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PAGE 1 1 PERPENDICULAR FIBER TRACKING FOR FIBER BUNDLE ANALYSIS By SIDDHARTH RAY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2012 PAGE 2 2 2012 Siddharth Ray PAGE 3 3 Dedicated t o my parents PAGE 4 4 ACKNOWLEDGMENTS I would first and foremost like to express my deep gratitude to my advisor Dr. needed clarifications and numerous discussions with him guided me through the project. His support and guidance throughout these years in graduate school ha ve m ade it a very productive and enjoyable experience. My sincere than ks extend to Dr. Angelos Barmpoutis, who was like my second advisor, for the generous support and encouragement to submit my work in various conferences. I would also like to thank Dr. Paul R. Carney my committee member, for the comments enabling me to understand the c aveats of that rat experiment s and Dr. Mansi Parekh for providing me real DW MRI rat brain datasets. I would like to extend my gratitude towards m y fellow lab mates Ankit Salgia, Rujuta Munje and Jiucheng Nie for numerous useful discussions and all the fun time we had. I would also thank Tifiny D McDo n ald for administrative and friendly support during various occasions. Finally, I sincerely thank my parents brother and my girlfriend for being supportive and understanding during stressful and happy times. I acknowledge funding support from Shands Cancer Center, University of Florida. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTIO N ................................ ................................ ................................ .... 12 1.1 Objectives ................................ ................................ ................................ ......... 12 1.2 Clinical Motivation ................................ ................................ ............................. 12 1.3 Current Methods for Diagn osing and Treating Brain Diseases/Disorders ......... 13 1.4 Need for Improvement ................................ ................................ ...................... 14 1.5 Organization of Report ................................ ................................ ...................... 15 2 METHODS ................................ ................................ ................................ .............. 16 2.1 Background ................................ ................................ ................................ ....... 16 2.2 Magnetic Resonance Diffusion Tensor Imaging (MR DTI) ................................ 16 2.3 Fiber Tracking ................................ ................................ ................................ ... 18 2.3.1 Deterministic Tractography ................................ ................................ ...... 19 2.3.2 Probabilistic T ractography ................................ ................................ ....... 21 2.3.3 Combination of Deterministic and Probabilistic Tractography ................. 22 2.4 Method ................................ ................................ ................................ .............. 22 2.4.1 DTI Reconstruction ................................ ................................ .................. 22 2.4.4 Perpendicular Fiber Tracking ................................ ................................ .. 24 2.4.4.1 Geometric cost ................................ ................................ ............... 25 2.4.4.2 Fiber cost ................................ ................................ ....................... 26 2.4.4.3 Total cost function ................................ ................................ .......... 27 2.4.4.4 Thresholds ................................ ................................ ..................... 27 2.4.5 Construction of 3D Cost Maps Through Dynamic Programming ............. 28 2.4.6 Algorithm: Pseudocode for 3D DP for Perpendicular Fiber Tracking ....... 30 3 TOWARDS VERIFICATION OF PERPENDICULAR FIBER TRACKING ............... 31 3.1 Validation on Synthetic Datasets ................................ ................................ ...... 31 3.2 Generation of Synthetic Dataset ................................ ................................ ....... 31 3.3 Implementation ................................ ................................ ................................ 31 3.4 Specifications ................................ ................................ ................................ .... 32 3.5 Data Set 1: Inclined Fibers ................................ ................................ ................ 32 3.6 Data Set 2: Conical Bundle with Parallel Fibers ................................ ................ 34 PAGE 6 6 3.7 Data Set 3: Linear and Curving Fibers ................................ .............................. 36 3.8 Data Set 4: Fibers Branching ................................ ................................ ............ 39 4 RESULTS ................................ ................................ ................................ ............... 41 4.1 Application on Real Datasets ................................ ................................ ............ 41 4.2 Implementation ................................ ................................ ................................ 41 4.3 Pre processing ................................ ................................ ................................ .. 41 4.4 Rat Hippocampus ................................ ................................ ............................. 43 4.4.1 Data Acquisition ................................ ................................ ...................... 43 4.4.2 Fiber Bundle Analysis Usi ng Perpendicular Fiber Tracking ..................... 44 4.4.3 Discussions ................................ ................................ ............................. 47 4.5 Control and Disease (Epilepsy) Rat Brain ................................ ......................... 50 4.5.1 Data Acquisition ................................ ................................ ...................... 51 4.5.2 Fiber Bundle Analysis of Control and Disease Rat Brain ......................... 51 4.5.3 Discussion ................................ ................................ ............................... 64 5 CONCLUSIONS AND FUTURE WORK ................................ ................................ 65 5.1 Conclusions ................................ ................................ ................................ ...... 65 5.2 Limitations ................................ ................................ ................................ ......... 65 5.3 Future Work ................................ ................................ ................................ ...... 66 5.3.1 Improvement of Perpendicular Fiber Tracking Method ............................ 66 5.3.2 Application on Real Datasets ................................ ................................ .. 66 LIST OF REFERENCES ................................ ................................ ............................... 68 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 70 PAGE 7 7 LIST OF TABLES Table page 2 1 List the factors and their formulation ................................ ................................ ... 25 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Diffusion encoding gradients ................................ ................................ .............. 17 2 2 Illustration of fiber trajectory ................................ ................................ ............... 19 2 3 Illustration of streamline and Fiber Assignment by Continuous Tracking (FACT) method of tractography.. ................................ ................................ ........ 20 2 4 Connectivity d istribution with seed point in posterior limb ................................ ... 21 2 5 Illustration of Split and Merge Tractography (SMT) ................................ ............ 