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A new multiparametric MRI protocol for diagnosis of prostate cancer Sabouri, Shirin 2017

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 A NEW MULTIPARAMETRIC MRI PROTOCOL FOR DIAGNOSIS OF PROSTATE CANCER by Shirin Sabouri  B.Sc. Physics, University of Tehran, 2005 M.Sc. Physics, Shahid Beheshti University, 2009 M.Sc. Physics, The University of British Columbia, 2011  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Physics)  The University of British Columbia (Vancouver)  August 2017  © Shirin Sabouri, 2017 ii  Abstract In this thesis, a new magnetic resonance imaging (MRI) quantitative T2 mapping technique, called Luminal water imaging (LWI), has been developed and used for non-invasive detection and grading of prostatic tumours.   Using this technique, we measured what we hypothesized to be the fractional amount of water content of luminal spaces in prostate, and called it Luminal Water Fraction, LWF. Based on the differences in tissue composition and fractional amount of luminal space between malignant and normal prostatic tissues and between tumors of different grades, we hypothesized that the measurements of LWF could be used for the detection and grading of prostatic tumours.  To verify these hypotheses, we performed two patient studies in which we compared MR measurements of LWI with whole-mount histology. In the first study, we evaluated the correlation between LWF and the percentage area of luminal space in the prostatic tissue. The results of this study demonstrated that LWF is significantly and strongly correlated with the percentage area of luminal space in the prostatic tissue. In the second study, we investigated the feasibility of LWI in the detection and grading of prostate cancer. The results of this study showed that LWI provides high accuracy both in the detection and grading of prostatic tumours.   After verifying our hypotheses, we performed a detailed comparison between the diagnostic accuracy of LWI and the more established MRI techniques: Dynamic Contrast-Enhanced (DCE) and Diffusion-Weighted MRI (DW-MRI). The results of this pilot study showed that iii  LWI alone performs better than DCE, DW-MRI, or their combination, in the detection of prostatic tumours and also in correlation with GS. Based on the results of this study, we proposed a guideline for making a more efficient, abbreviated multi-parametric MRI protocol for the diagnosis of prostate cancer. Finally, as a side project, we explored some potential areas of improvement in DCE-MRI by investigating the impact of temporal resolution on the accuracy of DCE-MRI in detection of prostatic tumours. Our results showed that within a certain range of temporal resolutions, the diagnostic accuracy of DCE-MRI would be independent of the temporal resolution.  iv  Lay Summary In this thesis, a new magnetic resonance imaging (MRI) technique has been developed and used for diagnosis of prostate cancer.   Prostatic tissue is composed of water compartments of different sizes. The fractional amount of these compartments varies between normal and malignant tissue, and between tumours of different grades. Our technique has been developed for diagnosis of prostate cancer by measuring the fractional amount of water content of different compartments. We evaluated the correlation between measurements of this MRI technique and the composition of prostatic tissue. We also investigated the feasibility of this technique in the detection and grading of prostate cancer by comparing MRI measurements with histology. In addition, we compared the diagnostic accuracy of this technique with the more established MRI techniques. Finally, as a side project, we explored some potential areas of improvement in dynamic contrast-enhanced MRI which is an established MRI technique for characterization of tumour microvasculature.     v  Preface This study was approved by the University of British Columbia (UBC) Clinical Research Ethics Board (CREB) (H02-70400), and supported by the Canadian Institutes of Health Research (CIHR) (MOP-115052). This study was performed in collaboration with multiple researchers. The idea of multi-component T2 mapping in prostate was created by Dr. Piotr Kozlowski, who had the vision for this project from the very beginning and supported it all the way through with grants and providing invaluable guidance as my primary supervisor and mentor for this research. He also supported the design and development of the protocol that was developed as one of the major contribution of this study, arranged patient studies, and provided valued insight in interpretation and analysis of results. The majority of the work of this project was performed by the author. The author’s contribution to this work includes: development, performance and interpretation of the simulation and phantom studies, assistance with MRI examinations for patient studies, aid in whole-mount histology preparation, and performance of image analysis and interpretation of the entire results.  This work would have not been possible without the contributions from the following collaborators: Dr. Silvia D Chang, an experienced radiologist and an Associate Professor at the Department of Radiology of UBC, assisted with protocol development and set up of MRI examinations for patient studies. Dr. Chang’s contribution also includes aid and confirmation of manually drawn regions of interest on the MR images. vi  Dr. Jing Zhang provided the pulse sequence for luminal water imaging (LWI), and assisted with the data acquisition of volunteer studies.  Dr. Edward C. Jones, an experienced pathologist at Vancouver General Hospital (VGH), performed cutting of the prostate glands using a custom made device, delineated tumours, and assigned the Gleason score (GS) on whole-mount histology slides.  Dr. Ladan Fazli, an experienced pathologist at Vancouver Prostate Center (VPC), delineated tumours, and assigned the GS on digital (high resolution) whole-mount histology slides.  She also assisted with colour segmentation of the digital histology images. Dr. S. Larry Goldenberg, a senior urology surgeon and researcher at VGH, assisted with the interpretation of the results of patient studies and with patient recruitment.  Dr. Peter Black, an experienced urology surgeon and researcher at VGH, assisted with the interpretation of the results of patient studies, and also supported this project by getting involved his fellow Dr. Richard Savdie. Dr. Savdie recruited all of the patients for this study. The contributions from this thesis have led to the following publications, submissions and presentations: 1) Sabouri S, Chang SD, Savdie R, Zhang J, Jones EC, Goldenberg SL, Black PC,  Kozlowski P. Luminal Water Imaging: A New MR Imaging T2 Mapping Technique for Prostate Cancer Diagnosis. Radiology 2017; 284(2): 451-9. A version of this article is also presented in Chapter 4.   vii  2) Sabouri S, Fazli L, Chang SD, Savdie R, Jones EC, Goldenberg SL, Black PC, Kozlowski P. MR measurement of luminal water in prostate gland: Quantitative correlation between MRI and histology. Journal of Magnetic Resonance Imaging, 2017; 46(3): 861-9. A version of this article is also presented in Chapter 3.  3) Sabouri S, Chang SD, Goldenberg SL, Savdie R, Jones EC, Black PC, Kozlowski P. Comparing Diagnostic Accuracy of Luminal Water Imaging with Diffusion-Weighted and Dynamic Contrast-Enhanced MRI in Detection and Grading of Prostate Cancer (Manuscript ready to be submitted). A version of this article is also presented in Chapter 5.   Sabouri S, Fazli L, Chang SD, et al. MR measurements of luminal water in prostate gland. In Proceedings of the 24thd Annual Meeting of ISMRM, Singapore, 2016. Abstract 2487.   Sabouri S, Chang SD, Savdie R, et al. Luminal water imaging: a novel MRI method for prostate cancer diagnosis. In Proceedings of the 24th Annual Meeting of ISMRM, Singapore, 2016. Abstract 2489.   Sabouri S, Chang SD, Goldenberg SL, et al. Comparing the Diagnostic Accuracy of Luminal Water Imaging with Diffusion-Weighted and Dynamic Contrast-Enhanced MRI for Evaluation of Prostate Cancer. In Proceedings of the 25th Annual Meeting of viii  ISMRM, Honolulu, Hawaii, 2017. Abstract 0670 (power-pitch oral presentation, awarded Suma Cum Laude). ix  Table of Contents  Abstract .................................................................................................................................... ii Lay Summary ......................................................................................................................... iv Preface ...................................................................................................................................... v Table of Contents ................................................................................................................... ix List of Tables ........................................................................................................................ xiii List of Figures ........................................................................................................................ xv List of Abbreviations ........................................................................................................... xix Acknowledgements ............................................................................................................. xxii Dedication ........................................................................................................................... xxiv Chapter  1: Introduction ........................................................................................................ 1 1.1 Magnetic Resonance Imaging (MRI) ........................................................................ 1 1.1.1 Magnetization Vector............................................................................................ 2 1.1.2 T1, T2, and T2* Relaxations ................................................................................... 5 1.1.3 Bloch Equations .................................................................................................... 9 1.1.4 RF Excitation and Signal Detection .................................................................... 10 1.1.5 Slice Selection ..................................................................................................... 12 1.1.6 Frequency Encoding ........................................................................................... 14 1.1.7 Phase Encoding ................................................................................................... 14 1.1.8 Fourier Transform and Image Reconstruction .................................................... 15 1.2 Prostate .................................................................................................................... 17 1.2.1 Anatomy .............................................................................................................. 17 x  1.2.2 Prostate Cancer ................................................................................................... 20 1.3 Objectives and Overview of this Thesis ................................................................. 23 Chapter  2: Development of a Multi-Exponential T2 Mapping Protocol for Prostate Imaging .................................................................................................................................. 28 2.1 Introduction ............................................................................................................. 28 2.2 Protocol Development ............................................................................................ 32 2.2.1 Simulations ......................................................................................................... 33 2.2.2 Phantom Study .................................................................................................... 37 2.2.3 Volunteer Study .................................................................................................. 40 2.3 Summary ................................................................................................................. 45 Chapter  3: MR measurement of Luminal Water in Prostate Gland: Quantitative Correlation between MRI and Histology ............................................................................ 46 3.1 Introduction ............................................................................................................. 46 3.2 Patient Selection...................................................................................................... 47 3.3 MRI Protocol .......................................................................................................... 48 3.4 Whole-mount Histology and Registration to MR images ....................................... 49 3.5 Image Segmentation................................................................................................ 51 3.6 Data Processing ....................................................................................................... 52 3.7 Statistical Analysis .................................................................................................. 56 3.8 Results ..................................................................................................................... 57 3.9 Discussion and Conclusion ..................................................................................... 63 Chapter  4: Luminal Water Imaging: A New MRI T2 Mapping Technique for Prostate Cancer Diagnosis ................................................................................................................... 67 xi  4.1 Introduction ............................................................................................................. 67 4.2 Patient Selection...................................................................................................... 67 4.3 MRI Protocol .......................................................................................................... 69 4.4 Histologic Examination and Registration to MR Images ....................................... 69 4.5 Data Processing ....................................................................................................... 70 4.6 Statistical Analysis .................................................................................................. 70 4.7 Results ..................................................................................................................... 71 4.8 Discussion and Conclusion ..................................................................................... 77 Chapter  5: Comparing Diagnostic Accuracy of Luminal Water Imaging with Diffusion-Weighted and Dynamic Contrast-Enhanced MRI in Detection and Grading of Prostate Cancer .................................................................................................................................... 81 5.1 Introduction ............................................................................................................. 81 5.2 Patient Selection...................................................................................................... 81 5.3 MRI Protocol .......................................................................................................... 83 5.4 Histologic Examination and Registration to MR Images ....................................... 84 5.5 Data Processing ....................................................................................................... 85 5.6 Statistical Analysis .................................................................................................. 86 5.7 Results ..................................................................................................................... 87 5.8 Discussion and Conclusion ..................................................................................... 93 Chapter  6: Optimization of Temporal Sampling of Dynamic Contrast-Enhanced MRI Protocol for Diagnosis of Prostate Cancer.......................................................................... 96 6.1 Introduction ............................................................................................................. 96 6.1.1 DCE-MRI ............................................................................................................ 96 xii  6.1.2 Significance of Temporal Resolution in Diagnostic Accuracy of DCE-MRI .... 98 6.2 Temporal Resolution and Accuracy of Fit Parameters ......................................... 100 6.3 An Alternative Analysis Technique for Low Temporal Resolution Data ............ 102 6.4 Temporal Resolution and Accuracy of Detection of Prostatic Tumours .............. 104 6.4.1 Data Processing ................................................................................................. 105 6.4.2 Results ............................................................................................................... 106 6.5 Discussion and Conclusions ................................................................................. 111 Chapter  7: Conclusions ..................................................................................................... 113 7.1 Summary ............................................................................................................... 113 7.2 Contributions......................................................................................................... 114 7.3 Future Work .......................................................................................................... 116 References ............................................................................................................................ 118 Appendix .............................................................................................................................. 124 Effect of the T1 relaxation on the measurement of Luminal Water Fraction ................... 124  xiii  List of Tables Table 1-1. Representative values of relaxation parameters T1 and T2, in milliseconds, for hydrogen components of different human body tissues at 1.5 T magnetic field and 37° C (human body temperature). ....................................................................................................... 7 Table 1-2. Estimated Canadian prostate cancer statistics (2016). .......................................... 20 Table 2-1. Summary of signal fractions and T2 relaxation times and bi-exponential decays. 32 Table 3-1. Clinical data of 17 patients participating in the study. .......................................... 48 Table 3-2. Percentage area (median values, with ranges in parentheses) of tissue components in different regions derived from histology. ........................................................................... 58 Table 3-3.  Average values (median values, with ranges in parentheses) of LWI parameters in malignant and normal tissue in different regions. ................................................................... 59 Table 3-4.  Spearman's rank correlation coefficient (ρ), with 95% confidence intervals  in parentheses, between MR measurements and the percentage area of tissue components. ..... 60 Table 4-1. Clinical data of 18 patients participating in the study. .......................................... 68 Table 4-2. Mean value, standard deviation, and range of MR measurements in malignant and non-malignant tissues of different regions. ............................................................................. 74 Table 4-3. Statistics of correlations between MRI multi-exponential decay parameters and Gleason score in PZ; data from 17 patients were included. .................................................... 76 Table 4-4. ROC analysis measures for MRI parameters in PZ, TZ, and entire prostate. ....... 76 Table 5-1. Clinical data of 15 patients participating in the study. .......................................... 82 Table 5-2. ROC analysis measures for single MRI parameters in the entire prostate, PZ, and TZ. ........................................................................................................................................... 90 xiv  Table 5-3. ROC analysis measures for combined MRI parameters in the entire prostate, PZ, and TZ. .................................................................................................................................... 91 Table 5-4. Statistics of correlations with Gleason score in PZ. .............................................. 92 Table 6-1. Results of multi-parametric ROC analyses. ........................................................ 110    xv  List of Figures Figure 1-1. Signal decay curve from a typical spin echo process showing the use of refocusing RF pulses to rephase the protons and to produce an echo signal. ............................................. 8 Figure 1-2. Slice selection by application of field gradient. ................................................... 13 Figure 1-3. Prostatic urethra. A, sagittal section. B, Oblique coronal view. .......................... 18 Figure 1-4. Zonal anatomy of the prostate as described by McNeal. ..................................... 19 Figure 1-5. Histologic patterns of prostatic adenocarcinoma in Gleason grading system. ..... 22 Figure 2-1. A series of spin-echo T2W images of a prostate gland (left), and hypothetical corresponding signal decay curve (right) ................................................................................ 28 Figure 2-2. A section of normal human prostatic tissue (20×) from peripheral zone, obtained from a whole-mount histology section of a participant in this study. ..................................... 31 Figure 2-3. A zoomed-in section (20×) of Hematoxylin and Eosin (H&E)-stained whole-mount histology slide ......................................................................................................................... 31 Figure 2-4. LT2F maps generated from simulated MR images using T2-short =50 ms, T2-long =200 ms, SNR=100, with variable TE and constant NE=25 (top), and variable NE and constant TE=25 ms (bottom). ................................................................................................................ 35 Figure 2-5. LT2F map generated from simulated MR images using T2-short =50 ms, T2-long =200 ms, SNR=100, NE=40. The values of TE that satisfy the second criterion are smaller than 50 ms. ........................................................................................................................................... 36 Figure 2-6. T2-short, T2-long, and LT2F map generated from formalin fixed celery for different TE and NE=32 (left), and NE=64 (right). ............................................................................... 39 Figure 2-7. 1st echo T2W images from 10 axial slices of a healthy prostate, with a) voxel size: 2×2×4 mm3, and b) voxel size: 1×2×4 mm3. .......................................................................... 42 xvi  Figure 2-8. SNR as a function of SENSE factor for 10 slices of MR images from a healthy prostate. ................................................................................................................................... 43 Figure 2-9. A) Axial T2W MR image of the prostate, B) LWF map, C) T2-short map, D) T2-long map of the same slice. Scale bar of C and D images is in ‘ms’. ............................................. 44 Figure 3-1. Representative example of segmentation of the whole mount histological images.................................................................................................................................................. 51 Figure 3-2. a: 1st echo T2W image of an axial cross section from a middle level of a prostate gland. b: NNLS fitting of the multi-exponential T2 decay curve ............................................ 55 Figure 3-3. Histogram of T2-short (blue) and T2-long (orange) for 4700 pixels. .......................... 56 Figure 3-4. Sample H&E-stained whole-mount histology sections (a,b), with the corresponding LWF map (c), and high resolution T2W image of the same slice (d). ................................... 61 Figure 3-5. Regression results and scatter plots of: a) LWF versus percentage area of luminal space ........................................................................................................................................ 62 Figure 4-1. Representative maps of MR parameters, T2-weighted image, and histology whole-mount section of the same slice. ............................................................................................. 73 Figure 4-2. Box and Whisker plot of the average values of LWF versus different Gleason patterns in PZ. ......................................................................................................................... 74 Figure 5-1. Representative maps of MR parameters, T2-weighted image, and histology whole-mount section of the same slice. ............................................................................................. 89 Figure 6-1. Comparison between numerical integration of the integral term in Equation 6-1, from a simulated Cp with temporal resolution of 12 s (left figures) and 14 s (right figures). . 99 Figure 6-2. Percentage errors in calculated fit parameters obtained from simulation. ......... 102 Figure 6-3. Percentage errors in calculated fit parameters obtained from simulation. ......... 104 xvii  Figure 6-4. Graphs of area under the (ROC) curve (AUC) as a function of down-sample factor (DSF) in the peripheral zone. ................................................................................................ 107 Figure 6-5. Graphs of AUC values as a function of DSF in the transition zone. ................. 108 Figure 6-6. Graphs AUC values as a function of DSF in the entire prostate. ....................... 109 Figure A-1. The ratio of LWF to LWF′ for T1-long equal to 4000ms, and 800ms<T1-short<1600ms................................................................................................................................................ 127 Figure A-2. The ratio of LWF to LWF′ for T1-short equal to 1250ms, and 2500ms<T1-long<5000ms. .......................................................................................................................... 