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Development of Diffusion Tensor Imaging Based-Computational Models of Direct Infusion into the Central Nervous System

Permanent Link: http://ufdc.ufl.edu/UFE0042413/00001

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Title: Development of Diffusion Tensor Imaging Based-Computational Models of Direct Infusion into the Central Nervous System
Physical Description: 1 online resource (140 p.)
Language: english
Creator: Kim, Jung
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: ced, cfd, dce, dti, intraparenchymal, modeling
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Despite the high therapeutic potential of many macromolecular drugs, delivery of these agents to targeted tissues for treatment of cancer and other degenerative diseases of the central nervous system remains challenging. One barrier to the systemic administration of macromolecules is low capillary permeability. Convection enhanced delivery (CED) is a promising local delivery technique for overcoming this barrier and treating diseases of the central nervous system. A new 3D interstitial transport modeling approach in which tissue properties and anatomical boundaries were assigned on a voxel-by-voxel basis using tissue alignment data from diffusion tensor imaging (DTI) is presented. The modeling approach is semi-automatic and utilizes porous media transport theory to estimate interstitial transport in isotropic and anisotropic tissue regions. Rat spinal cord DTI data sets were employed to develop the models, which provide predicted distributions of albumin tracer following infusion into anisotropic regions of the dorsal horn. The voxelized modeling methodology was adopted for CED into the rat brain. Surgical procedures and MR imaging protocols were developed to visualize in vivo heterogeneous and complicated distribution patterns during infusions in the hippocampus of the brain. Qualitative comparisons between predicted and measured distribution patterns, volumes and shapes demonstrated the model?s proficiency. The developed 3D porous media transport models for CED in the brain may be useful tools for surgical planning and may lead to improve treatment of neurological brain diseases by maximizing drug delivery to targeted regions and minimizing systemic and neurologic toxicities.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jung Kim.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Sarntinoranont, Malisa.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042413:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042413/00001

Material Information

Title: Development of Diffusion Tensor Imaging Based-Computational Models of Direct Infusion into the Central Nervous System
Physical Description: 1 online resource (140 p.)
Language: english
Creator: Kim, Jung
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: ced, cfd, dce, dti, intraparenchymal, modeling
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Despite the high therapeutic potential of many macromolecular drugs, delivery of these agents to targeted tissues for treatment of cancer and other degenerative diseases of the central nervous system remains challenging. One barrier to the systemic administration of macromolecules is low capillary permeability. Convection enhanced delivery (CED) is a promising local delivery technique for overcoming this barrier and treating diseases of the central nervous system. A new 3D interstitial transport modeling approach in which tissue properties and anatomical boundaries were assigned on a voxel-by-voxel basis using tissue alignment data from diffusion tensor imaging (DTI) is presented. The modeling approach is semi-automatic and utilizes porous media transport theory to estimate interstitial transport in isotropic and anisotropic tissue regions. Rat spinal cord DTI data sets were employed to develop the models, which provide predicted distributions of albumin tracer following infusion into anisotropic regions of the dorsal horn. The voxelized modeling methodology was adopted for CED into the rat brain. Surgical procedures and MR imaging protocols were developed to visualize in vivo heterogeneous and complicated distribution patterns during infusions in the hippocampus of the brain. Qualitative comparisons between predicted and measured distribution patterns, volumes and shapes demonstrated the model?s proficiency. The developed 3D porous media transport models for CED in the brain may be useful tools for surgical planning and may lead to improve treatment of neurological brain diseases by maximizing drug delivery to targeted regions and minimizing systemic and neurologic toxicities.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jung Kim.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Sarntinoranont, Malisa.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042413:00001


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1 DEVELOPMENT OF DIFFUSION TENSOR IMAGING BASEDCOMPUTATIONAL MODELS OF DIRECT INFUSION INTO THE CENTRAL NERVOUS SYSTEM By JUNG HWAN KIM A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Jung Hwan Kim

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3 To my parents, my wife and my son

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4 ACKNOWLEDGMENTS It would like to acknowledge the many people who made this dissertation possible. I am grateful to my supervisor, Dr. Malisa Sarntinoranont. She has provided encouragement, good teaching, and a lot of good ideas throughout my dissertationwriting period. I thank members of my committee Dr. Roger TranSon T ay, Dr. David W. Hahn and Dr. Thomas H. Mareci for thoughtful advice and mentoring. Especially it is a pleasure to mention Dr. Thomas Mareci who has provided great comments and insightful thought. He also gave me important guidance during my first steps into MR imaging studies. I would like to thank Dr. Paul Carney (Department of Pediatrics, Division of Pediatric Neurology, UF) who provided surgical suite for in vivo experiments. I would like to express my gratitude for my lab members: Garrett Astary, Tatiana Nobrega, Sung Jin Lee, and Greg Pishko, and, who provided encouragement, lots of great ideas. I would have been lost without them. I also thank Dr. Robert Yezierski, Sarah Berens and Mansi Parekh (Department of Neuroscience, UF ) who provided the fixed, excised the rat spinal cord and brain sample s. I would like to show appreciation to Svetlana Kantorovich, Mansi Parekh and Rabia Zafar (Department of Neuroscience, UF ) to teach me how to do the rat brain surgery. T hey also provide very useful advi ces about neuroanatomy. I owe my loving thanks to my parents, Choong Bong Kim, Kyung Hae Choi. It would have been impossible for me to finish this work with out their endless and priceless support. Lastly, and most importantly, I owe my deepest gratitude to my wife Gil Sun Jung and my son Peter Sangmin Kim. Their support and encouragement was in the end what made this dissertation possible.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................8 LIST OF FIGURES .........................................................................................................................9 LIST OF ABBREVIATIONS ........................................................................................................13 ABSTRACT ...................................................................................................................................14 INTRODUCTION .........................................................................................................................16 1.1 Mot ivation .........................................................................................................................16 1.2 Specific A ims ....................................................................................................................18 1.2.1 Specific Aim 1: Develop V oxelized M odel ing M ethodology for M acromolecular I nterstitial T ransport in the R at S pinal C ord U sing D iffusion T ensor I maging. ................................................................................19 1.2.2 Specific Aim 2: Develop Voxelized 3D C omputational T ransport M odel of CED into the R at B rain and Conduct P aramet er A nalysis ................................19 1.2.3 Specific Aim 3: Measur e I n V ivo T racer Di stributions during CED in the R at B rain ...........................................................................................................20 1.2.4 Specific Aim 4: Compare Predicted and Measured Infusate Distribution for CED in the Rat Brain ........................................................................................20 BACKGROUND AND PREVI OUS STUDIES ............................................................................21 2.1 Drug D elivery M et hods in the C entral N ervous S ystem ..................................................21 2.2 Convection E nhanced D elivery in the C entral N ervous S ystem ......................................22 2.3 Computational M odels of C onvection E nhanced D elivery ..............................................25 2.4 Visualization and T racking of I nfused A gents .................................................................28 DEVEL OPMENT OF VOXELIZED MODELING METHODOLOGY FOR MACROMOLECULAR INTERSTITIAL TRANSPORT IN THE RAT SPINAL CORD .....................................................................................................................................31 3.1 Introduction .......................................................................................................................31 3.2 Methods ............................................................................................................................31 3.2.1 Diffusion T ensor I maging ....................................................................................32 3.2.2 Semi Automatic Im age Segmentation .................................................................33 3.2.3 Tissue Transport Model .......................................................................................34 3.3 Results ...............................................................................................................................39 3.3.1 DTI and S egmentation .........................................................................................39 3.3.2 Interstitial Flow and Albumin Distribution ..........................................................40 3.3.3 Validation and Parameter Analysis ......................................................................41

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6 3.4 Discussion .........................................................................................................................42 3.5 Conclusions .......................................................................................................................45 DEVELOPMENT OF VOXEL IZED 3D COMPUTATIONAL TRANSPORT MODELING OF CED INTO THE RAT BRAIN AND PARAMETER ANALYSIS .................................54 4.1 Introduction .......................................................................................................................54 4.2 Methods ............................................................................................................................54 4.2.1 Diffusion Tensor Imaging ....................................................................................54 4.2.2 Interstitial Transport Model .................................................................................56 4.3 Results ...............................................................................................................................58 4.3.1 Predicted Fluid Flow and Tracer Distribution .....................................................58 4.3.2 Parameter analysis ................................................................................................60 4.4 Discussion .........................................................................................................................62 4.5 Conclusions .......................................................................................................................67 MEASUREMENT OF IN VI VO TRACER DISTRIBUTI ON DURING CED INTO T HE DORSAL AND VENTRAL HIPPOCAMPUS OF THE RA T BRAIN .................................73 5.1 Introduction .......................................................................................................................73 5.2 Materials and M ethods .....................................................................................................74 5.2.1 Infusion system ....................................................................................................74 5.2.2 Animal Preparation and Surgical Procedure ........................................................75 5.2.3 In Vivo MR Image Processing and Segmentation ................................................76 5.2.4 Brain Tissue Slice ................................................................................................77 5.3 Results ...............................................................................................................................78 5.3.1 Development of Surgical Procedure ........................................................78 5.3.2 Infusate Distribution in the Dorsal Hippocampus ................................................79 5.3.2 Infusate Distribution in the Ventral Hippocampus ..............................................81 5.3.4 Pressure Monitoring .............................................................................................82 5.4 Discussion .........................................................................................................................83 5.5 Conclusions .......................................................................................................................87 VOXELIZED 3D COMPUTATIONAL TRANSPORT MODELING IN THE VENTRAL HIPPOCAMPUS: COMPARI SON STUDIES BETWEEN MODELS AND EXPERIMENTS ...................................................................................................................102 6.1 Introduction .....................................................................................................................102 6.2 Materials and M ethods ...................................................................................................103 6.2.1 Animal Preparation and Diffusion Weighted Imaging ......................................103 6.2.2 Segmentation ......................................................................................................104 6.2.3 Tissue Properties and Computational Modeling ................................................104 6.2.4 In Vivo CED Experiments ..................................................................................106 6.3 Results .............................................................................................................................106 6.3.1 Segmentation ......................................................................................................106 6.3.2 Subject Variation and Similarity of Predicted Infusate Distribution .................107 6.3.3 Comparison between Predicted and Measured Distribution of Infusate ............108

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7 6.3.4 Predicted and Measured Transient Infusion Distribution ..................................109 6.3.5 Parameter Analysis of Isotropic Tissue Properties for White Matter ................111 6.4 Discussion .......................................................................................................................112 6. 5 Conclusions ....................................................................................................................116 CONCLUSIONS AND FUTURE WORKS ................................................................................129 7.1 Summary and Conclusions .............................................................................................129 7.2 Future Work ....................................................................................................................131 LIST OF REFERENC ES ......................................................................................................133 BIOGRAPHICAL SKETCH .......................................................................................................140

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8 LIST OF TABLES Table page 31 FA and So ranges used to segment the spinal cord DTI data. FA ranges were used to segment in vivo imaging data sets. So was used for excised, fixed tissue data and two different ranges were used over the axial length of the spinal cord. The values of So were normalized by the surrounding PBS value ................................................................46 32 Tissue transport properties used in the interstitial transport simulations. D and K values correspond to tensor components of Dt and K ........................................................46 41 Fractional anisotropy (FA) ranges used in tissue segmentation of the excised rat brain ...................................................................................................................................68 61 FA and AD ranges used in segmentation of the rat brain. ...............................................117

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9 LIST OF FIGURES Figure page 11 Brain capillaries which have tight junctions in the capillary lining, (Miller, 2002) ..........20 21 Tissue radioactivity concentrations following infusion into the rat brains after different routes of administration. CED data is shown from the center of infusion site. Intrathecal data is shown from the brain surface .......................................................30 22 Water diffusion carries information whether the environment is random (isotropic diffusion), or ordered (anisotropic diffusion) (M ori, 2007) ...............................................30 31 DTI based Segmentation ..................................................................................................47 32 Schematic diagram for computational modeling procedure ..............................................48 33 Predicted albumin distributions in the spinal cord using voxelized transport models generated from in vivo DTI (low resolution) dat a .............................................................49 34 Predicted albumi n distributions in the spinal cord using voxelized transport models generated from DTI of excised, fixed tissues (high resolution). ........................................50 35 Peclet number contour maps in the transverse plane of the spinal cord generated using voxel transport models ............................................................................................51 36 Comparison of predicted and measured distributions of albumin tracer in the rat spinal cord following direct infusion into the dorsal horn. Tracer tissue volumes calculated from the voxel transport models using in vivo and excised tissue data sets are plot ted. ..........................................................................................................................52 37 Parameter sensitivity analysis comparing the final distribution volume (Vd) and the total infusio n volume (Vi) on a loglog scal e ....................................................................53 41 Tissue segmentation of the excised rat brain using DTI derived FA ................................68 42 Variation in segmented white matter regions (red) within the corpus callosum (right co lumn) and hippocampus (left column) for different FA threshold values and DTI voxel resolutions. ...............................................................................................................69 43 Predicted velocity contours for infusions into the A) corpus callosum and B) hippocampus in coronal planes. C) Peclet number contour map for hippocampal infusion (coronal plane). CED infusion rate was 0.3 L/min. ..........................................70 44 Predicted albumin distributions during infusion into the corpus callosum in coronal planes. ................................................................................................................................70

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10 45 A lbumin distributions during infusion into the hippocampus in coronal planes.. .............71 46 Sensitivity of predicted tracer distribu tion volumes in the corpus callosum .....................72 51 In vivo surgical setup for direct infusion in the dorsal and ventral hippocampus of the rat brain ..............................................................................................................................88 52 Experimental setup for MR Imaging .................................................................................89 53 Schematic diagram of in vivo infusion system ..................................................................90 54 Flowchart of MR imaging procedure .................................................................................90 55 Dynamic coronal MR images at various times for A) infusate distribution without cannula clogging and B) delayed infusate distribution due to cannula clogging ..............91 56 Inline infusion pressure profiles and corresponding distribution patterns at given times frames during Evans Blue infusion in 2% hydrogel without retraction ...................92 57 Dynamic contrast enhanced MR images during infusion into the dorsal hippocampus for six individual subjects where the infusion rate was 0.3 L/min and the total infusion volume was 8 L ..................................................................................................93 58 Measured infusate distribution volumes for direct infusion in the dorsal hippocampus (n=6) to 8 L infusions. .....................................................................................................94 59 A) DCE MR images in the coronal plane B) Final distribution in high resolution T1 weighted images. C) Evans Blue dye distribution in the brain slice. D) Coronal slice in a brain atlas corresponding to MR images (Paxinos G., 2007). ....................................95 510 A) DCE MR images for different coronal slices at different time frames throughout infusion in the dorsal hippocampus, B) High resolution T1 weighted images post infusion and C) Evans Blue dye images progressing from posterior to anterior (left to right) after infusion.. ..........................................................................................................96 511 Dynamic contrast enhanced MR images during infusion into the ventral hippocampus(n=6) where the infusion rate was 0.3 L/min and total infusion volume was 10 L. Each trial shows the same coronal slices at various time frames. .................97 512 Measured infusate distribution volumes for direct infusion in the ventral hippocampus (n=6) for 10 L infusions. ...........................................................................98 513 A) DCE MR images in the coronal plane B) Final distribution in high resolution T1 weighted images. C) Evans Blue dye distribution in the brain slice. D) Coronal slice in a brain atlas corresponding to MR images (Paxinos G., 2007). ....................................99

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11 514 A) DCE MR images for different coronal slices at different time frames throughout infusion in the ventral hippocampus, B) High resolution post infusion T1 weighted images and C) Evans Blue dye images progressing from posterior to anterior (left to right) after infusion.. ........................................................................................................100 515 Inline infusion pressure profile in the ventral hippocampus of the rat brain with three consecutive T1 weighted coronal images at given time frames. .....................................101 61 Schematic diagram of the one side of the rat brain used in the computational model for direct infusion. ............................................................................................................118 62 Modeled infusion sites in the ventral hippocampus using a rat brain atlas ....................118 63 A) The segmentation map using FA threshold from the previous model where CSF regions and the skull were not accurately characterized. B) Improved segmentation map using FA and AD thresholds ....................................................................................119 64 Volume percentage of each brain region segmented for each subject .............................119 65 Predicted distribution pattern for direct infusion between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus for each subject ............120 66 Predicted distribution pattern for direct infusion in alveus/CC. ......................................121 67 Predicted volume distributions in each structure for direct infusion between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus (A) and direct infusion alveus/CC for each subject (B) .........................................................122 68 Predicted excised(A) and measured in vivo (B) final distribution patterns (Astary et al., 2010) in five consecutive coronal slices for infusion in the molecular layer of the dentate gyrus/CA1 subf ield of the ventral hippocampus In (C), three dimensional contours of t he final distribution .....................................................................................123 69 Predicted excised (A) and measured in vivo (B) final distribution patterns (Astary et al., 2010) in five consecutive coronal slices for infusion in alveus/CC (yellow dots: fimbria of the hippocampus). In (C), three dimensional con tours of the final distributions ......................................................................................................................124 610 Predicted (A) and measured (B)transient infusate distribution patterns in three cor onal slices for 10 L infusions between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus.. ...............................................................125 611 Predicted total distribution volumes (A) and predicted distribution volumes in white matter (B), gray matter (C) and CSF regions (D) fo r 10 L for direct infusion in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus (n=5) ...126

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12 612 Percentage of infusate in the tissue and CSF space at various time frames for 10 L infusions in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus. ...................................................................................................................127 613 T1 weighed MR images of final distributions in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus .............................................................128

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13 LIST OF ABBREVIATIONS AD A verage diffusivity BBB Blood brain barrier CC Corpus callosum CED Convection enhanced delivery CFD Computational fluid dynamics CSF Cerebrospinal fluid CNS Central nervous system DCE MRI Dynamic contrast enhanced magnetic resonance imaging DTI Diffusion tensor imaging DWI D iffusion weighted imaging FA Fractional anisotropy FOV Field of view Gd DTPA Gadolinium diethy lene triamine pentaacetic acid labeled albumin NA Number of average PBS P hosphate buffered saline Pe Peclet number PEEK P olyaryletheretherketone PID P roportional integral derivative S0 bdependent signal intensity without diffusion SPECT S ingle photon emission computed tomography TE Echo time TR Recovery time