22 2 6 Illustration of steps perpendicular fiber tracking ................................ .................. 24 2 7 Geometric cost ................................ ................................ ................................ ... 26 2 8 Fiber cost. ................................ ................................ ................................ ........... 26 2 9 Dynamic Programming ................................ ................................ ....................... 29 3 1 Resu lts from synthetic dataset#1. ................................ ................................ ....... 34 3 2 Results from synthetic dataset#2 ................................ ................................ ........ 35 3 3 Ellipsoidal representation of eigenvectors for dataset#3. ................................ ... 36 3 4 Results from synthetic dataset#3 ................................ ................................ ........ 37 3 5 Results from synthetic dataset#3 ................................ ................................ ........ 38 3 6 Ellipsoidal representation for eigenvectors of fibers branching ........................... 39 3 7 Results from synthetic dataset#4 ................................ ................................ ........ 40 4 1 Surf plots of a rat brain DWI dataset ................................ ................................ ... 42 4 2 Shown is the FA map ................................ ................................ ......................... 43 4 3 Results obtained from analysis of the rat hippocampus with seed point in the stratum lacunosum moleculare ................................ ................................ ........... 46 4 4 Results obtained from analysis of the rat hippocampus with seed point in the stratum oriens ................................ ................................ ................................ ..... 47 4 5 Visual depiction of the extend of the reconstructed fiber bundle in the stratum lacunosum moleculare ................................ ................................ ....................... 48 PAGE 9 9 4 6 Visual depiction of the extend of the reconstructed fiber bundle in the Stratum oriens ................................ ................................ ................................ .................. 48 4 7 [A] Shown is the colored FA map of control rat brain dataset ............................. 50 4 8 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 52 4 9 Results obtained from analysis of th e rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 53 4 10 Results obtained from analysis of the rat brain with seed point shown w ith black marker ................................ ................................ ................................ ....... 54 4 11 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 55 4 12 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 56 4 13 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 57 4 14 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 58 4 15 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 59 4 16 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 60 4 17 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 61 4 18 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 62 4 19 Results obtained from analysis of the rat brain with seed point shown with black marker ................................ ................................ ................................ ....... 63 4 20 Depicts the colored FA diagram of healthy r at brain ................................ ........... 64 PAGE 10 10 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science PERPENDICULAR FIBER TRACKING FOR FIBER BUNDLE ANALYSIS By Siddharth Ray May 2012 Chair: Walter G. Major: Biomedical Engineering Diffusion Tensor Imaging (DTI) is a well a ccepted Magnetic Resonance (MR) imaging technique that can non invasively analyze the diffusivity patterns of water in neural tissue and visualize neural fiber tract s inside the brain. However, the majority of existing fiber tracking techniques ignore s the featur es of diffusion perpendicular to the individual fiber which may contain unique information on the local patterns of diffusion. These secondary patterns have not been adopted for clinical use due to a vari ety of reasons, including high computational demands and high complexity involved in analyzing neural fiber tracking information. In this work I introduce the idea of perpendicular fiber tracking, for neural fiber bundle analysis and I present a novel dynamic program m in g method that tr aces surfaces that are locally perpendicular to axonal fibers This is achieved by using a cost function with a geometric as well as a fiber orientation term that is evaluated dynamically over the entire image domain starting from a given seed point. The p roposed method is validated using synthetic DW MRI datasets and is then applied to real brain datasets. The results demonstrate the accuracy and effectiveness of our method. The presented technique can be used for fiber bundle segmentation, as a clinical t ool for neural fiber analysis, and potentially as a PAGE 11 11 biomarker for various brain diseases cell migration PAGE 12 12 CHAPTER 1 INTRODUCTION 1.1 Objectives The long term objective of this project is to provide fiber bundle metrics, using an interactive algorithm for fiber bundle analysis. This algorithm could be used clinically as a biomarker for diagnosing and monitoring atrophy for epilepsy [1] Schizophrenia [2] [3] [4] and potentially other dementias, as well as to predict cancer cell migration in the brain [5] My specific objectives include To develop a perpendicular fiber tracking algorithm that computes in real time statistics on variation of the structure, size and curvature along a fiber bundle. Validate the method on synthetic data sets wi th known fiber geometry. Demonstrate the technique using real Diffusion Weighted Magnetic Resonance Imaging (DW MRI) data sets of control (healthy) and diseased (epilepsy) rat brains. 1.2 Clinical M otivation Each year in United States approximately 1.2 million people aged 18 years and older are newly diagnosed with the onset of brain disease. Approximately 14 million people, or approximately 14% of the population, are impaired with some type of brain disease/d isorder [6] disease (AD), epilepsy, P most prevalent brain disease and is expected that in the United States alone, there will be approximately 15 million people with AD by 2050 [7] As of now, AD is largely strongest risk factor. At present, AD is the fifth leading cause of death in the United States and the number of deaths has i ncreased by 66% between 2000 and 2008 [7] Following AD, epilepsy is the second most common brain disorder, with 250,000 people PAGE 13 13 diagnosed annually [7] Epilepsy can often be treated by surgery or medication. However, the development of epilepsy and its progression often cannot be properly diagnosed Also, epileptic seizures can sometimes have adverse effect on cognition. average, the total number of newly diagnosed PD patients is 50,000 annually. At present, PD is not curable and there is no objective, quantitative diagnostic test t hat can provide clinical efficacy for new treatments. Although the number of people diagnosed with primary brain cancer is not as many as for AD and epilepsy, cancer is the second leading cause for death in children and males. It has been estimated that in 2012 there will be 64,530 new cases of brain cancer, including 24,070 malignant cases [8] Some of the more common brain tumors types are: glioblastomas, astrocytomas, oligodendrogliomas and med ulloblastomas [9] At present, treatment for primary brain cancer involves surgery, chemotherapy and/or radiation therapy. Yet t he five year survival rate for patient with glioblastoma and of age 45 50 is only 6% and that for anaplastic astrocytoma is 29% [8] 1.3 Current M ethods f or Diagnosing a nd Treating Brain Diseases /Disorders As of now, there is no quantitative