segmenting CT scans. Global Registration vs. Manual Alignment The accuracy, precision and bias of the standa rd measurement was assessed by performing the measurements twice for each of ten patient data sets using global registration for bone alignment. These measurements were repeated twice more using manual procedures to align the pelvises and cups for all ten patients. The experiments provided a total of four RI (Radiographic Inclination) and RA (Radiographic Anteversion) measurements from the same data, two from the standard measurement, and two from the measurement using manual alignment. Paired two sample t tests were performed between two trials of each measurement, and the t test was also applied between two the measurement methods. Accuracy, precision and bias were calculated by treating the results of the standard measurement as the reference. Impact of t he Acetabulum During THA surgery the acetabulum is reshaped by reamers and removal of osteophytes, so the pre operative acetabular region is different from the post operative acetabular region. Since 3D registration is based upon alignment of similar surfa ces, it

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16 is important to know if the altered acetabular region will have an effect on registration accuracy. Therefore, the measurements were repeated on the ten patients by using full pelvis models with and without the acetabular bone included. A paired tw o sample t test was performed to compare the measurements with acetabular bone to the standard measurement, and accuracy, precision and bias were calculated. Impact of the Amount of Pelvis This experiment was designed to test the effect of post operative p elvis bone extent (in the superior inferior direction) on measurement accuracy. Both the pre and post operative pelvises were progressively reduced along z axis (longitude axis) from the full pelvis model. Bone model reductions were symmetric about the ac etabular center (the origin of the anatomic coordinate system). The bone model sizes evaluated were +/ 60mm, +/ 50mm, +/ 40mm and +/ 30mm from the acetabular center (Figure 2 4). Measurements were performed on all patients with these differing amounts of post op pelvis and a one factor ANOVA test was performed to detect if any measurements were significantly different from others. In addition, the accuracy, precision and bias of these measurements compared to the standard measurement using the full pelv is were calculated.

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17 Figure 2 1. Anatomic coordinates were derived from the pre op CT orientation and aligned to the medial/lateral axis formed by ASIS points. The x axis (red) is the medial/lateral direction and the z axis (blue) is the proximal/distal direction. The y axis (green, covered by the center) is the anterior/posterior direction, and is perpendicular to the image shown.

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18 Figure 2 2. The post operative pelvis model (white) is registered to the pre op pelvic model (orange), preserving the pr e op coronal plane. All measurement are recorded relative to the anatomic coordinates. In the standard measurement, full pre op and post op pelvises without acetabulum were used to measure the cup position.

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19 Figure 2 3. Flow chart of measuring the orientation of acetabular cup and list of uncertainty sources. The words in green frames show the process to measure the cup position. The words in blue frames show the systematic uncertainties. The words in orange frames show t he controllable uncertainties. The words in black frames show the uncertainty sources not discussed. Figure 2 4. Flow chart of measuring the orientation of acetabular cup and list of uncertainty sources. The words in green frames show the process to measure the cup position. The words in blue frames show the systematic uncertainties. The words in orange frames show the controllable uncertainties. The words in black fra mes show the uncertainty sources not discussed.

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20 CHAPTER 3 RESULTS Global Registration vs. Manual Alignment Repeated measures of cup orientation angles using global registration showed good accuracy (0.24), precision (0.65) and negligible bias (Table 3 1). Manual alignment had poorer results by all metrics. There were no significant differences detected for repeated measures or between method comparisons. The global registration based measurement is the standard for subsequent comparisons. Impa ct of the Acetabulum Inclusion of the periacetabular bone resulted in slight increases in accuracy, precision and bias results compared to the standard measurement (Table 3 2). Statistical comparison of radiographic inclination angles resulted in a p value of 0.07, which would be significant for a 90% confidence level. These results show inclusion of the periacetabular bone tends to degrade the measurement of cup orientation from pre and post operative CT scans. Impact of the Amount of Pelvis One factor ANOVA revealed no significant differences in cup orientation results using different amounts of pelvis bone (Table 3 3). There appears to be a slight improvement in the accuracy and precision results for measurements using 40mm or greater models but this is not a statistically supported observation. Comparison of Factors Comparing the results of the three separate evaluations shows that pelvis model extent had the smallest effect on cup orientation measurements, while manual alignment had the gr eatest effect (Table 3 4). (Assuming all measurements were