127    xviii  List of Symbols  Along                                                                                                                                              Area under the peak of long T2  Ashort                                                                                                                                         Area under the peak of short T2 Ktrans                                                                                                                                                           Volume transfer constant Ncomp                                                                                                                         Number of peaks in the T2 distribution T1                                                                                                                                                           Spin-lattice relaxation time T2                                                                                                                                                               Spin-spin relaxation time T2-long                                                                                                                                     Geometric mean value of long T2 T2-short                                                                                                                                   Geometric mean value of short T2 ve                                                                                 Fractional volume of the extra-vascular extra-cellular space vp                                                                                                                                                          Fractional volume of plasma  xix  List of Abbreviations  2D                                                                                                                       Two-Dimensional 3D Three-Dimensional ACR American College of Radiology ADC                                                                                              Apparent Diffusion Coefficient AFMS Anterior Fibromuscular Stroma AIC                                                                                                   Akaike Information Criterion AUC                                            Area Under the Receiver Operating Characteristic (ROC) Curve BIC                                                                                             Bayesian Information Criterion BPH                                                                                                  Benign Prostatic Hyperplasia BW                                                       Bandwidth CZ                                                                                                                              Central Zone DCE                                                                                                  Dynamic Contrast-Enhanced DCE-MRI                                                                                 Dynamic Contrast-Enhanced MRI DRE                                                                                                                Digital Rectal Exam DWI                                                                                                  Diffusion Weighted Imaging DW-MRI                                                                                                Diffusion Weighted MRI EES                                                                                           Extracellular-Extravascular Space EMF Electromotive Force ESUR European Society of Urogenital Radiology FOV                                                                                                                          Field of View xx  GLMM   Generalized Linear Mixed-Effect Model gmT2                                                                                                                 geometric mean T2 GS                                                                                                                           Gleason Score GRASE                                                                        Gradient Spin Echo H&E                                                                                                          Hematoxylin and Eosin IAE                                                                                                   Integral Approximation Error LT2F                                                                                                                   Long T2 Fraction MP-MRI                                                                                                      Multi-Parametric MRI MR                                                                                                                 Magnetic Resonance MRE                                                                                        Magnetic Resonance Elastography MRI                                                                                                 Magnetic Resonance Imaging MRSI                                                                                                   MR Spectroscopic Imaging NE                                                                                                                     Number of Echoes NMR                                                                                  Nuclear Magnetic Resonance Imaging NNLS                                                                                                Non-Negative Least Squares PCa                                                                                                                 Prostatic Carcinoma PD                                                                                                                           Proton Density PFMS                                                                                      Periurethral Fibromuscular Stroma PI-RADS                                                                 Prostate Imaging Reporting and Data System PSA                                                                                                        Prostate-Specific Antigen PZ                                                                                                                          Peripheral Zone RF                                                                                                                        Radio Frequency xxi  ROC                                                                                          Receiver Operating Characteristic ROI                                                                                                                   Regions of Interest SAR                                                                                                   Specific Absorption Rate SENSE                                                 Sensitivity Encoding SNR        Signal to Noise Ratio T1W                                                      T1-weighted T2W            T2-weighted TE                                                                                                                                 Echo Time TRUS                                                                                             Transrectal Ultrasound TR                                                                                                                       Repetition Time TZ                                                                                                                       Transition Zone   xxii  Acknowledgements First and foremost, I would like to express my deepest gratitude to my supervisor Dr. Piotr Kozlowski for his leadership, warm encouragement, never-ending patience and unlimited support. He created many rewarding opportunities for me, and his excellent knowledge and intuition was a great asset for this research. I consider myself fortunate and privileged to have had the opportunity to perform my research under his supervision. I would like to thank my committee members, Dr. Alex MacKay, Dr. Stefan Reinsberg, and Dr. Silvia Chang for their support, encouraging guidance, and helpful suggestions. I would also like to thank Dr. Chang for her technical support and her valuable feedback on the clinical aspects of this research. I would like to gratefully acknowledge Dr. Edward Jones, Dr. Ladan Fazli, Dr. Larry Goldenberg, Dr. Pater Black, and Dr. Richard Savdie for their technical support and beneficial advice on the clinical features of this research, and for providing constructive feedback on my publications. I sincerely thank Dr. Jing Zhang for providing the pulse sequence without which I could not have achieved this work. I would like to thank Dr. Martin Gleave, Dr. Alan So, and Dr. James Johnson for their valuable cooperation in patient recruitment, and Margaret Luk, Janet Liew, Dr. Alireza Moeen Rezakhanlou, and Dr. Antonio Hurtado for their kind support in preparation and handling of histology slides. xxiii  For their warm support, I sincerely acknowledge the supportive staff of UBC MRI Research Centre (3T); Laura Barlow, Alex Mazur, Jeannette Procter, Trudy Harris, and Tracey Maile.  I would like to express my gratitude to all amazing researchers (past and present) of our laboratory; Henry Chen, Andrew Yung, Barry Bohnet, Carlos Uribe, Firas Moosvi, Jennifer Moroz, and Haley Patrick for their continuous support and helpful feedbacks especially during our weekly group meetings. I would like to thank Dr. John Petkau, from UBC department of statistics for his valuable advice, and Tingting Yu for her assistance in our statistical analyses. My spatial thanks go to my kind friends, Soheyl Vakili and Seyed Mahdi Beheshtian, who volunteered to participate in this study despite their busy schedules. I would like to thank my former supervisors: Dr. Ezatollah Arzi, Dr. Siamak Sadat Goushe, and Dr. Hirohisa Tanaka to whom I attribute my passion for physics. Finally, I wish to express my endless gratitude to my parents, Mitra and Adel, and my dear brother Ali, for their unconditional love and unlimited support throughout my life and particularly during the course of this study. Last but not the least, I would like to thank Pirooz Darabi (my husband) for his continuous encouragement, endless support, and love during my PhD study. His help, patience and kindness made this research a satisfying experience to me. xxiv  Dedication  To my dearest parents, best brother, and beloved husband.  1  Chapter  1: Introduction  1.1 Magnetic Resonance Imaging (MRI) MRI is a non-invasive imaging technique that has been used for over 40 years to provide anatomical, physiological, and functional information from the human body, without use of ionizing radiation.  The fundamental finding, based on which MRI is developed, was achieved in 1938 by Isidor I. Rabi (1, 2). Rabi measured the nuclear magnetic moment by using Nuclear Magnetic Resonance (NMR), and explained how the magnetic orientation of nuclei could be flipped by use of oscillating magnetic fields. In 1946, two independent teams led by Felix Bloch and Edward Purcell simultaneously discovered NMR in condensed matter (3, 4, 5). The first NMR image was produced later in 1971 by Paul Lauterbur (6), and the first MRI scan of the human body was performed in 1977 by Raymond Damadian (7). In early 1980 commercial MRI scanners were introduced and became clinically available in hospitals. Since then, there have been many revolutionary improvements in the instrumentation, computer technology, and data processing techniques in the field of MRI. Nowadays, MRI is an essential imaging tool that provides a wide range of anatomical and physiological information from the human body for diagnostic purposes.   2  1.1.1 Magnetization Vector  In classical mechanics, the magnetic moment of an object is a measure of its tendency to align with an external magnetic field. An object with non-zero magnetic moment that is exposed to an external magnetic field, experiences a torque, and rotates about the direction of the magnetic field.  In quantum mechanics, particles possess an intrinsic form of angular momentum called spin, S. Particles with non-zero spin have a net magnetic moment and when exposed to a magnetic field will precess about the direction of the magnetic field. This motion is called Larmor precession, and the angular frequency of this precessing motion is known as Larmor frequency, 𝜔𝐿, which is related to the magnitude of the applied magnetic field, B, with the following equation: 𝜔𝐿 = −𝛾𝐵  Equation 1-1 where γ is the gyromagnetic ratio, i.e. the ratio of magnetic moment of a particle to its angular momentum. A rotating magnetic moment can be detected using a coil placed next to it. This is because precessing magnetic moment causes a change of magnetic flux in the coil, which, based on Faraday’s law, generates an induction current in the coil.  In each atom, electrons and the nucleus can be sources of magnetic moment. Both electronic and nuclear magnetic moments precess in the presence of an external magnetic field, and therefore, can be detected using magnetic resonance techniques (Nuclear Magnetic Resonance (NMR) for the nucleus, and Electron Paramagnetic Resonance (EPR) for the electron).  In MRI, the source of magnetism is the magnetic moment of nuclei. The MRI signal is generated  3  from Larmor precession of the magnetic moment of the hydrogen nucleus, 1H, which is a proton. 1H is used in MRI mainly due to the abundance of water in biological systems. An MRI signal is acquired from macroscopic pieces of tissue, rather than individual nuclei. In a macroscopic piece of tissue, there are billions of 1H nuclei. Magnetic moments of such nuclei in the absence of any external magnetic field are isotropically oriented, resulting in an almost net zero magnetic moment. Right after application of an external magnetic field, magnetic moments of spins precess about the magnetic field, still with an isotropic distribution of orientations. Therefore, the nuclear magnetic moments do not contribute to the magnetism of the material immediately after being exposed to a magnetic field. However, gradually nuclear spins exchange energy with the neighboring molecules, and eventually the isotropy of the distribution of magnetic moments’ orientation breaks. As a result of this a net magnetic moment along the direction of the magnetic field appears in the sample. A simplified explanation of this phenomenon, provided by quantum mechanics, is as follows.  The proton is a spin ½ particle, and hence has two spin eigenstates called spin-up and spin-down (with eigenvalues of S=+1/2, S=-1/2, respectively). Corresponding to the two spin eigenstates, there are two energy levels, E(S), given by the equation below: 𝐸(𝑆) = −𝛾 ℎ 2𝜋⁄ 𝑆𝐵 Equation 1-2 where h is the Planck constant = 6.626×10-34 m2kg/s, and B is the magnitude of the applied magnetic field.  4  The state of individual spins can be expressed as a linear combination of the eigenstates. In a system at finite temperature, the population of energy states, P(E), for an ensemble of spins is given by Boltzmann distribution equation, written as follows: 𝑃(𝐸) = 𝐴  𝑒(−𝐸𝑘𝑇)  Equation 1-3 where A is a constant of the system, k is the Boltzmann constant, equal to 1.381×10-23 m2kgs-2K-1, and T is the absolute temperature of the system. It can be easily observed from Equation 1-2 and  Equation 1-3 that the probability for proton spins to be in state up and down is different. Therefore, in an ensemble there is a slight tendency for the spins to point in the direction of the field rather than against it. For a large number of nuclear spins, N, with individual magnetic moments of m, where m=𝛾 ℎ 2𝜋⁄ 𝑆, the net macroscopic magnetization, M⃗⃗⃗ , can be calculated as below: ?⃗⃗? = ?⃗⃗? × 𝑁 × (𝑃(𝐸𝑑𝑜𝑤𝑛) − 𝑃(𝐸𝑢𝑝)𝑃(𝐸𝑑𝑜𝑤𝑛) + 𝑃(𝐸𝑢𝑝)) = ?⃗⃗? × 𝑁 × tanh (∆𝐸2𝑘𝑇) ≈ ?⃗⃗? × 𝑁 ×(∆𝐸2𝑘𝑇) = 𝑁𝛾2ℎ24𝜋2?⃗? 4𝑘𝑇 Equation 1-4 M⃗⃗⃗  is called the thermal equilibrium magnetization vector. In a macroscopic piece of tissue when M⃗⃗⃗  is tipped away from the direction of the magnetic field, B⃗ , it precesses and generates the signal that can be detected and used for image construction in MRI.            5  1.1.2 T1, T2, and T2* Relaxations As explained earlier, the first step to generate an MRI signal is having an external magnetic field to create a net magnetization vector in a macroscopic piece of matter. The second step would be to tip away the created net magnetization vector from the direction of the external magnetic field so that the net magnetization vector precesses and generates a signal. The procedure of tipping the net magnetization vectors from the direction of the magnetic field is performed by application of radio frequency (RF) excitation pulses, which is explained in more detail in Section 1.1.4. After the net magnetization vector is tipped away and the RF pulse is turned off, the precession does not last forever; eventually nuclei spins restore their equilibrium state and the net magnetization vector aligns itself with the direction of the magnetic field. The process by which the magnetization vector reaches its thermal equilibrium state is called relaxation and is divided into two independent mechanisms: spin-lattice, also known as longitudinal or T1 relaxation, and spin-spin, also known as transverse or T2 relaxation. T1 relaxation is the process by which the longitudinal component of the magnetization vector, which is along the direction of the magnetic field (here chosen to be ?̂?), is recovered. In this process, nuclei spins exchange energy with the surrounding molecules (or lattice, in solid samples) to return to the equilibrium state. Mathematically, longitudinal relaxation is modelled by an exponential growth function with the T1 relaxation time being defined as the time constant. This can be expressed as below:  6  𝑀𝑧(𝑡) = 𝑀𝑧(0)𝑒−𝑡𝑇1  + 𝑀0(1 − 𝑒−𝑡𝑇1)  Equation 1-5 where Mz is the component of magnetization vector along the direction of magnetic field (?̂?), and M0 is the equilibrium magnetization. T2 relaxation is the process by which the transverse component of magnetization vector decays toward its equilibrium value of zero. This mechanism occurs because the local fields that spins experience is a combination of the external magnetic field and the magnetic fields of spins’ neighbours. As a result of the differences in the local fields, individual spins precess at slightly different frequencies, which dephases the spins. Mathematically, transverse relaxation is modelled by an exponential decay function with the T2 relaxation time being the time constant. This can be expressed as below: 𝑀𝑇(𝑡) = 𝑀𝑇0𝑒−𝑡𝑇2  Equation 1-6 where MT (t), and MT0 are the magnitude of the transverse component of the net magnetization vector at time t, and before the beginning of relaxation, respectively.  Based on Equation 1-6, T2 relaxation time can be described as the time at which the transverse component of M decays to approximately 37% of its initial value. Representative values of T1 and T2 relaxation times in human body tissues are presented in Table 1-1.    7  Table 1-1. Representative values of relaxation parameters T1 and T2, in milliseconds, for hydrogen components of different human body tissues at 1.5 T magnetic field and 37° C (human body temperature).  These are only approximate values. The table is reproduced from (8). Tissue T1 (ms) T2 (ms) Gray Matter (GM) 950 100 White Matter (WM) 600 80 Muscle 900 50 Cerebrospinal Fluid 4500 2200 Fat (CSF) 250 60 Blood 1200 100-200  The decay of the transverse magnetization results from any processes causing spin dephasing. In addition to the processes involved in the T2 relaxation, spin dephasing can be caused by local static field inhomogeneity related to hardware imperfections and/or sample related local magnetic susceptibility effects. The general spin dephasing process is thus called T2* relaxation, with the static component called T2′ relaxation. T2, T2*, and T2′ relaxation times are related by the following equation: 1𝑇2∗ =1𝑇2+1𝑇2′  Equation 1-7  Unlike for T1 and T2 relaxations, the loss of magnetization due to T2′ effects can be recovered using spin-echo techniques. In these techniques, a series of refocusing RF pulses is applied, with time intervals t, following the initial spin excitation. By application of the refocusing pulses, the inhomogeneous static dephasing evolution reverses to form echoes at times n×2t (where n is an integer). The time between consecutive peaks of echoes, 2t, at which the MR  8  signal is sampled, is called echo spacing, TE. A signal decay curve obtained from a typical spin-echo technique is shown in Figure 1-1.   Figure 1-1. Signal decay curve from a typical spin echo process showing the use of refocusing RF pulses to rephase the protons and to produce an echo signal.  A spin echo was first discovered by E.L. Hahn in 1950 (9). The modified spin-echo technique, known as CP, was later developed by H.Y. Carr and E.M. Purcell (10).  The CP technique was further modified by S. Meiboom and D. Gill (11), and therefore was called CPMG (Carr Purcell Meiboom Gill). The CPMG sequence is nowadays widely used for T2 mapping experiments.   In MRI, most often a complete set of data is acquired from application of a series of RF excitation and gradient pulses. The time between two consecutive excitation pulses is called the repetition time or TR. In a spin-echo experiment, where the RF excitation pulses are applied at time interval TR and signal data are sampled at time interval TE, by combining Equation  9  1-5 and Equation 1-6, the transverse component of the magnetization vector, to which the signal is proportional, can be expressed as follows: 𝑀𝑇(𝑇𝐸) = 𝑀0 (1 − 𝑒−𝑇𝑅 𝑇1⁄ ) 𝑒−𝑇𝐸 𝑇2⁄   Equation 1-8  1.1.3 Bloch Equations The equation of motion for a net magnetization vector M from an ensemble of nuclei in an external magnetic field B, without considering the spin-lattice and spin-spin interactions, can be written as below (8): 𝑑𝑑𝑡?⃗⃗? = 𝛾?⃗⃗? × ?⃗?   Equation 1-9 The more accurate equation of motion, accounting for the spin-lattice and spin-spin interactions, in a coordinate system where B is in z direction, can be expressed by the following equation, also known as the Bloch equation: 𝑑𝑑𝑡?⃗⃗? = 𝛾?⃗⃗? × ?⃗? − 𝑀𝑥 ?̂?+𝑀𝑦 ?̂?𝑇2−(𝑀𝑧−𝑀0 )?̂?𝑇1  Equation 1-10 where Mx, My, and Mz are the components of the magnetization vector along the x, y, and z directions, respectively. The Bloch equation was introduced by F. Bloch in 1946 (4) and has the following general solutions: 𝑀𝑥(𝑡) = [𝑀𝑥(0) cos(𝜔𝐿𝑡) + 𝑀𝑦(0) sin(𝜔𝐿𝑡)]exp (−𝑡𝑇2)  Equation 1-11 𝑀𝑦(𝑡) = [−𝑀𝑥(0) sin(𝜔𝐿𝑡) + 𝑀𝑦(0) cos(𝜔𝐿𝑡)] exp (−𝑡𝑇2)  Equation 1-12 𝑀𝑧(𝑡) = 𝑀0 + [𝑀𝑧(0) − 𝑀0]exp (−𝑡𝑇1)  Equation 1-13  10  In complex space, the two transverse components can be combined to generate a single transverse magnetization vector, 𝑀𝑇 = 𝑀𝑥 + 𝑖𝑀𝑦, and accordingly Equation 1-11 and Equation 1-12 can be combined and expressed as below: 𝑀𝑇(𝑡) = 𝑀𝑇(0)exp (𝑖𝜔𝐿𝑡 −𝑡𝑇2)  Equation 1-14 As the MRI signal is generated by the transverse component of the magnetization vector, Equation 1-14 is a very practical equation and often referred to in MRI formalism.  1.1.4 RF Excitation and Signal Detection As mentioned earlier, tilted net magnetization vectors in a magnetic field will precess and generate a detectable signal until they reach a thermal equilibrium state. This process is called free induction decay, FID, and the signal that is generated during this process is called the FID signal. Tipping away of a magnetization vector from the direction of the primary magnetic field can be performed by applying either a strong secondary magnetic field (along a different direction) or a weak oscillating magnetic field as long as it oscillates at the same frequency as the frequency of precession, known as the resonance frequency. In MRI, the magnetization vector is tilted by using the second method, i.e. application of a (secondary) oscillating magnetic field, which is much smaller and perpendicular to the direction of the primary static magnetic field. The frequency of this oscillating magnetic field is in the RF range, and so the process of tilting the magnetization vector, or excitation of spins into a non-equilibrium state, is called RF excitation. The reason why the frequency of an excitation pulse must be in the RF range can be understood based on Equation 1-1. By substituting the gyromagnetic ratio of a proton (γ=2.675222×108 rad.sec.T-1) in Equation 1-1 and dividing it by 2π, the Larmor  11  frequency of protons per unit magnetic field will be calculated and is equal to 42.578 MHz.T-1. The magnitude of the static magnetic field used in typical MRI scanners ranges from 1 to 10 T. For this range, the Larmor frequency of protons ranges between 42 and 420 MHz, which is within the RF range (3 kHz – 300 GHz). If a coil whose surface vector is not parallel to the direction of the static magnetic field is located near the excited sample, the precession motion of the transverse component of the magnetization vector causes a change in the magnetic flux through the coil. As mentioned earlier, change of magnetic flux based on Faraday’s law induces electromotive force (EMF) in the coil. This induced EMF, generated from precessing magnetization, is the measurable signal in MRI experiments. The equation relating the detected signal to characteristics of the imaging system is derived in detail in (8). The final expression is as follows: 𝑠(𝑡) ∝ 𝜔𝐿 ∫𝑑3𝑟 𝑒−𝑡𝑇2(𝑟 )⁄𝑀𝑇(𝑟 , 0)𝐵𝑇(𝑟 )𝑒𝑖((𝛺−𝜔𝐿)𝑡+𝜑0(𝑟 )−𝜃𝐵(𝑟 ))  Equation 1-15 where s(t) is signal at time t, 𝑀𝑇(𝑟 , 0) and 𝜑0(𝑟 ) are the magnitude and phase of the complex magnetization vector at time 0 and location 𝑟  (𝑟  is a 3D vector) determined by the initial RF pulse condition. BT (𝑟 ) and 𝜃𝐵(𝑟 ) are the magnitude and phase of the receiver coil’s magnetic field per unit current produced at location 𝑟 , and 𝛺 is the reference signal frequency: frequency of precession in a reference frame rotating with the Larmor frequency L. It is important to note that in Equation 1-15 the signal is related to both magnitude and phase of the magnetization vector.    12  1.1.5 Slice Selection It has been mentioned earlier that excitation of spins happens only when the frequency of the applied RF pulse equates (or is close to) to the Larmor frequency of protons in the system. Larmor frequency is linearly related to the magnitude of the static magnetic field, expressed by Equation 1-1. Therefore, if an additional non-uniform magnetic field (generated by a series of coils called gradient coils), changing linearly in a desired direction is added to the existing static magnetic field during the application of the RF excitation pulse, only spins within a limited volume of the sample will be excited, and the detected signal can be spatially localized. To clarify this matter, let us suppose that a field gradient,G𝑟⃗⃗⃗⃗ , is applied along the 𝑟  direction (as demonstrated in Figure 1-2) to excite a desired slice perpendicular to 𝑟 . The linear perturbation of the magnetic field due to this field gradient along the 𝑟  direction can be calculated by below equation: ∆𝐵 = 𝑟  ⦁ G𝑟⃗⃗⃗⃗ = 𝑟𝐺𝑟  Equation 1-16 Accordingly, the total magnetic field along 𝑟  can be expressed as below: 𝐵(𝑟) = 𝐵0 +  𝑟𝐺𝑟  Equation 1-17 where 𝐵0 is the magnitude of the static magnetic field. By substituting Equation 1-17 in Equation 1-1 the precession frequency at position r can be expressed as below: 𝜔(𝑟) = 𝜔0 + 𝛾 𝑟𝐺𝑟  Equation 1-18 where 𝜔0 = 𝛾𝐵0. Equation 1-18 implies that under the impact of the field gradient precessing frequency is a linear function of position along the direction of the gradient. To excite a thin slice with  13  thickness ∆r, centered at r0, expanding from r0-∆r/2 to r0+∆r/2, the frequency of the excitation RF pulse must be tuned to a bandwidth ∆ω ranging from 𝛾 𝑟0𝐺𝑟 − 𝛾 ∆𝑟2⁄ 𝐺𝑟 to 𝛾 𝑟0𝐺𝑟 +𝛾 ∆𝑟 2⁄ 𝐺𝑟. The thickness of the excited slice, ∆r, and the bandwidth, BW, of the RF excitation pulse are related by the following equation: 𝐵𝑊 = ∆𝜔 = (𝛾 𝑟0𝐺𝑟 + 𝛾 ∆𝑟2⁄ 𝐺𝑟) − (𝛾 𝑟0𝐺𝑟 + 𝛾 ∆𝑟2⁄ 𝐺𝑟) = 𝛾 ∆𝑟𝐺𝑟  Equation 1-19   Figure 1-2. Slice selection by application of field gradient. Only spins within a plane perpendicular to field gradient, Gr, are excited by application of the RF pulse with a tuned bandwidth ∆ω.   