and objective method to diagnose and cure dementias. Current methods of diagnosis include standard medical test s a neurological exam and brain imaging (structural or functional). The standard group of medica l tests includes a blood test for anemia and blood glucose, a thyroid exam and a liver exam and are conducted to eliminate other diseases. The standard neurological exam includes checks of reflexes, muscle strength and, eye movement and are performed to d etect the type of disorder. Imaging exams PAGE 14 14 are typically acquired using X ray, computed tomography (CT) or magnetic resonance imaging (MRI). The standard of care of treatment includes medication, chemotherapy, radiation therapy and/or surgical resection. A n improved method for diagnosing the s everity of dementias would enable improved patient specific selection of treatment procedures. The U.S. Food and Drug Administration (FDA) has currently approved a class of cholinesterase inhibitors to treat AD. This i ncludes tacrine donepezil rivastigmine and galantamine However, their common side effect s include dizziness, agitation and d elusion. Namenda regulates glutamate activity and is also prescribed for people suffering from moderate to severe AD. The treatment regimen for epilepsy depends on the severity, frequency and types of seizure. Carbatrol, zarontin, topamax are the most comm on first line of treatment for epilepsy. When seizures cannot be controlled by medication, surgery is then considered. For tumors, complete resection is, generally, used as the initial therapy. However, some forms of brain cancer are highly infiltrative an d cannot be removed completely with surgery. Radiotherapy is often used to treat the microscopic spread of the cancer around the resection cavity. Temozolomide, BCNU and cisplatin are drugs that are frequently used as complement to surgical resection and r adiotherapy. 1.4 Need f or Improvement There is an urgent need for a non invasive structural biomarker to aid in the early diagnosis of brain disease and quantify disease progression. Also, early detection of epilepsy and PD in patients could avert surgical resection, while early diagnosis of AD could change the course of treatment. Finally an improved identification of white matter PAGE 15 15 tracts could add in the tracking of the migration of tumor cells in brain [5] and thereby may improve the treatment of aggressive brain cancer. 1.5 Organization o f Report The upcoming chapters of the thesis are organized as follows: Chapter 2 introduces the idea of perpendicular fiber tracking and method that implements it using Dynamic Programming (DP). It describes Diffusion Tensor Imaging (DTI) and tractography, a non invasive technique to track nerve fibers in white matter. It dis cusses the criteria used for case selection, DTI acquisition, DTI reconstruction, tractography methods and the algorithm for DP. Chapter 3 demonstrates the accuracy of the algorithm. The p erpendicular fiber tracking method is applied to several synthetic dataset s with known fiber geometry. The changes in area and curvature of the perpendicular surfaces/sections, for the synthesized data sets, are then computed and compared with the ground truth. Chapter 4 depicts the results obtained from a real rat brain DW MRI dataset. It contain s images that show the colored fractional anisotropy (FA) map, cost surfaces at 8 10 locations in dif ferent regions of brain and plot s of changes in cross sectional area and curvature of the surfaces. Chapter 5 summarizes the thesis, specifies the scientific and clinical contribution of this work, points out some limitations of the technique. It also discusses the improvements and potential future work PAGE 16 16 C HAPTER 2 METHODS 2.1 Background The overall structural information of axonal fibers in tissue can be acquired by analyzing the primary, secondary and tertiary orientation of fiber bundles using diffusion weighted magnetic resonance imaging. The aim of this study is to trace sections that are locally perpendicular to the a xonal fibers. This is achieved by using a cost function with a geometric as well as a fiber orientation term that is evaluated dynamically over the entire image domain starting from a given seed point. As applied to patients, the method is dependent upon d iffusion tensor imaging (DTI) data sets and methods to track fiber bundles through the tissue. I will first provide background information for MR DTI and several of more common tractography algorithms, including deterministic, probabilistic and their combin ations. 2.2 Magnetic Resonance Diffusion Tensor Imaging (M R D TI ) Diffusion weighted imaging is a magnetic resonance (MR) technique that uses a set of diffusion encoding gradient s in addition to imaging gradients (Figure 2 1) to g enerate the contrast in ima ge due to differences in diffusivity of water molecule s in the tissue. The degree of diffusion weighing depends on the strength of diffusion gradient, the time duration of the gradient pulses and the time separation between them. The cumulative effect of t hese parameters is expressed using the b value (2.1) where G amplitude of the diffusion encoding gradient, duration of diffusion encoding gradient, PAGE 17 17 Gyro magnetic ratio and t ime interval between the two diffusion encoding gradients. Figure 2 1 Diffusion encoding gradients. The blocks identified as 1 and 2 represent the bipolar diffusion weighting gradient pulses applied on either side of a 180 radio frequency excitation pulse (not shown) and are separated by the time the gradient direction (not depicted) and gradient 2 rephases the spins that have not moved. Spins that move along the direction of the applied diffusion gradient accrue a net phase. The signal strength reduction in DWI is given by the following equation: (2.2) where S = signal intensity with the diffusion encoding, S 0 = signal without diffusion gradient, b = b value, D = Apparent Diffusion Coefficient (ADC). From the above equation the signal intensity is low for a high diffusion coefficient. ADC describes the average di ffusion of water molecules in the region of interest which is usually the two dimensional (2D ) pixel or three dimensional ( 3D ) voxel The ADC is sufficient to describe isotropic diffusion. To better understand the anisotropy of diffusion, Peter Basser intr oduced diffusion tensor imaging (DTI) [10] in 1994. The diffusion tensor is a symmetric matrix with 6 unique values, PAGE 18 18 (2.3) In DTI, a data set contain images obtained with different b factors and gradients applied in different directions in addition to an image with no diffusion encoding (i.e. b=0 or B0 image). As the tensor has 6 unique values, a minimum of 6 measurements with different diffusion gradient s and one without the diffusion gradient are needed. DTI is generally obtained with more than 6 measurements and is solved to calculate the 6 diffusion coefficients (D xx D xy D yy D yz D zz and D xz ). After computing the coeffi 1 2 3 and the corresponding eigenvectors. The vector corresponding to largest eigenvalue, called principal eigenvector, gives the direction of maximal diffusion called the Principal Dif fusion Direction (PDD). The relative strengths of the 3 eigenvalues are often graphically represented with a diffusion ellipsoid that describes the directionality as well as magnitude of water diffusion. After calculating the eigen system, the mean diffusi vity and Fractional Anisotropy (FA) are calculated as: where (2.4) The FA value reflects the degree of anisotropy of the diffusion environment. An isotropic diffusion gives an FA value of zero, while an infinitely strong directional dependence gives an FA of one. 2.3 Fiber T racking DTI is a well established technique used to interpret neural trajectories and to track neural pathways. The principal eigenvector is assumed to be orientated parallel to PAGE 19 19 the local fiber tract. In the simplest form, mapping the principal