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21 independent, one would expect the measured accuracy, precision and bias figures for all measurements to be greater than twice the figures for the standard measurement, since they are measured by su btracting the standard measure.). Table 3 1. Cup orientation measurement results of RI using global registration and manual alignment methods. Radiographic Inclination Paired Two Sample T Test Global Registration Manual Alignment GR vs. MA Trial One Trial Two Trial One Trial Two GR MA Mean 38.73 38.36 38.14 39.25 38.73 38.70 Variance 35.33 35.88 28.33 32.18 35.33 28.99 P Value 0.9397 0.2546 0.5369 Global Registration Manual Alignment Accuracy Precision Bias Accuracy Precision Bias 0.2847 0.7462 0.0094 1.7972 4.7280 1.1059 GR = global registration; MA = manual alignment; Variance = the square of the standard deviation. Table 3 2 Cup orientation measurement results of RA using global registration and manual alignment methods. Radiographic Anteversion Paired Two Sample T Test Global Registration Manual Alignment GR vs. MA Trial One Trial Two Trial One Trial Two GR MA Mean 19.00 19.51 18.91 19.41 19.00 19.16 Variance 27.04 30.61 47.98 36.62 27.04 40.14 P Value 0.3091 0.3580 0.6115 Global Registration Manual Alignment Accuracy Precision Bias Accuracy Precision Bias 0.2361 0.5780 0.1005 1.8193 4.9955 0.2943 Table 3 3 The impact of using the periacetabular bone on the RI and RA. Radiographic Inclination Radiographic Anteversion Paired Two Sample T Test Paired Two Sample T Test Acetabulum Standard Acetabulum Standard Mean 38.35 38.73 Mean 19.17 19.00 Variance 39.92 35.33 Variance 26.67 27.04 P Value 0.0734 P Value 0.2608 Acetabulum Acetabulum Accuracy Precision Bias Accuracy Precision Bias 0.5723 1.1608 0.3794 0.3469 0.8442 0.1634

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22 Acetabulum = the measurement used full pelvis with acetabulum. Table 3 4 The impact of the a mount of pelvis on the RI Radiographic Inclination Single Factor ANOVA Test 30 40 50 60 Standard Mean 38.26 38.57 38.83 38.90 38.73 Variance 32.64 33.61 40.92 33.08 35.33 P Value 0.9993 30 40 Accuracy Precision Bias Accuracy Precision Bias 0.5630 1.2413 0.4688 0.4515 1.3221 0.1566 50 60 Accuracy Precision Bias Accuracy Precision Bias 0.4425 1.4760 0.0962 0.4821 1.1839 0.1694 The numbers (30, 40, 50 and 60) are the distances from acetabular center which indicates the amount of post op pelvis used in the measurement. Table 3 5 The impact of the a mount of pelvis on the RA Radiographic Anteversion Single Factor ANOVA Test 30 40 50 60 Standard Mean 19.32 18.91 19.23 18.91 19.00 Variance 27.48 25.57 26.63 24.22 27.04 P Value 0.9996 30 40 Accuracy Precision Bias Accuracy Precision Bias 0.6264 1.6260 0.3147 0.3861 1.1152 0.0989 50 60 Accuracy Precision Bias Accuracy Precision Bias 0.5248 1.3299 0.2305 0.5872 1.7338 0.0909 The numbers (30, 40, 50 and 60) are the distances from acetabular center which indicates the amount of post op pelvis used in the measurement. Table 3 6 Cup orientation measurement results of RI for all evaluations. Radiographic Inclination Standard 30 40 50 60 Acetabulum MA Accuracy 0.2847 0.5630 0.4515 0.4425 0.4821 0.5723 1.7972 Precision 0.7462 1.2413 1.3221 1.4760 1.1839 1.1608 4.7280 Bias 0.0094 0.4688 0.1566 0.0962 0.1694 0.3794 1.1059

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23 Table 3 7 Cup orientation measurement results of RA for all evaluations Radiographic Anteversion Standard 30 40 50 60 Acetabulum MA Accuracy 0.2361 0.6264 0.3861 0.5248 0.5872 0.3469 1.8193 Precision 0.5780 1.6260 1.1152 1.3299 1.7338 0.8442 4.9955 Bias 0.1005 0.3147 0.0989 0.2305 0.0909 0.1634 0.2943