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT OF DIFFUSION TENSOR IMAGING BASEDCOMPUTATIONAL MODELS OF DIRECT INFUSION INTO THE CENTRAL NERVOUS SYSTEM By Jung Hwan Kim December 2010 Chair: Malisa Sarntinoranont Major: Mechanical Engineering Despite the high therapeutic potential of many macromolecular drugs, delivery of these agents to targeted tissues for treatment of cancer and other degenerative diseases of the central nervous system remains challenging. One barrier to the systemic admini stration of macromolecules is low capillary permeability. C onvection enhanced delivery (CED) is a promising local delivery technique for overcoming this barrier and treating diseases of the central nervous system. A new 3D interstitial transport modelin g approach in which tissue properties and anatomical boundaries were assigned on a voxel byvoxel basis using tissue alignment data from diffusion tensor imaging (DTI) i s presented. The modeling approach i s semi automatic and utilizes porous media transpo rt theory to estimate interstitial transport in isotropic and anisotropic tissue regions. Rat spinal cord DTI data sets were employed to develop the models, which provide predicted distributions of albumin tracer following infusion into anisotropic regions of the dorsal horn. T he voxelized modeling methodology was adopted for CED into the rat brain Surgical procedures and MR imaging protocols were developed to visualize in vivo heterogeneous and complicated distribution patterns during infusions in the hippocampus of the

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15 brain. Qualitative comparisons between predicted and measured distribution patterns, volumes and shapes demonstrated the models proficiency. The developed 3D porous media transport models for CED in the brain may be useful tool s for surgical planning and may lead to improve treatment of neurological brain diseases by maximizing drug delivery to targeted regions and minimizing systemic and neurologic toxicities

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16 CHAPTER 1 INTRODUCTION 1.1 Motivation Many neurological disorders including epilepsy, Alzheimer disease, Parkinson disease and brain injuries result in abnormal behavior, memory loss, irregular cognition, and are potentially fatal. High potential therapeutic agents such as immunoglobulins, en zymes, micro particles and polynucleotides for treatment of neurological disorders have been introduced by recent advances in pharmaceutics ( Obbens et al. 1985; Zovickian et al. 1987; Harbaugh, 1989; Jain, 1989) However, effective delivery of these agents to the central nervous system (CNS) remains a challenge because the blood brain barrier (BBB) limits penetration of therapeutic agents into neuronal targets. The BBB consists of endothelial cells as tight junctions at the interface of blood capillaries and brain tissues and it acts to protect the CNS from exogenous substance s including therapeutic agents in Figure 11 ( Miller, 2002) Findings of previous studies have demonstrated that systemic, oral or intravascular drug administration often fails to deliver macromolecular agents to the brain because of this BBB at lower doses, and higher doses may result in systemic toxicity due to nontargeted distributions ( La nger, 1990) Several methods have been developed in past decades to overcome the BBB to improve drug delivery to the CNS. One approach to circumvent these barriers is intrathecal and intraventricular injections, which directly infuse the therapeutic ag ents into cerebrospinal fluid (CSF) regions. However, tissue penetration was limited due to low diffusivity of agents as well as exponentially declining concentrations away from the brain surface ( Groothuis et al. 1999) Another strategy is the implantation of drug eluting polymer wafers or bioceramic implants into that targeted regions of the brain ( Lopez et al. 2007) This approach allows local drug delivery that circumvents the BBB and prevents nontargeted distributions. In spite of overcoming

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17 transport barriers, only limited tracer distributions were obtained due to the low diffusivity of macromolecules in extracellular tissues. In addition, this approach causes greater local tissue damage and deformation because it requires a relatively large space for implants as compared to small diameter infusion catheters used in CED studies ( Rogawski, 2009) An alternative approach to accomplish drug delive ry in the CNS is direct infusion into extracellular tissues, i.e., convectionenhanced delivery (CED). This technique uses a bulk fluid motion, driven by a positive pressure gradient from a stereotactic guided cannula tip, to distribute therapeutic agents directly into the interstitial space (same as the extracellular space). The distribution volume has been shown to be significantly increased and well targeted over specific regions in the brain with uniform concentration ( Rogawski, 2009) Morrison, et al. simulated the infusion into homogeneous brain tissues for typical macromolecules (20 kDa ~ 180 kDa) commonly used for CED with different flow rates. They de monstrated that tracer distribution volumes generated by convection were much greater than by that of diffusion alone in homogenous brain tissues ( Morrison et al. 1994 ) The CED method not only circumvents the BBB but use s tight junctions surrounding the capillaries as a transport barrier for agents to remain in the extracellular spaces. Lonser et al. conducted direct infusion experiments into the nonhuman primate brainstem with Gdbounded albumin (72 kDa). A linear rel ationship between tracer distribution volumes and the infusion volumes (R2=0.94) was found. A homogeneous concentration profile was observed across perfused regions. A n eurological deficit was not observed. Histological analysis also showed evidence of minimal tissue damage due to the introduction of the infusion cannula ( Lonser et al. 2002 ) Computational models for predicting fluid flow patterns and spatial distribution volumes of agents during CED would be useful in treatment optimization and planning. In previous studies,

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18 porous me dia computational models of CED have been developed with isotropic and homogeneous tissue transport assumptions ( Barry & Aldis, 1992; Morrison et al. 1994; Chen et al., 2002; Netti et al. 2003; Chen & Sarntinoranont, 2007; Smith & Humphrey, 2007; Garcia & Smith, 2009) However heterogeneous and compl icated tissue boundaries and the underlying transport anisotropy of tissue structures should be major factors affecting distributions of the agents in the CNS for large infusion volumes. Few studies have introduced computational models with anisotropic t issue properties ( Raghavan et al. 2006; Sarntinoranont et al. 2006b; Linninger et al. 2008c ) and challenges still remain. For example, there is the need to generate realistic tissue boundaries rapidly and avoid the time consuming and labor intensive slice byslice geomet ric reconstruction methods employed in previous studies. Additional tissue segmentation schemes need to be developed, especially for heterogeneous tissue regions with complicated boundaries. Parameter analysis exploring the effects of infusion parameters tissue properties, resolution, and segmentation parameters is also necessary to determine significant factors affecting predicted interstitial flow and distribution patterns. In previous studies, simple infusion tests in homogeneous agarose gels and spi nal cord CED distribution studies from the literature were compared to developed computational models. However c omparisons of transient infusate distribution patterns, volume and shapes between experiments and computational models for CED in the brain ar e lacking. 1.2 Specific A ims The purpose of this study is to understand the effect of embedded tissue structures on local CED transport and provide an image based computational model as a surgical tool to optimize local targeting of CED in the brain A new 3D voxelized porous media transport model is introduced to predict interstitial flow and tracer distribution pattern s during CED. I n vivo

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19 infusion experiments in the rat brain were performed and compared to the developed c omputational model s 1.2.1 Specific Aim 1: Develop V oxelized M odel ing M ethodology for M acromolecular I nterstitial T ransport in the R at S pinal C ord U sing D iffusion T ensor I maging. A voxelized modeling approach was proposed. T issue properties and anatomical boundar ies of the rat spinal cord were assigned on a voxel by voxel basis using geometrical structure information from diffusion t ensor i maging (DTI). The introduced semi automatic voxelized approach employed fractional anisotropy (FA) and T2 weighted, protondensi ty dependent signal intensity without diffusion ( S0) from DTI for segmentation. This segmentation scheme allow ed for expedited building of computational model s and rapid prediction of interstitial flow and tracer distribution Simulations were performed using excised and in vivo DTI data to predict tracer distribution at high and low resolutions. P redicted distribution s of albumin tracer (molecular weight ~66 kDa) in rat dorsal white matter column following CED was compared to previous experimental distributions from the literature. 1.2.2 Specific Aim 2: Develop V oxelized 3D C omputational T ransport M odel of CED into the R at B rain and C onduct P aramet er A nalysis The developed voxelized modeling methodology in specific aim 1 was adopted for CED transp ort models of the rat brain to demonstrate feasibility in more complex structures. High resolution DTI data of excised and fixed rat brain was used to get geometrical structure information Two infusion sites (corpus callosum and ventral hippocampus) were selected to demonstrate differences in distribution patterns due to heterogeneous tissue structures. A paramet er analysis was executed to determine sensitivity of tracer distribution s to varying infusion parameters, tissue properties and computational pa rameters. Also additional segmentation schemes were developed to distinguish between tissue regions and internal CSF structures.

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20 1.2.3 Specific Aim 3: Measure I n V ivo T racer Di stributions during CED in the R at B rain Surgical procedures and MR imaging protocols were developed to visualize in vivo distribution patterns during infusions. T1weighted contrast enhanced MR imag es were acquired to measure Gd DTPA albumin tracer distributions during and after infusions into the dors al and ventral hippocampus Evans Blue dye images showing tracer distributions in histological slices were obtained to confirm the final tracer distribution in MR images. 1.2.4 Specific Aim 4: Compare Predicted and Measured Infusate Distribution for CED in the Rat Brain The developed model and segmentation scheme were used to predict CED transport in the ventral hippocampus and compared with experimental studies. I nfusions were modeled in five subjects using the same infusion sites Similar infusate distribution patterns were obtained demonstrat ing the reliability and repeatability of this modeling scheme Qualitative comparisons between predicted and measured distribution patterns, volumes and shapes were conducted to exhibit the models proficiency Figure 11. Brain capillaries which have tight junctions in the capillary lining, ( Miller, 2002)

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21 CHAPTER 2 BACKGROUND AND PREVI OUS STUDIES 2.1 Drug D elivery M ethods in the C entral N ervous S ystem The delivery of therapeutic agents to the central nervous system (CNS) for treating neurological and psychiatric disorders is still problematical due to low penetration of macromolecular therapeutic agents from blood capillaries to interstitial spaces. The blood brain barrier, discovered in the early 1900s by Ehrlich ( Ehrlich, 1885) surrounds the blood capillaries in the CNS and acts as a filter to protect the brain from toxins and viruses in the circulating blood. Only molecules escorted by selective transport proteins, or small (less than 500 Daltons) lipophillic molecules are able to pass through tight junctions of the barriers ( Miller, 2002) However, many potential therapeutic agents are high molecular weight compounds such as protein conjugates, enzymes, antibodies, and growth factors ( Oldendorf, 1974; Obbens et al. 1985; Zovickian et al. 1987; Harbaugh, 1989; Jain, 1989) Due to these barriers, intravenous or intravascular therapeutic delivery methods have limited penetration of the macromolecular agents in the CNS in spite of long dosage periods. Zhang and Pardridge have measured enzyme activities at one and four hours in the brain and peripheral organs after the intravenous injections of unconjugated beta galactosidase (116 kDa). Minimal uptake was observed in the brain compared to avid uptake by the liver and spleen ( Zhang & Pardridge, 2005) Therefore, high administered doses are needed to accomplish therapeutic outcomes in the CNS, which may result in unacceptable toxic ities on side effects. More effective delivery techniques are required to maintain therapeutic concentrations of agents and increase volume distribution in CNS without systemic toxicities and non targeted distribution. Intrathecal and intraventricular infusion techniques which deposit therapeutic agents into cerebrospinal fluid (CSF) regions such as the spinal canal and ventricles have also been studied.

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22 The driving force of these delivery methods is restricted to diffusion from CSF regions to the brain tissues, which is determined by the spatial concentration gradient and the molecular weight of the agents. Groothuis et al. demonstrated that 14C sucrose, which is a relatively small molecule (340 Da), is distributed in the brain tissues with high concentration in the vicinity of lateral ventricles. However, the local delivery efficiency declined approximately 10% at 1 mm and 5% at 2 mm from the ventricular surface because the concentration gradient exponentially decreased with distance from the ventricular surfaces ( Groothuis et al. 1999) Bioceramic wafers and polymer implants, which release agents in the CNS, are other potential continuous drug delivery methods ( Kokaia et al. 1994; Kubek et al. 1998; Tamargo et al., 2002; Lopez et al. 2007) These techniques allow the agents to circumvent the BBB and be released in a controlle d manner depending on the polymer compositions. However, the studies also show limited penetration of macromolecular therapeutic agents due to an exponentially decreasing concentration gradient with distance from the polymer implant, similar to previously developed diffusion based methods. Tamargo et al. studied intracerebral administration of phenytoin (250 Da) using a polymer implant to reduce experimental induced seizures in rats. Despite the small molecular weight of the agent and the large size of th e polymer reservoirs (5 mm diameter, 4 mm height, cylinder polymer) embedded in the rat brain, 23% of animals continued to have seizures due to the short duration of the administered therapy provided by drug reservoir ( Tamargo et al. 2002) In addition, greater local tissue damage and deformation was observed due to the large size of the polymer implants. 2.2 Convection E nhanced D eli very in the C entral N ervous S ystem In heat transfer, convection typically means the energy exchange between a surface and an adjacent fluid, but in mass transfer, the term convection more generally represents transport of molecules driven by fluid flow (advection) and the concentration gradient (diffusion).

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23 Convection enhanced delivery (CED) is a novel delivery technique for therapeutic agents that bypasses the BBB by creating continuous bulk fluid flow using a positive pressure gradient from a cannula tip which is inserted directly in nervous tissue. The fluids carrying the drug agents spread within the surrounding tissues through the extracellular space which is considered highly tortuous porous media. Moreover, molecular random motions which drive transport along concentration gradients also takes place simultaneously. Bobo et al. reported that fluid convection by interstitial infusion provides greater distribution volume of small and large molecules than by diffusion alone. In addition, CED takes advantage of the BBB by impeding the transport of therapeutic agents from the interstitial space into the blood capillaries ( Bobo et al. 1994) Morrison et al. simulated infusion of slowly degraded (~180 kDa) macromolecules into brain ti ssue gray matter to demonstrate that convective micro infusion provides five to ten fold increases in volume distributions with more uniform concentration than by diffusion alone. These results also illustrate that convective infusions prevent the undesir ed systemic toxicity due to non targeted distributions, which may be present with alternative methods ( Morrison et al. 1994) Groothuis et al. performed a comparison study of cytosine arabinoside (molecular weight 234 Da) delivery to the rat brain by intravenous, intrathecal, intraventricular infusion, and CED into the caudate nucleus. The results showed that CED is superior to the other methods for delivering and maintaining large distribution volumes with high concentrat ions of cytarabine in the brain tissues while minimizing systemic toxicity ( Groothuis et al. 2000) in Figure 2 1. In experimental CED studies, distribution volumes have been shown to be linearly propor tional to infusion volume regardless of the molecular weight of the infusate ( Lonser et al. 2002; Krauze et al. 2005; Saito et al.

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24 2005) Thus, CED may allow control over distribution volumes by adjusting infusion volumes to avoid an overdose of drugs in undesired regions. CED transport studies have been performed for differen t subjects, infusion sites and infusates to better understand the transport mechanisms and distribution patterns of agents ( Lieberman et al. 1995 ; Prabhu et al. 1998; Wood et al. 1999; Lonser et al. 2002; Krauze et al., 2005; Saito et al. 2006; Morrison et al. 2007) Chen and his coworkers conducted an experimental parameter analysis (infusion rate, cannula size, concentration of infusate, and pre sealing time) for the CED in the rat brain to optimize use of CED for the drug delivery in a clinical setting ( Chen et al. 1999) Systematical comparison for dis tributions of viruses, nanoparticles and albumin in CED were also studied by Chen et al. to show feasibility of convective delivery of therapeutic viral vectors in the CNS. The results demonstrated that the extracellular spaces of gray matter in brain ar e large enough to accommodate virus sized particles. It was also concluded that the surface characteristics, e.g. charge, of the particles are significant determinants for distributions of viruses by direction infusions ( Chen et al. 2005) Previous studies have indicated that the infusion of therapeutic agents into the hippocampus is a potential treatment method for epilepsy ( Rogawski, 2009) E der et al. reported that direct infusions of antiepileptic drugs into the hippocampus is useful in treating intractable partial seizures in rats ( Eder et al. 1997) It has also been shown that long term antiseizure dosing by CED of excitotoxin ibotenate into the amygdale and surroundin g regions produced an enduring suppression of seizure activity ( Pace et al. 2002) Distributions following hippocampal CED of particular therapeutic agents including galanin and musimol have also been investigated ( Schott et al ., 1998; Heiss et al. 2005) However, additional quantitative transport

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25 studies of CED in the hippocampus need to be undertaken to understand how the complex structure of these regions influences extracellular transport. CED has been also applied for treatment of brain malignant tumors. Due to heterogeneity of tumors, unexpected volume distributions of agents can be observed depending on the infusion site and the infusate. Even though CED provided the best distributions of chemotherapeutic agents, the recurrence of cancer cells may persist ( Patel et al. 2005) For this reason, many clinical studies investigating the use of CED for treatment of brain cancer attempt to monitor drug delivery during and after CED using MRI and/or histological te chniques to buildup a paradigm of treatment of brain tumors with minimal toxicity effects using CED ( Laske et al. 1997; Voges et al. 2003 ; Lonser et al. 2007; Fianda ca et al. 2008; Thomale et al. 2009) 2.3 Computational M odels of C onvection E nhanced D elivery The development of computational models of CED that predict interstitial flow and distributions of agents would facilitate planning of CED treatments that avoid undesired distribution patterns such as leakage into CSF, and neurologic toxicity to untargeted regions. The different regions of the brain have varying transport characteristics based on the structures of gray matter and white matter. Gray matter, which mainly consists of neuronal cell bodies, neuropil, and glial cells, is an approximatel y isotropic structure in which effective diffusivity and permeability (the rate of net fluid flow across a porous media) are relatively the same in all directions ( JohansenBerg & Behrens, 2009) On the other hand, white matter is composed of bundles of myelinated axons. Hence, preferential interstitial tra nsport takes place along the direction of aligned fiber tracts. Lonser and Wood et al. studied direct infusions of 14C labeled albumin in the white matter of spinal cord. These tracer distributions were observed to cover long segments of spinal cord along the white matter tracts ( Lonser et al. 1998 ; Wood et al. 1999) In the rat brain, Greer and