In two-dimensional (2D) MRI, during each RF excitation only spins within a single slice will be excited. Following the slice excitation, signal localization in two in-plane directions is performed using frequency encoding and phase encoding, which are briefly explained in Section 1.1.6, and 1.1.7, respectively.   14  1.1.6 Frequency Encoding In this localization technique, another non-uniform magnetic field, linearly varying in an in-plane direction, is applied after a slice was selected by simultaneous application of an RF excitation pulse and slice selective gradient.  Let us assume that the non-uniform magnetic field varies in the x direction. Then, during the application of a frequency encoding field gradient, spins at different locations along the x axis are affected by a different total magnetic field, and therefore they precess at different Larmor frequencies based on Equation 1-1. Through analysis of the detected signal and application of Fourier transformation it is possible to quantify the number of nuclei precessing at each frequency.  It must be noted that this technique only discriminates spins at different locations along one direction (x direction here). Therefore, the outcome of the Fourier transformation will be a projection of the 2D spin distribution onto the x axis. To complete spatial localization, another technique must be used to discriminate spins at different locations along the second dimension (y axis in here). The technique used for this purpose is phase encoding, and is explained in the following section.  1.1.7 Phase Encoding It was explained earlier, with the aid of Equation 1-15, that the induction signal contains information from both magnitude and phase of complex magnetization vectors. The phase encoding procedure, as its name suggests, encodes spatial information across one axis (y axis here) into the phase of magnetization vector. In this technique, a non-uniform magnetic field which varies linearly across the y axis is applied for a short period of time between slice  15  selection and frequency encoding. Similar to what was explained for frequency encoding above, during the application of the phase encoding gradient, spins at different locations across the y axis will be exposed to different total magnetic fields and will precess at different Larmor frequencies. Therefore, when the phase encoding gradient is turned off and followed by a frequency encoding gradient, nuclei at different positions across the y axis will have different initial phases, while nuclei at different position across x axis will precess with different Larmor frequencies. A complete set of MRI data may be collected from repeated RF excitations followed by the use of different configurations of the phase encoding gradient. By applying a 2D Fourier transformation on such a data set, images of nuclei distribution in the x-y plane can be constructed.  1.1.8 Fourier Transform and Image Reconstruction The Fourier transform is a mathematical theorem on the basis of which it is possible to transform a function into an alternative representation. In a 2D Fourier transform, a function f(x,y) can be related to its representative F(kx,ky), using  the following equations: 𝜌(𝑥, 𝑦) = ∬ S(k𝑥, k𝑦)𝑒+2𝜋𝑖(k𝑥𝑥+k𝑦𝑦)𝑑k𝑥  𝑑k𝑦∞−∞  Equation 1-20 S(k𝑥, k𝑦) = ∬ 𝜌(𝑥, 𝑦)𝑒−2𝜋𝑖(k𝑥𝑥+k𝑦𝑦)𝑑𝑥 𝑑𝑦∞−∞  Equation 1-21 The Fourier transform can be used to convert raw data collected as the induction signal to MR images that represent the distribution of spins or, correspondingly, the nuclei distribution. To explain this matter, let us look into the signal expression given by Equation 1-15. It can be shown (8) that in a proper rotating frame, the expression of a complex induction signal can be simplified to the following equation:   16  𝑠(𝑡) ∝ ∫𝑑3𝑟 𝜌(𝑟 )𝑒𝑖(𝜑(𝑟 ,   𝑡))  Equation 1-22 where 𝜌(𝑟 ) is nuclei density, and is proportional to the transverse magnetization, and 𝜑(𝑟 ,   𝑡) is the phase of the magnetization vector in the rotating frame. The phase can be written in terms of the precession frequency in the rotating frame, 𝜔, using the following equation: 𝜑(𝑟 ,   𝑡) = ∫𝜔 (𝑟 ,   𝑡) 𝑑𝑡 Equation 1-23 For a given magnetic field gradient, 𝐺 (𝑡), 𝜔(𝑟 ,   𝑡) would be equal to γ ?⃗⃗? ⦁𝐺(𝑡); therefore, Equation 1-23 can be re-written as below:  𝜑(𝑟 ,   𝑡) = γ ?⃗⃗? ⦁ ∫𝐺 (𝑡′) 𝑑𝑡′  Equation 1-24 Now let us define a new vector, ?⃗? , as below: ?⃗? ( 𝑡) = γ ∫𝐺 (𝑡′) 𝑑𝑡′   Equation 1-25 By combining Equation 1-24 and Equation 1-25, the following will be obtained:  𝜑(𝑟 ,   𝑡) =  ?⃗⃗? ⦁?⃗?   Equation 1-26 By substituting Equation 1-26 in Equation 1-22, the signal expression can be re-written as follows: 𝑠(?⃗? ) ∝ ∫𝑑3𝑟 𝜌(𝑟 )𝑒𝑖(𝑟 ⦁?⃗? )  Equation 1-27  Equation 1-27 is a Fourier transform relating nuclei density in an image space, 𝜌(𝑟 ), to a detected signal in k space 𝑠(?⃗? ). In MRI, 𝑠(?⃗? ) is sampled at a large area of k-space. By applying an inverse Fourier transform to the signal data, MR images can be reconstructed using the following equation:  𝜌(𝑟 ) ∝ ∫ 𝑑3𝑘 𝑠(?⃗? )𝑒−𝑖(𝑟 ⦁?⃗? )  Equation 1-28  17  1.2 Prostate 1.2.1 Anatomy  Prostate is an exocrine gland of the male reproductive system. The main function of the prostate is to secrete an alkaline fluid which is an important ingredient of semen. A normal human prostate is about the size and shape of a large chestnut, and weights between 17 and 19 grams (12). The lateral (left-right), vertical (superior-inferior), and sagittal (anterior-posterior) dimensions of normal prostate are about 4cm, 3cm, and 2cm, respectively. The prostate looks a like a compressed inverted cone, including a base, midgland, and an apex. Its anatomical position is between the vesicle neck of the bladder and the urogenital diaphragm’s apex. It surrounds the prostatic urethra just below the bladder, and is immediately anterior to the rectum (Refer to Figure 1-3).    18   Figure 1-3. Prostatic urethra. A, sagittal section. B, Oblique coronal view (Based on Hinman F Jr. Atlas of Urosurgical Anatomy. Philadelphia: WB Saunders, 1993). The image is obtained from (12), Skandalakis et al, Surgical Anatomy: The Embryologic and Anatomic Basis of Modern Surgery © 2004. Reproduced with the kind permission of McGraw-Hill Education (UK) Ltd. All rights reserved.  The prostate gland is usually described by four anatomical zones, which were first proposed by McNeal, in 1981 (13), as follows: peripheral zone, PZ, central zone, CZ, transition zone, TZ, and the anterior fibromuscular stroma, AFMS (See Figure 1-4). The key element in defining these four zones is the urethra. Posterior to the urethra, there is the glandular tissue, and anterior to the urethra there is the fibromuscular area. The transition zone is the region that surrounds the urethra proximal to the ejaculatory ducts. The central zone is the region that  19  surrounds the ejaculatory ducts and protrudes under the bladder base. The peripheral zone embodies the apical, the posterior and the lateral aspects of the gland. The anterior fibromuscular stroma is prolonged from the bladder neck to the striated urethral sphincter.    Figure 1-4. Zonal anatomy of the prostate as described by McNeal. The transition zone surrounds the urethra proximal to the ejaculatory ducts. The central zone surrounds the ejaculatory ducts and projects under the bladder base. The peripheral zone constitutes the bulk of the apical, posterior, and lateral aspects of the prostate. The anterior fibromuscular stroma extends from the bladder neck to the striated urethral sphincter. (Modified from Brooks JD. Anatomy of the lower urinary tract and male genitalia. In: Walsh PC, Retik AB, Vaughn ED Jr, Wein AJ (eds). Campbell's Urology, 7th Ed. Philadelphia: WB Saunders, 1998; with permission.) The image is obtained from (12), Skandalakis et al, Surgical Anatomy: The Embryologic and Anatomic Basis of Modern Surgery© 2004. Reproduced with the kind permission of McGraw-Hill Education (UK) Ltd. All rights reserved.  20   With aging, the prostate usually grows larger and most men develop some prostatic diseases.  Common diseases of the prostate include:  prostatitis (inflammation of the prostate gland), benign prostatic hyperplasia (BPH) (benign enlargement of the prostate gland) and prostate cancer.   1.2.2 Prostate Cancer Prostate cancer is the most common diagnosed cancer among the Canadian men. It was estimated that in 2016, 21,600 new cases will be diagnosed, and 4,000 men will die from this disease in Canada (14). These numbers represent 21%, and 10% of all new cases of cancer and cancer deaths in men, respectively. Estimated Canadian prostate cancer statistics are presented in Table 1-2.  Table 1-2. Estimated Canadian prostate cancer statistics (2016).  Table reproduced from (14), originally obtained from (15).  Category                                                      Estimate New cases 21,600 Incidence rate (for every 100,000 males)* 114.7 Deaths 4,000 Death rate (for every 100,000 males)* 24.2 5-year net survival (estimates for 2006–2008) 95% *Age-standardized to the 2011 Canadian Standard Population.    21  Over 95% of prostate cancers are adenocarcinomas originating from prostatic epithelial cells. Roughly 70-80% of prostate cancers originate from PZ, and 20-25% originate from TZ (16). The CZ of the prostate is rarely accosted with carcinoma, and only about 2.5% of carcinomas originate from this region (17). AFMS is only composed of stromal tissue; therefore, no carcinoma arises from this zone. Prostatic stromal tumours are also very rare (18).  Confirmation of prostate cancer is usually performed by pathological examination of biopsy samples. Histologic grading of prostate cancer is performed using the Gleason Grading system (19). In this system, as shown in Figure 1-5, 5 tumour patterns are defined based on the morphology of the cancerous tissue. Pathologists assign each tumour a primary grade, according to the most common pattern seen in the tumour, and a secondary grade, according to the next most common pattern with prevalence larger than 5%. The summation of two assigned grades is called the Gleason score, which is commonly used for prognostic evaluation of prostate cancer.  22   Figure 1-5. Histologic patterns of prostatic adenocarcinoma in Gleason grading system.  The image is copied from the original article by Gleason DF (19).  Pattern 1-Cancerous tissue is very similar to normal prostatic tissue, where glands are small, well-formed, and closely packed. Pattern 2- Glands are still well-formed but with larger separation spaces filled with more tissue. Pattern 3- Tissue still has recognizable glands while some gland tissues began to invade the surrounding tissue. Pattern 4-Very limited glands are recognizable, while many gland cells have invaded the surrounding tissue. Pattern 5- Sheets of invaded cells are seen, without recognizable glands.  23  1.3 Objectives and Overview of this Thesis Early diagnosis of prostate cancer is a difficult task due to the absence of common symptoms and signs in the early stages of this disease. Meanwhile, similar to most other cancers, if it is diagnosed in the early stages, there are significantly more treatment options and the survival chances increase drastically.  Currently, most prostate cancer cases are first detected by use of Prostate-Specific Antigen (PSA) serum screening or by Digital Rectal Exam (DRE). For the cases with suspected cancer, confirmation and staging of the disease is achieved by use of transrectal ultrasound-guided (TRUS) biopsy. Although the biopsy based techniques are very reliable, they have two unavoidable and major issues: 1) being invasive and 2) not being capable of screening the entire volume of the prostate gland, as only a limited number of samples obtained from a limited area is examined.  The second issue may result in discovery of inconsequential tumours in some cases, while missing significant tumours in other cases. To overcome the biopsy shortcomings, a non-invasive imaging technique that can provide pathological information through the entire prostate gland is in high demand. An accurate non-invasive imaging technique can potentially be used for: 1- detection and grading of prostate cancer, 2- monitoring treatment response, and 3- serving as a guidance for more accurate sampling of localized biopsy. Such an imaging technique will significantly decrease the probability of missing malignant tumours, which has a very high possibility when biopsies are performed.   Among the non-invasive imaging techniques, MRI is an excellent candidate for the purpose of detection and evaluation of prostate cancer. This is mainly because: 1- this technique provides high spatial resolution and high contrast in soft tissue, 2- it does not expose patients to ionizing  24  radiation, and 3- it is versatile and capable of quantifying a large number of tissue properties which can be used for characterization of prostatic lesions.   Using MRI, morphological properties can be obtained from T2 or T1-weighted data. Physiological properties can be investigated through a variety of techniques such as: Diffusion Weighted Imaging (DWI), which is sensitive to water diffusion processes (20, 21), Dynamic Contrast-Enhanced MRI (DCE-MRI), which can provide information about tissue structure and microvasculature properties (22), T2 mapping techniques, which can provide information about tissue composition, or Magnetic Resonance Elastography (MRE), which provides a quantitative assessment of mechanical properties of tissue (23).  While each MRI technique provides valuable information for diagnostic purposes, it has been shown that the highest accuracy is achieved when a combination of MRI techniques, known as Multi-Parametric MRI (MP-MRI) (24), is used. Over the past decade, various MP-MRI techniques have been studied and shown to improve the accuracy of prostate cancer diagnosis (25, 26, 27, 28). MP-MRI protocols typically consist of T2-weighted (T2W) imaging as an anatomical imaging technique, and a combination of at least two of the functional imaging techniques including DCE-MRI, diffusion-weighted MRI (DW-MRI), and MR Spectroscopic Imaging (MRSI).  The current guidelines for evaluation of prostate cancer based on a MP-MRI data (composed of T2W, DCE, and DW-MRI data) are called PI-RADS v2 (Prostate Imaging Reporting and Data System version 2) (29). This reporting system was developed by joint effort of the  25  European Society of Urogenital Radiology (ESUR), the American College of Radiology (ACR), and the AdMeTech Foundation in 2015. In the PI‐RADS v2 reporting system a score on a 5‐point scale is assigned to each lesion based on the likelihood that the overall findings from a combination of  T2W, DCE, and DW-MRI data correlates with the presence of a clinically significant cancer. Since it was published in 2015, PI‐RADS v2 has been validated and used as the main guideline for the evaluation of prostate cancer using MP-MRI in clinical practice and many research studies.  Despite the relative success of MP-MRI in diagnosis of prostatic carcinoma (PCa), similar to any other imaging techniques, it has accuracy limitations and there is still room for further improvement by implementing new technologies, sequences, and novel techniques.  The PI‐RADS Steering Committee also strongly supports the continued development of novel MRI methodologies for evaluation of prostate cancer by using new and/or advanced research tools that are not included in PI‐RADS v2,  The main goal of this research was to develop a novel multi-parametric MRI protocol to increase the accuracy of detection and grading of prostate cancer. This goal was planned to be achieved by fulfilling the following objectives:  1. Development and assessment of a novel protocol for quantitative T2 mapping in the prostate; 2. Investigating the relationship between the parameters measured from the developed T2 mapping technique and the corresponding tissue composition in the prostate;  26  3. Comparing the diagnostic accuracy of the developed T2 mapping technique with the more established MRI techniques. Also, finding the most accurate multi-parametric MRI protocol by selecting the best combination from the investigated techniques. Additionally, we believed that there is room for improvement in the existing DCE-MRI protocols that are used in prostate studies; therefore, we decided to explore some potential areas of progress. This supplementary goal was achieved by addressing the following objective in this thesis: 4. Investigating the effect of temporal resolution and data analysis technique in the accuracy of DCE-MRI in detection of prostatic tumours. This rest of this thesis is organized as follows:  In Chapter 2, it is described how the new multi-exponential T2 mapping protocol, Luminal water imaging (LWI), is developed.   In Chapter 3, the correlation between measurements of LWI and the corresponding tissue composition in prostate is investigated through a direct comparison between MRI data and histology images at cellular resolution.   In Chapter 4, the relationship between measurements of LWI and the histopathology of prostatic tissue is investigated by performing a direct comparison between MRI data and  27  whole-mount histology, and the accuracy of this technique in the detection and grading of prostatic tumours is determined.  In Chapter 5, the diagnostic accuracy of LWI is compared with the standard MP-MRI protocols which include DCE and DW-MRI. In addition, in this chapter the significance of adding LWI into a MP-MRI protocol, consisting of DCE-MRI and DW-MRI, in detection and grading of prostatic tumours is evaluated, and the most accurate MP-MRI protocol is proposed.  In Chapter 6, the impact of temporal resolution on the accuracy of DCE-MRI in the detection of prostatic tumours is investigated.  Chapter 7 provides a summary of the key findings and contributions of this thesis, and also establishes a framework for future work.  28  Chapter  2: Development of a Multi-Exponential T2 Mapping Protocol for Prostate Imaging  2.1 Introduction Magnetic resonance (MR) quantitative T2 mapping is an established imaging technique that has been used for non-invasive tracking of histopathologic changes in organs such as brain (30) and cartilage (31). In this technique, a series of T2-weighted (T2W) images is acquired by applying a spin-echo sequence, such as the CPMG sequence. From spin-echo images, a time-dependant signal decay curve can be extracted for each pixel, and consequently, the T2 relaxation time can be determined for each pixel (Figure 2-1).                                                                                                                                                                       Figure 2-1. A series of spin-echo T2W images of a prostate gland (left), and hypothetical corresponding signal decay curve (right) of a single pixel, from which the T2 relaxation time can be calculated for the outlined pixel. If the effect of T1 relaxation can be ignored (See the Appendix for details regarding the effect of T1 relaxation on multi-echo signal), in a homogenous spin system signal decay can be described by an exponential decay function with decay constant equal to the inverse of a well-defined T2 relaxation time. This can mathematically be expressed as below: t = 1×TE t=N×TE  t x y  29  𝑆(𝑡) = 𝐴𝑒−𝑡T2  Equation 2-1 where S(t) is the magnitude of the signal at a time t, and A is the amplitude of the signal at time zero (which is proportional to the proton density).  However, in inhomogeneous tissues, where each voxel contains various water compartments, the signal decay curve becomes multi-exponential, with several different T2 relaxation times. This is because hydrogen protons of water molecules experience different spin-spin interactions in different environments, and hence represent different T2 relaxation times. Therefore, in inhomogeneous tissue one may expect multi-exponential signal decay, which can mathematically be written as follows: 𝑆(𝑡) = ∑ 𝐴𝑖𝑒−𝑡T2i𝑖=𝑁𝑖=0   Equation 2-2 where N is the total number of exponential components, and is equal to the number of different water compartments, Ai is the amplitude of component i, and T2i is the T2 relaxation time of component i. Multiple T2 values reflect the underlying composition of the scanned tissue, and hence their measurement can reveal important information for diagnostic purposes.  The prostate is composed of glandular and non-glandular tissue. Non-glandular tissue of prostate, which is less important for diagnostic purposes, is mainly composed of stroma. Glandular tissue of the prostate, where 99% of prostate cancers originate (32), is composed of stromal tissue fused to several ducts and acini (Figure 2-2). These ducts and acini are relatively large in size (up to 0.2 mm in diameter) (33) and consist of luminal space filled with prostatic fluid and lined with two layers of basal epithelial cells (34, 35). In this tissue arrangement, there are two distinctive water environments in a typical voxel (1-10 mm3) of an MR image; the larger one being the lumen space, and the much smaller intra-/extra-cellular space of  30  epithelial and stromal tissue. Therefore, T2 decay curves will likely be bi-exponential, with a longer T2 related to the water inside the lumen and a shorter T2 to the water within the epithelial cells and stromal tissue.  The importance of multi-exponential T2 mapping in prostate can be understood by considering the fact that the relative percentage of luminal space in glandular tissue of prostate varies between tumour and normal tissue (36), and between different pathologic grades of cancer. Therefore, measurement of multiple T2 values and their relative ratio in prostate may potentially provide useful information for diagnostic purposes. Evidence of bi-exponential T2 decay in prostate has been shown in previous studies (37, 38, 39, 40). Reported values of T2 relaxation times of prostatic tissue from a previous study (38) are presented in Table 2-1. Potential contribution of bi-exponential T2 imaging in diagnosis of prostate cancer has also been investigated recently (41); however, no study with direct correlation between MRI and histology had been conducted by the time we started this study. This study was designed with the purpose of investigating the relationship between multi-exponential T2 mapping and the histopathology of prostatic tissue through a direct comparison between MRI and whole-mount histology. In our study, a new parameter called luminal water fraction (LWF), which represents the fractional amount of luminal space in prostatic tissue, was defined and used. Due to the differences in tissue composition and fractional amount of luminal space between normal and malignant tissues, we hypothesized that LWF could be used for the detection of prostatic tumours. Additionally, as the fractional amount of luminal space decreases with an increase in GS (See Figure 2-3), we also hypothesized that LWF could contribute to grading of prostate cancer. In summary, this study was designed to investigate  31  the feasibility of using multi-exponential T2 mapping in the detection and grading of prostatic tumours.  Figure 2-2. A section of normal human prostatic tissue (20×) from peripheral zone, obtained from a whole-mount histology section of a participant in this study.     Figure 2-3. A zoomed-in section (20×) of Hematoxylin and Eosin (H&E)-stained whole-mount histology slide  from a) normal tissue in PZ, b) Gleason 3+4 tumour in PZ, and c) Gleason 4+4 tumour in PZ.  It can be observed that with the progression of malignancy, the fractional amount of luminal space decreases.   32  Table 2-1. Summary of signal fractions and T2 relaxation times and bi-exponential decays.  The table is reproduced from (42).  Signal at TE=125 ms Bi-exp decays: number (total) Long T2 signal fraction (%) mean/median [range] T2 (ms): mean/median [range] Long component Short Component Peripheral Zone High 13 (14) 53/54 [28-80] 890/837 [490-1319] 70/73 [43-92] Intermediate 14 (14) 34/29 [29-57] 492/470 [161-828] 67/69 [48-79] Low 11 (14) 26/26 [18-34] 342/325 [201-516] 64/66 [50-80] Central Gland High 12 (14) 28/28 [16-45] 559/502 [297-1079] 63/64 [49-72] Intermediate 13 (14) 20/21 [5-30] 467/450 [193-928] 61/61 [51-71] Low 9 (14) 13/12 [3-21] 476/456 [230-821] 59/61 [45-67] All  72 (84) 30/27 [3-80] 546/490 [161-1319] 64/64 [43-92]  In the rest of this chapter, it is described how the imaging protocol for multi-exponential T2 mapping in prostate, named Luminal Water Imaging, has been developed. In Chapter 3, the relationship between measurements of this technique and the histopathology of the prostatic tissue is investigated by performing a direct comparison between MRI data and whole-mount histology, and the accuracy of this technique in the detection and grading of prostatic tumours is determined.  2.2  Protocol Development It has been previously shown that the sensitivity of T2 mapping techniques is highly dependent on the following scan parameters: TR, TE, number of echoes (NE), and signal to noise ratio  33  (SNR) (35, 40). Without using appropriate scan parameters, there will likely be a significant uncertainty in the measurement of T2 values and the relative ratio of each component. For scanning different organs, different sets of TR, TE, NE, and SNR must be determined during protocol development to maximize accuracy of T2 mapping measurements.  In this study, the value of TR (3073 ms) was chosen based on previous literature findings (37) such that the T1 contribution was minimized while still maintaining clinically feasible acquisition times. Using this relatively long TR imposed an indirect limitation on the range of SNR (average SNR within prostate gland, on the 1st echo images of a Gradient And Spin Echo (GRASE) sequence measured later during patient study, from 17 cases: 103, 81-125 95% CI). This was because any further improvement in SNR by increasing signal averaging would require a total scan time of greater than 25 minutes. Such a long scan time was avoided as it is not practical in clinical settings. With the selected values for TR and SNR (estimated from previously acquired data), the impact of variations of NE and TE on the accuracy of T2 mappings was investigated during the protocol development in this study. To find the optimum value of these parameters for T2 mapping of prostate gland, we performed several simulations and phantom testing followed by a series of volunteer scans. The details about simulations, phantom scans, and volunteer study are provided in the following sub-sections.  2.2.1  Simulations Simulations were performed using a fictitious two-compartment system described by two T2 relaxation times: T2-short and T2-long. Simulated MR images were generated for different values of T2-short and T2-long using an in-house program developed in Matlab (The Math Works Inc., Natick, MA, USA). The values of T2-short (25, 50, 75 ms) and T2-long (200, 400, 800 ms) used in  34  these simulations were chosen based on previously published T2 values of prostatic tissue in the literature (37, 38).  