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24 CHAPTER 4 DISCUSSION Post operative CT based measurement of acetabular cup position is accepted as a gold standard measurement method, yet its accuracy, precision and bias has not been reported. Therefore, we studied the impact of various sources of measurement uncertainty on acetabular cup angle measurements. Our results su ggest global registration of 3D pelvis bone models and cups provides the best results. Similar results can be obtained by using partial pelvis bone models with lesser extent in the proximal/distal direction. Our results suggest removing periacetabular bone from the pelvis model improves measurement accuracy, Manual alignment of pelvis models based upon the identification of bony landmarks resulted in less accurate measurements. This study has several limitations. The sample size is too small to provi de powerful statistical comparisons. Anonymous patient data were drawn from a single surgeon and clinic, so there may be some bias in patient anatomy or stereotypic differences in cup implantation. Finally, the impact of CT scan quality on cup measurement s was not included, because scans at different resolutions were not available for study. We expect that higher resolution CT images will provide better measurement results. Because the post op CT measurement has been accepted as a gold standard measurement, the bias and precision of the measurement had not been considered in reporting the precision and bias of other intraoperative cup measurement techniques. The bias an d precision figures reported for previous studies, e.g. [6, 7], represent the combination of errors from the intraoperative and CT based measurements. Based upon the bias and precision of our standard

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25 measurement (post op CT measurement), we can recalculat e the bias and precision of previous reports [Table 4 1 ]. The refined bias is smaller and the refined precision remains the same. Since the bias is the mean of differences, we may conclude that the results of of previous intraoperative measurements are clo ser to the true values than reported. The importance of this study is quantifying the standard measurement and impact of various sources of uncertainty in the post operative CT based measurement of acetabular cup position. The post op CT based measur ement that is accepted as a gold standard has an accuracy of less than 0.3, a precision less than 0.7 and an absolute bias less than 0.1. These data (including the accuracy, precision, bias of uncertainty resources) increase confidence in the use of res ults from post operative CT based measurements, help surgeons better to understand the accuracy of various implant placement technologies, and provide a rigorous method to demonstrate improvements in the techniques for implanting total hip replacements. T able 4 1 Original and refined results from other intro op measurement. Radiographic Inclination Radiographic Anteversion Original Standard Dorr et al. Ryan et al. Standard Dorr et al. Ryan et al. Bias 0.0094 0.03 0.52 0.1005 0.73 0.35 Precision 0.7462 4.4 3.4 0.578 4.1 5.5 Refined Dorr et al. Ryan et al. Dorr et al. Ryan et al. Bias 0.0261 0.5074 0.6253 0.2482 Precision 4.4326 3.5179 4.101 5.4959 Refined means that these results were calculated as considering the bias and precision of the post op CT standard measurement.

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26 APPENDIX MATLAB CODE USED TO CALCULATE CUP ORIENTATION functio n [anatomi c radiographic ] = THA_Accuracy_Analysis(P) % -----------------------------------------------------------------------% % % Compute s th e Anatomi c an d Radiographi c Inclinatio n an d Anteversio n of % Planned Adjuste d an d Post o p acetabula r cu p corientatio n accordin g to % Murra y 1993. % % Definitions: % % Anatomi c Inclinatio n (AI ) = angl e betwee n acetabula r axi s and % longitudina l axis. % % Anatomi c Anteversio n (AA ) = angl e betwee n th e transvers e axi s an d the % projecte d acetabula r axi s ont o th e tranvers e plane. % % Radiographi c Inclinatio n (RI ) = angl e betwee n th e longitudina l axi s and % th e projecte d acetabula r axi s ont o th e corona l plane. % % Radiographi c Anteversio n (RA ) = angl e betwee n th e acetabula r axi s an d the % corona l plane. % % -----------------------------------------------------------------------% % % INPUTS % % P -Vecto r o f patien t number s t o b e processe d ( eg [ 1 3 5 29 ] ) % % OUTPUTS % % n = numbe r o f inpu t patien t numbers % % anatomi c -(nx6 ) Matrix: % % [ Planned_AI Planned_AA Adjusted_AI Adjusted_AA Measured_AI, Measured_AA] % % radiographi c -(nx6 ) Matrix % % [Planned_RI Planned_RA Adjusted_RI Adjusted_RA Measured_RI, Measured_RA] % % -----------------------------------------------------------------------% % Loa d Sessio n Fil e Data [FileNam e PathNam e isok ] = uigetfile( '*.mat' 'Loa d sessio n fil e data...' ); i f isok dat a = load(fullfile(PathName,FileName)); end % -----------------------------------------------------------------------% %Initializ e Variables data.T_Anatomy_Plan = cell(29,1); anatomi c = zeros(length(P),6); radiographic = zeros(length(P),6); Mou t = zeros(2,1); Pou t = zeros(2,1); CPou t = zeros(2,1);