eigenvector direction at each voxel forms the basis for tractography the task of following a connected fiber bundle across many voxels 2.3.1 Deterministic Tractography In det erministic tractography, also called streamline tractogra p hy, there is a continuous agreement between connected points along the fiber bundle. Tracking starts at a seed point and follows a favored direction until reaches a new measurement (usually the adja cent voxel). The fiber tracking method developed by Basser et al. [11] is one of an illustrative example based on this technique. Basser et. al in [11] represented the fiber tract tractography in 3D space as a curve r (s) parameterized by arc length s The evolution of r (s) is described with a differential equation. Figure 2 2 Illustration of fiber trajectory. The tangent t (s) identifies the largest eigenvector of tensor D at r (s) (taken from [11] ). The tangent vector is equated to the principal eigenvector for a particular location in the tissue. The vectors in the above equation are computed by using PAGE 20 20 method or the Runge kutta method. The continuous representation of a tensor field is obtained by using B spline interpolation function over the 3D grid of voxel based DTI measurements. Based on the above formulation, Mori et al [12] introduced Fiber Assignment by Continuous Tracking (FACT ). In streamline tractography, F igure 2 3, tracking starts from the seed voxel and tracks to the center of the adjacent voxel in the eigenvector direction. This method restri cts the direction of the reconstructed fiber in 26 angle ranges. FACT overcomes this limitation by starting the tracing from within a seed voxel, taking sub voxel steps along the PDD until the tracing enters a neighbor voxel, and the sub voxel stepping pro cess continues along the new PDD. In comparison with the original method of Basser, the resultant fiber obtained through FACT deviates less from the underlying fiber bundle in regions of fiber cur vature, as shown in Figure 2 3. Figure 2 3 Illustration of streamline and Fiber Assignment by Continuous Tracking (FACT) method of tractography. The principal eigenvector in each voxel, assumed for illustration purposes to lie within a two dimensional plane, is represented by an arrow. The seed vox el is indicated by the asterix in the diagram. In the diagram on the left, the fiber is traced by connecting the center of each voxel towards the direction of eigenvector. While in the diagram on right, tracking starts from the seed voxel, follows the PDD inside PAGE 21 21 the voxel using sub voxel steps and continues along the PDD of each traced voxel (taken from [12] ). The computational cost of deterministic tractography is low and output tracts are easy to interpret. However, as calc ulations are made on local scale, error is accumulated along the tracts as one traces farther from the seed location. 2.3.2 Probabilistic Tractography In reality, the voxel size of a patient MRI scan is larger than an actual axon and also not every point i n brain has only one connection, but can have many. In probabilistic tractography, fiber tracts are computed by drawing a propagation from an underlying model of the distribution fiber orientations, rather than relying directly on the PDDs. The fiber track ing is done repeatedly, thousands of times, each time in a slightly different direction. The set of all the different paths are then collectively analyzed to compute the most highly probable direction. The method gives a more detailed picture of fiber con nectivity in brain and is more robust in complex intra voxel fiber configuration s However, this approach is computationally costly and the outcome connectivity maps are more difficult to interpret. Figure 2 4. Connectivity distribution with seed point in posterior limb (taken from [13] ). PAGE 22 22 2.3. 3 Combination of Deterministic a nd Probabilistic Tractography To combine the advantages of both approaches, methods to track short fiber tract clusters have been proposed. In [14] a method labeled Split and Me rge Tractography (SMT) tracks all of the fiber tracts inside an investigated area while minimizing the total energy. Although using short fiber tracts minimize s the error described for the determin istic approaches, the computational cost is still high. More recently, global energy minimization s based short track fiber clustering algorithms have been proposed [15] [16] [17] In these works, short fiber tracts are randomly generated and are allowed to move, rotate and assemble with other fibers to minimize internal and external energies. Figure 2 5. Illustration of Split and Merge Tractography (SMT). [ A ] Two short fibers S i and S j connected by bridge c that has been selected by Gaussian distribution D i [B] Shown are s hort tract clusters for a seed tract starting from the upper brain stem(taken from [14] ). 2.4 Method 2.4.1 DTI Reconstruction After obtaining the MR DTI data sets, calculations of the diffusion tensor, eigenvectors and FA values for each voxel were done in MATLAB version 2009b. The diffusio n data was reconstructed using the fanDTasia toolbox developed by Barmpoutis PAGE 23 23 et al. at the University of Florida Tutorial on Diffusion Tensor MRI using M ATLAB For each voxel, the principal diffusion direction (PDD) was determined by visualizing the di ffusion directions using the plot3 command in MATLAB. The color coded FA map was generated using the imshow () command in MATLAB. 2.4.2 Perpendicular Fiber Tracking Method Implementation The perpendicular fiber tracking algorithm was implemented in MATLAB o n a M 350 @ 2.27 Ghz, 4 GB RAM 2.4.3 Fiber Bundle Estimation The process of extracting parameters from a fiber bundle involves perpendicular fiber tracking and implements it using dynamic programming. Perpendicular fiber tracking reconstructs a perpendicular surface along the fiber bundle. The statistical variation in the cross sectional area and geometric curvature of the reconstructed surface are then analyzed. The metho d can be summarized in 4 main steps which were as follows: A fiber is traced along a given seed point. Any deterministic fiber tracking method can be used. The fiber is segmented in N equal length segments. (N should be an integer) For each segment, a surface is reconstructed, that is perpendicular to the fiber bundle. The section is constructed using a 3D cost map that is generated by dynamic programming. For every perpendicular section, properties such as curvature and the area of the surface are comp uted. PAGE 24 24 Figure 2 6 Illustration of steps perpendicular fiber tracking. [A] Shown is a fiber traced along seed point, [B] 6 equal length segments along the individual fiber [C] reconstruct ed cost surface for all segments, [D] area and curvature interpre tation for one of the surface s and, [E] and [F] statistics showing variation in area and curvature respectively. 