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26 Grossman determined that there was preferential fluid flow of interstitial fluid along the corpus callosum (a large region of white matter tracts) by histologic analysis an d autoradiography following infusions of rat albumin tagged with Evans blue and tritiated inulin ( Geer & Grossman, 1997) Prabhu et al. also infused tracers including Evans blue and Blue Dextran in the rat brain to obtain fluorescent histology images showing distribution patterns following CED into the caudate putamen. Their results also showed that CED distributions of both dyes tended to follow white matter tracts ( Prabhu et al. 1998) For large infusion volumes with CED, interstitial f luid flow and drug distributions are significantly affected by characteristics of tissue structures because distribution volumes could spread over both white matter and gray matter regions. Therefore, interstitial transport models of the CNS need to inco rporate tissue properties and boundaries. Kalyanasundaram et al. introduced a computational model incorporating regional differences in tissue properties and ventricular regions to predict local transport of interleukin 2 in the rabbit brain. T1weighted imaging was used to define realistic brain geometries and salient anatomic features for the model. However, only twodimensional transport using a single imaging slice was considered for the model ( Kalyanasundaram et al. 1997) Our group has developed a three dimensional finite element model of direct infusion into the rat spinal cord using anisotropic tissue properties ( Sarntinoranont e t al. 2003a ) This computational model was extended to predict distributions of SP diphtheria toxin fusion proteins and tracers for direct infusion in the human spinal cord ( Sarntinoranont et al. 2003 b) Few studies have incorporated diffusion tensor imaging (DTI) with computational models of tissue transport. S uch an approach could achieve more realistic boundaries between white and gray matter, and spatially varying tissue transport properties ( Sarntinoranont et al. 2006b;

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27 Sampson et al. 2007; Linninger et al. 2008a ; Linninger et al. 2008b; Linninger et al. 2008c ) DTI is a noninvasive quantitative measurement scheme for the self diffusion of water molecules in the intra and extracellular space of biological tissues ( Basser & Jones, 2002 ) This rank2 water diffusion tensor, De, provides a description of the averaged three dimensional translational self diffusion (in units of cm2/s) on voxel by voxel basis. Anisotropy in this diffusivity measurement results from restricted water movement in the underlying structure averaged over a large number of fibers in both the extracellular and intracellular spaces, as seen in Figure 2 2. Preferential directions of water diffusion have been found to correspond to the average aligned fiber directions within a voxel and this data has been used to calculate the fiber t ract trajectories within fibrous tissues ( Conturo et al. 1999; Basser et al. 2000; Mori et al. 2000; Basser & Jones, 2002 ) Tuch et al. derived cross property relations between tw o phenomenologically distinct transport processes. In structured media such as tissues, two different transport modes may be related through mutual respect of the boundary conditions imposed by underlying structure ( Tuch et al. 2001) Their results showed eigenvectors of De, to be the same as the eigenvectors of other transport properties such as permeability and diffusivity tensors of a drug agent in the interstitial space. Our group has previously used this relation to develop a computational modeling technique using DTI to assign anisotropic transport properties within a rat spinal cord model. Three dimensional heterogeneous and anisotropic interstitial flow as well as macromolecular distribution patterns during direct infusions of protein tracer were predicted ( Sarntinoranont et al., 2006b) Predicted axial and volumetric tracer distributio n compared well with previous tracer distribution studies by Wood et al. ( Wood et al. 1999) Sampson et al. also developed a

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28 computational model to predict CED distribution volumes of iodine 123labeled albumin (123I HSA) using DTI for malignant gliomas in the human brain. They compared predicted tracer distributions with actual distributions of a tumor targeted cytotoxin cintredekin besudotox tagged with 123I HSA by using single photon emission computed tomography (SPECT) ( Sampson et al., 2007) D iscrepancies, greater than 25% were observed between predicted and measured tracer distribution volumes Potential sources of error may be due to model assumptions (e.g. tissue properties, segmentation scheme) which were not well described and low r esolution of SPECT imagi ng; only one of eight cases yielded matching predicted and measured tracer distribution. Linninger et al. developed a twodimensional transport model to predict distribution patterns following infusion of a trophic factor (25 kDa) into the caudate nucleus of the human brain. DTI data was used to account for heterogeneous and anisotropic transport tissue properties ( Linninger et al. 2008a ) They applied this method to estimate three dimensional interstitial fluid flow and volume distributions of a trophic factor infused into the mid brain near the internal capsule putamen boundary. They also performed parameter analysis for catheter desig n parameters to maximize volume distributions. However, they performed only simple infusion tests of trypan blue dye in homogenous agarose gel to validate this computational model. Only spherical distributions and penetrated depths of the dye in agarose gel were used for validation ( Linninger et al. 2008 a ; Li nninger et al. 2008 b) 2.4 Visualization and T racking of I nfused A gents Computational models for direct infusions into the CNS are potentially useful tools to predict the spatial distributions o f drugs before CED surgeries. However, additional validation studies that compare predicted distribution s with experimental infusion tests are necessary. Quantitative measuring schemes for in vivo infusion experiments such as total distribution volume, 3D shape of drug distribution volumes, and/or concentration maps of the drug are

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29 needed to validate computational modeling results. There are several ways including histology, autoradiography, and fluorescent microscopy to quantify distribution patterns aft er infusion tests in post modern studies ( Bobo et al. 1994; Geer & Grossman, 1997; Krauze et al. 2005; Saito et al., 2005; Saito et al. 2006) However, by using these methods, only the final distribution can be measured since the animal need s to be sacrificed to obtain brain tissue slices for imaging. In vivo measurement schemes are required for a more comprehensive understanding of infusion mechanisms as well as to help co ntrol drug delivery in real time. MR imaging techniques provide a number of advantages for in vivo measurements including high spatial resolution with advances in MR hardware. Contrast agents such as Gd diethylenetriamine pentaacetic acid (Gd DTPA) tagged on therapeutic agents may be visualized in vivo with MR imaging. Krauze and Saito conducted direct infusions of liposomes tagged with Gadoteridol and fluorescent dyes into the corona radiate, putamen nucleus, and brains stem of the monkey brain. T1weig hted images were used to measure volume distributions of liposomal gadolinium, and histological results from fluorescent liposomes confirmed these measured volume distributions by MR images ( Krauze et al. 2005; Saito et al. 2005) Lonser et al. obtained T1weighted images during direct infusions of Gdbound albumin in the pontine regions of the nonhuman primate brain and they were able to visualize and calculated the volume of this tracer distribution ( Lonser et al. 2002) Clinically, they also performed coinfusions of therapeutic agents with GdDTPA in the brainstem on human patients. MR imaging results showed that GdDTPA could be used to track distributions of the therapeutic agents in i n vivo MR images without observing any evidence of toxicity ( Lonser et al. 2007) Recently our group has used MR imaging to track transport of Gdalbumin tagged with Evans blue after CED in the ventral and dorsal hippocampus of the rat brain. Final distribution patterns of a contrast agent were obtained by using in vivo T1 weighted

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30 imaging. Follow up fluorescent microscopy of the distributions of Evans blue in histological slices confirmed the distributions seen in MR imaging ( Astary et al. 2010 ) Figure 21. Tissue radioactivity concentrations following infusion into the rat brains after different routes of administration. CED data is shown from the center of infusion site. Intrathecal data is shown from the brain surface. The data for both the intraventric ular and intravenous experiments is shown from the ventricular surface. The vertical axis is represented on a log scale. ( Groothuis et al. 2000) Figure 22. Water diffusion carries information whether the environment is random (isotropic diffusion), or ordered (anisotropic diffusion) ( Mori, 2007)

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31 CHAPTER 3 DEVELOPMENT OF VOXEL IZED MODELING METHODOLOGY FOR MACROMOLECULAR INTERSTITIAL TRANSPORT IN THE RAT SPINAL CORD 3.1 Introduction This chapter introdu ces a new computational modeling methodology for CED using a semi automatic voxelized approach described in specific aim 1. The developed semi automatic modeling approach requires minimal user input and provides a rapid process relative to manual image segmentation and volume meshing processes previously used to construct complex white matter structures of the spinal cord. Diffusion tensor imaging of in vivo and excised rat spinal cord were used to provide preferential transport directions and anatomical boundaries based on underlying structures on a voxel by voxel basis. To validate the presented DTI based modeling methodology, the predicted distribution volume of albumin tracer following infusion into the dorsal horn was compared with experimentally mea sured tracer distributions with a similar infusion site and total infusion volume, <4 L by Wood and coworkers ( Wood et al. 1999) This study was published in the Journal of Biomechanical Engineering Transactions of the ASME in collaboration with Garrett Astary (Department of Biomedical Engineering, UF) and Xioming Chen (Department of Mechanical and Aerospace engineering, UF) and Dr. Thomas H. Mareci (Department of Biochemistry and Molecular Biology, UF) ( Kim et al. 2009) 3.2 Methods Dr. Robert Yezierski and Sarah Berens (Department of Neuroscience, Department of Orthodontics, UF) and provided the fixed, excised rat spinal cord tissue, and collected the DTI data for this study. Garrett W. Astary and Xioming Chen collected the in vivo spinal cord DTI data. All MRI data was collected at the Advanced Magnetic Resonance Imaging and Spectroscopy Facility in the McKnight Brain Institute (AMRIS) of UF.

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32 3.2.1 Diffusion T ensor I maging In vivo imaging : All animal studies were conducted in accordance to a protocol approved by the Animal Care and Use Committee of University of Florida. Adult female Sprague Dawley rats (~ 250 g) were anesthetized and MR imaging procedures were conducted using a Bruker Avance 11.1 Tesla magnet system (Bruker NMR Instruments, Billerica, MA). For DTI, a diffusionweighted spin echo sequence was used with a total acquisi tion time of 72 min, recovery time (TR) of 2000 ms, echo time (TE) of 30 ms and one average. Low diffusionweighted data (100 s/mm2) were acquired in 6 directions, defined by the tessellation of an icosahedron on a unit hemisphere, and highdiffusionweigh ted data (800 s/mm2) were acquired in 21 directions. A field of view (FOV) of 2.4 cm x 2.4 cm in 1 mm slices with a matrix of 80 x 80 in 15 slices covering vertebral levels T13 to L2. Excised, fixed tissue imaging : To obtain highresolution microstructur al information, excised and fixed rat spinal cord tissue was used in long scan time diffusion tensor measurements. The fixed (4% paraformaldehyde) rat spinal cord was imaged in phosphate buffered saline (PBS) after removal of the fixative, and DTI data set s were obtained using a 14.1 Tesla magnet (Bruker NMR Instruments, Billerica, MA). The spinal cord images were centered at vertebral levels L1 T13. Multiple slice images, weighted by water translational diffusion, were measured (~11 hrs) using a spin echo pulse sequence. Measurements was performed with TR=1400 ms, TE=25 ms. The diffusionweighted images had a FOV of 4.3 mm x 4.3 mm x 12 mm (60 m x 60 m x 300 m voxel resolution). Images with low diffusion weighting (100 s/mm2) and a higher diffusionw eighting (1250 s/mm2) were measured in 6 gradient directions and 46 gradient directions respectively.

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33 Image processing: The diffusionweighted images were interpolated (bilinear interpolation, with nearest neighbor sampling) by a factor of two in each dim ension (data matrix of 144 x 144 x 80 for excised data, 40 x 40 x 30 for in vivo data). After initial image processing, the multiple slice DTI data was fit to the water translational diffusion tensor, De, using multiple linear regression ( Basser et al. 1994 ) In the simplest case, a series of diffusion weighted images may be used to calculate Deij (a singlerate apparent diffusion tensor component) and So, by the relationship below ( Inglis et al. 2001) 0ln(/)ijeijSSbD ( 31) where bij is the diffusion weight f actor and S is the b dependent signal intensity. S0 value is T2 weighted, protondensity (i.e. free water density) dependent signal intensity in the absence of diffusion. A scalar measure of anisotropy is introduced by fractional anisotropy 222 13 222 1233 2 DDD FA () : Eigenvalue 3e iTrD D (3 2) FA takes on values between 0 (isotropic) and 1 (anisotropic). 3.2.2 Semi Automatic I mage S egmentation Tissue transport properties were assigned to each DTI voxel corresponding to S0 and FA threshold ranges for white matter, gray matter, bone, or surrounding tissues, Table 3 1. Since white matter is composed of bundles of myelinated axonal fibers running in parallel, water more freely undergoes translational diffusion in the direction of these fibers. However, gray matter consists of cell bodies and dendrites of neurons and gial cells which do not restrict water translational diffusion to a particular direction. The calculated S0 image does not include any diffusion information but reflects the proto n density and T2 relaxation time of the tissue and has

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34 been shown to be lower in white matter than in gray matter ( Narayana et al. 1999) due to differences in tissue structure, e.g. mainly lower proton density (water density) in white matter. However, contrast in the FA image reflects the underlying tissue structure, where anisotropy of the water diffusion tensor varies with the extent of tissue alignment within the image voxel. Therefore, oriented bundles of white matter result in higher FA values than gray matter tissue, which is more isotropic. Segmented tissue regions were highlighted in visualization software (Amira v.4.1, TGS, San D iego. CA) by adjusting threshold values ( S0 or FA) and these threshold values were confirmed by eye by matching qualitatively with anatomical boundaries defined in a rat spinal cord atlas ( Paxinos G., 2007) It was not possible to segment gray and white matter regions using the in vivo DTI derived S0 images because the signal to noise rat io and resolution were too low ( Figure 31B ) However, segmentation was possible using FA images, which has sufficient contrast between gray and white matter in Figure 3 1A. Since the excised tissue image had both high signal to noise ratio and resolution, gray and white matter could be segmented using either S0 or FA in Figure 31D and 31E. 3.2.3 Tissue Transport M odel Theory : This study assumes nervous tissue to be a rigid porous medium which is valid for low rate s of interstitial infusion where elastic expansion effects are small. The continuity equation is 0 v (3 3) where v is the tissueaveraged interstitial fluid velocity. Local sources and sinks of interstitial fluid were neglected in the infusion models because tissues of the CNS lack an active lymphatic system ( Abbott, 2004) Furthermore, these tissues are characterized by low rates of

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35 fluid transfer across the capillary walls at the pressures encountered during interstitial infusion at a moderate flow rate ( Haraldsson, 1986) and have negligibly low rates of water formation by metabolism ( Dykstra et al. 1992) Porous media fluid flow is governed by Darcys law for fluid flow in a rigid porous medium. p vK ( 34) where p is the pore fluid pressure, and K is the hydraulic conductivity tensor which is an empirical property dependent on the pore geometry of the media and viscosity of the fluid. Instead of the Navier Stokes equation, it is assumed that the momentum equation f or the CSF fluid region was simplified to Darcys law for rapid modeling since effects of external viscous flow along the exterior of the spinal cord on transport within the spinal cord were assumed to be small. In this case, porosity (fluid volume fractio n) of was used and the hydraulic conductivity was chosen to be higher than within white matter tissue since flow resistance within CSF should be lower than within tissues. Implications of this assumption are discussed in the section 3.4. For fluid ve locity solutions, zero fluid flux boundary conditions were applied along axial faces, and zero pressure boundary conditions were assigned along transverse faces. Albumin is a nonbinding and nonreacting macromolecule that is commonly used as an interst itial tracer in distribution studies. Assuming no sources or sinks for this molecule, tracer transport through tissue following infusion is governed by convection and diffusion, c cc t tvD ( 35) where t and are time and tissue po rosity, respectively. Dt is the diffusivity tensor of the macromolecule in the porous medium (a volume averaged term) and c is the tracer concentration averaged with respect to tissue volume. Albumin concentration was solved in terms of the normalized variable,

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36 ic c c ~ (3 6) where ic is the infusate concentration. Interstitial transport t ensors: Bulk porous media transport properties of hydraulic conductivity, K and tracer diffusivity, Dt, for gray matter and CSF were considered to be isotropic. In white matter, each nodal point in the computational mesh was assigned spatially varying, anisotropic K and Dt tensors using preferential transport directions extracted from De, with K and Dt tensors assumed to share the same maximum eigenvector (direction of maximum transport) as De ( Tuch et al. 2001) It should be noted that De was measured over a sufficient voxel volume such that water diffusion over a number of fibers was averaged to provide directional transport information for bundles of fibers. K and Dt tensors for each nodal point were assigned using the relati onships shown below. ||K00 0K0 00K TKV V ( 37) ||D00 0D0 00D T tDV V =123Vv v v ( 38) vi are the unit eigenvectors of De ordered according to the eigenvalues of De such that v3 is the uni t eigenvector corresponding to the largest eigenvalue. Tensor eigenvalues (K, K||, D, and D||) correspond to transport magnitudes in directions perpendicular and parallel to aligned fiber directions and were determined from literature, Table 3 2. The baseline value assigned to CSF hydraulic conductivity was taken to be approximately three orders of magnitude higher than that of gray matter to reflect less resistance to flow.

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37 Computational Model: To reduce computation times associated with a large mesh size, only the dorsal side of the spinal cord and surrounding CSF was modeled using a computational fluid dynamics (CFD) software package, FLUENT (v. 6.3.26, Fluent, Lebanon, NH), which solved for porous media transport. Isolating this tissue region is valid given the localized transport associated with the small infusion volumes simulated. For the 3D computational tissue model, a rectangular volume (6 mm 6 mm 15 mm for in vivo data, 2.12 mm 4.27 mm 11.85 mm for excised data) covering the dorsal side was created (GAMBIT v.2.4.6, Fluent, Lebanon, NH), see Figure 1. The FOV of the image data sets (i.e., the axial length of the tissue models) limited the transient tracer analysis to small infusion volumes, < 4 l. 8node brick elements were used, and the mesh consisted of 48,000 and 829,440 nodal points for models created from in vivo and exci sed image data, respectively. Each brick element corresponded to an interpolated image voxel (30 m 30 m 150 m for excised and 150 m 150 m 500 m for in vivo tissue data) from the DTI data set. (Only a portion of the DTI image data set for excised, fixed tissue was rendered for the model). Within FLUENT, a user defined function was used to assign K and Dt for nodes in each element using the segmentation and property assignment methodologies of the previous sections. Additionally, a cube infusion site corresponding to the outer diameter of a 31 gauge needle (150 m 150 m 150 m) was placed in the white matter dorsal column at depths of 0.84 (T13) and 0.68 mm (L1) from the dorsal surface in the in vivo and excised tissue models, respectively. The infusion site was modeled as a region with constant pressure, which corresponded to a constant infusion rate of 0.1 L/min similar to the Wood study ( Wood et al. 1999) Equation 33~3 5 for interstitial fluid flow, pressure, and albumin tracer transport were solved within FLUENT using a control volume based technique. The conservation of

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38 momentum equation was replaced with Darcys law by introducing a momentum source term corresponding to Darcys law ( K1v). A convective acceleration term, which is still in place, were assumed to be negligible due to low fluid velocity and velocity gradient (convection acceleration term at the highest velocity region were found to be approximately 10 orders of magnitude lower than the momentum source term corresponding to Darcys law). For tracer transport simulations, a user defined flux macro was used to account for tracer diffusion anis otropy (Equation 35). Also a weaklycoupled solution was employed which assumes that albumin transport was not significantly affected by osmotic effects or changes in viscosity with changes in concentration (Steady state flow was observed to be establish ed less than 1 second). Therefore, tracer concentration predictions were predicted using a steady state velocity field. A s chematic diagram for the computational modeling procedure is provided ( Figure 3 2) It was also assumed that external boundaries w ere a sufficiently long distance from the infusion site such that flows or variations in pressure at these boundaries did not have a significant effect in the region of interest, and p=0 was assigned at all outer boundaries A normalized concentration of c =1 was assigned at the infusion site boundaries, and c =0 was assigned at outer boundaries. Initial conditions for albumin transport assumed no tracer in the tissue ( c =0). Axial distribution lengths and tissue distribution volumes for predicted tracer distributions were calculated using a threshold of ~15% of the maximum concentration. Tracer distribution volumes were calculated as the spread (or integrated tissue volume) i n white and gray matter regions only. To calculate average velocity profiles from the point of infusion, 9 virtual lines through the cube infusion site (with separate nodal points) were averaged together for each orthogonal direction.