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27 % -----------------------------------------------------------------------% % Comput e Planne d Cu p Positio n Usin g Adjuste d Cu p Coordinates fo r i = 1:length(P) data.T_Anatomy_Plan{P(i) } = inv(data.T_Anatomy_Bone{P(i)})*data.T_Bone_Plan{P(i)}*inv(data.T_Cup1_Cup2{P(i)}); data.T_Anatomy_Plan2{P(i) } = inv(data.T_Cup1_Cup2{P(i)})*data.T_Bone_Plan{P(i)}*inv(data.T_Anatomy_Bone{P(i)}); end % Comput e Adjuste d Cu p Plane fo r i = 1:length(P) data.Cup_Plane{P(i) } = inv((inv(data.T_Anatomy_Bone{P(i)})*data.T_Pelvis_Bone{P(i)})')*data.Cup_Plane{P(i)}; data.Cup_Plane{P(i)} = data.Cup_Plane{P(i)}/norm(data.Cup_Plane{P(i)}(1:3)); end % ------------------------------------------------------------------------% % Fo r ever y patien t numbe r selected fo r i = 1:length(P) % Measure d cu p ------------------------------------------------------% % Anatomic % Comput e angl e betwee n acetabula r axi s an d longitudina l axis Mout(1) = acosd(dot(data.T_Anatomy_Cup2{P(i)}(1:3,3),[ 0 0 1])); % Projec t acetabula r axi s ont o transvers e plan e Bx(AxB ) and pro j = cross([ 0 0 1],cross(data.T_Anatomy_Cup2{P(i)}(1:3,3),[ 0 0 1])); % Comput e angl e betwee n projecte d axi s an d media l (transverse ) axis Mout(2) = acosd(dot(proj/norm(proj),[ 1 0 0])); i f proj(1 ) < 0 Mout(2) = acosd(dot(proj/norm(proj),[ 1 0 0])); end % Radiographic % Projec t acetabula r axi s ont o corona l plane rpro j = cross([ 0 1 0],cross(data.T_Anatomy_Cup2{P(i)}(1:3,3),[ 0 1 0])); % Comput e angl e betwee n projecte d axi s an d proxima l (longitudinal ) axis Mrout(1 ) = acosd(dot(rproj/norm(rproj),[ 0 0 1])); % Comput e angl e betwee n th e acetabula r axi s an d th e corona l plane Mrout(2 ) = 90 acosd(dot( 1*data.T_Anatomy_Cup2{P(i)}(1:3,3),[ 0 1 0])); % Planne d cu p -------------------------------------------------------% % Anatomic % Comput e angl e betwee n acetabula r axi s an d longitudina l axis Pout(1) = acosd(dot(data.T_Anatomy_Plan{P(i )}(1:3,3),[ 0 0 1])); % Projec t acetabula r axi s ont o transvers e plan e Bx(AxB ) and pro j = cross([ 0 0 1],cross(data.T_Anatomy_Plan{P(i)}(1:3,3),[ 0 0 1])); % Comput e angl e betwee n projecte d axi s an d media l (transverse ) axis Pout(2) = acosd(dot(proj/norm(proj ),[ 1 0 0])); i f proj(1 ) < 0 Pout(2) = acosd(dot(proj/norm(proj),[ 1 0 0])); end

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28 % Radiographic % Projec t acetabula r axi s ont o corona l plane rpro j = cross([ 0 1 0],cross(data.T_Anatomy_Plan{P(i)}(1:3,3),[ 0 1 0])); % Comput e angl e betwee n projecte d axi s an d proxima l (longitudinal ) axis Prout(1 ) = acosd(dot(rproj/norm(rproj),[ 0 0 1])); % Comput e angl e betwee n th e acetabula r axi s an d th e corona l plane Prout(2 ) = 90 acosd(dot( 1*data.T_Anatomy_Plan{P(i)}(1:3,3),[ 0 1 0])); % Cu p Plan e (Hessia n norma l for m assumed ) ---------------------------% % Anatomic % Comput e angl e betwee n acetabula r axi s an d longitudina l axis CPout(1) = acosd(dot(data.Cup_Plane{P(i)}(1:3),[ 0 0 1])); i f data.Cup_Plane{P(i)}(3 ) < 0 CPout(1) = acosd(dot( data.Cup_Plane{P(i)}(1:3),[ 0 0 1])); end % Projec t acetabula r axi s ont o transvers e plan e Bx(AxB ) and pro j = cross([ 0 0 1],cross(data.Cup_Plane{P(i)}(1:3),[ 0 0 1])); % Comput e angl e betwee n projecte d axi s an d media l (transverse ) axis CPout(2) = acosd(dot( proj/norm(proj),[ 1 0 0])); i f proj(1 ) < 0 CPout(2) = acosd(dot(proj/norm(proj),[ 1 0 0])); end % Radiographic % Projec t acetabula r axi s ont o corona l plane rpro j = cross([ 0 1 0],cross(data.Cup_Plane{P(i)}(1:3),[ 0 1 0])); % Comput e angl e betwee n projecte d axi s an d proxima l (longitudinal ) axis CProut(1 ) = acosd(dot(rproj/norm(rproj),[ 0 0 1])); i f CProut(1 ) > 90 CProut(1 ) = 180 CProut(1); end % Comput e angl e betwee n th e acetabula r axi s an d th e corona l plane CProut(2 ) = 90 acosd(dot(data.Cup_Plane {P(i)}(1:3),[ 0 1 0])); % Correc t sig n erro r du e t o righ t an d lef t sid e geometry % % Not e thi s assume s al l case s wer e implante d wit h positive % anteversion! CProut(2 ) = abs(CProut(2)); % -----------------------------------------------------------------------% % Updat e outpu t matrices anatomic(i,1:6 ) = [Pout(1 ) Pout(2 ) CPout(1 ) CPout(2 ) Mout(1 ) Mout(2)]; radiographic(i,1:6 ) = [Prout(1 ) Prout(2 ) CProut(1 ) CProut(2 ) Mrout(1 ) Mrout(2)]; end % Prin t t o screen radiographic anatomic