2.4.4 Perpendicular F iber T racking The goal is to reconstructs a 3D surface perpendicular to local fibers within the fiber bundle. Th e recons tructed surfaces consist of points whose normal vectors are parallel to the principal direction of diffusion of water inside the local fiber. The surface PAGE 25 25 constructi on is achieved using a 3D cost map, generated by dynamic programming, that is driven by a co st fun ction of two factors (1) fiber cost and (2) geometric c ost. The 3D cost map maps the total cost of each point in the reconstructed surface. Here, the optimality of the cost map is defined by the minimum total cost for a point from a starting point. The fiber cost ensures that the section is perpendicular to the dominant local fiber orientation at every point on the surface, while the geometric cost enforces a smoothness and connectivity constraint. Table 2 1 List the factors and their formulation Factors Formulation Fiber cost f Geometric cost g 2.4.4.1 Geometric cost The geometric cost ensures the connectivity and smoothness of the perpendicular surface by measuring the parallelism between the vectors of two adjacent voxels. In this work these vectors refer to the primary eigenvector s and were calculated from the diffusion tensor. The degree of parallelism between two vectors is measured by taking the ir vector dot product. The geometric cost at a point is given by: (2.5) where, g geometric cost, s principal eigenvector of seed point and r principal eigenvector of neighborhood point For the case shown in Figure 2 7 where two fibers are parallel, when calculating the geometric cost, all 26 neighboring voxels are considered except the vectors (black) in the voxels just above and below the seed voxel (red vector) that belong to same fiber, 1 So to consider those vectors (colored black) for cost surf ace reconstruction is not PAGE 26 26 correct, as the reconstructed section will not be perpendicular to fiber 1 but would reconstruct along the same fiber 1. Figure 2 7 Geometric cost. S how n are two parallel fibers 1 and 2. In fiber 1, the seed s is colored red and for fiber 2 is colored blue The voxel r for which the cost value is to be calculated is dark blue. 2.4.4.2 Fiber cost The fiber cost ensures that the surface is constructed perpendicular to the fiber bundle. It measures the perpendicularity between the eigenvector of a neighborhood voxel and unit vector connecting neighborhood voxel to the seed voxel. A less value of dot product of two vectors indicates more perpendicular ity between those two vectors. Figure 2 8 Fiber cost. S how n are vector is colored red and for fiber 2 is colored blue. The voxel with unit vector ch cost value is to be calculated is dark blue. The unit vector v colored green, connects the seed voxel to the neighboring vector PAGE 27 27 The fiber cost is defined as: (2.6) where, f fiber cost, v unit vector connecting from seed voxel to neighborhood voxel and r eigenvector of neighborhood voxel For the same a bove case now shown in Figure 2 8, when considering the 26 neighboring voxels to calculate cost function, the voxel vectors (colored black) just above and below the seed voxel will not be considered, as they belong to same fiber 1. Thus, the surface is constructed perpendicular to local fi bers. 2.4.4.3 Total cost function The total cost function ensures that both the cost functions, fiber and geometric, condition are fulfilled simultaneously. Since both cost s should be considered at the same time and a minimum total cost is desired, the geo metric cost is subtracted by 1 and is then multiplied by the fiber cost (2.7) 2.4.4.4 Thresholds Calculating the cost for each voxel can require a long execution time. To speed up the analysi s, as exclusion cost threshold were predefined for the fiber, geometric and total cost to exclude from future analysis voxels that have a cost value greater than the thresholds. Thus the reconstructed surfaces will only encompass voxels through which the f iber bundle is passing. PAGE 28 28 2.4. 5 Construction of 3D Cost Maps T hrough Dynamic Programming The dynamic programming (DP) step was formulated as a graph search for a minimum cost map. The 3D surface reconstruction of the perpendicular section uses a graph search similar to that in [18 ] but applied in three dimensions. Figure 2 9 demonstrates the fiber section algorithm realized through DP for a single slice of a 3D image, with the goal to reconstruct a perpendicular section of minimum total cost value. Here we have used a 2D e xample for a better underst anding of the method. Figur e 2 9 (a) is the initial local cost map with the seed point circled in red (Inf represents a very large number such as 100000 that is used to indicate that a cost has yet to be calculated). In figure 2 9 (b) the area around the seed point i s expanded (circle d grey), showing a portion of the map and cost of pixels where the local total costs are updated for some of the pixels while unchanged for rest of the pixels. The pixels that have higher cost value than the threshold s are not updated. However, the total c ost for the pixel can change later, in the algorith m. This can be seen in figure 2 9 (c) where the local costs for two points are updated fro m Inf to 0.8 and 0.9. Figure 2 9(d) and 2 9 (e) shows the map at variou s stage of completion. Figure 2 9 (f) depicts t he final 2D section reconstructed from the seed point. The surface includes pixels that have a total cost less than the cost threshold, that is here to 1.6. The same methodology is applied on 3D images and yields a 3D cost map. PAGE 29 29 Figure 2 9 D epiction of t he dynamic p rogramming approach (a) Shown is a map of the initial local total cost f or each point on the graph and where the seed point has an initial value zero (b) The region around the s eed point (circled gray) is expanded. (c) The region around the f irst 2 points (circled gray) is expanded. (d) The region around the first 3 points (circled gray) is expanded. (e) Shown is the final local cost matrix after computing local total cost for each point. ( f) Shown is the f inal reconstructed cost matrix, expanded around the se lected points {total cost threshold is 1.6} PAGE 30 30 2.4.6 Algorithm: Pseudocode for 3 D DP for Perpendicular Fiber Tracking Input: s {start voxel} g th f th T th { threshold s } {eigenvectors list} Data Structure: L {List of active voxel s sorted initially empty} N {Neighborhood set of active voxels (contains 26 neighbors of each voxel)} Ouput: C {Matrix of t o tal cost value for every voxel } Algorithm: {Set seed point cost value to 0 and initialize the active list with seed voxel} While do begin { If the list is not empty } p; {Find out the location of minimum cost and remove it } for each f= {Compute fiber cost for each neighborhood voxel } g {Compute geometric cost} if g PAGE 31 31 CHAPTER 3 TOWARDS VERIFICATION OF PERPENDICULAR FIB ER TRACKING 3.1 Validation on Synthetic Datasets The main objective of this thesis work is to study the differences in the structure of fiber bundles between normal and disease brains. The algorithm computes the area and curvature of each fiber bundle from the reconstructed 3D section, perpendicular to t he local dominant fiber orientation. To the best of our knowledge there is no prior literature on perpendicular fiber tracking and thus this approach requires a thorough validation. As the exact geometry of real brain datasets are not known, synthetic dat asets of different structure with known fiber geometry were used to test the accuracy of the algorithm. 3.2 Generation of S ynthetic D ataset Dr. Barmpoutis helped in synthesizing the DW MRI datasets using his free, open source Tutorial ( http://www.cise.ufl.edu/~abarmpou/lab/fanDTasia/tutorial.php utorial on Diffusion Tensor MR I using M ATLAB The datasets simulated fiber bundles with a variety of different fiber struct ures such as splaying, crossing and furcating. The simulation output is a series of simulated MR i mages representing a typical DW MRI exam but where the fiber orientation is specified a priori at each voxel and dictates the output DW images. 3.3 Implementation The generation of synthetic data was implemented using MATLAB software version 2009b. The dataset s were generated of different matrix sizes. It took 30 50 seconds to generate a typical data set on a Microsoft Windows 7 based laptop with the following specifica 50 @ 2.27 Ghz, 4 GB RAM PAGE 32 32 3.4 Specifications All of the datasets that were created consisted of a series of 22 images, representing different b values and gradient orientations. The first image corresponded to a low diffusion weighting (S0) and the remaining 21 images had a b value of 1500s/mm 2 and a unique gradient direction. 