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39 To determine the e ffect of voxel size (and element size) on predicted tracer transport, the highresolution DTI data set obtained for the excised spinal cord tissue was resampled at lower resolutions, and computational transport models with coarser grids were created from t hese lower resolution data. Predicted tracer distributions from these varying resolution data were compared (highresolution voxel size=30 m 30 m 150 m, mid resolution= 60 m 60 m 300 m, and low resolution=120 m 120 m 600 m). Threshold values used for tissue segmentation were adjusted with each data set to obtain comparable tissue volumes in each tissue region (~ 1% variation). 3.3 Results 3.3.1 DTI and S egmentation In vivo FA and excised tissue So scans of the rat spinal cor d show well defined regions of white and gray matter tissue ( Figure 31) The semi automatic segmentation scheme results in a small number of isolated white matterlabeled voxels in gray matter and some isolated gray matter labeled voxels in white matter. They result from locally high or low values of FA or S0 values, which may be due to local tissue structure variation. Since these small isolated tissue regions do not appear in the rat spinal cord atlas, we labeled thes e voxel regions as artifacts in Figure 31. Total artifact voxel volume was estimated less than ~2 % of the total spinal cord and CSF volume. Also, gray matter regions in the model generated from in vivo data were underestimated in dorsal horn regions and had an ~2 % smaller tissue vol ume than the spinal cord model generated from excised tissue data. Overall, white matter tissues volumes in this model were also ~1.5% smaller than in the excised tissue model.

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40 3.3.2 Interstitial Flow and Albumin D istribution Steady state interstitial fluid flow was predicted for 0.1 L/min infusion into the spinal cord white matter. The predicted interstitial fluid velocity dropped rapidly with penetration distance and was preferentially channeled along the axis of the spinal cord with larger velocity components in the z direction. Albumin distribution contours generated from in vivo and excised tissue data sets are overlaid on corresponding FA and S0 spinal cord images in Figures 33 and 3 4 respectively. Tracer spread conf ormed to anatomical white matter boundaries and was along the direction of the structured white matter tracts with preferential transport along the axis of the cord. Greater transverse spread of tracer was seen in the in vivo model with time due to connec ted dorsal and lateral white matter regions. Due to the lower hydraulic conductivity values assigned to gray matter ( Lonser et al. 1998; Wood et al. 1999) there was more limited tracer penetration into these regions over the time scales simulated (< 0.5 mm). While d istributions were relatively uniform within the white matter dorsal horn some dips in the concentration were noted in the vicinity of artifact voxels (assigned as gray matter). Conversely, local increases in concentration were predicted near artifact voxels (assigned as white matter) in the gray matter columns of the spinal cord. Convectiondominated regions estimated by Peclet number contours are presented in Figure 35. (Pe=v L / D where L is a length scale parameter, L =1 mm D is the tracer diffusivity coefficient (1.67107 cm2/s) and Pe >>1 in convection dominated regions.) These zones corresponded to white matter regions in the vicinity of the infusion site and extended significant distances from the point of infusion in the cranio caudal direction. The calculated Peclet number was as high as ~4900 (excised tissue model) and ~1800 ( in vivo data model) next to the infusion site and decreased proportionally with the velocity magnitude. Differences in the Peclet contours

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41 are due to local velocity differences that are confined to the immediate vicinity of the infusion site and are likely due to differences between embedded infusion sites. Overall, interstitial fluid flow in the excised spinal cord model is more confined by (1) gray matter horns that extend to the dorsal surface and (2) a more deeply embedded infusion site. Both of these effects results in greater channeling of flow and higher interstitial fluid velocities along the axis of the spinal cord. 3.3.3 Validation and Parameter A nalysis Predicted tissue distribution volumes for the albumin tracer were found to be consistent between the two computational spinal cord models generated from excised tissue and in vivo imaging data sets, as well as, the experimental distr ibution studies by Wood et al. ( Wood et al. 1999) that measured spread of 14C labeled albumin following CED into approximately the same region of the rat spin al cord ( Figure 36) Distribution volumes from models using the in vivo imaging (low resolution) data predicted larger distributions than those using excised (highresolution) data for the range of small infusion volume studied < 4 L. For simulations using baseline tissue transport parameters, normalized root mean square deviation values of 0.28 and 0.19 were achieved comparing predicted and experimental tracer distribution volumes for the models using in vivo and excised data, respectively. For the parameter sensitivity a nalysis varying the hydraulic conductivity of CSF, the relation between the tracer infusion volume and tissue distributions at the end of infusion (4 L) are presented in Figure 37A. This graph shows that tracer tissue distributions were within 3% of th e average distribution. The effect of varying the resolution or size of the imaging voxels used to create the computational model was also considered ( Figure 37B ) The voxel size range corresponded to highresolution scans for the excised tissue to lower resolution data comparable to in vivo scans. Final tracer tissue distributions versus the volume infused were compared and

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42 showed albumin tissue spread within 10% of the average distribution. This variation is likely due to changes in tissue boundaries with grid coarsening. This low variation shows consistency of predicted results within a range of likely imaging resolutions 3.4 Discussion This study presents a rapid, semi automatic segmentation approach for modeling interstitial transport in the spinal cord that avoids labor intensive and time consuming processes such as slice byslice contouring and polynomial surface reconstruction used in previous tissue transport modeling approaches ( Sarntinoranont et al. 2003a ; Sarntinoranont et al. 2003b; Sarntinoranont et al. 2006b; Linninger et al. 2008a ; Linninger et al. 2008b; Linninger et al. 2008c ) DTI derived FA and So values for both in vivo and excised tissue data sets were used to assign tissue transport properties for each voxel, and these properties were input into a voxelized computational model that predict ed interstitial transport using porous media equations. The computational model also accounts for interstitial transport anisotropy in white matter tissue Computational transport models using in vivo (low resolution) and excised tissue (high resolution) DTI data sets predicted tracer distribution trends observed experimentally including preferential transport along the axis of the cord and limited distribution in gray matter. Also, albumin concentration was dramatically decreased at boundaries between white matter and gray matter and CSF regions due to changes in K and D properties between these regions. Simulated tracer distributions showed an approximately linear relationship between distribution and infusion volumes ( Lonser et al. 1998; Wood et al. 1999) Non linear trends may increase with infusion volume as more tracer and fluid is channeled to adjacent CSF regions that offer less flow resistance.

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43 In addition, predicted tracer distributions were found to be comparable with experimental measures by Wood et al. in the rat spinal cord ( Wood et al. 1999) Predicted and measured tracer distribution volumes were comparable for small infusion volumes. Volume differences may be due to differences in spinal cord tissue volumes between animals, differences in infusion site location, and/or uncertainties in CNS transport properties such as porosity or hydraulic conductivity. It should be noted that few experimental data points are available for comparison at this time, e.g. 3 dat a points from Wood el al. Compared with experimental concentration profiles, the voxelized models also predicted greater variation in the concentration profiles (less uniform) due to the inclusion of artifact voxels within tissue regions, i.e., local tiss ue structure variations This tissue variation is a result of our semiautomatic segmentation scheme based on certain threshold values. However, the total volume for these artifact voxels was calculated to be small. Methods to account for the effects of fiber crossings in our DTI data set may further reduce the incidence of these voxels in the model. Tissue segmentation thresholds for FA or So were based on one DTI image data set each. Thus, the threshold values are specific to the particular image dat a set. In general, threshold values will vary between image data sets due to variation in signal to noise ratio, MR coil tuning, and other instrument factors, as well as differences between subjects. However, most of this variability will occur in the So value, since the FA value is more insensitive to these factors ( Bastin et al. 1998) and mainly depends on tissue structure. Some differences in tissue boundaries were noted between models generated using FA or So. In particular, substantia gelatinosa regions of the gray matter in the dorsal horn have larger FA values than adjacent gray matter due to fibers entering the spinal cord, so these regions were assigned as white matter in the in vivo data set model. The se tissue transition regions will likely exhibit some combination

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44 of white and gray matter transport behavior. However, additional experimental studies are required to determine how transport properties vary in these transition zones. In this study, assi gnment of these dorsal regions as white matter resulted in greater transverse spread of the albumin tracer due to connected white matter regions when compared with models that assign the same regions as gray matter using So thresholds. To allow for rapid m odeling, CSF regions were treated as a porous media with This assumption appears to be valid for our spinal cord transport model since fluid flow boundary layers that develop in the CSF likely have a small influence on transport within the spinal co rd. Parameter sensitivity studies showed that even after increasing CSF hydraulic conductivity, the relation between the tracer infusion volume and the final tissue distribution volumes were only slightly influenced. This showed insensitivity to this tr ansport parameter for small infusion volumes. The current model also does not account for local sources and sinks for interstitial fluid. This assumes an inactive lymphatic system, negligible water formation due to metabolism, and low rates of capillary uptake. However, this assumption may underestimate fluid transfer across the capillary walls and lead to some overestimation of interstitial tracer concentration, especially at higher infusion pressures or over longer infusion times than our current study. Parameter sensitivity studies for the effect of image voxel resolution showed greater tracer transport variation. After resampling the same DTI data set at varying resolutions, the predicted tracer distribution volumes decreased with resolution due t o the effect of discrete, stepwise boundary changes. Specifically, segmentation maps for the low resolution voxel model changed significantly with small changes in So threshold values resulting in changes in the predicted tracer distribution volumes. How ever after matching gray and white matter tissue volumes

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45 between models, the sensitivity of albumin tracer spread to changes in voxel resolution was reduced. In this study, MR scans of excised, fixed tissues were used to attain a high resolution DTI data set. The sample was surrounded by PBS fluid which was assigned CSF properties in our infusion transport model. As a result, greater CSF dilution of tracer is predicted than in vivo since the CSF volume is larger than the actual intrathecal space, see F igure 3. However, this effect appears to be minimal for small infusion volumes. For models generated using in vivo tissue data, a voxel layer of CSF was introduced surrounding the spinal cord to provide a low resistance pathway adjacent to the spinal cor d. Increasing in vivo DTI resolution scans may allow for direct segmentation of the intrathecal space in future studies. Other limitations of using excised, fixed tissue scans are associated with changes due to possible tissue shrinkage with fixation. F or example, nonuniform shrinkage may lead to changes in fiber orientation, i.e., the eigenvectors of De. We assume such changes to be small and fiber orientation will likely not change with uniform shrinkage. 3.5 Conclusions In this chapter a new voxelized modeling approach was developed using in vivo and excised MR diffusion tensor images to incorporate anisotropic tissue structure. This model provided estimations of 3D interstitial fluid flow and tracer distribution during CED Modeling results were compared with the experimental results performed by Wood et al. for validation. The developed computational models provided these useful insights into the effects of underlying transport forces and tissue structure on local CED transport; A new sem i automatic segmentation scheme provided the volume and shape of each structure in the central nervous system without labor intensive slice by slice volume reconstruction.

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46 Preferential interstitial fluid flow and tracer distributions were observed along t he white matter tracts with limited penetration into adjacent gray matter. The low resolution voxel model resulted in changes in the predicted distributions due to discrete, stepwise boundaries. Parameter analysis showed that CSF regions can be treated as porous media with for rapid modeling of small infusion volumes, < 4 L Table 31. FA and So ranges used to segment the spinal cord DTI data. FA ranges were used to segment in vivo imaging data sets. So was used for excised, fixed tissue data and two different ranges were used over the axial length of the spinal cord. The values of So were normalized by the surrounding PBS value Spinal Cord Region ( in vivo ) FA range White matter 0.466 1 Gray matter 0.05 0.466 Bone and surrounding tissues 0 0.05 Spinal Cord Region (excised) SO range (1 z 59) SO range (60 z 80) White matter 0 0.412 0 0.455 Gray matter 0.412 0.558 0.455 0.600 PBS fluid regions 0.558 1 0.600 1 ( z : Transverse plane slice number, slice thickness: 0.15 mm) Table 32. Tissue transport properties used in the interstitial transport simulations. D and K values correspond to tensor components of Dt and K Parameter Valu e Reference 0.26 ( Wood et al. 1999; Sarntinoranont et al. 2003a ) Dtgm 1.60 107 cm2/s ( Tao & Nicholson, 1996) Dtwm || 2.29 107 cm2/s ( Tao & Nicholson, 1996; Prokopova et al. 1997 ) Dtwm 1.34 107 cm2/s ( Tao & Nicholson, 1996; Prokopova et al. 1997 ) DCSF 1.34 107 cm2/s ( Tao & Nicholson, 1996; Prokopova et al. 1997 ) K wm|| 6.75 109 cm4/dyne s ( Sarntinoranont et al. 2006b) Kwm 4.22 1010 cm4/dyne s ( Sarntinoranont et al. 2006b) Kgm 4.22 1012 cm4/dyne s ( Sarntinoranont et al. 2006b) ( wm: white matter; gm: gray matter)

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47 Figure 31. DTI based Segmentation: A) FA image from a transverse DTI scan of the in vivo spinal cord at level T13 (voxel resolution=150 m 150 m 500 m). Gray matter tissue is hypo intense and white matter tissue is hyper intense. B) Corresponding S0 image with uniform intensity in gray and white matter, and C) tissue segmentation image used in the voxelized computational model (dark blue=white matter, li ght blue=gray matter, yellow=CSF, red=bone and surrounding tissues). D) FA image from a transverse DTI scan of excised tissue at L1 (voxel resolution = 30 m x 30 m x 150 m) and E) corresponding So image, where gray matter tissue is hyper intense and white matter tissues is hypo intense. F) Corresponding highresolution tissue segmentation image (blue=white matter, green=gray matter, red=free water region ). The yellow box outlines the dorsal tissue region used in the voxelized model. Artifact voxels res ulting from the semi automatic segmentation method are also identified.

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48 Figure 32. Schematic diagram for computational modeling procedure Steady State solver in Fluent (Conservation of mass equation and Darcys law) Interstitial velocity and pressure profiles Transient solver for tracer transport in Fluent (Convection diffusion equation ) Tracer distribution at different time frames We a kly coupled Diffusion Tensor Images Water diffusion (D e ) Fractional Anisotropy (FA) Signal intensity without diffusion ( S0) Segmentation (WM, GM, CSF regions) Max. eigenvector (Directions of max. transport) Eigenvalue s of tissue properties from literatures Hydraulic conductivity for each voxel Diffusivity for each voxel

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49 Figure 33. Predicted albumin distributions in the spinal cord using voxelized transport models generated from in vivo DTI (low resolution) data. Distribution contours in transverse and sagittal planes intersecting the infusion site are overlaid on FA images at varying times after the start of infusion (infusion rate=0.1 L/min). Tracer concentration contours are for normalized tissue concentrations.

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50 Figure 34. Predicted albumin distributions in the spinal cord using voxelized transport models generated from DTI of excised, fixed tissues (high resolution). Distribution contours from excised in transverse and sagit tal planes intersecting the infusion site are overlaid over So images at varying times after the start of infusion (infusion rate=0.1 L/min). Tracer concentration contours are for normalized tissue concentrations.

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51 Figure 35. Peclet number contour maps in the transverse plane of the spinal cord generated using voxel transport models from A) in vivo and B) excised tissue image data. Peclet contours are overlaid on So images in A) transverse and sagittal planes and B) transverse and coronal planes intersecting the infusion site. As an approximation, convectiondominated regions correspond to Peclet number > 300.

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52 Figure 36. Comparison of predicted and measured distributions of albumin tracer in the rat spinal cord following direct infusion into the dorsal horn. Tracer tissue volumes calculated from the voxel transport models using in vivo and excised tissue data sets are plot ted. Wood et al. measured distribution of 14C labeled albumin following CED into a similar region ( Wood et al. 1999) Bars correspond to 1 SD. The threshold value used for volume distribution analysis was 15% of the infusate concentration.

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53 Figure 37. Parameter sensitivity analysis comparing the final distribution volume (Vd) and the total infusion volume (Vi) on a loglog scale for A) the hydraulic conductivity of CSF and B) the image voxel resolution (highreso lution voxel size=30 m x 30 m x 150 m, mid resolution=60 m x 60 m x 300 m, and low resolution=120 m x 120 m x 600 m). Vd and Vi were calculated using the excised tissue data set. Vd was calculated for regions within the gray and white matte r tissue regions only. Solid lines correspond to the average Vd value 3% and 10% for the set of K ratios and voxel resolutions simulated, respectively.