Images of simulated T2 signal, Ss(t), were generated in the form of simple squares with 64×64 pixels using the following equation: 𝑆𝑠(𝑡) = 𝑆0(1 − 𝐿𝑇2𝐹) 𝑒−𝑡𝑇2−𝑠ℎ𝑜𝑟𝑡 + (𝑆0 × 𝐿𝑇2𝐹) 𝑒−𝑡𝑇2−𝑙𝑜𝑛𝑔  Equation 2-3 where t is time, S0 is the maximum signal of the short component, and LT2F is the fractional weighting of the long T2 component. In the simulations, time was varied between TE and NE×TE with intervals of TE, S0 was set at 104 (in accordance with the signal intensity in our actual scan data). The LT2F was increased from 0 to 0.2 in 64 equally spaced steps throughout the field of view. This range of LT2F was selected by using the lowest ends of the ranges of long T2 fraction observed in the prostate by Storas et. al (38) to mimic the tissues with low luminal content (such as tumours) for which the long T2 component is more likely to be misidentified during the fitting process. For each set of T2-short and T2-long (9 sets in total), images of simulated T2 signal, Ss(t), were generated for different combinations of TE and NE. The range of TE (7-55 ms) and NE (10-64) was chosen based on practical values for experimental settings. Gaussian noise was added to all simulated images to generate an SNR of 100 in similarity with the SNR of our previously acquired data. Images of simulated T2 signal, Ss(t), were fitted to a multi-exponential decay function using a software written in Matlab which handles the regularized Non-Negative Least Squares (NNLS) (43, 44) algorithm. From fitting, maps of LT2F were generated. More details about the software and fitting procedure are provided in Chapter 3, Data Processing (section 3.6).   35  From visual inspection on the series of LT2F maps obtained from simulated MR images, two criteria were identified to affect the accuracy of T2 mapping measurements. The first criterion applies a limit on the minimum value of TE×NE based on the value of T2-long. This criterion can be expressed mathematically as below: 𝑁𝐸 × 𝑇𝐸 ≥ 2 × 𝑇2−𝑙𝑜𝑛𝑔  Equation 2-4 Visual inspection on LT2F maps generated for different combinations of TE and NE showed that the relative ratio of long component is identified correctly if the last echo occurs at times bigger than 2×T2-long. To better explain this matter, two example sets of LT2F maps are presented in Figure 2-4: one is generated with identical value of NE and different values of TE, and the other is created with identical value of TE and different values of NE. It can be observed from these images that when the time of the last echo is smaller than 2×T2-long, maps of LT2F become very noisy, indicating a higher calculation error for the fractional amount of one or both T2 components.                                                                                                                                                                                                                                                         Figure 2-4. LT2F maps generated from simulated MR images using T2-short =50 ms, T2-long =200 ms, SNR=100, with variable TE and constant NE=25 (top), and variable NE and constant TE=25 ms (bottom). For the given value of NE (25), the minimum value of TE to satisfy the first criterion is equal to (2×200)/25=16. Similarly, for the given value of TE (25 ms), the minimum value of NE to satisfy the first criterion is equal to 16.  36  The second criterion applies a limit only on the value of TE, based on the value of T2-short.  From visual inspection on the set of LT2F maps generated for different values of TE, and investigation of the T2 distributions obtained from individual decay curves, it was concluded that the value and the relative ratio of T2-short and T2-long are identified correctly if TE is smaller than T2-short. This criterion can be mathematically written as below: 𝑇𝐸 < 𝑇2−𝑠ℎ𝑜𝑟𝑡  Equation 2-5 As an example, a set of LT2F maps generated for identical value of NE and various values of TE is represented in Figure 2-5. It can be observed in these images that when the second criterion is not satisfied, the map of LT2F is close to zero for the majority of the pixels, indicating that only one component was identified.                                                                                                                                                Figure 2-5. LT2F map generated from simulated MR images using T2-short =50 ms, T2-long =200 ms, SNR=100, NE=40. The values of TE that satisfy the second criterion are smaller than 50 ms.  Based on the results of our simulations, it was concluded that the following algorithm must be followed in order to find the optimum values of TE and NE for an accurate multi-exponential T2 mapping in prostate: 1- The ranges of T2-short and T2-long in prostatic tissue must be determined from literature reports;   37  2- The largest value of NE allowed by consideration of practical limitations of scanner and specific absorption rate (SAR) regulations must be determined;  3- Using the selected NE, the smallest value of TE which satisfies the first criterion, described earlier, must be calculated.  4- The last step would be to check whether the TE found in the third step satisfies the second criterion as well. If TE satisfies the second criterion, the set of TE and NE can be used to design a multi-exponential T2 mapping protocol. If TE does not satisfy the second criterion, a reliable T2 mapping protocol may not be possible.   2.2.2 Phantom Study A phantom study was conducted with the purpose of verifying the findings of the simulations. The first step for this task was to find a phantom that resembles prostatic tissue in terms of T2 relaxation properties. The first candidates were meat and celery. They were both scanned in fresh and formalin-fixed forms. Fixation was performed by immersing the sample in 10% formalin for a minimum of one week prior to scanning.  MR signals were acquired at a 7T animal scanner (Bruker, Germany) with a quadrature birdcage coil. Axial images were obtained with a multi-echo spin echo sequence (TR=1000-5000 ms, TE=6.8-25 ms, NE=32-80, field of view (FOV)=6×6cm2, voxel-size=0.47×0.47×4mm3, reconstruction matrix-size=128×128, slice thickness=4mm, flip angle=90°, number of averages=2). Similar to what was explained in the Simulations section, the MR images were fitted to a multi-exponential decay function using a software written in Matlab which handles NNLS algorithm. From fitting, a map of LT2F and also maps of T2-short, T2-long, were generated. More details  38  about the software and fitting procedure are provided in Chapter 3, the Data Processing (section 3.6).  A bi-exponential T2 decay was not observed in either fresh or formalin-fixed meat. But celery showed a bi-exponential T2 decay both in fresh and formalin-fixed form. The range of T2 relaxation times of formalin-fixed celery was found to be overlapping with the previously reported range of T2 relaxation times for prostatic tissue. In a previous quantitative T2 mapping study of prostate performed by Storas et al. (38) using a 1.5T scanner, the range of short and long T2 components was reported to be: 43-92 (ms) and 161-1319 (ms), respectively, and the range of fraction of long component was reported as: 0.03-0.8. In our study, using formalin-fixed celeries and a 7T scanner, the observed range of T2-short and T2-long was: 25-45 (ms) and 100-400 (ms), respectively, and the range of LT2F was: 0.1-0.2. Based on the similarity of T2 relaxation properties, formalin-fixed celery was selected as our phantom in this study to investigate the findings of our simulation study. Two sets of representative maps of T2-short, T2-long, and LT2F generated from MR images of formalin-fixed celery with different TE, and identical value of NE are presented in Figure 2-6. From these images, the necessity to satisfy the second criterion, which was described earlier in the simulation section, can be easily observed. Based on the second criterion, T2-short and T2-long are identified correctly if TE is smaller than T2-short. In this study the range of T2-short was 25- 45(ms), and based on the second criterion, we set TE to smaller than 45 ms in order to be able to identify both components. From Figure 2-6, it can be observed that for TE=50 ms the short component is entirely missing, which validates the second criterion. Recognition of the first criterion from the images of Figure 2-6 is not as easy as the second criterion. Comparison  39  between T2-long maps of different TE shows that as the value of TE × NE increases, T2-long becomes less noisy. When the first criterion (𝑁𝐸 × 𝑇𝐸 ≥ 2 × 𝑇2−𝑙𝑜𝑛𝑔) is satisfied (which happens at TE=25 for NE=32, and at TE=12.5 for NE=64, considering the maximum T2-long=400 ms), we see that the T2-long is identified, i.e. it has non-zero value for most of the pixels.  Figure 2-6. T2-short, T2-long, and LT2F map generated from formalin fixed celery for different TE and NE=32 (left), and NE=64 (right).  40  In summary, results of the phantom study confirmed our simulation finding; therefore, the two criteria obtained by the simulation study were used to design the preliminary protocol for multi-exponential T2 imaging of the prostate.  The preliminary protocol was designed by following the algorithm which was proposed at the end of the Simulations section. Based on the literature values for the T2 relaxation times in prostate (T2-short [43-92 (ms)] and T2-long [161-1319 (ms) ], reported by Storas et al. (38)) and taking into account the difference in the scanning system’s magnetic field (1.5 T used by Storas et al. vs. 3 T used in our study), we set the following parameters for the initial multi-exponential T2 mapping protocol: TE= 25 ms, and NE=64.  Prior to finalizing the protocol and using it for examination of participant patients, the proposed protocol was further investigated by scanning a number of healthy volunteers. Details of volunteer study are provided in the next section.   2.2.3 Volunteer Study  A volunteer study was performed with the purpose of testing and improving the preliminary protocol that was developed based on the results of the simulation and phantom studies. Five healthy volunteers (mean age, 35.4 years; age range 27-57 years) participated in this study, and provided informed signed consent prior to undergoing MRI examination. MRI examinations were carried out on a 3T MRI scanner [Philips Medical Systems, Best, The Netherlands]. MR signals were acquired using a pelvic phased-array coil (Medrad, Pittsburgh, PA, USA). To shorten the total scan duration, sensitivity encoding (SENSE), which is a parallel imaging technique, was used in this study. Angled axial images were obtained in the plane  41  perpendicular to the rectal wall-prostate interface, with a 3D multi-echo spin echo sequence developed by Jing Zhang at the University of British Columbia MRI Research Centre (45) (TR=3061 ms, TE=25 ms, NE=64, FOV=240×240×[24-40]mm3, voxel-size=[1×1×4 to 2×2×4]mm3, reconstruction matrix-size=240×240, slice thickness=4mm, flip angle=90°, number of averages=1, sense factor= [1.5-3]). To provide anatomical details for comparison with parametric maps of multi-exponential T2 mapping, high spatial resolution T2W  MR images were acquired by using a multi-slice Turbo Spin Echo (TSE) sequence (TR=1851 ms, effective TE = 80 ms, NE = 1, FOV=140×140×72 mm3, voxel-size=0.27×0.27×4 mm3, scan matrix-size=288×228, reconstruction matrix-size=512×512, slice thickness=4mm, flip angle=90°, number of averages=3, scan duration=285 sec). T2W images were acquired using the same orientation and slice location as multi-exponential T2 images.  By visual inspection of multi-exponential T2 images, two types of artifacts were identified: a aliasing (wraparound) artifact in the axial direction, and a Moire fringe artifact mainly in the center of images. The aliasing artifact was resolved by increasing the FOV in the axial direction, and Moire fringes were decreased (but not entirely removed) by decreasing the voxel size (increasing matrix size) in the frequency encoding (anterior-posterior) direction (See Figure 2-7).   42   Figure 2-7. 1st echo T2W images from 10 axial slices of a healthy prostate, with a) voxel size: 2×2×4 mm3, and b) voxel size: 1×2×4 mm3. Comparison between images of series a and b shows that Moire fringes were decreased by decreasing the voxel size in the frequency encoding (anterior-posterior) direction.  The effect of SENSE factor (a parameter in the parallel imaging technique, which is equal to the decrease of the number of phase encoding steps with respect to the full k-space sampling) on SNR was investigated by comparing SNR obtained from 1st echo images for SENSE factor ranging between 1.5 and 3. According to Figure 2-8, results showed an increase in SNR with  43  a decrease in SENSE factor, indicating a trade-off between scan time and SNR. For the rest of this study, SENSE=1.5 was fixed to maintain a reasonable SNR.  Figure 2-8. SNR as a function of SENSE factor for 10 slices of MR images from a healthy prostate.  Quantitative analysis was performed by fitting MR data to a multi-exponential decay function, as was explained in the Simulations section above. More details about the software and fitting procedure are provided in the sub-section 4.5: Data Processing From fittings, maps of T2-short, T2-long, and LWF were generated, and average values of T2-short, T2-long, and LWF were calculated within regions of interest (ROI) in the peripheral zone and central gland (which includes transition zone, central zone, and periurethral region). Representative parametric maps are shown in Figure 2-9. In the peripheral zone, two distinguishable T2 components were observed in almost all pixels. The mean value (averaged over the entire peripheral zone) of T2-short, T2-long, and LWF were 69±1 ms, 360±10 ms, and 0.34±0.01, respectively. In the central gland, some pixels showed two T2 components and some 010203040500 2 4 6 8 10 12SNRSlice NumberDependance of SNR on SENSE Factor SENSE 1.5SENSE 2SENSE 2.5SENSE 3 44  pixels showed only one T2 component. The mean value (averaged over the entire central gland) of the T2-short, T2-long, and LWF were 73.3±0.8 ms, 340±10 ms, and 0.108±0.007, respectively. It should be noted that in the central gland, pixels with only short T2 component, i.e. pixels with T2-long equal to zero, have not been accounted for in the calculation of average T2-long. Overall mean value (averaged over the entire gland) of the T2-short, T2-long, and LWF were 70.5±0.7 ms, 350±10 ms, and 0.236±0.008, respectively.  Literature data (46, 47) for the percentages of lumen, epithelium, and stromal tissue, averaged over the entire normal prostate gland; are: 30%±10%, 20%±5%, and 50%±10%, respectively. Therefore, LWF measured by our technique agrees reasonably well with the lumen percentage reported in the literature.  Figure 2-9. A) Axial T2W MR image of the prostate, B) LWF map, C) T2-short map, D) T2-long map of the same slice. Scale bar of C and D images is in ‘ms’.   45  2.3 Summary In summary, in this chapter we developed an initial multi-exponential T2 mapping protocol, for imaging of prostate, based on a series of simulations and phantom studies. We improved and finalized the protocol by performing a volunteer study. We identified two types of artifacts and resolved them by modifying the preliminary protocol. Using the final protocol, we were able to distinguish two T2 components in the T2 distributions obtained from glandular regions of prostate, and the average value of LWF agreed well with the literature data for percentage of luminal space in the prostatic tissue. Based on these results, we finalized the proposed protocol for multi-exponential T2 mapping of the prostate gland, and started to recruit patients to perform the main studies, i.e. 1) investigation of the relationship between the measurements of multi-exponential T2 mapping and composition of prostatic tissue, 2) assessment of diagnostic accuracy of multi-exponential T2 mapping in the detection and grading of prostate cancer, and 3) comparison between the diagnostic accuracy of this technique and the more established MRI techniques.  Our patient studies are presented in the following chapters.    46  Chapter  3: MR measurement of Luminal Water in Prostate Gland: Quantitative Correlation between MRI and Histology  3.1 Introduction In Chapter 2, it was described how the new multi-exponential T2 mapping protocol was developed.  As this technique measures LWF, which was hypothesized to be correlated with the fractional amount of luminal water in the prostatic tissue, we named this technique Luminal Water Imaging (LWI). In this chapter, the relationship between the measurements of LWI and composition of prostatic tissue will be investigated. It has been shown in the literature that there are differences in the distribution of tissue components between normal prostate and prostate affected by diseases such as PCa and BPH (46, 48, 49). Therefore, identification of the relationships between MR parameters and tissue components, and consequently using MR parameters as a surrogate for measurement of the corresponding tissue components, could be of high importance for disease characterization. Particularly, because the fractional cross sectional area of lumen changes significantly with disease progression in PCa (49), identification of the relationship between LWF and the true fractional amount of luminal space in tissue could potentially contribute to disease assessment and grading of PCa. This study was conducted to evaluate the correlation between LWF and the percentage area of luminal space in tissue through a direct comparison with histology. It was also aimed at evaluating the correlation between all other MR parameters measured with this technique, and  47  the percentage area of tissue components, including luminal space, nuclei, and cytoplasm plus stroma. 3.2 Patient Selection This was an institutional human ethics board approved prospective study. Seventeen patients (median age, 66.4 years; age range 58-80.3 years) were recruited consecutively during January 2015 to January 2016.  These were patients referred to the Vancouver General Hospital Urology Clinic and diagnosed with prostate cancer.  Additional inclusion criteria included biopsy-proven prostatic adenocarcinoma, no prior treatment, no contraindications to MRI, able to tolerate the endorectal coil and scheduled for radical retropubic prostatectomy. All patients gave informed signed consent prior to undergoing MRI examination shortly before surgery (median 11 days, range 1- 41 days). Clinical data for the 17 patients who participated in this study are summarized in Table 3-1.             48      Table 3-1. Clinical data of 17 patients participating in the study. Characteristic Value Median and range of patient age (y) 66.4 (58-80.3) Median and range of pre-op *PSA level (ng/mL) 7.9 (1.4-31.6) Pathologic tumour stage pT2a pT2c pT3a pT3b  1 4 11 1 Number of malignant *ROIs *GS=(3+3) GS=(3+4) GS=(4+3) GS=(4+4) GS=(4+5) GS=(5+3) GS=(5+4) GS=(5+5)  18 24 28 11 8 3 1 3 *PSA = Prostate-specific antigen, *GS = Gleason score, *ROI = Region of interest  3.3 MRI Protocol In this thesis all the MRI examinations of patient studies were carried out on a 3T MRI scanner [Philips Medical Systems, Best, The Netherlands], and MR signals were acquired with a combined endorectal/pelvic phased-array coils (Medrad, Pittsburgh,PA, USA). Angled axial images were obtained in the plane perpendicular to the rectal wall-prostate interface, with a 3D multi-echo spin echo sequence developed at the University of British Columbia MRI Research Centre (45) (TR=3073 ms, TE=25 ms, NE=64, FOV=240x240x56mm3, voxel-size=1x1x4mm3, scan matrix-size=240x119, reconstruction matrix-size=240x240, slice  49  thickness=4mm, flip angle=90°, number of averages=1, sense factor= 1.5, scan duration=673 sec). High spatial resolution T2-weighted  MR images were acquired with the same orientation, slice thickness, and slice location, by using a multi-slice Turbo Spin Echo (TSE) sequence (TR=1851 ms, effective TE = 80 ms, NE = 1, FOV=140x140x72mm3, voxel-size=0.3x0.3x4mm3, scan matrix-size=288x228, reconstruction matrix-size=512x512, slice thickness=4mm, flip angle=90°, number of averages=3, scan duration=285 sec). The number and positioning of the slices was set to cover the entire prostate. In addition to the multi-echo and the high resolution T2-weighted images, we also acquired DWI and DCE-MRI data, to be used in another study for a direct comparison between the diagnostic accuracy of these techniques. The details of this study are provided in Chapter 5.  3.4 Whole-mount Histology and Registration to MR images After the surgery, the excised specimens were immersed in 10% formalin for a minimum of 48 hours, and then dissected and examined histopathologically in a uniform and consistent manner. The seminal vesicles and vas deferens were amputated, and the remainder of the specimen was cut perpendicularly to the posterior surface of prostate, into 4 mm transverse slices by using a multi-blade cutting device, developed in-house (50). The entire prostate slices and dissected tissues were sent for histological examination and all slices were stained with hematoxylin and eosin (H & E). Areas of prostate infiltrated by tumour were manually identified and marked by an experienced genitourinary pathologist. All stained slides were then digitalized with the SL801 autoloader and a Leica SCN400 scanning system (Leica Microsystems; Concord, Ontario, Canada) at magnification equivalent to ×40 (Spatial resolution: 0.25 µm/pixel at ×40 magnification). The images were subsequently stored in the  50  SlidePath digital imaging hub (DIH; Leica Microsystems) of the Vancouver Prostate Centre. Using DIH software, the high resolution histology sections were examined by an experienced pathologist, who outlined the tumours and the border between peripheral zone and central gland and assigned the Gleason scores on each slide. The digitized whole-mount histology sections were registered to MR images with a software package developed in-house (51) using Matlab. As described previously (51), the multi-step process involved registration of histology sections and high resolution T2W and multi-echo images. In the first step, histology images (as moving images) were registered to their corresponding high resolution T2W images (as fixed targets). The corresponding slices of histology and MR images were determined based on anatomical details. Prior to application of the transformations, contour of prostate was manually outlined on histology and MR images. The initial alignment of the images was performed by an affine transformation involving a 2D multi-resolution algorithm with a b-spline. The required deformation was then applied by another non-rigid b-spline transformation. The measurement of the similarity of the registration was performed by advanced mattes mutual information metric from elastix (52). The precision of registration was evaluated using the Dice Similarity Coefficient (DSC), while the exclusion criteria was set at DSC<0.85. In the second step, multi-echo images were registered to high resolution T2W images (in a similar manner to what was explained for the first step) and the inverse function of this transformation was determined. In the last step, the inverse transformation of step two was applied to the registered histology from step one, which generated the histology images that were registered to multi-echo images.  This process resulted in deforming the original manually drawn ROIs, rather than MRI images, and thus the  51  ROI averages were calculated from the non-deformed parametric maps, ensuring their accuracy.   3.5 Image Segmentation Identification of tissue components was performed by use of color-based segmentation using DIH software on H&E stained whole-mount histology sections. As depicted in Figure 3-1, pixels were categorized as luminal space, nuclei, or cytoplasm plus stroma, based on a manually defined set of training data for each component. Any pixel that was not categorized in any of the above classes by the software was referred to as unclassified. For each ROI, the total number of pixels identified for each component was counted, and the percentage area for each component was calculated as the ratio of the segmented pixels to all ROI pixels.   Figure 3-1. Representative example of segmentation of the whole mount histological images.  a) A magnified (20×) H&E–stained histology section; b) Tissue components are segmented into cytoplasm plus stroma (blue), lumen (yellow), and nuclei (orange).   52  3.6 Data Processing All MR data were processed offline. For each pixel of the multi-echo MR images within prostate, signal decay curves were fitted to a multi-exponential decay function. Fitting was performed with a software package developed in-house which handles NNLS algorithm using Matlab. The software made no prior assumption about the number of contributing T2 components in the multi-exponential decay function, and it decomposed each decay curve into multiple T2 distributions, S(T2), with distinct peaks, as explained by Bjarnason and Mitchell (43) (see Figure 3-2). The number of the observed peaks for the T2 distributions in this study ranged from one to three. The T2 distributions with three peaks were mostly seen in discrete individual pixels. The third peak in these cases were likely an artifact, potentially due to lower SNR. Regions of continuous pixels with three peaks in T2 distributions were only seen in three out of seventeen cases analyzed in this study. In these cases the 3rd peak was observed within the long T2 relaxation time range. Although the reason for two distinct long T2 components is not entirely clear, it may be related to distinct populations of glands with different sizes. Since the majority of T2 distributions were seen to have two peaks, parameterization of the distributions was performed based on bi-exponential decay modeling with the following parameters: Ncomp, gmT2, T2-short, T2-long, Ashort, Along, and LWF. Ncomp is the number of peaks in the distribution. gmT2, which is the mean T2 time of the entire distribution on a log scale, was calculated as explained previously (43) by the following equation: 𝑔𝑚𝑇2 = 𝑒𝑥𝑝 [∑ 𝑆(𝑇2) 𝑙𝑜𝑔 𝑇2𝑇2−𝑚𝑎𝑥𝑇2−𝑚𝑖𝑛∑ 𝑆(𝑇2)𝑇2−𝑚𝑎𝑥𝑇2−𝑚𝑖𝑛] Equation 3-1  Where T2-min and T2-max were set at 20 ms and 2000 ms respectively.  