3.5 Data S et 1: Inclined F ibers The first DW MRI dataset was created by simulating a single fiber bundle with straight fibers inclined at 45 angle fro m x axis. The matrix size of this dataset was 212110. As the fibers were straight and linear, the ground truth curvature of the dataset was zero and area was constant throughout the fiber bundle T his is reflect ed in Figure 3 1 which shows that the curva ture of all the segmented points is zero while the area of the cost surface remains constant for the segmented points, which agrees with the ground truth. PAGE 33 33 A B PAGE 34 34 Figure 3 1 Results from synthetic dataset#1: inclined straight fibers. The plot on the top [A] demonstrate s the ellipsoidal representation of eigenvector s at each voxel for synthetic dataset#1. [B] The cost surface is depi cted at 5 different locations along the fibe r bundle and a n individual fiber is traced from a seed point (marked in red). The number of fibers remains constant and straight along the length of the bundle from the seed point (red) to the end point (blue). [C] The change in the cross sectional area de termined from the algorithm is plotted using red blue color graded curve. The red to blue gradation indicates the distance along the fiber segment, increasing from seed location to the end location. The plot remains constant as the number of fibers remains constant. [D] The plot of curvature remains zero throughout because the fibers were all parallel and bundle was straight. 3.6 Data Set 2: Conical Bundle w ith Parallel F ibers The second DW MRI dataset was created by simulating a single fiber bundle with straight fibers, and a linearly increasing cross sectional area. The matrix size of the dataset was 60*60*60. As the fibers were all straight, the ground truth curvature of the perpendicular section was zero throughout the bundle. Figure 3 1 demonstrates the accuracy of the algorithm. The area of the surface s increases linearly along the fiber which agrees with the ground truth and the curvature of the surface is zero, which also agrees with the ground truth. C D Ground Truth = 9.732 Ground Truth = 0 degree PAGE 35 35 Figure 3 2 Results from synthetic dataset#2: conical bundle with parallel fibers [A] The cost surface is depicted at 9 different segment locations along the length of the bundle ( al though there are really 18 sections). The number of fibers and the corresponding bundle cross sectional area, increase linearly along the bundle from the seed point (marker red) to end point (marked blue). The number of fibers increases linearly and so the section width also increases. [B] Th e change in area is plotted using red blue gradation scale. The ground truth is indicated by the matches it well. The plot decreases after 16th location because the dataset reached to t he edge of the imaging matrix and is a result of artifact at the PAGE 36 36 edges [C] The plot of the curvature remains zero throughout because fibers were all parallel and bundle was straight. 3.7 Data Set 3: Linear a nd C urvi ng F ibers The third dataset was synthesized by simulating 2 f iber bundles, one with straight fibers oriented along the z axis (out of the plane of the paper ) inside a cylinder and the second bundle with circ ularly oriented fibers outside the cylinder and with the number of fibers increasing with radius (Figure 3 3). The dataset created was of matrix size 211510. As the fibers, inside the cylinder were all straight and linear (along z axis), the cross sectional area and curvature remain ed constant and zero along the segmented location of the fiber bundle. While fibe rs outside the cylinder area increase d in numbers with radius, t he cross sectional area and the curvature of the bundle increase d as we move away from the center Figure 3 3 Ellipsoidal representation of eigenvectors for dataset#3. A PAGE 37 37 Figure 3 4 Results from synthetic dataset#3: linear and curving fibers. [A] The circular cost surface is depicted at 4 different segment locations along the length of the bundle (inside the cylindrical region). The number of fibers, and the corresponding bundle cros s sectional area, remains constant along the bundle from the seed point (marker red) to end point (marked blue). [B] The change in area is plotted using the red blue gradation scale. The cross sectional area remains constant along the bundle as all fiber w ere parallel and straight inside the bundle. [C] The plot of the curvature remains zero throughout because fibers were all parallel and bundle was straight. A B C Ground Truth=12.1244 Ground Truth= 0 degree PAGE 38 38 Figure 3 5 Results from synthetic dataset#3: linear and curving fibers. [A] The cost surface is depicted at 5 different segment locations along the length of the bundle (outside the cylindric al region). The number of fibers and the corresponding bundle cross section al area increases along the bundle from mid point (marked brown) to the seed point (marked red) and end point (marked blue). [B] The change in area is plotted using the red blue gradation scale. The cross sectional area increases no n linearly along the bun dle as the number of fibers increases at extremes (start and end point). [C] The plot of the curvature also increases from the mid point to the start and end point s because the fibers are parallel in the middle region and are curving more along the corners A B C PAGE 39 39 3.8 Data Set 4: Fibers B ranching The fourth synthetic dataset was synthesized by simulating a fiber bundle with splaying fibers in a 2D plane, and then extruding this geometry upwards through the entire image stack. The data set was of in plane matrix size 2114 and with 10 extruded slic es. The fibers were constructed as two cylinders, each with inner radius of 9 pixels and outer radius 13 pixels. Since the centers for the cylinders we re (0,0) and (22,0), they share d a common region initially which spli t as you move upwards along the fiber s (Figure 3 6 ). Figure 3 6 Ellipsoidal representation for eigenvectors of fibers branching in synthetic datasets#4. The bubbles get wider approaching t he bifurcation as the FA value decreases due to the two different pathways. The fiber bundle area and curvature increases until the branching, and decreases after the branching because the fibers initially, at bottom, starts splaying in both the directions and the cost surface tends to include all. The curvatu re again decreases after branching, as fibers get aligned horizontally while the area rema ins constant after branching. Each segmented locations ar e marked in white circle s A PAGE 40 40 Figure 3 7 Results from synthetic dataset#4: branching fibers. [A] The cost surface is depicted at 3 different locations along the length of t he bundle. The number of fibers and the corresponding bundle cross sectional area, decreases, suddenly, after the branching and remains constant afterwards. [B] The change in area is plotted using the red blue gradation scale. The cross sectional area, first decreases along the bundle as the number of fibers suddenly decreases after the branching and remains constant afterward s. [C] The plot of the curvature also decreases suddenly after branching, because the fibers are parallel in the middle region and are curving more along the corners. B C A PAGE 41 41 CHAPTER 4 RESULTS 4.1 Application on Real Datasets After validating the algorithm on synthetic data, we then applied it on a real rat brain datasets to examine its clinical viability. Cost surfaces/sections were reconstructed at 8 and10 different locations in two different regions (stratum lacunosum molecu lare and stratum oriens) of the rat hippocampus. 4.2 Implementation The results for the rat brain datasets were obtained using MATLAB version 2009b. The experiments are performed on a Microsoft Windows 7 based laptop with the following specification: Intel CPU M 350 @ 2.27 Ghz, 4 GB RAM With these specifications, it took < 2 second s to generate the cost surfaces and plots of area and curvature for a typical bundle. 