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54 CHAPTER 4 DEVELOPMENT OF VOXELIZED 3D COMPUTATIONAL TRANSPORT MODELING OF CED INTO THE RAT BRAIN AND PARAMETER ANALYSIS 4.1 Introduction Chapter 3 explained the development of the voxelized modeling methodology for the rat spinal cord. Namely, DTI data was used to assign tissue boundaries, transport properties, and preferential transport directions within a 3D spinal cord transport model. This chapter aims to adopt the developed methodology for the rat brain. By using this technique, tissue transport models for the rat corpus callosum and hippocampus were developed and interstitial pressure, interstitial velocity fields, and tracer transport were predicted for CED. High resolution DTI data that was obtained from a fixed brain provided sufficient mesh resolution for rapidly converging transport predictions. In parameter analyses, sensitivities of predicted CED tracer distribution to changes in FA thresholds used for segmentation, DTI voxel resolution, tissue porosity, infusion site, and transport properties were demonstrated. This study was published in Medical and Biological Engineering and Computing ( Kim et al., 2010) This work was done in collaboration with Dr. Thomas H. Mareci (Department of Biochemistry and Molecular Biology, UF). 4.2 Methods 4.2.1 Diffusion Tensor I maging Dr. Paul Carney (Department of Pediatrics, Division of Pediatric Neurology, UF) provided the fixed, excised rat brain sample. Mansi Parekh (Department of Neuroscience, UF) collected DTI data at the Advanced Magnetic Resonance Imaging and Spectroscopy Facility in the McKnight Brain Institute (AMRIS) of UF. Animal preparation: Use of excised, fixed tissue in DTI scans allowed for the long scan times necessary to obtain high resolution micro structural information of the rat brain. S urgery was conducted in accordance with the NIH guidelines on the use of animals in research and the

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55 regulations of the Animal Care and Use Committee of the University of Florida. Once anesthetized, rats were exsanguinated then perf usion fixed with a 4% solution of paraformaldehyde in phosphate buffered saline (PBS). After overnight fixation, the brain was removed and stored in the fixative solution. Before imaging, the tissue was soaked overnight in PBS to remove the fixative. The rat brain was imaged in fluorinated oil, and DTI data sets were obtained using a 17.6 Tesla magnet. Image processing: Multiple slice images, weighted by water translational diffusion, were measured (~11 hrs) using a spinecho pulse sequence. Measurement s w ere performed with recovery time of 1400 ms, and echo time of 28 ms. The diffusionweighted images were acquired with a field of view 30 mm x 15 mm in a matrix of 200 x 100 in 32 slices of 0.3 mm thickness. This is a resolution of 150 m 150 m 300 m. Images with low diffusionweighting (100 s/mm2) and high diffusionweighting (1250 s/mm2) were measured with 5 averages in 6 gradient directions and 46 gradient directions, respectively, specified by the tessellations of an icosahedron on the unit hemisphere. Diffusion weighted images were interpolated (bilinear interpolation with nearest neighbor sampling) by a factor of two in the slice direction (data matrix of 200 x 100 x 64). After initial image processing, the multiple slice DTI data was fit to a rank 2 tensor model of water translational diffusion, De, using multiple linear regression ( Basser et a l. 1994) The effect of gradient crossterms was included in the calculation of the diffusion tensor. The diffusion tensor, the T2 weighted signal intensity in the absence of diffusionweighted gradients (So), and fractional anisotropy (FA) which is a scalar measure of anisotropy were calculated using methods previously describe in section 3.1.2.

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56 Segmentation: A semi automatic methodology which was developed in the C hapter 3 was implemented to reconstruct a three dimensional rectangular tissue volume with regions delineated for isotropic gray matter and anisotropic white matter and CSF spaces (free water). FA values from the DTI data set were used to differentiate between voxels of different tissues and free water regions. Ranges of FA threshold val ues, Table 4 1, were adjusted, using visualization software (Amira v.4.1, TGS, San Diego, CA) until selected tissue regions conincided with anatomical boundaries for white matter, gray matter and CSF spaces in a rat brain atlas ( Paxinos G., 2007) Figure 41 4.2.2 Interstitial Transport M odel For the interstitial transport model of the brain, the semi automatic voxelized modeling methodology was applied. Details of the method are described in section 3.1.3. Computational model: For the 3D transport models, two rectangular volumes covering portions of the rat brain were created using meshing software (GAMBIT v.2.4.6, Fluent, Lebanon, NH). Meshed tissue volumes were 9 mm 7.5 mm 9.45 mm for the corpus callosum region and 12 mm x 7.35 mm x 9.45 mm for the hippocampal region. Eight node brick elements were used and each mesh element corresponded to an interpolated image voxel element (150 m 150 m 150 m) from DTI data. Cube shaped infusion sites corresponding to the outer diameter of a 31 gauge needle (150 m 150 m 150 m) were placed in the middle of the tissue volumes according to the following approximate stereotactic coordinates within the corpus callosum (AP = 0.72 mm, ML = 3.75 mm, DV = 3.6 mm) and the hippocampus (AP = 6.00 mm, ML = 5.00 mm, DV = 5.00 mm) A constant infusion rate of 0. 3 L /min, similar to that used in the Greer and Grossman study ( Geer & Grossman, 1997) was simulated at these sites.

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57 Parameter analysis: In all parameter studies, final tissue distribu tion volumes for 5.1 L tracer infusions were compared. These tissue distributions volumes were calculated by adding together voxels that exceeded a threshold value of ~5% of maximum concentration. Computational modeling parameters of interest included t he FA thresholds used for segmentation and the voxel resolution of DTI data sets. FA thresholds used for white matter segmentation were varied over three different ranges: 0.275 to 1.0 (baseline), 0.30 to 1.0, and 0.34 to 1.0. FA ranges of 0.30 to 1.0 and 0.34 to 1.0 slightly under estimated white matter regions ( Figure 4 2A 4 2D ) The effect of varying image resolution was also considere d and the high resolution DTI data set was resampled at lower resolutions. However at low voxel resolutions of 600 m x 600 m x 600 m, difficulties were encountered in obtaining segmentation maps that were representative of the selected rat brain structures with major features of the corpus callosum, internal capsule, and hippocampus (i.e., granular layer of dentate gyrus and CA3) being lost. As a result, only data resampled at 300 m x 300 m x 300 m resolution was used to generate trans port models with coarser meshes ( Figure 4 2E and 42F ) The effect of varying FA threshold values on the lower resolution data set was also evaluated and predicted tracer distributions for two different FA threshold ranges (0.275 to 1.0 and 0.29 to 1.0) for white matter segmentation were compared. Parametric studies were conducted to evaluate the effects of changing tissue propert ies varied tissue porosity (0.22, 0.26, 0.30), the ratio of the hydraulic conductivity parallel to the fiber tracts to the conductivity perpendicular to fiber tracts ( K||/ K=16 and 24) and the ratio of white matter to gray matter hydraulic conductivity (Kw m/Kgm=50, 100, and 150 where Kwm is the hydraulic conductivity perpendicular to the fiber tracts). These tissue property ranges were selected based on a previous parameter analysis of a spinal cord CED model ( Sarntinoranont et

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58 al., 2006b) The effect of endogenous fluid flow on CED transport was also considered. For these cases, a fluid mass generation term corresponding to fluid sources from capillaries, microvasculature and active secretion by the cerebral endothelium was applied uniformly in all tissue regions (0.1 0.3 L/ming as estimated by Abbott ) ( Abbott, 2004) 4.3 Results 4.3.1 Predicted Fluid Flow and T racer D istribution Interstitial f low : Steady state interstitial fluid flow fields were predicted for 0. 3 L/ min infusions into the corpus callosum and hippocampus ( Figure 43) Simulated flow was directed outwardly from the infusion site with highest velocities (~ 1.96 105 m/s in the corpus callosum and ~ 1.99 105 m/s in the hippocampus ) and highest pressures (~2.01x105 dyne/cm 2 in the corpus callosum and ~3.57 x105 dyne/cm 2 in the hippocampus) adjacent to the infusion site For corpus callosum CED, preferential fluid flow was found along white matter tracts and fluid velocities in white matter regions were two orders of magnitude greater than in neighboring gray matter ( Figure 4 3A ) These flow patterns were as expected since white matter tissues have more conducive fluid transport properties than gray matter. For hippocampal CED, the predicted highest velocity flows were al so confined within white matter ( Figure 43B ) However, a more convoluted fluid flow pattern was predicted since the hippocampus has a more complicated structure consisting of layers of white matter (i.e., molecula r and pyramidal cell layers) and gray matter (granular cell layers). Infusion pressures at the hippocampal site were predicted to be higher than for the corpus callosum where the infusion site was embedded in a larger volume of white matter, since gray ma tter has a lower hydraulic conductivity (greater resistance to fluid flow) than white matter.

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59 Albumin t ransport : Corpus callosum and hippocampus CED models showed different tracer distribution patterns due to differing tissue structures. Predicted albumin distributions for corpus callosum CED are shown in Figure 44 for infusions up to 4.5 L Preferential spread of albumin was along the direction of the structured white matter tracts as shown in the FA map of Figure 41. Spatial distribution profiles showed relatively flat concentration profiles with steep concentration drops at the advancing front. At the final simulated infusion time ( t = 17 min; 5.1 L total infusion volume; not shown), the albumin tracer was predicted to penetrat e less than 1 mm i nto adjacent gray matter regions. Tracer distributions for hippocampal CED are shown in Figure 45. Tracers were predicted to distribute rapidly within white matter regions, most likely along granule cell dendrites (mossy fibers and pyramidal cells) in t he molecular layer of the dentate gyrus in the ventral hippocampus, and then spread throughout interspersed gray matter Within this hippocampal model, tracer volumes within gray matter hippocampal regions were found to be larger than within white matter hi ppocampal regions. Overall, albumin tracer was predicted to penetrate greater distances into gray matter compared to the predicted penetration within the corpus callosum. In both models a linear relationship was predicted between total infusion volumes and total tissue distribution volumes over the range of infusion volumes studied, < 5.1 L. Albumin tracer was also predicted to spread into CSF regions once a threshold infusion volume was reached (~0.3 L). For the chosen infusion sites, the volume of tracer entering CSF regions was minimal compared with the total distribution volumes simulated. The maximum Peclet numbers (1.18x103) for corpus callosum CED and 1.19x103) for hippocampal CED) were determined to be adjacent to the infusion site Pe was f ound to decrease proportionally with velocity magnitude and distance from the infusion site Figure 43C. C onvectiondominated transport regions ( Pe >> 1) estimated using Pe values of 30 were found to

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60 extend significant distances from the point of infusion and corresponded to white matter and adjacent tissue regions. 4.3.2 Parameter analysis Computational model parameter analysis: By increasing the FA threshold value from 0.275 to 0.34, segmented white matter volumes were decreased by 28% in the corpus ca llosum model with minimal effect on the connectivity of the fiber structure. Segmented white matter volumes in the hippocampus model decreased by a greater amount, 54%, and there was significant loss of connectivity of white matter structures. This dispro portionate change is due to the fact that FA values within fiber tract regions of the corpus callosum were relatively higher resulting in less sensitivity to FA changes. Correspondingly, predicted tracer distributions in the corpus callosum were changed <1% by changes in FA thresholds Figure 46A. In the hippocampus, predicted tracer distributions were minimally effected changing the FA threshold from 0.275 to 0.3. However, increasing the threshold to 0.34 resulted in an ~10% decrease in the predicted distribution volume after 5.1 L infusion, Figure46B since connectivity within the white matter structures was lost. This local dependent sensitivity is likely due to differing tissue composition; the corpus callosum consists primarily of bundles of myel inated axons with strong alignment and greater tissue density ; whereas, the hippocampus has more varied neuronal tissue and a less dense structure that results in weaker alignment ( Freund & Buzsaki, 1996) Spatial variation of FA values within differing brain regions has been previously reported by Le Bihan ( Le Bihan et al. 2001) CED simulations using lower resolution voxels ( 300 m3) resulted in 6.5% and 6.7% decreases in final tracer distribution volumes within the hippocampus and corpus callosum, respectively, after 5.1 L infusions ( Figure 46C and 46D ) The larger voxel size resulted in a

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61 loss of structural information and connectivity of finer white matter structures was again lost within the hippocampus. The effect of varying the segmentation threshold at this lower resolution was also considered. Predicted tracer distribution volumes within the hippocampus and corpus callos um increased by 11% and 2% when the FA threshold was varied between 0.275 and 0.29. Overall increases in tracer distributions were likely due to changes in tissue boundaries with grid coarsening. In higher resolution simulations predicted distributions were more sensitive to changes in FA threshold values when compared to lower resolutions. Infusion p arameter analysis : The effect of varying tissue porosity (0.2, 0.26 and 0.3) on final tracer distribution volumes is shown in Figure 46E and 46F. As expected, lower tissue porosities resulted in greater tracer distributions for the same infusion volume and tracer distribution volumes varied approximately inversely with porosity. This trend was expected since a smaller fluid volume per unit tissue volume results in greater pore level velocity. Tissue transport parameter analyses for K||/K and Kwm/Kgm ratios were also conducted (not shown). However, f inal albumin distribution volumes were only changed by less than ~0.4% (hippocampus) and ~0.1% (corpus c allosum) when the white matter K||/K ratio was varied between 16 and 24. Relative changes between white and gray matter transport properties, ( i.e. the Kwm/Kgm ratio ) were found to affect the predicted albumin distribution volumes to some extent. Increasing the Kwm/Kgm ratio from 50 to 150 resulted in ~5% to ~7% increases in tracer tissue volumes within the hippocampus and corpus callosum after 5.1 L infusions. T he effect of endogenous fluid flow on CED transport in the corpus callosum and hippoc ampus was also considered The resulting CED tracer distribution volumes changed less than ~1% over the CED infusion period for the endogenous flow rates investigated.

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62 4.4 Discussion The voxelized modeling approach of this study utiliz ed DTI data to assign tissue boundaries, transport properties, and preferential transport directions within 3D brain transport models. This methodology reli ed on minimal user input and provide d a relatively rapid process when compared with previous manual image segmentation and volume meshing processes used for construc ting models of the brain with complex white matter structures. By using this technique, tissue transport models for the rat cor pus callosum and hippocampus were developed, and estimates of interstitial pressure and velocity fields and tracer transport were predicted. The high resolution DTI data obtained from a fixed brain provided sufficient mesh resolution for rapidly converging transport predictions. In parametric analyses, predicted CED tracer transport was stable over the variable ranges tested and CED tracer distributions were most sensitive to changes in FA thresholds used for segmentation, DTI voxel resolution, tissue por osity and infusion site. To a lesser extent, predicted distributions were also sensitive to relative differences in gray matter and white matter transport properties. For CED into the corpus callosum, the computational model predicted preferential tracer transport along white matter tracts in the mediallateral direction with limited penetration into adjacent gray matter. Significant tracer spread in the white matter wa s consistent with experimental observations by Greer and Grossman ( Geer & Grossman, 1997) following infusions int o the corpus callosum and experimental observations by Prabhu et al ( Prabhu et al. 1998) for infusions into the putamen. In the hippocampus, previous researchers have investigated the therapeutic response of compounds following CED ( Schott et al. 1998 ; Zhung et al. 2002; Heiss et al. 2005) ; however, corresponding distribution studies in the hippocampus are sparse and difficult to compare.

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63 Differences in CED transport between the two brain sites were determined by comparing tracer distribution volumes and infusion pressures. Tracer di stribution volumes in the hippocampus were predicted to be greater in gray matter than in white matter; whereas, tracer infusions into the corpus callosum followed the opposite trend. These distributions may be explained by differences in aligned tissue structures and tissue composition between the two infusion sites. At the hippocampal infusion site, there is a relatively smaller volume of white matter (likely corresponding to aligned mossy fibers extending from granule cell laye rs). Once white matter tissue wa s filled, tracer was transported into the surrounding gray matter. Gray matter penetration may also be facilitated by the greater cell connectivity between the layers of white and gray matter within this region which was reflected in the underlying fiber structure. With CED into the corpus callosum, tracers preferentially distribute d within the relatively larger white matter structure before transporting into adjacent tissues, resulting in a greater ratio of white matter spread. Also, s ince gray matter has lower hydraulic conductivity (greater resistance to fluid flow) than white matter, infusion pressures at the hippocampal site were predicted to be higher than for the corpus callosum where the infusion site was embedded in a larger vol ume of white matter. CED transport predictions were found to be sensitive to tissue segmentation parameters. Varying the FA range used for white matter segmentation changed the tissue composition within models and the hippocampus model was more sensitive to changes in FA thresholds. Location dependent sensitivity wa s likely due to differing tissue composition; the corpus callosum primarily consists of bundles of mylenated axons with strong alignment and greater tissue density, whereas, the hippocampus has more varied neuronal tissue and a less dense structure that results in weaker alignment ( Freund & Buzsaki, 1996) Spatial variation of FA volume

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64 within di ffering brain regions has been previously reported by Le Bihan ( Le Bihan et al. 2001) In addition, it should be noted that CSF regions were not always correctly assigned using this FA based segmentation approach. Assigned CSF regions did not completely match those of the brain atlas ( Paxinos & Watson, 1998) This may have led to some error of tissue distributions near CSF regions. However, loss of tracer into adjacent CSF regions was found to be small for the selected infusion sites. Artifact voxels as described in the results section were also introduced with FA bas ed segmentation. Tracer predictions were found to be insensitive to the presence of these voxels with no concentration jumps found near infusion sites due to the fact that total artifact voxel volumes were a small percentage of total model volumes. Incre asing the number of these voxels could lead to variation in concentration and pressure profiles For example, our voxe lized spinal cord models predicted comparable distribution volumes to those measured experimentally, but concentration profiles were less uniform in the vicinity of artifact voxels ( Sarntinoranont et al. 2006a ) These artifact voxels are likely due to local tissue structure variation s, e.g., cros sing fibers, or maybe due to other imaging limitations, e.g., edge boundary effects. Methods to account for the effects of fiber crossings in the DTI data set may further reduce the incidence of these voxels ( Tuch et al. 2002; Hess et al. 2006 ; Ozarslan et al. 2006) Model predictions were also found to be s ensitive to the DTI resolution. Simulations that resampled the DTI data at lower resolutions predicted lower tracer distribution volumes This wa s likely due to partial voxel volume effect s since the entire volume of all voxels under the concentration t hreshold were added together to calculate distribution volumes. Thus, it is possible that at the lower resolutions used in in vivo studies, voxelized transport models will underestimate CED tissue distributions depending on the concentration threshold val ue. Also, distribution patterns will likely change with spatial averaging and fine transport pathways within