53  T2-short and T2-long were defined as the geometric mean T2 of the short and long T2 components, and were calculated as:              where T2-threshold was the cut-off T2 time between the short and long component and was set at 200 ms, based on a graphical analysis of the T2 distributions as follows. The geometric T2 value of the short and long components were determined from bi-exponential decay modeling for 4700 pixels (from four slices, each obtained from a different patient) without setting a cut-off time. The distributions of the short and long T2 components were generated as the number of observation per time bin, and the corresponding histograms were plotted (See Figure 3-3). The distributions were then fitted using Matlab. The best fit curves were double Gaussian functions (f(x) =  a1×exp(-((x-b1)/c1)2) + a2×exp(-((x-b2)/c2)2)) with the following parameters: a1 = 59.89, b1 = 121.8, c1= 15.21, a2 = 375.8, b2 = 122.2, c2= 43.29, and a1 = 149, b1 = 597.1, c1= 181.5, a2 = 167.2, b2 = 943.4, c2= 442.5 for T2-short  and T2-long respectively. The crossing point of the fits was chosen as the cut-off value between the short and long T2 components. Ashort and Along, were defined as areas under the short and long components (See Figure 3-2), and were calculated by summing S(T2) within the region of [T2-min - T2-threshold] , and [T2-threshold -T2-max] respectively.; LWF, defined as the ratio of area under the long component over the 𝑇2−𝑠ℎ𝑜𝑟𝑡 = 𝑒𝑥𝑝 [∑ 𝑆(𝑇2) 𝑙𝑜𝑔 𝑇2𝑇2−𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑𝑇2−𝑚𝑖𝑛∑ 𝑆(𝑇2)𝑇2−𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑𝑇2−𝑚𝑖𝑛] Equation 3-2 𝑇2−𝑙𝑜𝑛𝑔 = 𝑒𝑥𝑝 [∑ 𝑆(𝑇2) 𝑙𝑜𝑔 𝑇2𝑇2−𝑚𝑎𝑥𝑇2−𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑∑ 𝑆(𝑇2)𝑇2−𝑚𝑎𝑥𝑇2−𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑] Equation 3-3  54  total area under the entire distribution, is equivalent to the area function described by Bjarnason and Mitchell (43) and was calculated as: 𝐿𝑊𝐹 =∑ 𝑆(𝑇2)𝑇2−𝑚𝑎𝑥𝑇2−𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑∑ 𝑆(𝑇2)𝑇2−𝑚𝑎𝑥𝑇2−𝑚𝑖𝑛 Equation 3-4               For T2 distributions with only one peak (N=1), depending on the gmT2 of the distribution compared to the cut-off T2 , either the pair of T2-short and Ashort or T2-long and Along were set to zero. For cases in which the pair of T2-short and Ashort was set to zero, LWF was set to 1; and for cases in which the pair of T2-long and Along was set to zero, LWF was set to zero. T2 distributions with three peaks (N=3) were parameterized bi-exponentially where one peak was considered individually and the other two peaks were averaged geometrically. Maps of the seven parameters (Ncomp, gmT2, T2-short, T2-long, Ashort, Along, and LWF) were generated for every slice. Average values of MR parameters were calculated within a total of 359 (263 non-malignant, and 96 malignant) ROIs manually outlined on the registered whole-mount histology images in malignant PZ and TZ, non-malignant PZ and TZ, normal AFMS, and Periurethral Fibromuscular Stroma (PFMS). Malignant ROIs were selected by accurately outlining the tumour boundaries delineated by pathologist. Non-malignant ROIs were selected by avoiding the tumour boundaries. Since regions of BPH were not outlined by a pathologist, non-malignant ROIs in TZ could consist of BPH.  55   Figure 3-2. a: 1st echo T2W image of an axial cross section from a middle level of a prostate gland. b: NNLS fitting of the multi-exponential T2 decay curve (left-hand side) generated from the pixel in non-malignant PZ (red marker in a.), and its correspondent T2 distribution (right-hand side). c: NNLS fitting of the multi-exponential T2 decay curve (left-hand side) generated from the pixel in malignant PZ (yellow marker in a.), and its correspondent T2 distribution (right-hand side). d: histology whole-mount section of the same slice.  56   Figure 3-3. Histogram of T2-short (blue) and T2-long (orange) for 4700 pixels. Time-axis is shown in logarithmic scale. The solid lines represent the best fit to the data, described in terms of double Gaussian functions (f(x) =  a1×exp(-((x-b1)/c1)2) + a2×exp(-((x-b2)/c2)2)) with the following parameters: a1 = 59.89, b1 = 121.8, c1= 15.21, a2 = 375.8, b2 = 122.2, c2= 43.29, and a1 = 149, b1 = 597.1, c1= 181.5, a2 = 167.2, b2 = 943.4, c2= 442.5 for T2-short (dark blue) and T2-long (red) respectively.  3.7 Statistical Analysis All statistical analyses were performed using MedCalc (MedCalc Software, Mariakerke, Belgium). The Kolmogrov-Smirnov test showed that none of the MR parameters and percentage areas of tissue components were normally distributed. Median and ranges of all MR parameters and percentage areas of the tissue components were calculated, with each data point corresponding to an ROI averaged value. It should be noted that as each median value was calculated from a large number of ROI averaged data points, a fraction value was obtained for Ncomp, while Ncomp calculated for each individual pixel had only an integer value.  57   Evaluation of the correlation between MRI measurements and histology data was performed by including the whole data set from the entire prostate, including both malignant and non-malignant ROI averaged data points. The correlations between average values of MR parameters and percentage area of tissue components were evaluated with Spearman’s rank correlation test. In all analyses P<0.05 was considered statistically significant. For each of the tissue components, the MR parameter with the highest correlation was identified. Scatter plots of each histology-MRI pair (with strongest correlation) were generated and slopes of the regression lines were calculated.  3.8 Results Median values and ranges of the percentage area of all tissue components and the MR parameters are summarized in Table 3-2 and Table 3-3, respectively.  Spearman's rank correlation coefficients between MR parameters and tissue components are presented in Table 3-4. Five MR parameters (T2-short, gmT2, Along, LWF, and Ncomp) showed significant correlation with percentage area of luminal space and percentage area of cytoplasm plus stroma. Two MR parameters (T2-short, gmT2) also showed significant correlation with percentage area of nuclei. The overall highest correlation coefficient was obtained between percentage area of luminal space and LWF (Spearman's coefficient: 0.75, P<0.001).  A sample histology section and the corresponding LWF map, presented in Figure 3-4, show good correspondence between LWF and luminal space identified with histology. The highest correlation coefficient between the percentage area of cytoplasm plus stroma and MR parameters was obtained for gmT2 (Spearman's coefficient: -0.64, P<0.001), and for the nuclei  58  was obtained for T2-short (Spearman's coefficient: 0.33, P<0.001). Scattered plots of these histology-MR pairs are demonstrated in Figure 3-5.   Table 3-2. Percentage area (median values, with ranges in parentheses) of tissue components in different regions derived from histology. Tissue Component Non-malignant *PZ Non-malignant *TZ Normal *AFMS Normal *PFMS Malignant PZ Malignant TZ Luminal space 27.2 a, b, c, d (13.7-65.4) 33.9 a, b, c, d (7.2-64.0) 4.8 c, d, e, f (1.1-21.5) 3.7 c, d, e, f (0.7-15.6) 11.6 a, b, e, f (2.8-31.1) 10.8 a, b, e, f (2.4-26.9) Cytoplasm plus stroma 42.9 a, b  (5.9-63.2) 40.7 a, b, c (7.7-63.6) 78.0 c, d, e, f (34.3-86.3) 68.3 c, d, e, f (50.8-81.6) 49.0 a, b, f (21.6-63.2) 47.4 a, b (23.1-67.2) Nuclei 7.5 a, b, c, d (2.3-28.9) 7.3 a, b, c, d (2.4-18.3) 2.4 c, d, e, f (1.4-7.6) 4.1 c, d, e, f (1.5-20.6) 11.5 a, b, e, f (3.8-38.4) 12.0 a, b, e, f (6.4-38.4) *PZ= peripheral  zone, *TZ= transition  zone, *AFMS= anterior fibromuscular stroma , *PFMS= and periurethral fibromuscular stroma. a Significantly different than normal AFMS (P<0.01). b Significantly different than normal PFMS (P<0.01).  c Significantly different than malignant PZ (P<0.01). d Significantly different than malignant TZ (P<0.01).  e Significantly different than non-malignant PZ (P<0.01). f Significantly different than non-malignant TZ (P<0.01).   59  Table 3-3.  Average values (median values, with ranges in parentheses) of LWI parameters in malignant and normal tissue in different regions. MR Measurement Non-malignant *PZ Non-malignant *TZ Normal *AFMS Normal *PFMS Malignant PZ Malignant TZ T2-short (ms) 75 a, b, c (50-152) 83 a, b, c (49-176) 64 c, d, e, f (32-80) 69 e, f (40-111) 72 a, e, f (25-116) 83 a (36-108) T2-long (ms) 503 a, b, d (249-904) 551 b, d (283-948) 617 c, e (348-1074) 726 c, e, f (306-1300) 507 a, b, d (290-923) 722 c, e, f (249-1135) gmT2 (ms) 114 a, b, c, d (58-295) 107 a, b, c, d (57-237) 66 c, d, e, f (36-86) 74 e, f (41-120) 84 a, e, f (30-139) 89 a, e, f (41-120) LWF 0.20 a, b, c, d, f (0.03-0.50) 0.14 a, b, c, d, e (0.02-0.40) 0.03 c, e, f (0.02-0.11) 0.03 c, e, f (0.00-0.13) 0.07 a, b, d, e, f (0.01-0.18) 0.04 c, e, f (0.00-0.12) Ashort (×105) 159 a, c (98-290) 164 a, c (109-268) 138 c, d, e, f (84-198) 162 c (111-211) 185 a, b, c, f, (64-300) 170 a (96-219) Along (×105) 39.2 a, b, c, d, f (8.0-116.0) 28.2 a, b, c, d, e (3.5-112.7) 4.3 c, e, f (2.4-14.6) 5.8 c, e, f (0.2-26.1) 14.1 a, b, d, e, f (1.9-59.8) 6.7 c, e, f (0.1-22.0) Ncomp 2.00 a, b, c, d, f (1.22-2.47) 1.90 a, b, c, d, e (1.27-2.61) 1.55 c, e, f (1.03-2.02) 1.44 c, e, f (1.01-2.09) 1.82 a, b, e, f (1.15-2.22) 1.70 e, f (1.08-2.13)  *PZ= peripheral  zone, *TZ= transition  zone, *AFMS= anterior fibromuscular stroma , *PFMS= periurethral fibromuscular stroma. a Significantly different than normal AFMS (P<0.01). b Significantly different than normal PFMS (P<0.01).  c Significantly different than malignant PZ (P<0.01). d Significantly different than malignant TZ (P<0.01).  e Significantly different than non-malignant PZ (P<0.01). f Significantly different than non-malignant TZ (P<0.01).        60  Table 3-4.  Spearman's rank correlation coefficient (ρ), with 95% confidence intervals  in parentheses, between MR measurements and the percentage area of tissue components. MR Measurement Luminal Space Cytoplasm plus stroma Nuclei T2-short 0.42 (0.33 to 0.50) P<0.001 -0.50 (-0.57 to -0.42) P<0.001 0.33 (0.23 to 0.42) P<0.001 T2-long -0.13 (-0.23 to -0.03) P=0.01 0.03 (-0.07 to 0.13) P=0.58 0.06 (-0.05 to 0.16) P=0.27 gmT2 0.69 (0.64 to 0.74) P<0.001 -0.64 (-0.70 to -0.58) P<0.001 0.26 (0.16 to 0.35) P<0.001 LWF 0.75 (0.70 to 0.79) P<0.001 -0.52 (-0.59 to -0.44) P<0.001 0.02 (-0.09 to 0.12) P=0.77 Ashort -0.11 (-0.26 to -0.01) P=0.03 -0.04 (-0.14 to 0.06) P=0.44 0.13 (0.02 to 0.23) P=0.02 Along 0.71 (0.65 to 0.76) P<0.001 -0.51 (-0.58 to -0.43) P<0.001 0.04 (-0.07 to 0.14) P=0.47 Ncomp 0.43 (0.34 to 0.51) P<0.001 -0.26 (-0.35 to -0.16) P<0.001 0.03 (-0.07 to 0.13) P=0.58   61   Figure 3-4. Sample H&E-stained whole-mount histology sections (a,b), with the corresponding LWF map (c), and high resolution T2W image of the same slice (d). In figure (a), color-based segmentation algorithm was applied only for identification of luminal space (shown in green). Notice good correspondence between LWF values (c) and the amount of luminal space (a).   62   Figure 3-5. Regression results and scatter plots of: a) LWF versus percentage area of luminal space (regression line: y = 0.45 x + 0.03, P<0.001 ) , b) gmT2  versus percentage area of cytoplasm plus stroma (regression line: y = - 0.2 x + 0.19, P<0.001 ), and c) T2-short versus percentage area of nuclei (regression line: y = 0.1 x + 0.079, P<0.001 ). Each data point on graphs represents average value of MR parameter and corresponding percentage area value for a chosen ROI.  63  3.9 Discussion and Conclusion In this study, we investigated the relationship between MR parameters of LWI and the underlying composition of prostatic tissue through a direct comparison with histology. We were particularly interested to verify and establish if there is any relationship between LWF and percentage area of lumen in prostatic tissue. The median values of T2-short, T2-long, and LWF (75, 503, 0.2 in PZ and 83, 551, 0.14 in TZ) measured in normal tissue in this study are comparable to the values of the corresponding parameters previously measured with bi-exponential analyses by Storås et. al (38). In their study, three median values, corresponding to high, intermediate, and low intensity, were reported for each MR parameter in peripheral zone and central gland. Reported median values in their study are as follows: short T2: 73, 69, 66 (ms), long T2: 837, 470, 325 (ms), long T2 signal fraction (%): 54, 29, 26 in peripheral zone, and short T2: 64, 61, 61 (ms), long T2: 502, 450, 456 (ms), long T2 signal fraction (%): 28, 21, 12 in central gland. The median and range of LWF values in the entire prostate measured in this study are in good agreement with the previously published values for percentage of lumen in the composition of normal prostatic tissue (48). The median value and range of percentage area of luminal space measured in normal and malignant tissues in PZ are also in good agreement with previously published data (48). However, median values of percentage area of cytoplasm plus stroma and nuclei measured in this study are lower than published values (48) both in normal PZ (42.9, and 7.5 vs. 54.9, and 14.5) and in malignant PZ (49.0, and 11.5 vs. 61.1, and 23.7). This underestimation could be due to inaccuracy of the segmentation algorithm, since in the calculation of percentage areas for each ROI, an average of 23% of pixels were unclassified. Because luminal space has a simpler color-based pattern (mostly plain white areas in the histology images) in comparison to the rest of the tissue, it is safe to assume  64  that minimum error had occurred in the calculation of luminal space percentage, and that most of the unclassified pixels belonged to cytoplasm plus stroma or nuclei. Our correlation analyses showed that LWF is positively and significantly related to the percentage area of luminal space. With the exception of fibromuscular stroma, such strong correlation between LWF and luminal space was present in all types of tissue (data not shown).      The slope of the regression line obtained from a plot of LWF vs. fractional amount of luminal space was equal to 0.45, rather than 1. This observation implies that LWF, while proportional to the fractional volume of luminal space, is not identical to this histological measure. Several factors could have potentially contributed to this discrepancy between LWF and the fractional volume of luminal space measured with histology.  Firstly, LWF measured in this study is likely to be weighted by proton density and T1 values (See the Appendix for details regarding the effect of T1 relaxation on the LWF measurements). In addition, we compared the 2D percentage area of lumen to the 3D fractional volume of the luminal water. Since the glands are ellipsoids, rather than elliptical cylinders aligned in the axial direction, the area of lumen is not linearly proportional to its volume. Simple comparison between the volumes of ellipsoids and elliptical cylinders suggests that the 2D percentage area of luminal space, measured with histology, overestimates the luminal volume by as much as 33%. In reality, this effect is expected to be less than 33%, taking in to account that the glands are not perfect ellipsoids and are not necessarily aligned in the axial direction.  Another contributing factor to be considered is morphological differences between in vivo prostate, imaged with MRI, and excised, fixed prostate, analysed with histology. However, this could make justification of the observed discrepancy even harder.  That is because histological processing involves heat-induced  65  dehydration during which the water content is removed. Water-filled cavities are therefore more prone to shrinkage than stromal tissues. Consequently, tissue shrinkage may be non-uniform (53, 54, 55). Therefore, luminal space and the luminal water fraction may be smaller in whole-mount histology than in vivo. However, it is worth noting that the slopes of the regression lines varied very little between different types of tissue (data not shown), suggesting that the tissue composition is likely not the reason for the LWF underestimating the luminal space. Presumably a systematic error in the histology segmentation procedure resulting in an overall overestimation of percentage area of luminal space might have also been a contributing factor. Finally, water exchange between different compartments within the prostatic tissue (e.g. intra-/extra- cellular vs. luminal water) might have resulted in LWF underestimating the volume of luminal space.  Determination of the true relationship between LWF and the amount of lumen in prostatic tissue is not trivial and requires further investigations. The main limitation of this study was related to the segmentation procedure. The software that has been used in this study was not capable of differentiating loose stroma from the epithelial cytoplasm. Therefore, stroma and epithelial cytoplasm were combined into one tissue component in this study. However, according to Langer et al. (48), in cancer there is an increase in percentage area of cytoplasm, and hence in our study measuring the percentage of cytoplasm separate from stroma would be very informative and useful. In order to investigate the relationship between MR measurements of LWI and percentage area of cytoplasm more accurately, a prospective study with a more accurate segmentation algorithm, or better staining techniques, and higher number of patients is required. Another limitation to be noted here is related to the scan time. The relatively long scan time (11 min) of this technique increases the  66  chance of patient movement during the scan. This may result in a mismatch of data in signal decay curves and consequently the uncertainty of the data fitting procedure can be increased. Therefore, a potential future work is to reduce the total scan time of this technique. The results of this pilot study demonstrate that LWF measured with MRI is significantly correlated with the percentage area of luminal space in the prostatic tissue. This is an important finding, considering that in PCa the amount of luminal space correlates strongly with Gleason grade, which is a key prognostic marker. With higher Gleason grade, the glands first coalesce and then disappear in solid sheets of cells (55). Therefore, LWF could potentially differentiate the aggressive forms of PCa from the more biologically benign.   In conclusion, the methodology established for measuring LWF can potentially be used as a surrogate for measurement of fractional amount of lumen in diagnosing various prostatic diseases in which the amounts of lumen differ between normal and abnormal tissues.     67  Chapter  4: Luminal Water Imaging: A New MRI T2 Mapping Technique for Prostate Cancer Diagnosis  4.1 Introduction In Chapter 3, the correlation between measurements of LWI and the corresponding tissue composition in prostate was investigated, and our hypothesis that LWF represents the fractional amount of MR signal generated by water content of luminal spaces in prostate was verified. In this chapter, the relationship between the measurements of LWI and the histopathology of prostatic tissue is investigated. The diagnostic accuracy of this technique in the detection and grading of prostatic tumours is determined by direct comparisons between MRI data and whole-mount histology.  4.2 Patient Selection  The patient selection process was similar to what was explained for the previous study described in Chapter 3.  Clinical data for the 18 patients who participated in this study are summarized in Table 4-1. A portion of the patient population used in this study has been previously reported in Chapter 3.        68  Table 4-1. Clinical data of 18 patients participating in the study. Patient Age (y) PSA level (ng/mL) Prostate volume (cc) Lesion characteristics Pathologic tumour stage Size (cc) Gleason grade Location Total number of ROIs per lesion (from different slices) P01 65 13.1 32.3 5.8 4+3 PZ 7 pT3a P02 65 4.6 67.5 0.1 0.1 2×0.1 3+4 3+3 3+3 TZ TZ PZ 1 1 2 pT2c P03 67 8 94.7 0.7 2×0.2 0.5 0.3 3+3 3+3 3+3 3+3 PZ PZ TZ TZ 4 4 2 3 pT2c P04 62 6.5 31.0 3.2 0.2 0.1 0.5 4+3 4+3 3+3 3+3 PZ PZ PZ TZ 6 2 1 4 pT3a P05 80 7.2 128.3 0.1 3+3 PZ 2 pT2a P06 64 7.6 32.3 7.5 0.9 4+3 3+3 PZ PZ 8 4 pT3a P07 75 18.2 41.1 3.3 1.5 3×0.1 4×0.1 5×0.2 4+3 3+3 3+3 3+3 3+3 PZ PZ PZ TZ TZ 5 4 3 4 9 pT2c P08 62 13.5 23.4 6.8 0.3 3×0.1 4+5 3+3 3+3 PZ PZ PZ 8 2 3 pT3b P09 75 7.9 31.0 0.9 0.5 0.3 4+5 4+3 3+3 PZ PZ TZ 2 1 2 pT3a P10 69 18.4 39.5 6.2 4+5 TZ 5 pT3a P11 66 7.4 32.5 1.0 3+4 PZ 1 pT3a P12 67 6 17.7 1.3 0.1 0.6 3+4 3+3 3+3 PZ PZ TZ 3 1 2 pT3a P13 58 6.7 31.4 6.1 3.3 3+4 3+4 PZ PZ 8 5 pT3a P14 58 12 20.2 3.9 0.1 0.2 3+4 3+3 3+3 PZ PZ TZ 5 1 1 pT3a P15 66 31.6 44.9 6.6 4+3 PZ 9 pT3a P16 75 8.5 36.6 3.2 0.4 0.1 4+5 4+5 3+3 PZ PZ PZ 4 2 1 pT3a P17 63 51 26.4 9.5 4+5 PZ 6 pT3b P18 62 13.3 33.3 2.1 4+4 PZ 4 pT3a  69  4.3 MRI Protocol Imaging protocols were similar to what was explained in the previous study. Multi-echo data were acquired using a 3D multi-echo spin echo pulse sequence and high resolution T2W images were acquired using a multi-slice TSE sequence. More details about imaging protocols can be found in Chapter 3, MRI protocol.  4.4 Histologic Examination and Registration to MR Images Following prostatectomy, the excised specimens were immersed in 10% buffered formalin for a minimum of 48 hours. The formalin-fixed specimens were dissected and examined histopathologically in a uniform and consistent manner. The external surfaces were inked and the seminal vesicles and vas deferens amputated. The apical and bladder neck tissue were each removed as 0.5 cm thick tissue doughnuts. The complete prostate gland was then cut perpendicularly to the posterior surface of the prostate into 4 mm transverse slices with a multi-blade cutting device as explained before (section3.4). These Hematoxylin and Eosin (H&E) stained whole-mount slides were histologically examined by a genitourinary pathologist, who outlined the tumours and assigned the Gleason scores on each slide under the light microscope.  The whole-mount histology sections, digitized using a flatbed scanner, were registered to MR images with a software package developed in-house as explained in the previous Chapter (section 3.4). Tumour ROIs were manually drawn on the registered histology images, by accurately overlapping the tumour outlines drawn by the pathologist on the non-deformed histology sections. Non-malignant ROIs were manually drawn on the registered histology images while avoiding the tumour outlines.   70    4.5 Data Processing All MR data were processed offline. Maps of the seven LWI parameters: Ncomp, gmT2, T2-short, T2-long, Ashort, Along, and LWF were generated for all slices across the entire prostate similarly to what was explained for the previous study described in Chapter 3. Average values of MR parameters were calculated within a total of 378 (226 non-malignant, and 152 malignant) ROIs manually outlined on the registered whole-mount histology images. ROIs were defined in six types of tissue: malignant PZ and TZ, non-malignant PZ and TZ, AFMS, and PFMS.  4.6 Statistical Analysis Statistical analyses were performed using MedCalc and R packages (56, 57, 58). None of the MR parameters were normally distributed, as confirmed by the Kolmogorov-Smirnov test. Significant differences between malignant and non-malignant tissues were determined with paired t-test. In order to account for the correlations of MR parameters within each patient, the values of MR parameters for each type of tissue were averaged for each patient prior to the application of the paired t-test. Correlations between MR parameters and GS were evaluated by averaging Spearman’s correlation coefficients calculated for individual patients. It should be noted that the calculation of correlation coefficients for each individual patient was based on the ROIs defined in separate slices, and the ranges of Gleason scores were sufficient to calculate correlation coefficients in 17 out of 18 patients. Significance of the correlation between MR parameters and GS was evaluated with the application of a one sample t-test. P<0.05 was considered statistically significant. Area under the receiver operating characteristic (ROC) Curve (AUC) was calculated by ROC analysis (59) of individual and combined MR  71  parameters, performed in PZ, TZ, and the entire prostate. ROC analyses were performed based on logistic generalized linear mixed effect models (GLMMs) with the dependant (output) variable being malignant vs non-malignant (1 vs 0). Correlation within each patient was incorporated by having a random intercept in the model with the grouping factor for the random intercept being each patient. Multi-parametric ROC analyses were performed using logistic GLMM. In order to prevent data overfitting, only parameters that contributed significantly (P<0.05) to the model, and also minimized Akaike information criterion (AIC) and Bayesian information criterion (BIC), were included in the logistic GLMM.   4.7 Results Representative maps of MR parameters are shown in Figure 4-1, and their mean values and ranges are provided in Table 4-2. A Box and Whisker plot of the average values of LWF versus different Gleason patterns in PZ is shown in Figure 4-2 . Results of the paired t-test indicate that the average values of gmT2, Ashort, Along, and LWF are significantly different between malignant and non-malignant tissue in the entire prostate. Results of paired t-test in PZ showed that all MRI parameters except for T2-long have significantly different average values between malignant and non-malignant tissue. Paired t-test could not be conducted in TZ due to the insufficient number of patients with tumours in TZ.  Average Spearman's rank correlation coefficients between MR parameters and GS, and the results of t-test in PZ are presented in Table 4-3. T-test could not be conducted in TZ due to  72  the insufficient number of patients with tumours in TZ.  LWF showed the strongest correlation with Spearman's coefficient values of -0.78 ± 0.01.  The values of AUCs calculated from ROC analysis are summarized in Table 4-4. LWF had the highest AUC in PZ (0.97), TZ (0.98), and the Ashort had the highest AUC in the entire gland (0.82). Multi-parametric ROC analysis in PZ showed slightly increased AUC (0.98 vs. 0.97), with only gmT2 and T2-short contributing significantly to the logistic regression model (Regression coefficients: -9±2 (P<0.0001), 6±1 (P<0.0001), respectively). Multi-parametric ROC analysis could not be performed in TZ, since the only parameter that contributed significantly to the model was LWF. In the entire prostate, multi-parametric ROC analysis again showed increased AUC (0.86 vs. 0.82), with gmT2, T2-short, Ashort, and Ncomp contributing significantly to the model (Regression coefficients: -5.4±0.9 (P<0.0001), 4.4±0.7 (P=0.0002), 0.7±0.2 (P=0.002), 0.9±0.2 (P=0.0001), respectively).   73   Figure 4-1. Representative maps of MR parameters, T2-weighted image, and histology whole-mount section of the same slice. Scale bar of gmT2, T2-short, and T2-long images are in ‘s’. Zero pixels on the T2-long  map indicate mono-exponential decay.     74   Figure 4-2. Box and Whisker plot of the average values of LWF versus different Gleason patterns in PZ.    75  Table 4-2. Mean value, standard deviation, and range of MR measurements in malignant and non-malignant tissues of different regions. Location  T2-short (ms) T2-long (ms) gmT2a(ms) LWFb Ashort  (×105) Along  (×105) Ncomp Non-malignant PZc Mean 90±26 545±115 138±46 0.24±0.09 165±51 52±23 2.09±0.22 Range [52-150] [300-887] [68-298] [0.09-0.45] [90-350] [16-116] [1.4-2.67] Malignant PZ Mean 81±21* 548±188 94±27* 0.10±0.05* 188±46* 22±12* 1.81±0.28* Range [44-157] [207-1408] [46-187] [0-0.3] [89-303] [0.2-73] [1.06-2.52] Non-malignant TZd Mean 104±38 548±183 138±49 0.20±0.08 168±40 41±21 1.94±0.19 Range [56-202] [281-914] [65-276] [0.06-0.43] [104-250] [13-97] [1.52-2.52] Malignant TZ  Mean 90±22 609±270 101±30 0.08±0.05 165±36 15±11 1.66±0.37 Range [37-124] [372-1035] [39-158] [0-0.15] [118-292] [0-34] [1-2] Normal AFMSe Mean 57±12 639±281 58±14 0.06±0.05 154±30 9±9 1.39±0.25 Range [31-84] [219-1323] [28-97] [0-0.21] [95-262] [0-40] [1-1.92] Normal PFMSf  Mean 75±22 639±271 77±22 0.04±0.03 165±31 8±5 1.39±0.27 Range [37-115] [258-1078] [38-116] [0-0.11] [107 -228] [0-21] [1-1.96] Entire prostate Mean Range 84±28  [31-202] 569±204 [207-1408] 106±45 [28-298] 0.14±0.10 [0-0.45] 172±46 [89-350] 29±23  [0-116] 1.80±0.36 [1-2.67] agm T2: geometric mean T2, bLWF: luminal water fraction, cPZ: peripheral zone, dTZ: transition zone, eAFMS: anterior fibromuscular stroma,  fPFMS: periurethral fibromuscular stroma, *Malignant PZ significantly different than non-malignant PZ (P<0.05) based on paired t-test. Paired t-test could not be conducted in TZ due to the insufficient number of patients with tumours in TZ.    76  Table 4-3. Statistics of correlations between MRI multi-exponential decay parameters and Gleason score in PZ; data from 17 patients were included.  