4.3 Pre processing All images were first filtered using a moving average operato r. The filtering operation was performed for a single slice at a time and using a 33 averaging kernel. Additional n oise elimination wa s done with the help of the surf command in MATLAB. Command surf creates a 3D shaded surface, where the color is proporti onal to the height. The height of the 3D surface, here, corresponds to the strength of DWI image signal at each pixel at that particular slice The un wanted signal, the noise, outside the brain region can be easily detected by observing the plot and then t he undesirable noise can be cut off by using surf (S(:,:,m,:),t). Here, S is signal obtain ed from the data set, of size 4D matrix, m is the slice number and t is the threshold by which the signal is cut off. Figure 4 1 shows the use of the above command wit h S of PAGE 42 42 matrix size 90905624 (see 4.4.1 for details), where there are 60 slices of size 9490 pixels taken in 24 gradient directions, m is taken as 28 and t=8, which means the base line is shifted to 8 (Figure 4 1B). Now for calculating the DTI coefficie nt s we consider only those signals that have intensity greater than 8 The procedure not only eliminates the noise but also reduces the time to calculate DTI (From eq. 2.2). Figure 4 1 demonstrate s th is use of surf Figure 4 1 Surf plots of a rat brain DWI dataset. The p lot on the left shows the signal intensity before setting threshold, the disturbances around t he image signal can be seen. The plot on the right shows signal intensity after setting threshold level to 8, almost all noise i n the signal are removed. noise PAGE 43 43 4.4 Rat Hippocampus Figure 4 2 Shown is the FA map of the 28th slice out of 56 slices of a representative rat dataset. Shown is s sagittal view through the hippocampus. 4.4.1 Data A cquisition The acquisition pro tocol included 56 images using a pulsed gradient spin echo pulse sequence with repetition time (TR) =1.5s, echo time (TE) =28.3 ms, bandwidth =35 kHz, field of view ( FOV ) =4.5 x 4.5 mm, imaging matrix =90 x 90 with 20 30 continuous 200 micron axial slices. After the fi rst image set was collected with no diffusion weighting (b~0 s/mm), 21 diffusion weighted image sets with gradient strength (G) = 415 mT/m, gradient duration delta = 2. 4 ms, gradient separation Delta =17.8 ms, and diffusion time T delta (T ) = 17 ms were collected. The reader is referred to Figure 2.1 for a schematic of these parameters. These parameters create a b value of approximately 1250s/mm 2 Each of these image sets used a different diffusion gradient direction whose orientations were de termined from the second order PAGE 44 44 tessellation of an icosahedron projected onto the surface of a unit hemisphere. The image without diffusion weighting had 36 signal averages (time =81 min), and each diffusion weighted image had 12 averages (time = 27 min per diffusion gradient orientation) to give a total imaging time of 10.8 h ours per hippocampus. The t emperature was maintained at 20 0.2C throughout the experiments using the temperature control unit of magnet previously calibrated by methanol spectroscopy [ 19 ] 4.4.2 Fiber Bundle Analysis Using Perpendicular Fiber T racking The algorithm was performed at two regions on th e rat hippocampus dataset. The first one was at the stratum lacunosum moleculare (Figure 4 3 A) and the second one at the stratum oriens (Figure 4 4 A). In each run, a primary fiber was defined as starting from a manually selected seed point and traced throu gh the brain using deterministic tractography and 8 10 cost surfaces were constructed along the length of the primary fiber. All of the fibers passing along the cost surfaces were trace d to ensure that the surfaces did not include the fibers outside the b undle region. The output, fiber sections/surfaces, plot of area of each surface and curvature of each surface, obtained from the algorit hm are demonstrated in Figure 4 3. PAGE 45 45 B C A PAGE 46 46 Figure 4 3 Results obtained from analysis of the rat hippocampus with seed point in the stratum lacunosum moleculare: [A] Shown is the colored FA map where the green red and blue color indicate the direction of the underlying fibers being the horizontal, vertical o r perpendicular (out of plane) respectively. The approximate location of the seed point within the stratum lacunosum moleculare is indicated by the yellow arrow. [B] The primary fiber was traced from the seed point (marked in red) and cost surfaces were co mputed at 8 different locations along the length of the primary fiber, from the seed point to the end point (blue). [C] The whole fiber bundle is depicted. [D] and [E] The change in the cross sectional area and curvature determined from the algorithm is pl otted using the red blue color graded curve. The red to blue gradation indicates the distance along the fiber from the seed location to the end location. D E A PAGE 47 47 Figure 4 4 Results obtained from analysis of the rat hippocampus with seed point in the stratum oriens: [A] Shown is the colored FA map where the green red and blue color indicate the direction of the underlying fibers being the horizontal, vertical or perpendicula r (out of plane), respectively. The approximate location of the seed point within the stratum oriens is indicated by the yellow arrow. [B] The primary fiber was traced from the seed point (marked in red) and cost surfaces were at 10 different locations alo ng the length of the primary fiber, from the seed point to the end point (blue). [C] The whole fiber bundle is depicted. [D] and [E] The change in the cross sectional area and curvature determined from the algorithm is plotted using red blue color graded c urve. The red to blue gradation indicates the distance along the fiber from the seed location to the end location. 4.4.3 Discussions To help verify that the reconstructed bundle contained all possible fibers in the hippocampus region of interest, a zero ei genvector value was assigned to all the voxels B C D E PAGE 48 48 that had been covered while tracing the fiber bundle. The zero valued eige nvectors appears as a black pixel (dot) in the colored FA plot. Figure 4 5 Visual depiction of the extent of the reconstructed fiber bundle in the stratum lacunosum moleculare: the colored FA map is depicted with eigenvector value [0 0 0] for all the voxels covered in the fiber bundle. The region in black depicts appr oximately the bundle traced by the perpend icular fiber tracking method. Figure 4 6 Visual depiction of the extent of the reconstructed fiber bundle in the Stratum oriens: the colored FA map is depicted with eigenvector value [0 0 0] for all the voxels covered in fiber bundle. The region in blac k depicts appr oximately the bundle traced by the perpendicular fiber tracking method. PAGE 49 49 From t he above observation (Figure 4 5 and Figure 4 6 ) the calculated area and curvature used to construct the fiber bundle approximately fits the two regions, stratum la cunosum moleculare and stratum oriens, of the rat hippocampus PAGE 50 50 4.5 Control and Disease ( E pilepsy) Rat B rain Figure 4 7 [A] Shown is the colored FA map of control rat brain dataset and [B] colored FA map of disease (epilepsy) rat brain where the green red and blue color indicate the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. PAGE 51 51 4.5.1 Data A cquisition T he acquisition protocol [ 20 ] included 63 images collected with TR = 1 5 00 ms, TE = 30 ms, Twelve contiguous slices of 0.9 mm thickness were imaged with a FOV of 30 mm 30 mm and imaging matrix size of 100 100 Low diffusion weighted image data sets ( b value of 100 s/mm 2 ) were acqu ired in 6 directions and high diffusion weighted image data sets ( b value of 800 s/mm 2 ) were acquired in 21 directions, determined from the level 1 triangular subdivision of an icosahedron tessellated onto the surface of a unit hemisphere. 