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65 complex fiber regions may be lost. Care must be taken when determining if DTI data sets possess sufficient resolution to capture underlying transport characteristics. Future studies will focus on validating this modeling method using lower resolution DTI data sets obtained in vivo After varying tissue transport properties, CED transport was predicted to be most sensitive to changes in tissue poro sity with lower porosities resulting in greater tracer spread. This trend was expected since a smaller fluid volume per unit tissue volume results in greater porelevel velocity. Thus, tracer convection was inversely proportional to tissue porosity. Por osity values were estimated from previous experimental CNS studies for normal and edematous states but were not measured at the specific brain regions used in this study. Given the sensitivity of the models to this parameter, additional measures of porosi ty, especially under CED conditions, are necessary. Varying the white matter K||/K ratio was found to have only a small effect on predicted tracer distribution volumes. Transport sensitivity to hydraulic conductivity anisotropy was found to be less than in our previous spinal cord CED model ( Sarntinoranont et al. 2006a ) in which white matter was adjac ent to CSF. In the brain, the different embedded nature of the white matter tracts provides a significant difference since flow from white matter is primarily distributed into adjacent gray matter and not into CSF. CED transport was slightly more sensiti ve to relative changes in white and gray matter transport properties, Kwm/Kgm. Fluid velocities in white matter increased with increases in Kwm/Kgm, and convective tracer transport was enhanced in these regions. Changes in cannula placement and infusion rates within the same brain structure were also investigated. Tracer distribution patterns and tissue volumes were minimally affected by small changes in location. However, significant changes in infusion pressure were predicted depending on if the cann ula was placed within either white or gray matter. Again, higher

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66 infusion pressures were predicted in gray matter due to its lower hydraulic conductivity. These results suggest that pressureinduced effects including fluid efflux or tissue damage may var y with cannula location. Varying infusion rates did not affect predicted tracer distribution volumes. This result was expected for the rigid porous media model since transport properties did not change with flow rate or pressure. E ndogenous flows over a range of flow rates were previously estimated by Abbott (0.1 0.3 L/ming ( Abbott, 2004) ) and predicted to minimally effect tracer distributions during the course of CED infusions. The effect of this underlying tissue flow on tracer transport was expected to be small over short time scales. T he effect of such flows over longer time periods fo llowing CED may be more substantial, e.g., affecting tracer clearance, since endogenous flows will continue to spread tracer after the end of infusion. In this study, limitations of using fixed tissues were associated with changes due to tissue shrinkage with fixation or expansion due to infusion in tissue during CED. With uniform shrinkage, fiber orientation wa s not expected to change ; thus FA fields were not expected to significantly change. Also, CSF regions surrounding the brain were overestimated s ince the skull region was not included in the fixed tissue scans. However dilution of tracer in CSF likely has a small effect on internal tissue distributions, which are dominated by transport that occur s primarily in one direction, from the tissue into the CSF. In this study, a methodology for incorporating DTI data to rapidly develop interstitial transport models of the brain is presented. The developed computational models provide d useful insight into the effects of underlying transport forces and t issue structure on local CED transport. To advance these models, improved segmentation schemes may be incorporated and additional measures of tissue porosity should be obtained given the sensitivity of mo del results to

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67 segmentation and porosity. Also, further experimental CED and DTI imaging studies are needed to test this modeling approach in vivo It should be noted that while high field magnets and long imaging times were required to develop these models for the small animal rat brain, similar DTI met hods have been developed for clinical use. These methods allow fast data measurement at a resolution on a human scale ( Le Bihan et al. 2001) that captures the structural features similar to the resolution on the size scale used in this study. Thus with further development these imagebased models may eventually be used as surgical tools to guide CED 4.5 Conclusions This study demonstrated that the voxelized modeling methodology developed in C hapter 3 was applied for CED in more complex structures such as the rat brain. It was also shown that tracer distribution and interstitial fluid flow patterns at different infusion sites (corpus callosum and hippocampus) change d due to tissue structures surrounding infusion sites. The following aspects were highlighted in this chapt er : Three dimensional computational transport models were performed for CED in the corpus callosum and the ventral hippocampus, and predicted interstitial velocity field and tracer distribution. Sensitivity of models to changes in infusion parameters, transport properties, and modeling parameters was determined. Predicted tracer distributions were most sensitive to changes in segmentation threshold, DTI resolution, tissue porosity, and infusion site.

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68 Table 41. Fractional anisotropy (FA) ranges used in tissue segmentation of the excised rat brain Brain Region FA range White matter 0.275 FA 1 Gray matter 0.1 FA < 0.275 Free water regions( CSF ) 0 FA < 0.1 Figure 41. Tissue segmentation of the excised rat brain using DTI derived FA: (Left) FA map of the coronal plane; (Right) corresponding tissue segmentation map of a reflected image (green: gray matter, red: white matter, blue: free water region). In FA images, white corresponds to FA=1 and black cor responds to FA=0. Solid arrows point to artifact voxels. Colored lines correspond to planes intersecting the point of infusion within the corpus callosum.

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69 Figure 42. Variation in segmented white matter regions (red) within the corpus callosum (right column) and hippocampus (left column) for different FA threshold values and DTI voxel resolutions. (A & B) white matter range of 0.275
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70 Figure 43. Predicted velocity contours for infusions into the A) corpus callosum and B) hippocampus in coronal planes. C) Peclet number contour map for hippocampal infusion (coronal plane). CED infusion rate was 0.3 L/min. Contours are overlaid on corresponding FA image s (white corresponds to FA=1 and black corresponds to FA=0). Figure 44. Predicted albumin distributions during infusion into the corpus callosum in coronal planes. Tracer distributions at increasing times A) 5 min, B ) 10 min, and C ) 15 min are shown. CED infusion rate was 0.3 L /min. Concentration contours are normalized and overlaid on corresponding FA images (white corresponds to FA=1 and black corresponds to FA=0).

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71 Figure 45. A lbumin distributions during infusion into the hippocampus in coronal planes. Tracer distributions at increasing times A) 5 min, B ) 10 min, and C ) 15 min are shown. CED infusion rate was 0.3 L /min. Concentration contours are normalized and overlaid on c orresponding FA images (white corresponds to FA=1 and black corresponds to FA=0).

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72 Figure 46. Sensitivity of predicted tracer distribution volumes in the corpus callosum (left column) and hippocampus (right column) to varying (A & B) FA threshold val ues, (C & D) DTI voxel resolution, and (E & F) tissue porosity. Baseline tissue properties used in simulations: K||/K =16, Kwm/Kgm =100, and infusion rate =0.3 L/min

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73 CHAPTER 5 MEASUREMENT OF IN VI VO TRACER DISTRIBUTI ON DURING CED INTO THE DORSAL AND VENTRAL HIPPOCAMPUS OF THE RAT BRAIN 5.1 Introduction In this chapter, in vivo experimental studies of direct infusion in the rat brain were performed to investigate infusate distribution patterns in complex tissue structures during local drug delivery The dorsal and ventral hippocampus were selected as infusion sites. Surgical procedures and MR imaging protocols were developed to visualize in vivo tracer distribution patterns during infusions. Albumin tracers tagged with MR visible contras t agents and Evans Blue dyes were infused to visualize distribution in MR and histological slice images, respectively. T1 weighted dynamic contrast enhanced MR imaging (DCE MRI) provide d consecutive MR images to track the evolution of tracer distribution patterns during CED. T1 weighted imaging after direct infusion also provided final tracer distributions with high resolution. Evans Blue images showing tracer distributions in histological slices were obtained to confirm the final tracer distributions in MR images. Due to the nature of this experiment, several people provided assistance in their respective areas. The experimental procedure mentioned in the method sections were performed with assistan ce from Garrett Astary and Tatiana L. Nobrega (Department of Biomedical Engineering, UF) Garrett Astary helped to develop the MR imaging protocols and MR segmentation scheme, and collaborat e in collecting MR data Tatiana L. Nobrega assisted in assembling infusion system and measuring inline pressu re. Dr. Thomas H. Mareci (Department of Biochemistry and Molecular Biology, UF) provide d technical advice for analyzing MR imaging data. Surgery was performed at Dr. Paul Carneys lab (Epilepsy Research Laboratory, UF). MR data was collected at the Adva nced Magnetic Resonance Imaging and Spectroscopy Facility (AMRIS) in the McKnight Brain Institute of UF.

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74 5.2 Materials and M ethods 5.2.1 Infusion system Gadolinium diethylene triamine pentaacetic acid labeled albumin [(Gd DTPA)35Albumin] tagged with Evans Blue dye (R. Brasch Labortory, University of California, San Francisco, CA) was prepared as a tracer used for contrast enhancement in MR imaging. Phospate buffered saline (PBS) was used to dilute (GdDTPA)35Abumin to obtain a 10 mg/mL concentration of (GdDTPA)35Albumin (MW ~ 87 kDa with ~35 GdDTPA molecules per albumin molecule) for optimal contrast enhancement in MR images. A 100 L gas tight syringe (Hamilton, Reno, NV) driven by a syringe pump (Cole Parmer 749000, Col e Parmer, Vernon Hills, IL) was used in the CED infusion system. The syringe pump, which is not MR compatible, was placed outside of the MR room containing the magnet. The syringe was connected to 3 m of polyaryletheretherketone (PEEK) tubing (ID = 0.254 mm, OD= 1.5875 mm, Valco Instrument Houston, TX). The PEEK tubing was connected to a silica infusion cannula. The silica cannula (ID = 40 m, OD = 104 m, Polymicro Technology, Phoenix, AZ) was implanted into the brain. The twoway valve served as a connection between the syringe and a PEEK tubing adapter to prevent undesired infusion during transportation and handling. For experiments including pressure measurements, an additional threew ay connector (Valco Instrument, Houston, TX) was placed between the twoway valve and PEEK tubing to couple a fiber optic pressure sensor (FISO Technologies, Qubec, CA ). Fiber optic pressure transducers have an extrinsic optical cavity which interfaces w ith the optical fiber on one end and a diaphragm on the opposing end. The diaphragm deforms in response to applied pressure in turn changing the cavity length. Prior to infusion the transducers were zeroed to obtain baseline intracranial pressure values. The transducers operational range was 460 1960 mmHg with a

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75 resolution of less than 1 mmHg. Data was acquired using a UMI4 signal conditioner (FISO Technologies, Quebec, CA) at a sampling frequency of 20Hz. Dynamic pressure calibrations were performed to obtain apparent pressure without the pressure drop across the infusion system, from the transducer to the cannula tip, under the given infusion parameter. 5.2.2 An imal Preparation and Surgical Procedure Experiments were conducted on male Spra gue Dawley rats (n=6) weighing 250350 g using protocols and procedures approved by the University of Florida Institutional Animal Care and Use Committee. Animals were initially anesthetized with xylazine (10 mg/kg, SQ) and isoflurane (4%) in 1L/min oxygen, and then pla ced in the head holder of a stereotaxic frame (David Kopf Instruments, CA), where inhalation anesthesia (0.4 L/min oxygen with 1.5% isoflurane) was delivered via a nose mask. A heating pad was placed under the rat to maintain core temperature. A mid sagi ttal incision was made between the eyes and extended ca udally to the level of the ears and the cranium was exposed by scraping off underlying muscle and periosteum. The coordinates for each infusion site were determined using stereotactic coordinates based on a brain atlas ( Paxinos G., 2007) Three m illimeter diameter burr holes were drilled into the skull above the infusion sites. A silica cannula, connected to the infusion system primed with Gd DTPA albumin with Evans Blue dye, was then stereotaxically implanted into the dorsal dentate gyrus of the hippocampus (AP = 3.7 mm, ML = 2.2 mm, DV = 2.75 mm) The silica cannula was secured in place using skull fixture adhesive (Cerebond, Coretech Holdings company, MO). The second silica cannula was implanted into the ventral CA1 subregion of the hippocampus (AP = 5.88 mm, ML = 5.1 mm, DV = 5.2 mm) in the same manner Figure 51 shows the surg ical setup for implanting cannulas into the brain. Immediately following the infusion surgery (~2 hours), animals were transport to the 11.1 Tesla magnet. Saline (2 ml) was provided to animals to avoid dehydration during experiments. Animals were placed on a MR

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76 compatible stereotaxic frame for proper positioning of an RF coil in a magnet bore, while maintaining anesthesia (2% isoflurane in 1 L/min oxygen) for MR imaging, Figure 5 2. R espirat ion and body temperature were also measured (SAI Inc., Stony Brook, NY) to monitor physiological conditions A proportional integral derivative (PID) air temperature controller was used for maintain ing body temperature. After animals were placed w ithin the magnet bore, 8 L and 10 L of Gd DTPA albumin were infused into the dorsal and ventral hip pocampus respectively with infusion lines extending from the bore of the magnet to a safe operational distance for the syringe pumps, Figure 53. At the end of the experiment, animals under inhalation anesthesia (1.5% in 1.5 L/min oxygen) were given xylazine (10 mg/kg, SQ) and ketamine (80 mg/kg, IP). Upon ensuring deep anesthesia, the chest activity was opened to expose the heart, and a needle connect ed to an infusion pump was inserted into the left ventricle and clamped in place and an incision was made in the right atria. Two to three hundred milliliters of 0.9% saline solution was circulated by the he art, followed by 200300 ml of 10% paraformaldeh yde solution. Following decapitation, the brain was extracted from the skull and stored in 10% paraformaldehyde solution overnight. 5.2.3 In V ivo MR Image P rocessing and Segmentation In vivo MR imaging was conducted using a Bruker Avance imaging console (Bruker NMR Instruments, Billeria, MA) connected to a 11.1 Tesla horizontal bore magnet system (Varina Inc., Magnex Scientific Products, Walnut Creek, CA). A custom made 130 degree arc, 3.5 cm rectangular l inear surface coil constructed on a 4 cm diameter half cylinder was used for linear transmission and detection of MR signal. Before infusion, three transverse T1 weighted spinecho images were obtained with a 20 x 20 x 10 mm3 (read x phase x slice) field of view (FOV) in a matrix 1 04 x 104 with 10 slices with read in the lateralmedial direction to determine the

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77 baseline signal in the brain tissue. M easurements were performed with a recovery time, TR = 330 ms, echo time (TE) of 9.4 ms, and number of avera ged signals, NA = 6. During the infusion, T1 weighted spinecho images were repeated serially to capture the evolution of the infusate distribution. Each scan was obtained with a total acquisition time of ~ 3.5 min Following the infusion, t he highresol ution T1weighted spin echo images (TR = 1000 ms, TE = 15 ms, 30 slices at 0.5 mm thickness, NA = 8, 2.4 x 2.4 cm FOV with 200 x 200 matrix) were acquired to confirm the final distribution pattern. Figure 54 shows the schematic diagram summar izing these MR imaging procedures Final distribution volumes of Gdalbumin were calculated by performing semi automatic image segmentation on the highresolution T1 weighted coronal images using the ITK SNAP opensource medical image segmentation tool (Yushkevich et. al; http://www.itksnap.org/). Dorsal and ventral hippocampus infusion volumes were segmented separately with the following specific threshold criteria. Voxels were included in the infusion volume if their signal intensity was at least 6 standard deviation s of noise higher than the signal intensity in the corresponding region contralateral to the site of infusion. Final distribution volumes in the dorsal and ventral hippocampus were calculated by counting the number of voxels included in each segmented regi on and multiplying by the volume of a single voxel. 5.2.4 Brain T issue S lice The fixed brain was mounted on a vibratome (Lecica VT 1000A, Leica Microsystems Inc., Germany) and cut into 300 m thick coronal slices. The brain was sliced 2 mm from the infusion site in both the anterior and posterior direction to obtain all slices where infusate was distribut ed T he sliced brain tissue was placed on glass slides. The slides were mounted on an Optixcam microscope (Microscope Store, LLC, Wr irtz, VA) to obtain distributions of Evans

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78 blue in the brain slices. Th is data was used to confirm the final distribution of tracer in MR images at given coronal slice locations. 5.3 R esults 5.3.1 Develop ment of Surgical Procedure Initially C ED experiment s were performed using the surgical procedure previously described in section 5.2.2 However, experimental results (n=14) were not useful due to unexpected factors such as severe backflow, delayed infusion and administration of a bolus injection due to cannula clogging. The cannula clogging resulted in backflow and misleading total infusion volume T ime required for the infusate to be observed was at least 17 min in most cases, and in some cases, it never came out Figure 55 showed dynamic MR images at various times for normal distribution and delayed distribution during the infusion. Seven min utes after the start of infusion, a significant amount of the infusate distributed in the CA1 of the dorsal hippocampus and then continued to fill up the hippocampus, Figure 55A Only m ild backflow became visible in the corpus callosum ~ 10.5 min into infusion. In Figure 55B infusate was not observed until ~ 17.5 min. Even if the infusate was observed ~ 21 min after the infusion pump started, it was distributed slowly in the hippocampus until ~ 49 min and then significant amount of infusate was seen in the dorsal hippocampus, corpus callosum and the surface of the brain due to the administration of a bolus injection. Tissue and/or coagulated blood were likely clogged in the tip of the cannula when the ca nnula was inserted into the brain tissue and prevented the infusate from exiting the cannula To develop surgical procedure s for prevent ing bolus injections infusion t ests were performed in hydrogel (Trevigel 5000 powder, Trevigen, Inc., Gaithersburg, MD) The same infusion system and infusion rate were used for the hydrogel test. T he infusion pressure and distribution shapes of Evans Blue dyes are shown at various ti me frames in Figure 5 6. B olus

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79 injection in tissues was mimicked in 2% hydrogel. Figure 5 6A shows the pressure profile and distribution pattern when the cannula was blocked or clogged. The pressure dramatically increased up to approximately 350 mmHg until ~ 11 min without observing infusate in the media; then a bolus injection of infusate was observed with significant backflow. After the bolus injection, the pressure stabilized around 100 mmHg followed by rapid pressure decrease. To reduce a bolus in jection, a cannula retraction method was proposed. The cannula was inserted in the media and after a 5 10 min wait period and it was pulled out 0.25 mm. T he results of five infusion tests in hydrogel using this retraction method are shown in Figure 56B Infusate was observed to distribute in the hydrogel immediately. The pressure increased after infusion and asymptotically reached a steady state pressure around 100 mmHg. All reported pressure values included the infusion system pressure drop of 52 mmH g. The infusate distribution pattern showed a spheric al shape without any backflow. This retraction method was used for all animal experiments below. 5.3.2 Infusate Distribution in the Dorsal Hippocampus Direct infusions in the right side of the dorsal hippocampus were performed (n=6), Figure 57. DCE MR images showed high enough resolution to visualize contrast agent in the tissue and CSF space. In all subjects, the i nfusion si te targeted the molecular layer of the dentate gyrus directly under the fissure in the dorsal hippocampus. The cannula placement within the hippocampus was observed; however, t he exact cannula position within the hippocampus was not visible in pre infusion MR scans. P ost infusion high resolution T1 weighted images and histo logical images confirmed the cannula was placed within the targeted regions. All six trials showed a similar final distribution pattern and transient distribution patterns of the infusate traveling along underlying structures in the dorsal hippocampus H owever, discrepancies were also observed possibly due to delay of the infusion, backflow, variation of the infusion site and