Characteristic T2-short T2-long gmT2 LWF Ashort Along Ncomp  Average ρ* ± standard deviation -0.34±0.49 0.17±0.45 -0.66±0.34 -0.78±0.11 0.38±0.48 -0.76±0.11 -0.56±0.30 PZ 95% Confidence Interval for ρ -0.596 to -0.093 -0.065 to 0.399 -0.832 to -0.485 -0.834 to -0.726 0.133 to 0.628 -0.814 to -0.697 -0.716 to -0.408  Significance level P = 0.010 P = 0.146 P < 0.0001 P < 0.0001 P = 0.005 P < 0.0001 P < 0.0001  Test statistic t 2.902 1.525 8.046 30.500 3.263 27.349 7.736 ρ*: Spearman’s coefficient of rank correlation Table 4-4. ROC analysis measures for MRI parameters in PZ, TZ, and entire prostate.                      Characteristic T2-short T2-long gmT2 LWF Ashort Along Ncomp    PZ Area under the  ROC curve (AUC)  0.84±0.05 0.76±0.06 0.96±0.03 0.97±0.02 0.85±0.05 0.97±0.02 0.88±0.05 Significance level P (Area=0.5) <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001  Sensitivity (95% CI) 0.89 (113/127) (0.82-0.94) 0.86 (109/127) (0.79-0.91) 0.93 (118/127) (0.87-0.97) 0.94 (119/127) (0.88-0.97) 0.86 (109/127) (0.79-0.91) 0.93 (118/127) (0.87-0.97) 0.89 (113/127) (0.82-0.94)  Specificity (95% CI)  0.62 (53/86) (0.51-0.72)  0.43 (37/86) (0.32-0.54)  0.81 (70/86) (0.72-0.89)  0.91 (78/86) (0.82-0.96)  0.69 (59/86) (0.58-0.78)  0.88 (76/86) (0.80-0.94)  0.70 (60/86) (0.59-0.79)  Area under the  ROC curve (AUC)  0.97±0.03 0.89±0.07 0.98±0.02 0.98±0.02 0.94±0.05 0.95±0.04 0.92±0.05  TZ Significance level P (Area=0.5) <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001  Sensitivity (95% CI) 0.8 (20/25) (0.59-0.93) 0.64 (16/25) (0.43-0.82) 0.84 (21/25) (0.64-0.95) 0.76 (19/25) (0.55-0.91)  0.72 (18/25) (0.51-0.88) 0.76 (19/25) (0.55-0.91) 0.52 (13/25) (0.31-0.72) Specificity (95% CI) 0.94 (61/65) (0.85-0.98) 0.89 (58/65) (0.79-0.96) 0.95 (62/65) (0.87-0.99) 0.97 (63/65) (0.89-1.00) 0.89 (58/65) (0.79-0.96) 0.95 (62/65) (0.87-0.99) 0.97 (63/65) (0.89-1.00)  Area under the  ROC curve (AUC)  0.70±0.05 0.69±0.05 0.72±0.05 0.74±0.05 0.82±0.04 0.71±0.05 0.69±0.05 Significance level P (Area=0.5) <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 Entire prostate  Sensitivity (95% CI) 0.2 (30/152) (0.14-0.27) 0.2 (30/152) (0.14-0.27) 0.35 (53/152) (0.27-0.43) 0.53 (81/152) (0.45-0.61) 0.62 (95/152) (0.54-0.7) 0.44 (67/152) (0.36-0.52) 0.22 (33/152) (0.15-0.29)  Specificity (95% CI)  0.89 (202/226) (0.85-0.93)  0.93 (210/226) (0.89-0.96)  0.81 (183/226) (0.75-0.86)  0.76 (171/226) (0.7-0.81)  0.88(199/226) (0.83-0.92)  0.74 (168/226) (0.68-0.8)  0.92 (209/226) (0.88-0.96)          77  4.8 Discussion and Conclusion The results of this pilot study demonstrate the feasibility of multi-exponential T2 mapping for PCa diagnosis. Although multi-component nature of T2 decay in prostate has been shown before (37, 38, 39, 40, 41) only one recent study investigated the application of this technique for cancer diagnosis (41); however, no direct correlation between MRI and histology has been published. In our study, we validated MR measurements with whole-mount histology, and performed statistical analysis to assess the accuracy of this technique in the detection and grading of PCa. In addition, we used a regularized NNLS algorithm, which provides an unbiased assessment of the number of T2 components and the increased accuracy of T2 estimation in the presence of noise (60). We also introduced a new parameter: the fractional volume of the long T2 component, or LWF, which outperformed all the other MRI parameters in detecting and grading PCa. In addition, LWF represents a morphological feature of the tissue, i.e. the percentage of the luminal space, and thus lends itself to a physiological interpretation more easily than most other MRI parameters.      The mean and range of LWF values  measured in non-malignant PZ in this study is in good agreement with the published values of the percentage area of lumen in normal prostatic tissue (0.24 (0.09-0.45) vs. 29.6% (15.9%-43.9%)) (48), suggesting that LWF can be a good measure of luminal space in prostate. This is strongly supported by our recent study (61), which showed a significant correlation between LWF and the histological measure of luminal space (Details of this study were provided in Chapter 3). The mean and range of gmT2, T2-short, and T2-long also correspond well to the previously published values (38, 39).   78  Our results showed lower gmT2, Along, and LWF values in tumours and in normal dense stroma than in the non-malignant glandular tissue. In general, in PCa, some of the loose stroma that fills the area between ducts and acini is replaced by densely packed malignant epithelial cells, decreasing the percentage of lumen. Therefore it is not surprising to see a decrease in Along and LWF in these cancers.  There was no significant difference in Ncomp, T2-long and T2-short between non-malignant and malignant tissues. This is likely because T2 will depend not only on the size of the water compartment, but also on its shape, or more accurately, its surface to volume ratio (62, 63). Thus one would not necessarily expect significant differences of T2-long between tumour and normal tissue. We observed fairly large variability in T2-long, most likely related to the variability of individual glands’ sizes and surface to volume ratios.  Average values of Ncomp were lower in tumour and normal dense stroma than in the non-malignant glandular tissue in PZ; thus Ncomp can be considered an indicator of how glandular the tissue is. Generally, in higher grade tumours the lumen shrinks significantly and more T2-decay curves become mono-exponential, thus decreasing the average Ncomp values. Therefore one would expect Ncomp to be significantly different between normal glandular and higher grade cancerous tissue. Since the analysis of the entire prostate included normal stroma (Ncomp ≈1) and lower grade tumours (Ncomp ≈2), it is not surprising to see no significant difference in Ncomp between non-malignant and malignant tissue.   Our results demonstrate significant correlation between LWF and GS in PZ.  The decreasing LWF with increasing GS is aligned with the published values for percentage of lumen in normal tissue and in tumours of Gleason scores 6 and 7 (48). Such dependence underscores  79  the role of LWF as a morphologic parameter that correlates with known histologic features.  It is recognized that Gleason pattern 4 carcinoma has poorly formed fused glands and is often characterized by a dense cribriform pattern. Gleason pattern 4 carcinoma has significant collapse and loss of luminal formation, contrasting with Gleason 3 carcinoma that has malignant glands with open lumina (19). Thus one may expect lowered LWF with this loss of luminal space and increased cell density.  LWF had much higher AUC in PZ and TZ than in the entire prostate. This is likely because, with regards to the luminal space, the normal dense stroma mimic the tumours in PZ and TZ. Our results show that combining Ncomp with any other MR parameter improves specificity and AUC within the entire prostate; this suggests that Ncomp can potentially be useful in tissue classification algorithms. The main limitation of this pilot study was the relatively low number of patients. Also, the range of Gleason Score in this study was limited, with 35 lesions of GS=6, 13 GS=7, 1 GS=8, 6 GS=9 and none with GS=10. Another limitation of this study includes lack of distinction between normal gland, BPH, and prostatitis.  Also, the patient selection process was potentially biased, as the recruited patients were selected from those who were scheduled for retropubic prostatectomy, indicating that the sampled lesions were weighted toward more advanced tumours. However, any study that requires validation with histology will suffer from a similar bias. Areas of future research with this technique include expanding this study with a larger number of patients and wider range of Gleason Scores, with larger numbers in each category, to access the accuracy of this technique. Comparison of this technique with the current PI-RADS v2  80  protocol (29) would also be useful in determining its clinical utility. Also combining it with current PI-RADS version 2 protocol to determine if it further increases accuracy and its incremental benefit should be investigated. In conclusion, the results of this pilot study demonstrate the feasibility of Luminal Water Imaging for diagnosis and grading of prostate cancer. Four MR parameters showed significant differences between malignant and non-malignant tissue in the prostate. LWF showed very high accuracy in detection of prostatic tumours, and a strong correlation with Gleason score. Ncomp was found to increase the specificity of this technique in the entire prostate. Our preliminary results have shown that the proposed MRI technique can be applied for both the detection and grading of prostate cancer with high accuracy. To accurately assess the suitability of this technique for clinical application, a prospective study with much larger number of patients and broader range of tumour grades, and a comparison to the current clinical PI-RADS version 2 protocol should be done.    81  Chapter  5: Comparing Diagnostic Accuracy of Luminal Water Imaging with Diffusion-Weighted and Dynamic Contrast-Enhanced MRI in Detection and Grading of Prostate Cancer  5.1 Introduction In Chapter 4, we investigated the feasibility of LWI in the detection and grading of prostate tumours, and showed that this technique provides high accuracy in the detection of tumours and high correlation with GS. Although the results of this study were very promising, it was only performed as a hypothesis-generating pilot. In order to involve LWI in clinical settings further investigation on the accuracy of this technique is required.  In this prospective trial, we performed a detailed comparison of the diagnostic accuracy of LWI with the standard MP-MRI protocols, including dynamic contrast-enhanced (DCE) and DW-MRI. In addition, in this study efforts were made to evaluate the significance of adding LWI into a MP-MRI protocol, consisting of DCE-MRI and DW-MRI, for the detection and grading of the prostatic tumours.  5.2 Patient Selection The patient selection process was similar to what was explained in Chapter 3.  Clinical data for the 15 patients who participated in this study are summarized in Table 5-1. The entire patient population used in this study has been previously reported in Chapters 3 & 4.      82  Table 5-1. Clinical data of 15 patients participating in the study. Patient Age (y) PSA level (ng/mL) Prostate volume (cc)  Lesion characteristics Pathologic tumour stage Size (cc) Gleason grade Location Total number of ROIs per lesion (from different slices)  P01 65 13.1 32.3 5.8 4+3 PZ 7 pT3a P02 67 8 94.7 0.7 2×0.2 0.5 0.3 3+3 3+3 3+3 3+3 PZ PZ TZ TZ 2 3 2 3 pT2c P03 62 6.5 31.0 3.2 0.2 0.1 0.5 4+3 4+3 3+3 3+3 PZ PZ PZ TZ 6 2 1 2 pT3a P04 80 7.2 128.3 0.1 3+3 PZ 2 pT2a P05 64 7.6 32.3 7.5 0.9 4+3 3+3 PZ PZ 8 4 pT3a P06 75 18.2 41.1 3.3 1.5 3×0.1 4×0.1 5×0.2 4+3 3+3 3+3 3+3 3+3 PZ PZ PZ TZ TZ 5 4 3 1 9 pT2c P7 69 18.4 39.5 6.2 4+5 TZ 5 pT3a P8 66 7.4 32.5 1.0 3+4 PZ 1 pT3a P9 67 6 17.7 1.3 0.1 0.6 3+4 3+3 3+3 PZ PZ TZ 3 1 2 pT3a P10 58 6.7 31.4 6.1 3.3 3+4 3+4 PZ PZ 8 5 pT3a P11 58 12 20.2 3.9 0.1 0.2 3+4 3+3 3+3 PZ PZ TZ 4 1 1 pT3a P12 66 31.6 44.9 6.6 4+3 PZ 8 pT3a P13 75 8.5 36.6 3.2 0.4 4+5 4+5 PZ PZ 4 1 pT3a P14 63 51 26.4 9.5 4+5 PZ 6 pT3b P15 62 13.3 33.3 2.1 4+4 PZ 4 pT3a  83  5.3 MRI Protocol As mentioned before, MRI examinations were performed with a 3T MRI scanner, using a combined endorectal/pelvic phased-array coil. The scanning session included: T2W imaging, LWI, DCE-MRI and DW-MRI. Orientation of axial images was set perpendicular to the rectal wall-prostate interface, and identical slice thicknesses and positioning were used for all imaging techniques.  LWI protocol was similar to what was explained for the previous study described in Chapter 3. Multi-echo data were acquired using a 3D multi-echo spin echo pulse sequence developed at the University of British Columbia MRI Research Centre (8). More details about the LWI protocol can be found in Chapter 3, MRI protocol. DW-MRI used a multi-slice diffusion weighted single shot echo-planar  spin echo sequence (TR=3129-3488 ms, TE=50-64 ms, FOV=240×240×72-375×375×72mm3, voxel-size=1.4×1.4×4-1.5×1.5×4mm3, scan matrix-size=120×120-188×186, slice thickness=4mm, flip angle=90°, number of averages=4, sense factor= 2, scan duration=241-269 sec). During each DW-MRI scan, four sets of images were acquired; one without and three with diffusion gradient (b values: 0, 100, 500, and 1000 sec/mm2). DCE-MRI data consisted of T1-weighted (T1W) and proton density (PD) images. PD data were obtained for calculation of T1 values which consequently were used for calculation of the contrast agent concentration in the tissue (64). PD images were acquired prior to the acquisition of T1W images using a 3D ultrafast spoiled gradient echo sequence (T1-TFE) (TR=50 ms, TE=0.93 ms, FOV=295×375×72mm3, voxel-size=1.2×1.5×4mm3, scan matrix-size=188×188, slice thickness=4mm, flip angle=4°, number of averages=1, sense factor= 2, scan duration=127 sec). A series of 170 T1W images were acquired prior to and after (4, and 166 images,  84  respectively) the injection of contrast agent (Magnevist (Gadopentetate dimeglumine, Bayer HealthCare, NJ), 469mg/mL (0.5 mmol/mL), 0.2 mL/Kg, rate: 2mL/s, flush: 20 mL]), using a 3D T1-TFE sequence (TR=2959 ms, TE=1.35 ms, temporal resolution= 3.4 ms, FOV=295×375×72mm3, voxel-size=1.2×1.5×4mm3, scan matrix-size=188×188, slice thickness=4mm, flip angle=12°, number of averages=1, sense factor= 2, scan duration=581 sec).   High spatial resolution T2W images were acquired to provide anatomical details and facilitate the process of image registration, using a multi-slice Turbo Spin Echo (TSE) sequence (TR=1851 ms, effective TE=80 ms, FOV=140×140×72mm3, voxel-size=0.3×0.3×4mm3, scan matrix-size=288×228, slice thickness=4mm, flip angle=90°, number of averages=3, scan duration=285 sec).   5.4 Histologic Examination and Registration to MR Images Similar to what was explained in Chapters 3 & 4, following radical prostatectomy, the excised specimens were fixed by immersion in formalin and cut in to 4mm transverse slices. Whole mount histology sections were stained by H&E and submitted for histological examination. On the whole-mount slides, tumours with a minimum Gleason grade of 3 were outlined and Gleason scores were assigned.  Image registration was performed to align MR images with the corresponding histology slides.  Due to the differences in the field of view, artifacts and apparent distortions between images of LWI, DCE and DW-MRI, image registration was performed separately for each technique. Digitized histology sections were generated by scanning whole-mount slides using a flatbed  85  scanner.  Histology sections were registered to MR images with a software package developed in-house (51) using Matlab similar to what was explained before. For more information about the registration process please refer to Chapter 3, Whole-mount Histology and Registration to MR images.  5.5 Data Processing Processing of all MR data was performed offline. From LWI data, for each voxel the signal decay curve was extracted and fitted to a multi-exponential function to generate maps of 7 parameters: T2-short, T2-long,  geometric mean T2 (gmT2), LWF, Ashort, Along, and Ncomp as described in Chapter 3, Data Processing.  From the set of four DWI images the apparent diffusion coefficient (ADC) was calculated using the Stejskal-Tanner equation (65): Sb=S0 e –b*ADC   Equation 5-1 where Sb is the signal intensity with non-zero b, and S0 is the signal intensity with b=0. For processing DCE-MRI data, first the concentration of contrast agent in the tissue was calculated from T1W and PD images as described in (64). The extended Tofts (also known as Kety) model (66) was used to relate the concentration of contrast in the tissue to the arterial input function (AIF). For each patient, the AIF function was generated by fitting the concentration of contrast agent in the voxels within the external iliac or femoral arteries to a double Gaussian function (67). By fitting the concentration of contrast agent in tissue to the extended Tofts model, maps of pharmacokinetic parameters: volume transfer constant (Ktrans), fractional volume of the extra-vascular extra-cellular space (ve), and fractional volume of  86  plasma (vp) were generated. These parameters, and how they were calculated, are described in greater details in Chapter 6. Fitting was performed for all the voxels within the prostate gland. Average values of MR parameters obtained from LWI, DCE, and DW-MRI were calculated within a total of 304 (186 non-malignant, and 118 cancers) ROIs manually outlined on the registered histology sections. Tumours with dimensions of equal or higher than 4×4 mm2 were included in data processing. For statistical analysis, data were divided into six categories based on the location and malignancy status of tissue as follows: malignant PZ, malignant TZ, non-malignant PZ, non-malignant TZ, normal PFMS, and normal AFMS. For selection of malignant ROIs the outlines of tumours, delineated by pathologist, were accurately replicated during the image registration process. Selection of non-malignant ROIs was performed by avoiding the tumour boundaries. Considering that in this study regions of BPH were not delineated by the pathologist, non-malignant ROIs could consist of normal or BPH tissue.  5.6 Statistical Analysis Statistical analyses were performed using MedCalc and R packages (56, 57, 58). Diagnostic accuracy of individual and combined MR parameters was investigated through ROC analysis (59). Values of sensitivity, specificity, and AUC were calculated separately in PZ, TZ, and the entire prostate. ROC analyses were performed based on logistic GLMMs with the dependant variable being malignant vs non-malignant. Correlation within each patient was incorporated by having a random intercept in the model with the grouping factor for the random intercept being each patient. Multi-parametric ROC analyses were performed using logistic GLMM,  87  while in order to prevent data overfitting only parameters that contributed significantly to the model, and also minimized AIC and BIC, were used in the calculations. Prior to correlation testing, normality of MR data was investigated with the Kolmogorov-Smirnov test. Since none of the MR parameters were normally distributed, correlations between MR parameters and GS were evaluated by averaging Spearman’s correlation coefficients calculated for individual patients. Significance of the correlation between MR parameters and GS was evaluated with the application of one sample t-test. In the entire study, P<0.05 was considered statistically significant.   5.7 Results Representative MR parametric maps are shown in Figure 5-1. Values of sensitivity, specificity and AUC calculated from single and multi-parameter ROC analyses are summarized in Table 5-2 and Table 5-3, respectively.  In single parameter ROC analysis (Table 5-2), the highest value of AUC obtained from LWI was equal to or higher than the highest value of AUC obtained from DCE and DW-MRI in PZ (0.97 vs 0.9 and 0.9 respectively), TZ (0.99 vs 0.9 and 0.98), and entire prostate (0.81 vs 0.76 and 0.81). In comparing the accuracy of individual techniques, using multi-parameter ROC analysis (except for DWI which only had one parameter) (Table 5-2 and Table 5-3), the AUC value obtained from LWI was higher than the AUC value obtained from DCE and DW-MRI in PZ (0.98 vs 0.89 and 0.9), and the entire prostate (0.85 vs 0.75 and 0.81). Multi-parametric ROC analysis could not be performed for DCE in TZ since there were no combinations of DCE parameters that contributed significantly to logistic GLMM.  88  Comparison of the diagnostic accuracy of combinations of techniques (Table 5-3) showed that: in PZ the highest AUC value (0.98) was obtained from LWI combined with either or both DCE and DW-MRI; in TZ, the highest AUC value (0.99) was obtained from combination of LWI and DW-MRI; and in the entire prostate the highest value of AUC (0.88) was obtained from combination of all three techniques. In PZ, the differences between AUC values obtained from the combination of LWI with DCE, DW-MRI, or both were not statistically significant, but the AUC value obtained from any combination including LWI was significantly different than the AUC value obtained from the combination of DCE and DW-MRI. In TZ, none of the differences between AUC values obtained from different combinations were statistically significant. In the entire prostate, the difference between the AUC value obtained from combination of all three techniques and combination of LWI and DCE-MRI was not statistically significant.  But the AUC values obtained from combination of LWI and DW-MRI or DCE and DW-MRI were significantly different than AUC values obtained from combination of all three techniques or combination of LWI and DCE-MRI.     Average Spearman's rank correlation coefficients between MR parameters and GS in PZ are presented in Table 5-4. A T-test could not be conducted in TZ due to the insufficient number of patients with tumours in TZ. The data presented in Table 5-4 indicates  that the highest correlation coefficient obtained from the LWI technique was higher than the highest correlation coefficient obtained from DCE and DW-MRI (0.81 vs 0.59 and 0.53 respectively). Overall, the strongest correlation with GS was obtained from the LWF parameter with a Spearman's coefficient of -0.81±0.09.  89   Figure 5-1. Representative maps of MR parameters, T2-weighted image, and histology whole-mount section of the same slice.      90  Table 5-2. ROC analysis measures for single MRI parameters in the entire prostate, PZ, and TZ. a Significantly (P<0.05) different than value of AUC obtained from Ktrans, based on Delong’s test. b Significantly different than AUC value obtained from ve. c Significantly different than AUC value obtained from vp.d Significantly different than AUC value obtained from ADC. e Significantly different than AUC value obtained from T2-short.f Significantly different than AUC value obtained from T2-long. g Significantly different than AUC value obtained from gmT2. h Significantly different than AUC value obtained from LWF.  i Significantly different than AUC value obtained from Ashort. j Significantly different than AUC value obtained from Along. k Significantly different than AUC value obtained from Ncomp.Location Entire Prostate PZ  TZ    Technique MR Parameter  Sensitivity 95% CI  Specificity 95% CI  AUC 95%Cl Significance level  (P value)  Sensitivity 95% CI  Specificity 95% CI AUC 95%Cl Significance level  (P value)  Sensitivity 95% CI  Specificity 95% CI  AUC 95%Cl Significance level  (P value) DCE Ktrans 0.42 (50/118) 0.33-0.52  0.85 (158/186) 0.79-0.9 0.76 b, e, f, k (0.71-0.81) <0.001 0.86 (85/99) 0.77-0.92 0.78 (54/69) 0.67-0.87 0.9 b, f, g, h, j (0.85-0.95) <0.001 0.68 (13/19) 0.43-0.87 0.88 (50/57) 0.76-0.95 0.9 d, e, g, h, j (0.83-0.97) <0.001 ve 0.25 (29/118) 0.17-0.33 0.91 (170/186) 0.86-0.95 0.70 a, d, i (0.64- 0.76)  <0.001 0.89 (88/99) 0.81-0.94 0.52 (36/69) 0.4-0.64 0.77 a, c, d, e, g, h, i, j, k (0.70-0.84)  <0.001 0.63 (12/19) 0.38-0.84 0.93 (53/57) 0.83-0.98 0.93 e, g, h (0.87-0.99) <0.001 vp 0.42 (49/118) 0.33-0.51 0.87 (162/186) 0.81-0.92 0.73 d, i (0.67-0.79)  <0.001 0.81 (80/99) 0.72-0.88 0.65 (45/69) 0.53-0.76 0.85 b,f, g, h, j (0.79-0.91) <0.001 0.58 (11/19) 0.33-0.8 0.84 (48/57) 0.72-0.93 0.89 d, e, g, h, j (0.82-0.96) <0.001 DWI ADC 0.61 (72/118) 0.52-0.7 0.85 (159/186) 0.8-0.9 0.81 b, c, e, f, g, h, j, k (0.76-0.86) <0.001 0.87 (86/99) 0.79-0.93  0.78 (54/69) 0.67-0.87 0.9 b, f, g, h, j (0.85-0.95) <0.001 0.74 (14/19) 0.49-0.91 0.98 (56/57) 0.91-1.00 0.98 a, c, f (0.96-1.00) <0.001 LWI T2-short 0.2 (24/118) 0.13-0.29  0.9 (168/186) 0.85-0.94 0.68 a, d, g, i (0.62-0.74) <0.001 0.86 (85/99) 0.77-0.92 0.67 (46/69) 0.54-0.78 0.87 b, f, g, h, j (0.82-0.92) <0.001 0.79 (15/19) 0.54-0.94 0.95 (54/57) 0.85-0.99 0.98 a, b, c, f, i (0.96-1.00) <0.001 T2-long 0.19 (23/118) 0.13-0.28 0.94 (174/186) 0.89-0.97 0.69 a, d, i (0.63-0.75)  <0.001 0.89 (88/99) 0.81-0.94  0.43 (30/69) 0.32-0.56 0.76 a, c, d, e, g, h, i, j, k (0.69-0.83)  <0.001 0.68 (13/19) 0.43-0.87 0.88 (50/57) 0.76-0.95 0.89 d, e, g, h, j, k (0.82-0.96) <0.001 gmT2 0.31 (37/118) 0.23-0.41 0.81 (150/186) 0.74-0.86 0.72 d, e, i (0.66-0.78)  <0.001 0.93 (92/99) 0.86-0.97  0.86 (59/69) 0.75-0.93 0.97 a, b, c, d, e, f, i, k (0.94-1.00)  <0.001 0.89 (17/19) 0.67-0.99 0.96 (55/57) 0.88-1.00 0.99 a, b, c, f, i (0.98-1.00)  <0.001 LWF 0.47 (56/118) 0.38-0.57 0.75 (139/186) 0.68-0.81 0.73 d, I, j (0.67-0.79)  <0.001 0.93 (92/99) 0.86-0.97  0.91 (63/69) 0.82-0.97 0.97 a, b, c, d, e, f, i, k (0.95-0.99)  <0.001 0.89 (17/19) 0.67-0.99 0.96 (55/57) 0.88-1.00 0.99 a, b, c, f, i (0.98-1.00) <0.001 Ashort 0.58 (68/118) 0.48-0.67  0.91 (170/186) 0.86-0.95 0.81 b, c, e, f, g, h,j,k (0.76-0.86)  <0.001 0.84 (83/99) 0.75-0.9 0.72 (50/69) 0.6-0.83 0.85 b, f, g, h, j (0.79-0.91) <0.001 0.74 (14/19) 0.49-0.91 0.89 (51/57) 0.78-0.96 0.93 e, g, h (0.87-0.99) <0.001 Along 0.42 (49/118) 0.33-0.51 0.74 (138/186) 0.67-0.8 0.70 d, h, i (0.64-0.76)  <0.001 0.92 (91/99) 0.85-0.96 0.9 (62/69) 0.8-0.96  0.97 a, b, c, d, e, f, i, k (0.94-1.00)  <0.001 0.89 (17/19) 0.67-0.99 0.96 (55/57) 0.88-1.00 0.98 a, c, f (0.95-1.00) <0.001 Ncomp 0.21 (25/118) 0.14-0.3 0.9 (167/186) 0.85-0.94 0.69 a, d, i (0.63-0.75) <0.001 0.90 (89/99) 0.82-0.95 0.71 (49/69) 0.59-0.81 0.91 b, f, g, h, j (0.87-0.95) <0.001 0.58 (11/19) 0.33-0.8 0.98 (56/57) 0.91-1.00 0.95 f (0.90-1.00) <0.001   91  Table 5-3. ROC analysis measures for combined MRI parameters in the entire prostate, PZ, and TZ.     