4.5.2 Fiber Bundle Analysis of C o ntrol and Disease Rat B rain The algorithm was performed at 12 differe nt points on the two rat brain dataset s In each run, a seed point (manually selected) wa s placed on a healthy rat brain (37 th slice) and epilepsy rat brain (38 th slice) and a primary fiber was traced from seed point using deterministic tractography, and 4 cost surfaces were constructed along the length of the primary fiber (not shown) The average of all 4 cost surface cross sectional area s were taken at 5 different cost thresholds (0.4, 0.5, 0.6, 0.7, 0.8). All of the fibers passing along the cost surface s were trace d to ensure that the surfaces did not include the fibers outside the bundle region (not shown). The output, plot s of area at each threshold, for control as well as disease brain were obtained from the algorithm and are demonstrated in the follo wing figures PAGE 52 52 Figure 4 8 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain respectively where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from the alg orithm is plotted. PAGE 53 53 Figure 4 9 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the green red and blue color indicat e s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 54 54 Figure 4 10 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the green red and blue color ind icate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from t he algorithm is plotted. PAGE 55 55 Figure 4 11 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color ) determined from the algorithm is plotted. PAGE 56 56 Figure 4 12 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red co lor) determined from the algorithm is plotted. PAGE 57 57 Figure 4 13 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the gree n red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 58 58 Figure 4 14 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 59 59 Figure 4 15 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where t he green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilep sy (red color) determined from the algorithm is plotted. PAGE 60 60 Figure 4 16 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, wher e the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 61 61 Figure 4 17 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control a nd epileptic rat brain, respectively, where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost thresho ld in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 62 62 Figure 4 18 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of contro l and epileptic rat brain, respectively, where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost thre shold in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 63 63 Figure 4 19 Results obtained from analysis of the rat brain with seed point shown with black marker : [A] and [B] Shown is the colored FA map of control and epileptic rat brain, respectively, where the green red and blue color indicate s the direction of the underlying fibers being the horizontal, vertical or perpendicular respectively. [ C ] The change in the cross sectional area for 5 different cost threshold in a healthy brain (blue color) and epilepsy (red color) determined from the algorithm is plotted. PAGE 64 64 4.5.3 Discussion After running algorithm at all of the above mentioned points, we observe difference in the fiber bundle area between healthy and epileptic rats in the marked (circled white) regions, shown in Figure 4 20. Figure 4 20 Depicts the colored FA diagram of hea l thy rat brain where the green, red and blue color indicates the direction of fib er in horizontal, vertical or perpendicular respectively. The white ellipse s indicate region s where difference s in the fiber bundle area between healthy and epileptic rats w ere observed. PAGE 65 65 CHAPTER 5 CONCLUSIONS AND FUTU RE WORK 5.1 Conclusions In conclusion, the results of my experiments obtained from real DTI datasets of rat hippocampus, diseased (epilepsy) and control (healthy) brain demonstrate the use of method. Furthermore, verification of the algorithm on synthetic datasets, including line arly increasing fibers along a fiber bundle branching fibers and crossing fibers, demonstrate the accuracy of our technique. The algorithm produces interactively comprehensive statis tics on area and curvature along fiber bundle s with potential for near re al time clinical use. The algorithm is successful in tracking fiber s in direction s other than theprincipal direction of diffusion and provides new information on l ocal patterns of diffusion. The technique can be used as a tool for fiber bundle segmentation for neural fiber analysis, and potentially as a biomarker for various brain disease that involve some kind of change in white matter, including A D isease P D isease epilepsy, autism and other dementias. 5.2 Limitations A MR DTI data and the many limitations associated with MR DTI. F irst, MR DTI is incapab le o f differentiat ing efferent nerves, anterograde and retrograde pathways, inhibitory and excitatory conn ections as well as direct indirect route s in data. Second, the regions of fiber crossing, sma ller pathways and fibers interrupted by synapses may not be detected with DTI. Last long and complex nerve fiber pathway s are less likely to be traced. PAGE 66 66 Another po tential problem i s the need to optimize the cost threshold for different cases F or example, the image quality and resolution of MR data sets can differ the number of receive coils, and a different optimal threshold may be need ed for each case.Although in most practical cases the error due to small deviation from the optimal threshold is not dramatic, a different cost threshold was used for each of the animal and synthe tic data set s is presented here. Thus future work should be directed towards overcoming the above limitations to derive more accurate and reproducible results and interpretations. 5.3 Future Work 5.3.1 Impr ovement of Perpendicular Fiber Tracking M etho d The errors evident in the analysis of the synthetic crossing fiber data set may be overcome with improved MR DTI acquisition and reconstruction. High angular resolution diffusion imaging (HARDI) has been demonstrated to permit the identification of multi ple crossing fibers within the same voxel. Perpendicular fiber tracking based on HARDI is expected to allow us to compute the fiber metrics for region s of fiber crossing. HARDI data may also enable improved the analysis of small pathways and long tortuous pathways. Future work should be directed towards implementing a global cost threshold that can be run effectively on various data sets. One possible approach would be to employ self learning (machine learning) feature in the algorithm 5.3.2 Application on Real D atasets Since the algorithm was successfully validated on dif ferent synthetic data sets and wa s also applied to real brain data set s, t he method can be applied to some diseased PAGE 67 67 brains (A D isease epilepsy, P D isease cancer) da ta sets to diagnose changes in the fiber geometry. PAGE 68 68 LIST OF REFERENCES [1] Diffusion Tensor Imaging in Epilepsy Curr vol. 8, no. 4, pp. 85 89, Jul. 2008. [2] M. S. Buchsbaum, J. Friedman, B. R. Buchsbaum, K. W. Chu, E. A. Hazlett, R. Newmark, J. S. Schneiderman, Y. Torosjan, C. Tang, P. R. Hof, D. Stewart, K. L. Biol. Psychiatry vol. 60, no. 11, pp. 1181 1187, Dec. 2006. [3] Ne uropsychiatr Dis Treat vol. 4, no. 4, pp. 737 742, Aug. 2008. [4] L. L. Chan, H. Rumpel, K. Yap, E. Lee, H. V. Loo, G. L. Ho, S. Fook Chong, Y. Yuen, and E. J. Neurol. Neur osurg. Psychiatr. vol. 78, no. 12, pp. 1383 1386, Dec. 2007. 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Mareci, the onset of spontaneous seizures in an animal model of chronic limbic epilepsy, Experimental Neurology vol. 224, no. 1, pp. 258 270, Jul. 2010. PAGE 70 70 BIOGRAPHICAL SKETCH Siddharth Ray received his Bachelor of Engineering in Biomedical from Shri Govindram Sekseriya Institute of Technology and Science (SG S ITS) in 2006. He began gradu ate studies at the University of Florida in 2011. He pursued his research in the area of understanding the nerve fiber bundle using Magnetic Resonance Diffusion since March 20 11. 