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80 variation between subjects. Contrast agent was visualized within 47 min for two subjects and 710 min for the remaining four subjects. One trial showed pre infusion. Backflow was prevalent in all six trials. In Figure 5 8, transient infusion volumes at various time frames were calculated for each subject. Similar linear increases in total distribution volume were obse rved for all six subjects after infusate was visible in the tissue. For the six subjects after 8 L infusion in the dorsal hippocampus, m ean distribution volumes w as 39.37 3.42 mm3. Infusate distribution wa s highly dependent on tissue structure, Figure 59. The dynamic MR scans demonstrated the evolution of the infusate throughout the infusion period. Initially, the infusate was visible in the molecular layer of the dentate gyrus and the CA1 region of the hippocampus as represented in Figure 5 9A Subse quently the infusate followed the boundaries of these structures distributing medially. Backflow was observed along the cannula tract and spread medially along the fiber tracts of the corpus callosum located superior to the hippocampal infusion site. The dots (blue = the molecular layer of the dentate gyrus, red = the CA1 of the dorsal hippocampus, yellow = the corpus callosum ) in Figure 59B indicate the evolution of infusate distribution based on the dynamic images obtained. The highresolution T1 weighted images showed the final infusate distribution and the sectioned coronal brain slices confirmed this distribution, Figure 59B and C. After filling the dorsal hippocampus, i nfusate reached the boundary between the CSF space and tissue and then entered the CSF space (red dots), Figure 510A I nfusate also traveled along the fissure near the infu sion site and then entered the CSF space (yellow dots) Only a small portion of the infusate was observed in the ventral hippocampus after 8 L were infu sed ( dashed blue circle in Figure 5 10A ). Post infusion highresolution T1 weighted images were in agreement with the distribution patterns seen in the dynamic MR scans, Figure 510 B Images of

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81 sliced brain tissue with E vans B lue dye showed the same distribution pattern as the high resolution T1 weighted images These images also confirmed the distribution of infusate in the ventral hippocampus and CSF space, red dots in Figure 5 10 B and C 5.3.2 Infusate Distribution in the Ventral Hippocampus Direct infusions in the left side of the ventral hippocampus were also conducted (n=6), Figure 511. DCE MR images visualized contrast agent in the tissue and CSF space at various time frames In all subjects, the targeted infusion si te was between the molecular layer of the dentate gyrus and the CA1 subfield in the ventral hippocampus. Although t he infusion sites for two (trial 4 and 5) trials were slightly more anterior and/or lateral compared to the remaining four trials a ll six trials showed a sim ilar dynamic distribution pattern where infusate traveled along underlying structure s within the ventral hippocampus and CSF spaces. However, time delay of the infusion was observed. Contrast agent was visualized within 4 7 min for three subjects and 7 10 min for remaining three subjects. Pr e infusions were shown in five out of six subjects. Mild backflow was present toward the end of infusion in all six trials. In Figure 5 11, transient infusion volumes at various time frames were calc ula ted for each subject. Similar l inear increases in total distribution volume were observed in four subjects after infusate was visible in the tissue. Distribution volumes for subject 4 and 5 were lower when compare to the remaining four subjects. For the six subjects after 10 L infusion in the ventral hippocampus, m ean distribution volume was 45.91 9.19 mm3. Infusate traveled along the molecular layer of the dentate gyrus and the CA1 subfield, Figure 513 A The dynamic MR scans also indicated the infusate penetrated the granular cell layer near the infusion site and distributed mediall y. The degree of the infusion penetration across this layer decreased with distance from the infusion site. The infusate was confined

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82 within the ventral hippocampus At the start of infusion mild backflow was observed and at the end of infusion more backflow was observed in the corpus callosum and cortex. Infusate also traveled into the lateral ventricle placed between the corpus callosum and alveus of the hippocam pus due to backflow in two trials (data was not shown). T1 weighted high resolution images and brain slices confirmed final distribution patterns in these structures of the ventral hippocampus, Figure 51 3B and C. Figure 514 A shows the dynamic images of four different coronal slices progressing anteriorly from left to right. A significant amount of the infusate le aked into the CSF space due to infusion in the other side of the brain. Thus, pre enhancement of the CSF space was observed. O nce the infusa te reached the boundaries between the tissue and the CSF spaces (yellow and red dots) it entered the CSF space as noted by greater enhancement of this region toward the end of infusion. Some of the infusate also distributed in the dorsal hippocampus ( da shed red circle). Final distribution in T1 weighted highresolution images and brain slices were confirmed these distribution pattern s Figure 514B and C. 5.3.4 Pressure Monitoring Figure 515 demonstrates pressure during the infusion with three consecutive T1weighted coronal images near the infusion site. Pressure profiles were measured for two trials for each infusion site. The dynamic pressure and infusate distribution data were coll ected simultaneously during infusion. Although the infusi on pressure increased linearly at the start of infusion, t he infusate was not seen in the first scanned images, Figure 515 A T he infusate became visible in the next scan, Figure 515B After a transient period of over 500 sec, infusion pressure stabilize d reaching a steady state value. Only minimal backflow was detected for the trial presented

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83 5.4 Discussion In vivo CED experiments in the dorsal and vent ral hippocampus were performed. A cannula retraction method was introduced to reduce tissue clogging. Transient distribution patterns were visualized with DCE MRI. Post infusion T1 weighted images and histological brain slice images provided finer resolution to visualize final infusate distributions Real time infusion pressure measurement s were introduced to show t he feasibility of monitoring CED infusions. DCE MR images exhibited preferential distribution of the contrast agent based on anatomical tissue structure during infusion. In the dorsal hippocampus infusate was initially observed in the CA1 subfield and the molecular layer of the dentate gyrus Infusate traveled medially along the CA1 field until it filled up CA1 regions. The infusate also distributed in the molecular layer of the dentate gyrus along the dense granul ar cell layer and continued to occupy this structure by distributing in the curved region of the molecular layer of the dentate gyrus superior to the thalamus The fissure is a cell free region connected to the CSF space, filled wit h CSF and blood vessels. Infusate likely opened and traveled along the fissure until it reached the CSF space, where it then occupied the CSF space. A s mall amount of the infusate was observed in the ventral hippocampus adjacent to the dorsal hippocampus A prospective reason for this occurrence is that the adjacent CSF space acts as a mass sink due to its inherent lower resistance compared with tissue Infusate appeared to move easily toward this low resistance region. P ost infusion, T1 weighted image s and Evans B lue image brain slice images exhibited the same distribution of the infusate in the aforementioned underlying structures in DCE MR images. All six trials demonstrated these transient distribution patterns, but the distribution volume for each time frame does not match up perfectly for each trial. A cause of these differences may be due to a variable time delay associated with mild clogging of the cannula tip. A nother possibility is

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84 slightly different infusion site s between trials. T he same infus ion site was targeted in each trial according to a rat atlas; however, disparities from individual anatomical differences errors associated with determining baseline points such as bregma and the surface of the brain contributed to the variability of the infusion site. This variation contributed to different final distributions among subjects. The a mount of backflow also affect ed the distribution pattern in the dorsal hippocampus due to smaller total infusion volume s in the dorsal hippocampus. The infusion experiment in the ventral hippocampus also showed similar preferential distribution according to a natomical structure as seen in the dorsal hippocampus. Infusate was initially observed in the molecular layer of the dentate gyrus and then traveled along the molec ular layer of the dentate gyrus following the dense granular cell layer of the dentate gyrus and CA1 subfiel d of the ventral hippocampus These preferential distributions were likely observed because the molecular layer consists of mossy fibers (white matter) which have less fluid resistance than the granular cell layer of the dentate gyrus consisting of dense cell bodies (gray matter). However, some infusate was observed to penetrate th is dense granular cell layer close to the infusion site. Hyperintense regions were observed in the transient and final MR images within and surrounding the cistern (ventral border between the hippocampus and thalamus: CSF regions). Evan B lue dye was also observed with high intensity in t he regions surrounding the cistern in the histological images. The CSF fluid space could be a significant factor affecting the infusate distribution volume and pattern for CED. Although similar distribution patterns and volumes of the contrast agents were observed in all six subjects, infusate distributions in the ventral hippocampus for each subject were slightly different due to variations of the inf usion site, backflow and individual anatomical differences between subjects.

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85 Retraction methodology was pr oposed to reduce the administration of a bolus injection in this study. In the hydrogel test, approximately 3.5 times higher pressure was loaded in the infusion system and released with backflow for the clogging case. This increased infusion pressure would be unpredictably high and likely result in backflow Figure 55B (the image for 51min 30sec) Additionally, the total infusion volume in targeted regions could be affected because infusate would not distribute until the obstruct ion at the tip of a cannula is cleared With small infusion volume, infusate might not be released in the tissue due to the cannula clogging, Figure 55B (the images before 17 min 30sec). The implemented r etraction method reduced the severity of clogging and its associated effects. Retraction of the cannula may create a small fluid pocket or decrease compression of the deformed tissue under the tip of the cannula providing less resistance allowing the infusate to push out the tissue fragment. Although the retraction method reduced clogging, the delay of infusate administration still existed in some subjects. More studies are needed to characterize cannula retraction methods and determine the optimal retraction length. In spite of reducing back flow due to a bolus injection, backflow was observed alo ng the cannula during infusion in most cases. Cannulas were attached on the skull using skull adhesive. However, the floating brain inside the skull could move around due to vibration s during transport to the MR room It is also possible that the cannula was not placed perfectly straight and tissue tearing occurred Although a stereotaxic frame was used for cannula placement, a cannula could be bent. Th is could cause tissue damage an d create a gap between the cannula and the surrounding tissue Infusate could travel through this low resistance pathway along the cannula and possibly spread to undesired regions such as the corpus callosum, lateral ventricle and cortex

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86 More research i s needed to prevent backflow and provide more consistent infusion distribution pattern s and infusion volume (i.e. polymer coated cannula). For some of the experimental cases, infusion pressure was measured to show the feasibility of monitoring infusions by measuring inline pressure. T he pressure data provided a quantitative understanding of infusion in tissue while dynamic MR images provided visual insight into the tiss ue response throughout infusion. However, in this study, limited pressure data was collected. M ore inline pressure measurement s with variations of parameter s such as infusion rate, infusion site and backflow existence are need ed for comprehensive understanding of the infusion experiment. In this study, transient infusion distributi on was successfully observed using MR imaging to better understand hippocampal infusions in the rat hippocampus. In each trial, infusate distribut ed in the landmark structures of the hippocampus as previously described in section 5.3. However, 3D infusate distribution volumes were not identical. The amount of infusate within the targeted tissue and the regions in which infusate distributed due to backflow are remarkably different between cases. Additionally, i nfusion volume distribution was affected by e ven slight variations of the infusion site. For example, the difference between the final cannula placements for subject s 4 and 5 for ventral hippocampus infusion, differed by approximately 200~300 m in anterior and/or l ateral direction when compared to the other four subjects In these cases, infusate occupied more of the CA1 subfield than the molecular layer of the dentate gyrus and l ess infusate was distributed in the CSF space between the ventral hippocampus and thalamus In some cases, preinfusions were observed. This possibly occurred when handling and transporting the animal with the surgically implanted infusion system to the MR room. The use

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87 of an MR comparable infusion system and pump could simplify the infusion system and possibly help prevent pre infusion. Initially MR imaging scans such as T2 weighted imaging and/or diffusion weighted imaging (DWI) was planned to obtain structural information before infusion. However, in troubleshooting experiments, it was noted that longer time period between cannula insertion and infusion le d to an increase in the probability and severity of clogging. Therefore, dynamic scans were performed after transporting the rat to the MR room. Improved surgical procedures could be implemented to reduce this time frame allowing T2 weighted and/or DWI scans to be acquired pre infusion. This would provide more detail anatomical information allowing for better quantification of infusion volume in each brain structure and direct development of com putational model 5.5 Conclusions In this chapter, in vivo infusion experiments in the rat hippocampus were performed to investigate transient infusate distribution patterns in complex tissue structures. Surgical procedures and MR imaging protocols were developed to visualize in vivo distribution patterns throughout infusion. Albumin tracers tagged with MR visible contrast agents and Evans Blue dye were infused to visualize distribution in MR and brain slice images, respectively. T1 weighted dynamic contrast enhanced MR imaging (DCE MRI) provided consecutive MR images to track contrast agent distribution during CED. The following aspects were highlighted in this chapter : A cannula retraction method was proposed to reduce tissue clogging and the administration of bolus injections during CED. Inline pressure measurements were introduced to show the feasibility of monitoring direct infusions in biological tissue in real time

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88 Transient preferential distributions of contrast agent were observed along underlying structures in the hippocampus Significant leakage into adjacent CSF spaces was observed toward the end of infusion with 8 L and 10 L infusion in the dorsal and ventral hippocampus respectively. With the provided infusion parameters, the infusate occupied the entire dorsal and ventral hippocampus Figure 51. In vivo surgical setup for direct infusion in the dorsal and ventral hippocampus of the rat brain Cannula Stereotaxic frame Adhesive Stereotaxic frame

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89 Figure 52. Experimental setup for MR Imaging Cannula MR comparable stereotaxic frame Cannula MR comparable stereotaxic frame RF coil Anesthesia Line Anesthesia Line RF coil Rat Bore of the magnet MR Room

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90 Figure 53. Schematic diagram of in vivo infusion system Figure 54. Flowchart of MR imaging procedure Infusion pump Syringe PEEK tubing Micro connector PEEK holder Magnet Cannula MR room

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91 Figure 55. Dynamic coronal MR images at various times for A) infusate distribution without cannula clogging and B) delayed infusate distribution due to cannula clogging

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92 Figure 56. Inline infusion pressure profiles and corresponding distribution patterns at given times frames during Evans B lue infusion in 2% hydrogel without retraction (A) and with retraction (B) Distribution pattern f or B corresponds to trial 5. Maximum pressure Steady state pressure Steady state pressure Backflow Spherical infusion

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93 Figure 57. Dynamic contrast enhanced MR images during infusion into the dorsal hippocampus for six individual subjects where the infusion rate was 0.3 L/ min and the t otal infusion volume wa s 8 L. Each trial show s the same coronal slices at various time frames. B efore infusion 7 min 10 min 30 se c 14 min 17 min 30 se c 28 min 14 min Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Subject 6

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94 Figure 58. Measured infusate distribution volumes for direct infusion in the dorsal hippocampus (n=6) to 8 L infusions 0 5 10 15 20 25 30 35 40 45 0 200 400 600 800 1000 1200 1400 1600 1800Distribution volume (mm^3)Time (sec) subject 1 subject 2 subject 3 subject 4 subject 5 subject 6

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95 Figure 59. A) DCE MR images in the coronal plane show preferential transport behavior dorsally along the molecular layer of the dentate gyrus (blue dots) and CA1 (red dots) in the hippocampus at different time frames. Tracers were also observed enterin g the corpus callosum and traveled along white matter tracts (yellow dots). B) Final distribution in high resolution T1 weighted images. C) Evans B lue dye distribution in the brain slice. D) Coronal slice in a brain atlas corresponding to MR images ( Paxinos G., 2007)

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96 Figure 510. A) DCE MR images for different coronal slices at different time frames throughout infusion in the dorsal hippocampus, B) High resolution T1 weighted images post infusion and C) Evans B lue dye images progressing from posterior to anterior (left to right) after infusion. Yellow dots indicate fissure. The dashed red circle indicates the leakage in to CSF spaces. The dashed blue circle shows infusate distribution in the ventral hippocampus.

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97 Figure 511. Dynamic contrast enhanced MR images during infusion into the ventral hippocampus (n=6) where the i nfusion rate wa s 0.3 L/min and t otal infusion volume wa s 10 L. Each trial show s the same coronal slices at various time frames. B efore infusion 7 min 10 min 30 se c 17 min 30 se c 35 min 14 min Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Subject 6 24 min 30 se c

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98 Figure 512. Measured infusate distribution volumes for direct infusion in the ventral hippocampus (n=6) for 10 L infusions 0 10 20 30 40 50 60 70 0 500 1000 1500 2000Disbituion volume (mm^3)Time (sec) subject 1 subject 2 subject 3 subject 4 subject 5 subject 6

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99 Figure 513. A) DCE MR images in the coronal plane show preferential transport behavior along the molecular layer of the dentate gyrus (blue dots) and CA1 (red dots) in the ventral hippocampus at different time frames. Tracers were also observed entering the corpus ca llosum and traveled along white matter tracts (yellow dots). B) Final distribution in high resolution T1 weighted images. C) Evans B lue dye distribution in the brain slice. D) Coronal slice in a brain atlas corresponding to MR images ( Paxinos G., 2007)

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100 Figure 514. A) DCE MR images for different coronal slices at different time frames throughout infusion in the ventral hippocampus B) High resolution post infusion T 1 weighted images and C) Evans B lue dye images progressing from posterior to anterior (left to right) after infusion Yellow and red dots indicate the leakage into CSF space. The dashed red circle shows infusate distribution in the dorsal hippocampus.

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101 Figure 515. Inline infusion pressure profile in the ventral hippocampus o f the rat brain with three consecutive T1 weighted coronal images at given time frames.