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29 LIST OF REFERENCES [1] Berry DJ. Unstable total hip arthroplasty: detailed overview. Instr Course Lect. 2001:50:265 274. [2] Fackler CD, Poss R. Dislocation in total hip arthroplasties. Clin Orthop Relat Res. 1980:151:169 178. [3] Jolles BM, Zangger P, Leyvraz PF. Factors predisposing to dislocation after primary total hip arthroplasty: a multivariate analysis. J Arthroplasty. 2002;17:282 208. [4] Kennedy JG, Rogers WB, Soffe KE, Sullivan RJ, Griffen DG, Sheehan LJ. Effect of acetabular component orientation on recurrent dislocation, pelvic osteolysis, polyethylene wear, and component migration. J Arthroplasty. 1998;13:530 534. [5] Hedlundh U, Ahnfelt L, Hybbinette CH, Weckstrom J, Fredin H. Surgical experience relate d to dislocations after total hip arthroplasty. J Bone Joint Surg Br. 1996;78:206 209. [6] Ryan JA, Jamali AA, Bargar WL. Accuracy of computer navigation for acetabular component placement in THA. Clin Orthop Relat Res 2010;468:169. [7] Dorr LD,Malik A,Wan Z, Lon gWT,HarrisM. Precision and bias of imageless computer navigation and surgeon estimates for acetabular component position. Clin Orthop Relat Res. 2007;465:92 99. [8] Jenny JY, Boeri C, Dosch JC, Uscatu M, Ciobanu E. Navigated non image based positioning of the acetabulum during total hip replacement. Int Orthop. 2009;33:83 87. [9] Ybinger T, Kumpan W, Hoffart HE, Muschalik B, Bullmann W, Zweymuller K. Accuracy of navigation assisted acetabular component positioning studied by computed tomography measurements: method s and results. J Arthroplasty. 2007;22:812 817. [10] McArthur B, Cross M, Geatrakas C, Mayman D, Ghelman B. Measuring acetabular component version after THA CT or plain radiograph. Springer. 2012:10:2810 2818. [11] Jaramaz, B., Eckman K., 2006. 2D/3D registration for measurement of implant alignment after total hip replacement. In: Larsen, R., Nielsen, M., Sporring, J. (Eds.), Ninth International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2006), P art 2, Lecture Notes In Computer Science, vol. 4191. Springer, Copenhagen, Denmark, pp. 653 661. [12] Murray DW. The definition and measurement of acetabular orientation.J Bone Joint Surg Br. 1993;75:228 232.

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30 [13] Paul A. Yushkevich, Joseph Piven, Heather Cody Hazl ett, Rachel Gimpel Smith, Sean Ho, James C. Gee, and Guido Gerig. User guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability. Neuroimage 2006 Jul 1;31(3):1116 28.

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31 BIOGRAPHICAL SKETCH Zenan Zhang was born in Zou cheng, Shandong Province, China He got his Bachelor of Science in m echanical e ngineering from Beijing Jiaotong University, Beijing, China by studying bio inspired robots from 2007 to 2011. From 2011 to 2013, Zenan was enrolled in University of Florida, US to pursue his Master of Science in m echanical e ngineering. His interest is the postoperative CT measurement of measuring positions of acetabular cup s and stems guided by Dr. Scott A. Banks.