Location        Entire Prostate                      PZ                                       TZ   Technique   Contributing Parameters  Sensitivity 95% CI  Specificity 95% CI  AUC 95%Cl Significance level (P value) Contributing Parameters  Sensitivity 95% CI  Specificity 95% CI  AUC 95%Cl Significance level (P value) Contributing Parameters  Sensitivity 95% CI  Specificity 95% CI  AUC 95%Cl Significance level (P value)   LWI T2-short   Ncomp  gmT2 Ashort  0.64 (76/118) 0.55-0.73 0.82 (153/186) 0.76-0.87 0.85 b, c, f (0.81-0.89) <0.001 T2-short gmT2 0.97 (96/99) 0.91-0.99 0.88 (61/69) 0.78-0.95 0.98 b, e (0.95-1.00) <0.001 LWF 0.89 (17/19) 0.67-0.99 0.96 (55/57) 0.81-1 0.99 ┼ (0.98-1.00) <0.001 DCE Ktrans  vp  0.43 (51/118) 0.34-0.53  0.84 (156/186) 0.78-0.89 0.75 a, c, d, e, f (0.69-0.81) <0.001 Ktrans ve  vp 0.86 (85/99) 0.77-0.92 0.83 (57/69) 0.72-0.91 0.89 a, c, d,, f (0.84-0.94) <0.001 - - - - - LWI+ DCE T2-short     gmT2   Ncomp Ashort Ktrans ve  0.73 (86/118) 0.64-0.81 0.82 (153/186) 0.76-0.87 0.87 a, b (0.83-0.91) <0.001 T2-short gmT2 vp 0.96 (95/99) 0.9-0.99 0.9 (62/69) 0.8-0.96 0.98 b, e (0.96-1.00) <0.001 Along Ncomp , Ktrans 0.79 (15/19) 0.54-0.94 0.95 (54/57) 0.85-0.99 0.96 ┼ (0.92-1.00) <0.001 LWI+ DWI T2-short gmT2 Ncomp   ADC  0.71 (84/118) 0.62-0.79 0.82 (152/186) 0.75-0.87 0.86 b, f (0.82-0.90) <0.001 T2-short   gmT2, ADC 0.98 (97/99) 0.93-1 0.93 (64/69) 0.84-0.98 0.98 b, e (0.95-1.00) <0.001 LWF 0.89 (17/19) 0.67-0.99 0.96 (55/57) 0.88-1 0.99 ┼ (0.98-1.00) <0.001 DCE+DWI ve ADC 0.64 (76/118) 0.55-0.73  0.88 (163/186) 0.82-0.92 0.84 b, f (0.79-0.89) <0.001 ve  vp ADC 0.89 (88/99) 0.81-0.94 0.84 (58/69) 0.73-0.92 0.91 a, c, d, f (0.87-0.95) <0.001 ADC 0.74 (14/19) 0.49-0.91 0.98 (56/57) 0.91-1 0.98 ┼ (0.96-1.00) <0.001 LWI+ DCE+DWI T2-short gmT2  Ncomp ve ADC 0.75 (88/118) 0.66-0.82  0.84 (157/186) 0.78-0.89 0.88 a, b, d, e (0.84-0.92) <0.001 T2-short  gmT2  vp 0.96 (95/99) 0.9-0.99 0.9 (62/69) 0.8-0.96 0.98 b, e (0.96-1.00) <0.001 Along, Ncomp , Ktrans 0.79 (15/19) 0.54-0.94 0.95 (54/57) 0.85-0.99 0.96 ┼ (0.92-1.00) <0.001  a Significantly (P<0.05) different than value of AUC obtained from LWI, based on Delong’s test. b Significantly different than AUC value obtained from DCE.  c Significantly different than AUC value obtained from combination of  LWI and DCE. d Significantly different than AUC value obtained from combination of LWI and DWI. e Significantly different than AUC value obtained from combination of  DCE and DWI. f Significantly different than AUC value obtained from  combination of LWI, DCE, and DWI. ┼ Not significantly different than AUC value obtained from any other technique in TZ.   92  Table 5-4. Statistics of correlations with Gleason score in PZ.   Technique MR Parameter Average Spearman’s coefficient of rank correlation (ρ) ±standard deviation 95% Confidence Interval for ρ Significance level Test statistic t  DCE Ktrans 0.59±0.36 0.37 to 0.80 P = 0.0001 5.927 ve 0.36±0.31 0.16 to 0.55 P = 0.0016 4.058 vp 0.46±0.41 0.22 to 0.71 P = 0.0014 4.120 DWI ADC -0.53±0.43 -0.79 to -0.27 P = 0.0008 4.417   LWI T2-short -0.46±0.40 -0.70 to -0.22 P = 0.0014 4.124 T2-long 0.13±0.43 -0.13 to 0.39 P = 0.3021 1.078 gmT2 -0.76±0.10 -0.82 to -0.70 P < 0.0001 26.298 LWF -0.81±0.09 -0.86 to -0.75 P < 0.0001 31.663 Ashort 0.38±0.50 0.07 to 0.68 P = 0.0192 2.702 Along -0.80±0.10 -0.86 to -0.74 P < 0.0001 29.598 Ncomp -0.68±0.19 -0.80 to -0.57 P < 0.0001 13.211   93  5.8 Discussion and Conclusion Our results showed that LWI alone performs better than either DCE or DW-MRI, and equally well or better than the combination of DCE and DW-MRI in the detection of prostate cancer. Using LWI alone rather than a combination of DCE and DW-MRI provides advantages of being completely non-invasive as it does not require administration of contrast agent. This results in reduction of costs of contrast agent and intravenous injection materials. Also, LWI can be used as an alternative for patients who cannot undergo DCE-MRI due to potential adverse reaction to a gadolinium based contrast agent, as well as patients with metallic hip implants, for whom DWI is likely to be non-diagnostic. Finally, LWI can potentially be the basis for developing an abbreviated protocol for prostate cancer screening and diagnostics. A similar concept is becoming standard of care for breast cancer (68).  However, it should be noted here that the acquisition time of LWI protocol is currently relatively long (11 minutes). Therefore, for the development of an abbreviated protocol based on this technique, further improvements of the proposed LWI technique are necessary to reduce its acquisition time.  Reducing the scan time of LWI is a feasible task by for example increasing the GRASE factor and/or under-sampling the k-space in conjunction with the Compressed Sensing reconstruction. We showed that LWI provides significantly higher correlation coefficients with Gleason score than DCE and DW-MRI.  This is to be expected because LWF strongly correlates with the fractional amount of luminal space in prostate tissue (61), and the relative amount of luminal space decreases with increase in GS (19, 48). Both ADC and Ktrans also correlated significantly with GS in PZ, albeit with significantly lower values of the correlation coefficient. The ADC’s   94  significant correlation with GS is most likely related to the higher cellularity of high GS tumours (69), since it has been shown that ADC values correlate with tissue cellular density (70). The likely reason for significant correlation between Ktrans and GS is the increased tumour vascularity, as compared to normal tissue, since Borren et al. have shown a statistically significant dependence between GS and micro-vessel density (71). However, the results of our study suggest that the amount of luminal space is a much stronger factor than cellularity or vascularity in distinguishing between different Gleason scores.   In this study the highest accuracy for detecting PCa in the entire prostate was achieved when LWI was combined with both DCE and DW-MRI. However, the difference between the AUC value obtained from combination of all three techniques and combination of LWI and DCE-MRI was not statistically significant. Also, in PZ the difference between the AUC value obtained from LWI when combined with either or both DCE and DW-MRI was not statistically significant, and in TZ there was no significant difference between the AUC value obtained from any combination. Based on accuracy alone, the combination of LWI and DCE-MRI could be the preferred methodology for diagnosis of prostate cancer. But if scan time is also taken into consideration, the combination of LWI and DW-MRI would be preferred, as it still provides the highest accuracy in PZ, and TZ, with a very minor reduction in accuracy in the entire prostate. This study has several limitations, primarily the relatively small number of patients and the limited range of GS. Also, in this study, there was no differentiation between normal gland, BPH, and prostatitis in non-malignant regions. Another limitation was related to patient selection: as the recruited patients were selected from those who were scheduled for retropubic   95  prostatectomy, the sampled lesions were weighted toward more advanced tumours. We had relatively long scan times (70 minutes) which increased the chance of patients’ movement, possibly resulting in data processing errors of each technique or a mismatch of images between different techniques. Another limitation was that a high b value of > 1400 was not used, which is recommended as per PI-RADS v2. This study was a pilot study and a final decision on whether to incorporate LWI in clinical MP-MRI protocols requires further investigations. Potential future research includes expanding this study with a larger number of patients and wider range of GS, and comparison to PI-RADS version 2. Also, future work will involve further development of the LWI technique to reduce its acquisition time by increasing the Gradient Spin Echo (GRASE) factor and/or using sparse k-space sampling together with the Compressed Sensing reconstruction.  In conclusion, the results of this pilot study show that LWI alone performs better than DCE and DW-MRI in detection of PCa and in correlation with GS. LWI, when combined with either DCE or DW-MRI, provides significantly higher accuracy than either of the other two techniques individually or combined. Therefore, it can be concluded that incorporating LWI in MP-MRI protocols may result in a significant increase in accuracy of detection and grading of PCa and that a more efficient, abbreviated MP-MRI protocol for diagnosis of PCa can be achieved by combining LWI with either DCE or DW-MRI, but not both.         96  Chapter  6: Optimization of Temporal Sampling of Dynamic Contrast-Enhanced MRI Protocol for Diagnosis of Prostate Cancer  6.1 Introduction 6.1.1 DCE-MRI DCE-MRI is a MRI technique that is widely used for diagnosis of cancer and monitoring response to anticancer treatments due to its capability for characterization of tumour microvasculature (64, 72).  In this technique, a paramagnetic contrast enhancing agent is injected intravenously into the patient. Consecutive T1W MR images are acquired prior to, during, and following the administration of the contrast agent. As the contrast agent passes through the body, it leaks from the vascular system to the surrounding tissue, and decreases the T2 and T1 relaxation times of the adjacent tissue. The T2 shortening effect of the contrast agent results in a decrease of signal intensity while the T1 shortening effect of the contrast agent results in an increase of signal intensity of the T1W images. In clinical settings, depending on the tissue of interest, different DCE-MRI techniques with different contrast agents are used. For DCE-MRI of prostate, the contrast agent is usually Gadolinium-based. The dominant effect of Gadolinium on signal intensity is the decrease of T1 relaxation time. Therefore, following the injection of Gadolinium, a signal enhancement can be obtained in the tissue in proximity to the contrast agent. The rate and level of signal enhancement is different in normal tissues and tumours. It has been shown that the signal enhancement in malignant tumours is generally faster and greater than the signal enhancement in normal tissue (73). This is mainly caused by (but not   97  limited to) the higher vascularity and also higher endothelial permeability of malignant tumours compared to the normal tissues. Based on these differences, by monitoring the contrast-driven enhancement, it can be determined whether a tissue is normal or not. Moreover, by knowing the amount of signal enhancement, and accordingly estimating the change in T1 relaxation time of the tissue, concentration of contrast agent in the tissue can be calculated at any time. Then, by use of a pharmacokinetic model, the concentration of contrast agent in the tissue can be related to its physiological parameters such as vessel density, blood flow, endothelial permeability, and the volume of Extracellular-Extravascular Space (EES).  Among the pharmacokinetic models that are used in the literature, the Tofts (also known as Kety) (74) and extended Tofts model (75) are the most common pharmacokinetic models used for DCE-MRI. In this study, we only used the extended Tofts model which relates the concentration of the contrast agent in the tissue to three useful physiological parameters: 1) the influx volume transfer constant (Ktrans), 2) the volume of EES per unit volume of tissue (ve), and 3) the volume of plasma per unit volume of tissue (vp). In the extended Tofts model, the equation relating the concentration of contrast agent in the tissue (Ct), the concentration of contrast agent in the plasma (Cp), and the three physiological parameters (Ktrans, ve , vp) is expressed as below:  𝐶𝑡(𝑡) = 𝑣𝑝𝐶𝑝(𝑡) + 𝐾𝑡𝑟𝑎𝑛𝑠 ∫ 𝐶𝑝(𝑇)𝑡0𝑒−(𝐾𝑡𝑟𝑎𝑛𝑠𝑣𝑒⁄ )(𝑡−𝑇)𝑑𝑇 Equation 6-1 Following a DCE-MRI examination, Ct(t) and Cp(t) can be calculated from scan data. By using the calculated Ct(t) and Cp(t) and an appropriate fitting program, physiological parameters (Ktrans, ve, vp) can be calculated (from Equation 6-1) for every pixel of a DCE image.   98  6.1.2 Significance of Temporal Resolution in Diagnostic Accuracy of DCE-MRI The data fitting process based on Equation 6-1 is complicated due to the presence of the integral term.  If the functional form of Cp(t) is known, the integral term can be replaced by its analytical solution to simplify the fitting procedure. Otherwise, the integral term can only be estimated numerically. The difference between the result of numerical integration and the analytical solution introduces an uncertainty in the fitting procedure. Let us call the difference between the outcome of numerical integration and analytical integration, the integral approximation error, IAE. IAE can affect the accuracy of the fitting process and increase the uncertainty in calculation of physiological parameters. This error depends on the temporal resolution.  It has been shown (76) that the accuracy of DCE data analysis can be maximized by using very high temporal resolution (as high as 1s). Based on this result and by considering the source of IAE, one may assume that the accuracy of DCE data analysis perhaps always increases with an increase of temporal resolution. But we will show that this is not necessarily the case for the problem at hand. In fact the IAE depends both on the temporal resolution, and the shape of Cp(t). To better understand this matter, let us look at Figure 6-1. Based on this figure, as explained in its caption, it can be observed that it is possible to have a bigger IAE for a higher temporal resolution. Thus, there potentially could be an optimum value of temporal resolution minimizing the IAE. Based on the observation of this figure, one has to be cautious when choosing the temporal resolution for a DCE-MRI protocol.     99   Figure 6-1. Comparison between numerical integration of the integral term in Equation 6-1, from a simulated Cp with temporal resolution of 12 s (left figures) and 14 s (right figures). In the top figures (a & b) the integration is performed using the rectangle method, and in the bottom figures (c & d) the integration is performed using the trapezoid method. The red curves show Cp(T) exp (− (Ktransve⁄ ) (t − T)). Pink and blue colors show the areas that are overestimated and underestimated by integration, respectively. Green color shows the area that is correctly calculated by the integration. In the above figures, the total integration approximation error (IAE) can be calculated by subtraction of the pink area from the blue area. Here we can see that for both of the rectangular and trapezoidal integration techniques, in the first three steps of the integration, in the right figures (∆t=14s), the overestimated region roughly cancels the underestimated region. However, in the left figures (∆t=12s) the dominant effect is underestimation. Therefore, the cases shown at the left, while having a higher temporal resolution, have a higher IAE than the cases shown at the right. Although many studies have investigated the effect of temporal resolution on the diagnostic accuracy of DCE-MRI (77, 78, 79, 80), to the best of our knowledge, no study has been conducted to investigate the effect of temporal resolution on the accuracy of prostate cancer diagnosis using the extended Tofts model. Therefore, the first objective of this study was to   100  investigate the relationship between the accuracy of calculated fit parameters (Ktrans, ve, vp) that are used in the extended Tofts model, and the temporal resolution, by using simulation. The second objective of this study was to increase the accuracy of calculated fit parameters (obtained from simulation) for low temporal resolution data, by using an alternative data analysis technique. The third objective was to investigate the relationship between the temporal resolution and the detection accuracy of prostatic tumours, using patient data. The details of the implementation and the results of these three projects are presented in sections 6.2, 6.3, and 6.4. 6.2 Temporal Resolution and Accuracy of Fit Parameters In this study the relationship between the accuracy of calculated fit parameters (Ktrans, ve, vp) and temporal resolution was investigated by performing a series of simulations. In these simulations, Cp(t) was generated for a series of time data points separated by ∆t by using a double-Gaussian function as described by Parker et. al (67). Ct(t) was generated, with the same temporal spacing as Cp(t), by substituting Cp(t) and presumed values (obtained from (81)) of Ktrans, ve, vp, in Equation 6-1. A Gaussian noise was then added to the Ct(t), and Cp(t) values. These Ct(t) and Cp(t) were then substituted in Equation 6-1, and by using a fitting program written in Matlab Ktrans, ve, and vp were calculated for each pixel. For evaluating the accuracy of calculated fit parameters, the percentage error for each of the fit parameters was calculated by the following equation: %𝐸𝑟𝑟𝑜𝑟 =(𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒−𝑝𝑟𝑒𝑠𝑢𝑚𝑒𝑑 𝑣𝑎𝑙𝑢𝑒)𝑝𝑟𝑒𝑠𝑢𝑚𝑒𝑑 𝑣𝑎𝑙𝑢𝑒× 100  Equation 6-2   101  Maps of percentage error were generated as a function of temporal resolution and the standard deviation of the Gaussian noise that was added to Ct(t) and Cp(t). These maps are presented in Figure 6-2.a-c.  Figure 6-2.d shows a graph of all three percentage errors as a function of temporal resolution at a single standard deviation. From Figure 6-2, it can be observed that within a certain range of temporal resolution (3-30s), the effect of standard deviation is dominated by the effect of temporal resolution. Also, from the same figure, it can be observed that the decrease in temporal resolution has a significant impact on vp values [%error: -100%-0%], while the impact on Ktrans is smaller [%error: -25%-0%], and ve remains almost unaffected [%error: -2%-+2%].    102   Figure 6-2. Percentage errors in calculated fit parameters obtained from simulation.  a-c) Maps of percentage error as a function of temporal resolution and the standard deviation of the Gaussian noise. d) Graph of all three percentage errors as a function of temporal resolution at standard deviation=0.05.  6.3 An Alternative Analysis Technique for Low Temporal Resolution Data We proposed using a different analysis technique for cases when Cp(t) has to be measured with low temporal resolution. This technique is proposed based on the fact that in order to numerically calculate the integral term of Equation 6-1 with a desirably small element size, we do not necessarily need to know the Cp(t) with temporal spacing equal to that element size. Instead, a lower temporal resolution Cp(t) can be first fitted to an appropriate model to find its   103  functional form. The functional form of Cp(t) can then be used to calculate the integral numerically with any desirably small element size. For testing the proposed technique, a number of simulations were performed using the methodology as explained in section 6.2 with the following modification: 1) only the noiseless condition was investigated (as it was concluded in the previous section that the effect of noise is dominated by the effect of temporal resolution), and 2) regardless of temporal resolution of Cp(t), the integral term was numerically calculated with 1 s element size (while in section 6.2 the element size of the integral term was always equal to the temporal spacing of Cp(t)). Percentage errors were calculated similar to what was explained in Equation 6-2 of Section 6.2. Results are shown in Figure 6-3.    104   Figure 6-3. Percentage errors in calculated fit parameters obtained from simulation. The green and red graphs represent cases where the integral term is calculated with and without the proposed technique, respectively.  Figure 6-3 shows graphs of percentage error as a function of temporal resolution for the cases where the integral term is calculated with and without the proposed technique. From Figure 6-3, it can be observed that our proposed technique is successful in decreasing the error in calculation of all fit parameters, particularly vp.  6.4 Temporal Resolution and Accuracy of Detection of Prostatic Tumours In this section, we investigate the effect of temporal resolution on the diagnostic accuracy of prostate cancer detection, by using DCE-MRI data acquired from 15 patients. Scan data were   105  down-sampled in time by a down-sample factor, DSF, of 2, 3, 4, and 5. Parametric maps were generated for the original and the down-sampled data, and correlated to the whole-mount histology using image registration. Diagnostic accuracies were evaluated using ROC analysis. Patient selection, DCE-MRI protocol, histologic examination and registration process of this study is exactly the same as Chapter 5; therefore, they are not repeated here again. However, data processing is slightly different which is explained in the following section.  6.4.1 Data Processing  Data processing was similar to Chapter 5 with one modification. In addition to processing the original data, the down-sampled data were also generated and processed in this study. In an effort to mimic the lower temporal resolutions, down-sampling of data was performed by averaging every 2, 3, 4, and 5 time frames, which generated data sets with temporal resolutions of 6.8s, 10.2s, 13.6 s, and 17s (original temporal resolution=3.4 s). It must be noted that averaging the signal to generate down-sampled data may not be identical to acquiring data at slower sampling rate.  Particularly, averaging the data points increases the SNR of the time course of the down-sampled data to a larger degree than for the actual data acquired with lower temporal resolutions.  The original data were processed in the same manner as what was explained in Chapter 5 (Section 5.5). For processing the down-sampled data, first concentration of contrast agent in the tissue, Ct(t), was calculated from down-sampled T1W images and the PD image in a similar manner as what was explained in Section 5.5. Then, by using the extended Tofts model, Ct(t) was related to the concentration of contrast agent in plasma, Cp(t). For each patient, the   106  functional form of Cp(t) was determined by fitting the concentration of contrast agent in the voxels within the external iliac or femoral arteries to a double Gaussian function (67). By fitting the Ct(t) to the extended Tofts model, maps of Ktrans, ve, and vp were generated. For each of the original and down-sampled data sets, the fitting procedure was performed twice; once with and once without using the alternative data analysis technique (which was explained in section 6.3). In both cases the functional form of Cp(t) was used for numerical calculation of the integral term in Equation 6-1. Using the alternative data analysis technique, the integral term was numerically calculated with 1 s element sizes, regardless of the temporal spacing of Ct(t). Without using the alternative analysis technique, the integral term was numerically calculated with the same element size as temporal spacing of Ct(t). Average values of MR parameters were calculated within a total of 304 (186 non-malignant, and 118 cancers) ROIs. Statistical analyses were performed using MedCalc. Diagnostic accuracy of individual and combined MR parameters was investigated by using ROC analysis. Multi-parametric ROC analyses were performed using logistic regression, while in order to prevent data overfitting only parameters that contributed significantly to the model were used in the calculations. Values of AUC were calculated separately in PZ, TZ, and the entire prostate.   6.4.2 Results Graphs of AUC values as a function of DSF, in PZ, TZ, and the entire prostate are shown in, Figure 6-4, Figure 6-5, and Figure 6-6, respectively. Results of multi-parameter ROC analyses are summarized in Table 6-1.    107   Figure 6-4. Graphs of area under the (ROC) curve (AUC) as a function of down-sample factor (DSF) in the peripheral zone. The green and the red graphs represent the cases where the data were analysed with and without using the alternative technique (that was explained in section 6.3), respectively.    108   Figure 6-5. Graphs of AUC values as a function of DSF in the transition zone.  The green and the red graphs represent the cases where the data were analysed with and without using the alternative technique (that was explained in section 6.3), respectively. Multi-parametric ROC analyses were performed using logistic regression, while only parameters that contributed significantly to the model were used in the calculations. For DSF=3 multi-parametric ROC analysis could not be performed as no parameter was retained in the model.   109   Figure 6-6. Graphs AUC values as a function of DSF in the entire prostate. The green and the red graphs represent the cases where the data were analysed with and without using the alternative technique (as explained in section 6.3), respectively.      110  Table 6-1. Results of multi-parametric ROC analyses.  Location Fitting Technique Characteristic †DSF=1 DSF=2 DSF=3 DSF=4 DSF=5    PZa Without AT* Contributing Parameters Ktrans Ktrans,vp Ktrans Ktrans,vp Ktrans,ve,vp cAUC 0.768 0.748 0.773 0.754 0.818 With AT Contributing Parameters Ktrans ve,vp Ktrans Ktrans,vp vp AUC 0.764 0.788 0.757 0.769 0.697    TZb Without AT Contributing Parameters ve ve ∆N/A Ktrans,ve,vp ve,vp AUC 0.721 0.64 - 0.82 0.776 With AT Contributing Parameters ve ve N/A ve ve AUC 0.74 0.659 - 0.671 0.687   Entire Prostate Without AT Contributing Parameters Ktrans Ktrans,ve Ktrans,ve ve,vp Ktrans,ve,vp AUC 0.654 0.632 0.645 0.646 0.707 With AT Contributing Parameters Ktrans vp Ktrans,ve ve,vp vp AUC 0.658 0.63 0.652 0.638 0.677 AT*: Alternative (data analysis) technique, †DSF: down-sample factor. aPZ: peripheral zone, bTZ: transition zone, cAUC: area under the (ROC) curve. Multi-parametric ROC analyses were performed using logistic regression, while only parameters that contributed significantly to the model, were used in the calculations. ∆For DSF=3 Multi-parametric ROC analysis could not be performed in TZ since no parameter was retained in the model.    111  Overall, our results showed a non-linear relationship between the AUC values and temporal resolution in all locations. And, we did not observe a noticeable difference between AUC values obtained with or without using the proposed alternative data analysis technique.  We had a few interesting observations: 1) In the multi-parametric ROC analysis in PZ and the entire prostate, there is not a considerable difference between AUC values that are obtained for different temporal resolutions, ranging from 3.4s to 13.6 s. 2) for vp, the impact of temporal resolution on AUC values observed here is not as dramatic as the impact of temporal resolution on the accuracy of calculation of vp which was observed in the simulation study, Section 6.2. This can be explained by hypothesizing that although a decrease in temporal resolution increases the uncertainty in the calculation of vp, if the vp of both tumour and normal tissue vary in the same manner (i.e. both decrease or both increase), it is possible to have the same contrast between tumour and normal tissue in vp maps of different temporal resolutions.  6.5 Discussion and Conclusions In this study, first we investigated the impact of temporal resolution on the accuracy of calculation of fitting parameters of Equation 6-1 by performing a simulation study. From this investigation, we concluded that a decrease in the temporal resolution has the highest impact (as decrease of accuracy) on vp, less impact on Ktrans, and almost no impact on ve. Second, we proposed an alternative data analysis technique to increase the accuracy of calculation of fitting parameters of Equation 6-1 for data that have been acquired with low temporal resolution. We verified the suitability of this technique against a standard data   112  analysis technique, using simulation. The results showed that our proposed technique successfully decreases the calculation error of all fitting parameters, particularly vp. Finally, we investigated the impact of temporal resolution on the accuracy of detecting prostatic tumours, using patient data. Our results demonstrated that when temporal resolution varies within a certain range (3.4-13.6 s), the diagnostic accuracy of DCE-MRI is not affected considerably. This result may be surprising at first, especially considering that following the bolus injection the contrast agent in arterial blood increases very fast, such that this signal may contain significant high frequency components. Thus, in order to fully capture the shape of the signal the Nyquist criterion must be satisfied by sampling the signal at greater than twice the rate of the highest frequency components. Using lower sampling rates results in a greater fitting error and inaccurate values of the fit parameters. However, our results show that cancer detection accuracy is not significantly affected by the temporal resolution. A possible reason for that is that, the calculated fit parameters for both tumour and normal tissue may be affected by a systematic error to a similar degree, resulting in a similar contrast between the tumour and normal tissue for different temporal sampling rates.  The significance of this finding can be understood by considering that if two temporal resolutions provide similar accuracy, the lower temporal resolution may be preferred to allow for improvement of spatial resolution or SNR (while maintaining the same scan time) to achieve better results. An increase in spatial resolution of DCE-MRI decreases false-negative diagnoses and improves specificity as demonstrated by Furman-Haran et al. (82).   113  Chapter  7: Conclusions   7.1 Summary In this work, LWI, a new quantitative T2 mapping technique, has been developed for diagnosis and grading of prostate cancer. This technique was developed to measure the fractional amount of water content in luminal space of prostate tissue. As the fractional amount of luminal space is different between normal and malignant tissue, and between tumours of different grades, it was hypothesized that this technique can be used for both detection and grading of prostatic tumours. We developed the LWI protocol based on a series of simulations and phantom studies. The preliminary protocol was then improved and validated by acquiring data from a number of healthy volunteers.  We investigated the correlation between parameters measured with LWI, particularly LWF, and the corresponding tissue composition in prostate. The results demonstrated that LWF is significantly and strongly correlated with the percentage area of luminal space in the prostatic tissue. Hence, our hypothesis that LWF represents the fractional amount of MR signal generated by water content of luminal spaces in prostate was verified. We evaluated the diagnostic accuracy of the proposed MRI technique by performing a patient study.  In this pilot study, we demonstrated the feasibility of LWI for diagnosis of prostate cancer. Our results showed that LWI measurements provide high accuracy in detection of tumours, and strong correlation with Gleason score.    114  Additionally, we compared the diagnostic accuracy of LWI with the more established MP-MRI protocols: DCE and DW-MRI. We also investigated the significance of combining LWI with DCE and/or DW-MRI, in the accuracy of detection and grading of prostatic tumours. The results showed that LWI alone performs better than DCE and DW-MRI in the detection of tumours as well as in correlation with GS. LWI, when combined with either DCE or DW-MRI, provided significantly higher accuracy than either of the other two techniques individually or combined. Combination of all three techniques did not provide significant improvement on the accuracy that is obtained from combination of LWI with either DCE or DW-MRI. Therefore, it was concluded that a more efficient, abbreviated MP-MRI protocol for the diagnosis of prostate cancer could be achieved by combining LWI with either DCE or DW-MRI, but not necessarily with both.    Finally, as a side project, we investigated the impact of temporal resolution on the accuracy of DCE-MRI in detection of prostatic tumours. Our results showed that for a temporal resolution ranging between 3.4s to 13.6 s, the diagnostic accuracy of DCE-MRI in prostate cancer is independent of the temporal resolution.   7.2 Contributions The contributions of this thesis can be summarized as follows:   Development of a novel MRI technique for measurement of luminal water content in prostate.   115  A clinically applicable protocol was developed for non-invasive measurement of luminal water content in prostate.   Verification of the hypothesized relationship between MR measurement of luminal water and the fractional amount of luminal space in prostatic tissue. Correlation between LWF and the fractional amount of luminal space in prostatic tissue was evaluated. Establishment of the relationship between LWF and fractional amount of luminal space allows for potential application of LWI for the diagnosis and evaluation of prostatic diseases (including but not limited to prostate cancer) in which the extent of luminal space differs between normal and abnormal tissues.   Clinical evaluation of diagnostic accuracy of LWI. Preliminary clinical assessment of LWI for the diagnosis of prostate cancer was performed, and the feasibility of this technique in detection and grading of prostatic tumours was demonstrated. Incorporation of LWI in clinical settings could potentially result in a significant increase in the accuracy of detection and grading of prostate cancer.   Evaluation of the diagnostic accuracy of LWI compared to DCE and DW-MRI. A detailed comparison of the diagnostic accuracy of LWI with the standard MP-MRI protocols was performed. It was demonstrated that LWI performs better than DCE and DW-MRI in diagnosis of prostate cancer; therefore, this technique could become clinically preferred to DCE-MRI as it does not require administration of any contrast agent. Substitution of DCE-  116  MRI by LWI saves the cost of contrast agent and intravenous injection materials; moreover, LWI could be the alternative option for patients who cannot undergo DCE-MRI at all due to the potential adverse reaction to a gadolinium-based contrast agent. Finally, substitution of DW-MRI by LWI could be the alternative option for patients with metallic hip implants, for whom DWI is likely to be non-diagnostic.    Proposing a potential area of improvement in accuracy of DCE-MRI for diagnosis of prostate cancer. The impact of temporal resolution on the accuracy of DCE-MRI in the detection of prostatic tumours was investigated. It was demonstrating that when temporal resolution varies within a certain range, the diagnostic accuracy of DCE-MRI is not affected considerably; hence a lower temporal resolution can be used, allowing for improvement of spatial resolution or SNR compared to a higher temporal resolutions, to achieve better results.  7.3 Future Work The main limitation of the LWI pilot studies in this thesis is having access to the data from a relatively low number of patients, and also, a limited range of Gleason Scores. Another limitation of LWI studies is the lack of distinction between normal gland, and BPH. Another important area of improvement for LWI is reduction in its scan time. Based on above limitations, areas of future research with our developed LWI technique are as follows:   117   Expanding the study of diagnostic accuracy of LWI with a larger number of patients and wider range of Gleason Scores with larger numbers in each category to better access the accuracy of this technique.   Comparing LWI with the current PI-RADS (version 2) protocol to further assess the clinical utility of LWI.   Further development of our proposed LWI technique to reduce its acquisition time by increasing the GRASE factor and/or under-sampling the k-space in conjunction with the Compressed Sensing reconstruction.  Investigating the accuracy of LWI in distinction between normal tissue and BPH. For the DCE-MRI study, the future research direction could include:  Performing a simulation study to investigate the impact of temporal resolution on the contrast between the calculated physiological parameters of a presumed normal tissue and a presumed malignant tissue. This result can be compared to our clinical result to better characterize the relationship between the temporal resolution and the diagnostic accuracy of DCE-MRI.        118  References 1. A New Method of Measuring Nuclear Magnetic Moment. Rabi II, Zacharias JR, Millman S, Kusch Physical Review, 1938;53(4):318-318. 2. The Molecular Beam Resonance Method for Measuring Nuclear Magnetic Moments. The Magnetic Moments of L6,Li7, and F19. Rabi II, Millman S, Kusch P, Zacharias JR. Physical Review, 1939;55:526-535. 3. Nuclear Induction. Bloch F, Hansen WW, Packard M. Physical Review, 1946; 69:127. 4. Nuclear Induction. Bloch.F. Physical Review., 1946; 70:460. 5. Ressonance Absorbtion by Nuclear Magnetic Moments in a Solid. Purcell EM, Torrey HC, Pound RV. Phyical Review, 1946; 69:37-38. 6. Image formation by induced local interactions: examples employing nuclear magnetic resonance. PC., Lauterbur. Nature, 1973; 242:190-191. 7. Raymond V. Damadian, M.D.: magnetic resonance imaging and the controversy of the 2003 Nobel Prize in Physiology or Medicine. Macchia RJ, Termine JE, Buchen CD. J Urol., 2007;178(3):783-5. 8. Haacke EM, Brown RW, Thompson MR, Venkatesan R. Magnetic Resonance Imaging: Physical Principles and Sequence Design, Second Edition.  Wiley & Sons, Inc, 2014. ISBN 978-0-471-72085-0. 9. Spin Echoes. EL, Hahn.  Physical Review, 1950;50:580. 10. Effect of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments. Carr HY, Purcell EM.  Physical Review, 1954; 94:630. 11. Modified SpinEcho Method for Measuring Nuclear Relaxation Times. Meiboom S, Gill D.  Rev.Sci.Instrum., 1958; 29:688. 12. Skandalakis, John E. Skandalakis Surgical Anatomy: The Embryologic and Anatomic Basis of Modern Surgery.  Paschalidis Medical Publication Ltd., 2004. ISBN: 9789603990741. 13. The zonal anatomy of the prostate. JE., McNeal. 1,  Prostate, 1981; 2:35-49. 14. Prostate cancer statistics. Canadian Cancer Society. Retrived on 19/04/2017 from http://www.cancer.ca/en/cancer-information/cancer-type/prostate/statistics/?region=bc. 15. Canadian Cancer Society’s Advisory Committee on Cancer, Statistics. Canadian Cancer Statistics 2016. Toronto, ON : Canadian Cancer Society, 2016. 1-142.   119  16. Biologic differences between peripheral and transiotion zone prostate cancer. Lee JJ, Thomac IC, Nolley R, Ferrari M, Brooks JD, Leppert JT.  Prostate, 2014; 75(2):183-90. 17. Central zone carcinoma of the prostate gland: a distinct tumor type with poor prognostic features. Cohen RJ, Shannon BA, Phillips M, Moorin RE, Wheeler TM, Garrett KL.  J Urol, 2008;179(5):1762-7. 18. The 2016 WHO Classification of Tumours of the Urinary System aand Male Genital Organs-Part B: Prostate and Bladder Tumours. Humphrey PA, Moch H, Cubillia AL, Ulbright TM, Reuter VE.  Eur Urol., 2016; 70(1):106-19. 19. Histologic grading of prostate cancer: a perspective. Gleason. DF, Hum Pathol,1992;23(3):273-9. 20. Basic principles of diffusion-weighted imaging. R., Bammer. European Journal of Radiology, 2003; 45(3):169-184. 21. Diffusion-weighted MRI in the body: applications and challenges in oncology. Koh DM, and Collins DJ.  American Journal of Roentgenology., 2007;188:1622-1635. 22. Dynamic contract enhanced MRI in prostate cancer. Alonzi R, Padhani AR, Allen C. European Journal of Radiology, 2007; 63(3):335-350. 23. The state of prostate MRI in 2013. Gupta RT, Kauffman CR, Polascik TJ, Taneja SS, Rosenkrantz AB. Oncology, 2013; 27(4):262-270. 24. Prostate cancer detection with multi-parametric MRI: logistic regression analysis of quantitative T2, diffusion-weighted imaging, and dynamic-enhanced MRI. Langer DL, Van der Kwast TH, Evans AJ, Trachetenberg J, Wilson BC, Haider MA.  J Magn Reson Imaging, 2009;30:327-334. 25. Prostate cancer detection with multi-parametric MRI: logistic regression analysis of quantitative T2, diffusion-weighted imaging, and dynamic contrast-enhanced MRI. Langer DL, van der Kwast TH, Evans AJ, Trachtenberg J, Wilson BC, Haider MA. J Magn Reson Imaging, 2009;30(2):327-34. 26. Prostate cancer: multiparametric MR imaging for detection, localization, and staging. Hoeks CM, Barentsz JO, Hambrock T, et al.  Radiology, 2011;261(1):46-66. 27. The role of magnetic resonance imaging in the diagnosis and management of prostate cancer. Thompson J, Lawrentschuk N, Frydenberg M, et al. BJU Int., 2013;112(2): 6-20. 28. Role of multiparametric magnetic resonance imaging in the diagnosis of prostate cancer. Rais-Bahrami S, Turkbey B, Grant KB, et al.  Curr Urol Rep, 2014;15(2):387. 29. PI-RADS. Prostate Imaging – Reporting and Data System, Version2. : American College of Radiology Web site. , 2015. Retrived on 19/04/2017 from http://www.acr.org/~/media/ACR/Documents/PDF/QualitySafety/Resources/PIRADS/PIRADS%20V2.pdf    120  30. In Vivo Visualization of Myelin Water in Brain by Magnetic. Mackay A, Kenneth W, Julian A, Li D,Paty D, Graeb D.  Magn Reson Med, 1994; 31(6):673-7. 31. Evaluation of the articular cartilage of the knee joint: value of adding a T2 mapping sequence to a routine MR imaging protocol. Kijowski R, Blankenbaker DG, Munoz Del Rio A, Baer GS, Graf BK. Radiology, 2013;267(2):503-13. 32. Pathology and Genetics of Tumours of the Urinary System and Male Genital Organs. International Agency for Research on Cancer (IARC). [ed.] Sauter G, Epstein JI, Sesterhenn IA Eble JN.  IARCPress, 2004: 160-160. 33. Zonal Anatomy of Prostate. Amin M, Khalid A, Tazeen N,Yasoob M. Annals of KEMU, 2010;16(3):138-142. 34. The state of prostate MRI in 2013. Gupta RT, Kauffman CR, Polascik TJ, Taneja SS, Rosenkrantz AB. Oncology, 2013; 27(4):262-270. 35. MRI relaxometry: methods and applications. O. Carnerio AA, Vilela GR, Araujo DB de, Baffa O,.  Braz J. Phys, 2006; 36:9-15. 36. Prostate Cancer Grading: Use of Graph Cut and Spatial Arrangement of Nuclei. Nguyen K, SarkarA, Jain AK.  IEEE Transactions on Medical Imaging, 2014; 33(12):2254-70. 37. In Vivo Estimation of Relaxation Processes in Benign Hyperplasia and Carcinoma of the Prostate Gland by Magnetic Resonance Imaging. Kjaer L, Thomsen C, Iversen P, et al.  Magnetic Resonance Imaging, 1987; 5(1):23-30. 38. Prostate Magnetic Resonance Imaging: Multiexponential T2 Decay in Prostate Tissue. Storås TH, Gjesdal KI, Gadmar Ø.B, et al. J Magn Reson Imaging, 2008;28(5):1166-72. 39. Three-dimensional Balanced Steady State Free Precession Imaging of the Prostate: Flip Angle Dependency of the Signal Based on a Two Component T2-decay Model. Storås TH, Gjesdal KI, Gadmar OB, et al.  J Magn Reson Imaging, 2010; 31(5):1124-31. 40. Minimization of Errors in Biexponential T 2 Measurements of the Prostate. Gilani N, Rosenkrantz AB2, Malcolm P, et al. J Magn Reson Imaging, 2015;42(4):1072-7. 41. Two-compartment T2 Decay for Prostate Cancer Diagnosis. Wang S, Agarwal H, KarczmarGS, Oto A.  In:Proceedings of the 23rd Annual Meeting of ISMRM, Toronto,Ontarion, Canada, 2015. Abstract 944.. 42. Prostate magnetic resonance imaging:Multiexponential T2 decay in prostate tissue. 4. Storås, T. H., Gjesdal, K.-I., Gadmar, Ø. B., Geitung, J. T. and Kløw, N.E.,. Journal of Magnetic resonance Imaging, 2008; 28(5):1166-1172.   121  43. AnalyzeNNLS: magnetic resonance multiexponential decay image analysis. Bjarnason TA, Mitchell JR. J Magn Reson, 2010; 206(2):200-4. 44. Applications of Stimulated Echo Correction to Multicomponent T2 Analysis. Prasloski T, Mädler B, Xiang QS, et al. Magn Reson Med, 2012;67(6):1803-14. 45. Advanced Myelin Water Imaging Techniques for Rapid Data Acquisition and Long T2 Component Measurements. Zhang J, Vavasour I, Kolind SH, et al.  In:Proceedings of the 23rd Annual Meeting of ISMRM, Toronto, Ontario, Canada, 2015. Abstract 824. Vol. 73. 46. Morphometry of the prostate: I. Distribution of tissue components in hyperplastic glands. Marks LS, Treiger B, Dorey FJ, Fu YS, deKernion JB. Urology, 1994; 44(4):486-92. 47. Regional Variations of Insulin-Like Growth Factor I(IGF-I), IGF-II, and Receptor Type 1 in Benign Prostatic Hyperplasia Tissue and Their Correlation with Intraprostatic Androgens. Monti S. et. al. Journal of Clinical Endocrinolgy& amp Metabolism , 2001; 86:1700-06. 48. Prostate tissue composition and MR measurements: investigating the relationships between ADC, T2, K(trans), v(e), and corresponding histologic features. Langer DL, van der Kwast TH, Evans AJ, et al. Radiology, 2010;255(2):485-94. 49. Changes in Epithelium, Stroma, and Lumen Space Correlate More Strongly with Gleason Pattern and Are Stronger Predictors of Prostate ADC Changes than Cellularity Metrics. Chatterjee A, Watson G, Myint E, Sved P, McEntee M, Bourne R. Radiology, 2015; 277(3):751-62. 50. Device for sectioning prostatectomy specimens to facilitate comparison between histology and in vivo MRI. Drew B., Jones E.C., Reinsberg S., et al. Journal of Magnetic Resonance Imaging, 2010;32(4):992-996 . 51. In vivo 3T and ex vivo 7T diffusion tensor imaging of prostate cancer: Correlation with histology. Uribe CF, Jones EC, Chang SD, et al. Magn Reson Imaging, 2015; 33(5):577-83. 52. Elastix: a toolbox for intensity-based medical image registration. Klein S, Staring M, Murphy K, Viergever MA, Pluim JP. IEEE Trans Med Imaging 2010;29:196–205. 53. Patterns of progression in prostate cancer. Mcneal JE, Kindrachuk RA, Freiha FS, Bostwick DG, Redwine EA, Stamey TA. Lancet, 1986; 1(8472):60-63. 54. Tissue shrinkage and stereological studies. MJ., West.  Cold Spring Harb Protoc, 2013; 3. 55. Gleason grading and prognostic factors in carcinoma of the prostate. PA, Humphrey.  Modern Pathology, 2004; 17(3):292-306. 56. Dragulescu, AA. Apache XMLBeans POI, and Maintainer Dragulescu AA. "Package ‘xlsxjars’.". 2014.   122  57. Fitting Linear Mixed-Effects Models Using lme4. Bates D, Maechler M, Bolker B, Walker S.  Journal of Statistical Software, 2015; 67(1):1-48. 58. pROC: an open-source package for R and S+ to analyze and compare ROC curves. Robin X, Turk N, Hainard A, et al.  BMC Bioinformatics, 2011; 12:77. 59. Receiver operating characteristic curves and their use in radiology. NA, Obuchowski.  Radiology, 2003; 229(2):3-8. 60. Insights into brain microstructure from the T2 distribution. MacKay AL, Laule C, Vavasour I, Bjarnason T, Kolind S, Mädler B. Magnetic Resonance Imaging, 2006; 24(4):515-25. 61. MR measurement of luminal water in prostate gland: Quantitative correlation between MRI and histology. Sabouri S, Fazli L, Chang SD, et. al.  Journal of Magnetic Resonance Imaging, 2017;46(3):861-9.. 62. An NMR determination of the physiological water distribution in wood during drying. Menon RS, MacKay AL, Hailey JRT, Bloom M, Burgess AE, Swanson JS.  Journal of Applied Polymer Sciences, 1987;33(4):1141-55. 63. Application of spin-spin relaxation to measurement of surface area and pore size distributions in a hydrating cement paste. Halperin WP, Jehng JY, Song YQ. Magn. Reson. Imaging, 1994;12(2):169-73. 64. Probing tumor microvascularity by measurement, analysis and display of contrast agent uptake kinetics. Parker GJ, Suckling J, Tanner SF, Padhani AR, Revell PB, Husband JE, Leach MO.  J Magn Reson Imaging, 1997;7(3):564-74. 65. Spin Diffusion Measurements: Spin Echoes in the Presence of a Time‐Dependent Field Gradient. TannerJE, Stejskal EO and.  The Journal of Chemical Physics, 1965;42:288-292. 66. Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols. Tofts PS, Brix G, Buckley DL, Evelhoch JL, Henderson E, Knopp MV, Larsson HB, Lee TY, Mayr NA, Parker GJ, Port RE, Taylor J, Weisskoff RM. J Magn Reson Imaging, 1999;10(3):223-32. 67. Experimentally-derived functional form for a population-averaged high-temporal-resolution arterial input function for dynamic contrast-enhanced MRI. Parker GJ, Roberts C, Macdonald A, Buonaccorsi GA, Cheung S, Buckley DL, Jackson A, Watson Y, Davies K, Jayson GC., 2006; 56(5):993-1000. 68. Abbreviated breast magnetic resonance imaging (MRI): first postcontrast subtracted images and maximum-intensity projection-a novel approach to breast cancer screening with MRI. Kuhl CK, Schrading S, Strobel K, Schild HH, Hilgers RD, Bieling HB.  J Clin Oncol, 2014;32(22): 2304-10.   123  69. In vivo measurement of the apparent diffusion coefficient in normal and malignant prostatic tissues using echo-planar imaging. B., Issa.  J Magn Reson Imaging, 2002;16(2):196-200. 70. Correlation of ADC and T2 measurements with cell density in prostate cancer at 3.0 Tesla. Gibbs P, Liney GP, Pickles MD, Zelhof B, Rodrigues G, Turnbull LW.  Invest Radiol., 2009;44(9):572-6. 71. Accurate prostate tumour detection with multiparametric magnetic resonance imaging: dependence on histological properties. Borren A, Groenendaal G, Moman MR, et al. Acta Oncol, 2014;53(1):88-95. 72. Dynamic Contrast-enhanced MRI in Clinical Oncology: Current Status and Future Directions. AR., Padhani.  J Magn Reson Imaging, 2002;16:407-422. 73. Dynamic contrast-enhanced MRI in normal and abnormal prostate tissues as defined by biopsy, MRI, and 3D MRSI. Noworolski S.M., et al. MAgnetic Resonance in Medicine, 2005;53(9):249-255. 74. Modeling tracer kinetics in dynamic Gd-DTPA MR imaging. P.S., Tofts. Journal of Magnetic Resonance Imaging, 1997; 7(1):91-101. 75. Estimating kinetic parameters from dynamic contrast-enhanced t1-weighted MRI of a diffusable tracer: Standardized quantities and symbols. Tofts P.S., et al.  Journal of Magnetic resonance Imaging, 1999;10(3):223-232. 76. Investigation and optimization of parameter accuracy in dynamic contrast-enhanced MRI. Margaret, Cheng Hai-Ling.  Journal of Magnetic Resonance Imaging, 2008;28(3):736-743. 77. Temporal sampling requirements for the tracer kinetics modeling of breast disease. Henderson E, Rutt BK, Lee TY. Magn Reson Imaging., 1998;16(9):1057-73. 78. Temporal Sampling Requirements for Reference Region Modeling of DCE-MRI Data in Human Breast Cancer. Planey CR, Welch EB, Xu L, et al.  J. MAgn Reson Imaging, 2009;30:121-34. 79. The effect of temporal sampling on quantitative pharmacokinetic and three-time-point analysis of breast DCE-MRI. Fluckiger JU, Schabel MC, Dibella EV. Magn Reson Imaging, 2012;30(7):934-43. 80. The influence of temporal resolution in determining pharmacokinetic parameters from DCE-MRI data. Heisen M, Fan X, Buurman J, van Riel NA, Karczmar GS, ter Haar Romeny BM.  Magn Reson Med, 2010; 63(3):811-6. 81. Comparision between Population Average and Experimentally Measured Arterial Input Function in Predicting Biopsy Results in Prostate cancer. Meng R, Chang SD, Jones EC, Goldenberg SL, Kozlowski P.  Academin Radiology, 2010; 17(4):520-5. 82. Critical Role of Spatial Resolution in Dynamic Contrast-Enhanced Breast MRI. Furman-Haran E, Grobgeld D, Kelcz F, Degani H. J Magn Reson Imaging. 2001;13(6):862-7.   124  Appendix Effect of the T1 relaxation on the measurement of Luminal Water Fraction  In Chapter 2, for the development of a mathematical model to describe the T2 decay in prostatic tissue, the effect of T1 relaxation was ignored. In this appendix, we will demonstrate the effect of including T1 relaxation in the modeling of the T2 decay.  By including the effect of T1 relaxation in the decay model the signal decay which was previously described by Equation 2-2, can be expressed as below: 𝑆(𝑡) = ∑ 𝐴𝑖𝑒−𝑡𝑇2𝑖 (1 − 𝑒−𝑡𝑇1𝑖)𝑖=𝑁𝑖=0   Equation A-1 where S(t) is the signal magnitude at a time t, A is the amplitude of the signal at time zero, and T2i, and T1i are respectively the T2, and T1 relaxation times of water compartment i.   As described in chapters 2 and 3, in the absence of T1 relaxation effects, LWF is defined as: 𝐿𝑊𝐹 =𝐴𝑙𝑜𝑛𝑔𝐴𝑠ℎ𝑜𝑟𝑡+𝐴𝑙𝑜𝑛𝑔  Equation A-2 where Ashort and Along are the maximum amplitudes of the short and long T2 components, respectively.   By considering the effect of T1 relaxation, the Ashort and Along terms of Equation A-2 can be expressed as below:   125  Ashort =A′short (1 − 𝑒−𝑇𝑅𝑇1−𝑠ℎ𝑜𝑟𝑡)   Equation A-3 Along =A′long (1 − 𝑒−𝑇𝑅𝑇1−𝑙𝑜𝑛𝑔)   Equation A-4  where T1-short  and T1-long  are the T1 relaxation times of the small and the large water compartments, respectively, and A′short and A′long are the maximum amplitudes of the short and long T2 components when the effect of T1 relaxation is taken into account.    By substituting Equation A-3 and Equation A-4 in Equation A-2 LWF can be expressed as below: 𝐿𝑊𝐹 =𝐴′𝑙𝑜𝑛𝑔(1−𝑒−𝑇𝑅𝑇1−𝑙𝑜𝑛𝑔),𝐴′𝑠ℎ𝑜𝑟𝑡(1−𝑒−𝑇𝑅𝑇1−𝑠ℎ𝑜𝑟𝑡)+𝐴′𝑙𝑜𝑛𝑔(1−𝑒−𝑇𝑅𝑇1−𝑙𝑜𝑛𝑔),  Equation A-5  From Equation A-5 we can see that LWF no longer represents the fractional amount of water within the luminal space, unless T1-short and T1-long are equal in value. Therefore we can define the true luminal water fraction as:  By comparing Equation A-5 and A-6 it can be realized that the measurements of luminal water fraction that were reported in Chapters 2 - 5 were in fact T1-weighted measures of the true fractional amount of luminal water content.  𝐿𝑊𝐹′ =𝐴′𝑙𝑜𝑛𝑔𝐴′𝑠ℎ𝑜𝑟𝑡+𝐴′𝑙𝑜𝑛𝑔  Equation A-6   126  To better understand the effect of T1 relaxation on the measurements of luminal water fraction, let us perform a very simplistic analysis. In this analysis we calculate the values of LWF and LWF′ for some assumed values of A′short, A′long, T1-short, T1-long and TR. A′short, and A′long are assumed to be equal to Ashort, and Along measured in normal PZ (165×105, and 52×105 respectively, see Table 4.2). T1-short is assumed to be equal to the T1 relaxation time in human muscle (1250 ms) at 3T, and T1-long is assumed to be equal to the T1 relaxation time of free water (4000 ms). TR = 1473 ms (which is the effective TR of our LWI protocol = 3073 ms – (64×25 ms)). By substituting these values in Equations A-5 and A-6, LWF and LWF′ values will be calculated as: 0.12, and 0.24, respectively. In this example, the effect of ignoring T1 relaxation appears as underestimation of the true luminal water fraction.   Now, let us perform another simple analysis and calculate the ratio of LWF/LWF′ for two more general cases where; 1) T1-long is presumed to be equal to 4000 ms but T1-short varies between 800ms and 1600ms, and 2) T1-short is presumed to be equal to 1250 ms but T1-long varies between 2500ms and 5000ms. The results of these analyses are shown in figure A-1 and Figure A-2.    127   Figure A-1. The ratio of LWF to LWF′ for T1-long equal to 4000ms, and 800ms<T1-short<1600ms.   Figure A-2. The ratio of LWF to LWF′ for T1-short equal to 1250ms, and 2500ms<T1-long<5000ms.  From Figure A-1 and Figure A-2, we can see that for the interested ranges of T1-short and T1-short LWF always underestimates LWF′. 0.40.450.50.550.6800 900 1000 1100 1200 1300 1400 1500 1600LWF/LWF'T1-short (ms)LWF/LWF' for T1-long=4000 ms0.40.450.50.550.60.650.72500 3000 3500 4000 4500 5000LWF/LWF'T1-long (ms)LWF/LWF' for T1-short=1250 ms  128  In conclusion, T1 relaxation affects measurement of luminal water fraction in prostatic tissue. Ignoring the effect of T1 relaxation in the modeling of T2 decay results in underestimation of the true fractional amount of luminal water. This is the most likely reason for the slope of the correlation between LWF measured with MRI vs. fractional volume of the luminal space measured with histology to be about 0.45 (See the Results section of Chapter 3).  It should be noted that the simplistic analyses presented in this appendix was only performed by using a single set of values for A′short, and A′long. Determination of the T1 relaxation effect on measurements of luminal water under general conditions requires further investigation in form of an extensive simulation study.  

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