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102 CHAPTER 6 VOXELIZED 3D COMPUTATIONAL TRANSPORT MODELING IN THE VENTRAL HIPPOCAMPUS: COMPARI SON STUDIES BETWEEN MODELS AND EXPERIMENTS 6.1 Introduction In vivo CED experimental studies in C hapter 5 gave some feedback to the computational model. F or hippocampal infusion, the CSF spaces were found to be one of the significant factors affect ing the infusate distribution. Experimental observation showed the infusate leaked into the CSF space when it reached at the boundary between tissue and CSF spaces In this chapter, more realistic segmentation map s were used, which consider ed the CSF space, subarachnoid space and skull regions F ive DTI data sets from fixed brains samples were used to create computational models that determine transient and final infusate distribution in different rat s Although slight anatomical differences existed between the five subjects, the predicted final distributions were similar. Differences noted in infusate distributions can be attributed to individual variation from subject to subject. The predicted infusate distribution was compared with distributions of contrast agents in MR images from a previous paper ( Astary et al. 2010) and Chapter 5. Additional parameter analysis was performed to demonstrate the sensitivity of infusate distribution to assigned isotropic tissue properties for white matter. Garrett Astary (Department of Biom edical Engineering, UF) and Svetlana Kantorovich (Department of Neuroscience, UF) provided their experimental results ( As tary et al. 2010) for comparison. Mansi Parekh (Department of Neuroscience, UF) collected DTI data sets at the Advanced Magnetic Resonance Imaging and Spectroscopy Facility in the McKnight Brain Institute (AMRIS) of UF. Dr. Thomas H. Mareci (Department of Biochemistry and Molecular Biology, UF) and Dr. Paul Carney (Department of Pediatrics, Division of Pediatric Neurology, UF) provided technical advice for analyzing experimental data.

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103 6.2 Materials and M ethods 6.2.1 A nimal Preparation and Diffusion Weighted Imaging Five male S prague Dawley rats weighing 250350g were used to obtain the high resolution DTI data set s collected by Mansi Parekh (Department of Neuroscience, UF) Rats were placed under anesthesia and euthanized by perfusion fixation with 10 % paraformaldehyde solution. The brains were removed from the skull and stored in 10 % paraformaldehyde solution. All procedures followed the guidelines provided by the NIH and the regulations of the University of Florida Institutional Animal Care and Use Committee. Fixed rat brains were imaged in phosphate buffered solution (PBS) after removal of the fixative. To obtain high r esolution images, MR imaging was conducted using a Bruker Advance imaging console (Bruker NMR Instruments, Billeria, MA) with a 17.6 Tesla, 89 mm vertical bore magnet system (Varian, Inc., Magnex Scientific Products, Walnut Creek, CA). Diffusion tensor imaging data sets for five different excised brains were collected using a diffusionweighted sp in echo sequence. For two DTI data sets, horizontal diffusionweighted scans were performed with recovery time (TR) of 4000 ms and echo time (TE) of 28 ms and eight averages. Forty slices of 0.3 mm thickness were acquired with a field of view (FOV) 27 mm x 18 mm in a matrix of 180 x 120. Another two DTI data sets were obtained by coronal slice images weighted by water diffusion. The diffusionweighted images had a FOV of 18 mm x 12 mm in 0.3 mm slices with a matrix of 120 x 80 in 32 slices. Measurement s were performed with TR=1400 ms, TE=25 ms, and four averages. Imaging parameters for the remaining DTI data set were the same as those used previously described in section 3.2.1 : 32 horizontal slices of 0.3 mm thickness, FOV 30mm x 15 mm in a matrix of 200 x 100, TR=1400 ms, TE=25 ms, and fiv e averages. For all DTI sets, i mages with low diffusionweighting (100 s/mm2) and higher diffusionweighting (1250 s/mm2) were measured in 6 gradient directions and 46 gradient

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104 directions respectively. Bilinear interpolation was performed for diffusionweighted images by a factor of two in the slice direction. The resolution for all data sets is 0.15 mm3. 6.2.2 Segmentation A semi automatic voxelized segmentation scheme developed in C hapter 3 was employed to reco nstruct regions of isotropic gray matter, anisotropic white matter and the CSF spaces (free water). In Chapter 4, only FA threshold value was used for segmentation. However, in this chapter, average diffusivity (AD) was used to obtain more realistic CSF regions. Average diffusivity is defined as a mean of the diagonal elements of the water diffusion tensor De, for each voxel. AD provides information about the overall mobility of water molecules within the voxel. AD in the CSF space (free water) is higher than in tissue structures. AD threshold values were adjusted until tissue regions and CSF spaces (free water) were delineated and in accordance with an anatomical atlas ( Paxinos G., 2007) Then, t issue regions were segmented as either white matter or gray matter regions using FA threshold value. Threshold values of FA and AD for each region were provided, Table 61. In chapter 4, CSF regions surrounding the brain were overestimated since DTI data from excised brain s did not provide information for subarachnoid spaces. In this model, a 0.15 mm thick layer of cerebrospinal fluid was manually assigned on the surface of the brain to provide more realistic boundaries surrounding the brain. The outer r egion of subarachnoid spaces w as assigned as the skull, which was defined as a non permeable region. 6.2.3 Tissue Properties and Com putational M odeling Transport properties were assigned in the same manner described in section 3.2.3. It should be noted that hydraulic conductivity in CSF spaces and subarachnoid spaces was three orders of magnitude higher than that of white matter in the maximum transport direction along fibers to replicate low resistance fluid flow regions. The hydraulic conductivity of the outer

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105 region of subarachnoid spaces was five orders of magnitude lower than that of gray matter to mimic the nonpermeable skull region. The same assumptions and equations previously described in 4.2.2 were used. Only one hemisphere of the brain was considered. P ortions of the rat brain were modeled to reduce calculating time. This volume covered coronal slices from bregma 0.0 mm to 9.0 mm anterior, Figure 61. Two infusion sites, similar to the experimental infusion sites were selected to observe the effect of infusion site variation on final distribution patterns in the ventral hippocampus. Cube shaped infusion sites (0.15 mm3) were placed at the interface between the molecular layer of the dentate gyrus and CA1 subfield of the hippocampus (AP = 5.88mm, ML = 5.1 mm, DV = 5. 2 mm), and at the interface between the alveus of the hippocampus and the corpus callosum ( AP = 5.04 mm, ML = 5.6 mm, DV = 5.2 mm ) A constant pressure condition at the infusion site was applied to simulate an infusion rate of 0.3 L/min. The t otal infusion volume was 5 assigned at the infusion site boundaries at time zero. A sagittal cut was used to divide the cerebral hemispheres and symmetric boundary conditions were applied to the internal surface of each hemisphere. Zero pressure and normalized concentration values were assigned t o the external bou ndaries. The i nitial concentration of alb umin tracer in tissue was assumed to be 0 at time zero. Parameter analysis was performed to demonstrate the feasibility of modeling white matter as an isotropic tissue (Kwm, Dwm) instead of an anisotropic tissue (Kwm ||, Kwm Dwm ||, Dwm ) White matter was assumed to be an isotropic structure with higher hydraulic conductivity and diffusivity than gray matter. Two isotropic analyses were performed. T he hydraulic conductivity (Kwm: 4.22 1010 cm4/dyne s) a nd diffusivity (Dwm: 1.60 107 cm2/s) values

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106 perpendicular to the fiber tracts were used for one analysis Tissue properties parallel to the fiber tract (Kwm: 6.75 109 cm4/dyne s, Dwm: 2.29 107 cm2/s) were assigned in the second analysis. Both of the infusion sites were used to evaluate the effect of variable infusion site. 6.2.4 In Vivo CED Experiments CED tracer infusion experimental results on seven male Sprague Dawley rats were provided from previous publication ( Astary et al. 2010) In summary, 5 microliters of Gd DTPA albumin (10 mg/mL in PBS solution; MW ~ 87 KDa, ~35 GdDTPA molecules per albumin molecule; R. Brasch Laboratory, University of California, San Francisco, CA) tagged with Evans Blue dye was infused at a rate of 0.3 L/min. T he ventral CA1 subfi eld of the hippocampus (AP = 5.0 mm, ML= 4.9 mm, DV=5.0 mm) w as initially targeted, but MR images confirmed two different infusion sites previous described in 5.2.3, were actually obtained. High resolution spin echo T1weighted images were acquired to de termine final infusate distribution: FOV 20 mm x 20 mm in a matrix of 160 x 160 with 20 slices, TE= 20 ms, TR= 1000 ms. Coronally oriented data w as acquired with 8 averages. 6.3 Results 6.3.1 Segmentation Figure 63 demonstrates two segmentation techniques implemented in this study. The white and gray matter regions were segmented using FA thresholds as described in Chapter 4, Figure 63A. However, this segmentation technique does not accurately account for the CSF regions in the brain. Additionally, the large regions outside of the brain were characterized as free water without skull regions, which proved to be a limitation of this method. In efforts to improve the model, the CSF regions within and surrounding the brain were successfully segmented in accordance with atlas boundaries as shown in Figure 63B where blue, green, yellow and red represent white matter, gray matter, CSF and a mimicked skull, respectively. The

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107 volumetric percentages occupied by each brain structure (white matter, gray matter and CSF regions ) were calculated for each subject, Figure 6 4. The average percentages for white matter, gray matter and CSF spaces were 32.75 2.89, 56.10 2.69 and 11.07 1.01, respectively. The CSF sp ace proved to comprise a noticeable percentage of the total volume and little variation was noted across subjects. 6.3.2 Subject Variation and Similarity of Predicted Infusate Distribution Tracer distributions were predicted in 5 subjects where a total i nfusion volume of 5L was administered. Figure 65 presents coronal, horizontal and sagittal plane views of the predicted final tracer distribution in each subject where the infusion site was between the molecular layer of the dentate gyrus and CA1 subfie ld of the hippocampus Infusate concentration w as normalized and values less than 5% of the maximum concentration was cutoff. In all subjects, it was predicted that the tracer would occupy the molecular layer of the dentate gyrus and CA1 region of the ventral hippocampus I nfusate was predicted to enter CSF regions. However, the predicted final infusion distributions were slightly different such as degree of infusate penetration into adjacent gray matter and CSF regions. Figure 66 presents coronal, horizontal and sagittal plane views of the predicted final tracer distribution in each subject where the infusion site was at the interface between the alveus of the hippocampus and the corpus callosum. In the simulations, most of the infusate was confined within the hippocampal alveus, corpus callosum and fimbria of the hippocampus. Preferential distribution patterns were observed due to anisotropic tissue properties and limited penetration of neighboring gray matter regions was predicted. Across subjec ts, variations in the degree of preferential distribution in the corpus callosum and fimbria were noted. The predicted final distribution volumes for each brain structure were calculated. Figure 67 shows the predicted total distribution volume as well a s the distribution volumes in white

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108 matter, gray matter and CSF filled regions. For the infusion site near the molecular layer of the dentate gyrus and CA1 subfield of the hippocampus (Figure 67A), the average final distribution volumes for gray matter, white matter and CSF spaces were 12.21 1.14, 11.58 2.96 and 5.56 0.52 mm3, respectively. The average total distribution volume was 29.37 1.94 mm3. Subject 2 demonstrated a larger distribution in the white matter regions than in the gray matter re gions; this observation differs from the trend observed in all other subjects where the distribution volume in gray matter is higher than in white matter. For the infusion site near the interface between the alveus of the hippocampus and the corpus callos um (Figure 6 7B), the average final distribution volumes for gray matter, white matter and CSF spaces were 12.92 1.97, 26.67 2.11 and 1.5 0.64 mm3, respectively. The average total distribution volume was 41.10 0.76 mm3. In these simulations, the distribution volume in white matter regions was approximately twice the distribution volume in gray matter regions. The predicted volume in CSF regions was minimal when compared to tissue due to limited access to the CSF space with the applied parameters (infusion site and volume). 6.3.3 Comparison between Predicted and Measured Distribution of Infusate P redicted infusate distribution and high resolution MR images after 5 L infusion for each infusion sites are juxtaposed in Figure 68 and 69. Red regions in Figure 68A and 69A represent predicted distribution volumes where normalized concentration values less than 0.05 were omitted. In Figure 68, the targeted infusion site in both simulated and experimental results, was between the molecul ar layer of the dentate gyrus (blue dots) and CA1 subfield (green dots) in the ventral hippocampus. It should be noted that a significant amount of infusate was observed in the CSF space in the predicted result and MR images (yellow dots). Minimal distribution of the infusate in the dorsal hippocampus was observed in both cases ( dashed orange

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109 circle), Figure 6 8A and B. Three dimensional renderings of final distribution s were segment ed from the predicted infusate distribution (left in Figure 68C) and contrast enhanced MR images (right in Figure 6 8C) provided from ( Astary et al. 2010) P redicted and measured final distributions of the infusate for the infusion site near the interface between the alveus of the hippocampus and the corpus callosum are shown in Figure 6 9. Preferential distribution patterns along the fiber tracts of the corpus callosum and limited pene tration into adjacent gray matter w as observed (green dots in Figure 6.9A). In predicted infusate distribution, a considerable amount of infusate was observed in the fimbria of the hippocampus (yellow dots in Figure 6.9A) and a small amount was found in t he internal capsule. However, minimal infusate w as observed in the fimbria of the hippocampus in MR images (yellow dots in Figure 6 9B) provided from ( Astary et al. 2010) Three dimensional contours for predicted and measured infusion distributions were also provided. The mean and standard deviation of predicted and measured total distribution volumes for the infusion s ite between the molecular layer of the dentate gyrus and CA1 in the ventral hippocampus were 29.37 1.94 mm3 (n=5) and 33.22 0.76 mm3 (n=4) respectively. The predicted total distribution volume was 11.6% lower than the measured total distribution volume For alveus/corpus callosum infusion, the mean and standard deviation of predicted and measured total distribution volumes were 41.10 0.76 mm3 (n=5) and 32.59 0.05 mm3 (n=3) respectively. The p redicted distribution volume was 20.7 % higher tha n the measured distribution volume. The total infusion volume for both infusion sites was 5 L. 6.3.4 Predicted and Measured Transient Infusion Distribution Simulations were also performed with infusion volumes up to 10 L and compared with dynamic infusi on distribution MR images provided in Chapter 5. The infusion site between the

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110 molecular layer of the dentate gyrus and CA subfield in the ventral hippocampus was used for comparison. Three different coronal slices progressing anteriorly from left to right are presented at each time frame for the simulation and experimental results. The best experimental result with the least amount of backflow, minimal clogging, and no pre infusion was selected to compare to the simulation result, which is an idealized case since the model does not predict backflow Infusate exhibited preferenti al spread along the underlying structures in both the simulation and experiment. Infusate reached the boundary of the CSF space and continued to enter the CSF spaces in both cases. However, the evolution of infusate distributions did not exactly match between the simulation and experiment at various time frames. For 10 L infusions, predicted transient distribution volumes in each structure were shown for five subjects, Figure 611. The m ean and standard deviation of predicted total distribution volume were 53.48 8.02 mm3, which is higher than the measured total distribution volume ( 45.14 9.19 mm3) in C hapter 5. Total infusion distribution volumes are almost identical up to approximately 5 L and then showed minor discrepancies between subjects. The infusion distribution volume in white matter was predicted to be much higher for subject 2 than for the remaining f our subjects. Considerable infusion distribution volumes in CSF spaces were observed in all five subjects. It should be noted that the distribution volume in CSF spaces tappers off after infusing 6 L infusion. Figure 6 12 shows the percentage of infusat e in the tissue and CSF spaces at various time frames. The percentage of distributed infusate in CSF spaces increased by approximately 20% of the total distribution for the first 4 L infusions and maintained this proportion throughout infusion.

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111 6.3.5 Parameter Analysis of Isotropic Tissue Properties for White Matter Variations in predicted infusate distribution patterns for two isotropic white matter simulations are shown along with final infusate distributions in MR images in Figure 6 13( Astary et al. 2010) Figure 613B and F show the predicted infusate distributions using anisotropic white matter tissue properties for comparison (red distributions). In Figure 613C and G, white matter was assigned as an isotropic region where the implemented hydraulic conductivity and diffusivity were literature values for the white matter parameters perpendicular to the fiber trac t. Predicted final distributions of infusate are shown in green. For both infusion sites, a similar distribution pattern was predicted for this isotropic case when compared with experimental results and the anisotropic modeling. However, for the infusion in hippocampal alveus/corpus callosum, more infusate was predicted in neighboring gray matter for this isotropic case (Figure 6 13G) when compared to the anisotropic prediction ( Figure 613F) Average percent differences between anisotropic (Figure 6 13 B and F) and isotropic (Figure 613 C and G) 3D volume shapes of the infusate distribution s were calculated for five subjects for both infusion sites : 19.60 11.46 % for the infusion between the molecular layer of the dentate gyrus and CA subfield in the ventral hippocampus, 21.44 4.39 % for the infusion between the alveus of the hippocampus and the corpus callosum. Figure 613D and H shows the predicted infusate distribution (blue distributions) where isotropic white matter assumptions associated with the highest hydraulic conductivity and diffusivity values (properties parallel to the fiber direction) were applied. Infusate was predicted to occupy and be confined in white matter for both two infusion site s and barely penetrate into adjacent gray matter which does not coincide with experimental results. Average percent differences between anisotropic (Figure 613 B and F) and isotropic (Figure 613 D and H) 3D volume shapes of the infusate distribution were calculated for five subjects for both infusion sites :

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112 48.30 4.36 % for the infusion between the molecular layer of the dentate gyrus and CA subfield in the ventral hippocampus, 28.58 0.80 % for the infusion 6.4 Discussion The voxelized model developed in Chapters 3 and 4 was used to predict the infusate distribution during direct infusion. Average diffusivity values of DTI were employed to provide more realistic CSF spaces in the brain. The five DTI data sets were used t o generate models that were used to simulate for two different infusion sites. Modeling infusions in five subjects using the same infusion sites and obtaining similar distribution patterns demonstrated the reliability and repeatability of this modeling sc heme. Qualitative comparisons between predicted and measured distribution patterns, volumes and shapes demonstrated the models proficiency for direct infusion in the ventral hippocampus The parameter analysis for assuming isotropic tissue properties in white matter demonstrated the possibility of obtaining useful predictions using a simplified model without DTI when appropriate value s for tissue properties and infusion sites are selected. The segmentation scheme was improved by modeling more realistic C SF spaces using average diffusivity values. The result from the infusion experiments described in Chapter 5 highlighted the importance of CSF spaces in modeling direct infusions in the brain. U sing this segmentation scheme, similar proportions of white m atter, gray matter and CSF space were obtained between subjects. It should be noted that thresholds for each subject were not exactly the same, but had similar ranges. This variation was likely due to variation in signal to noise ratio, MR coil tuning an d other instrument factors, as well as differences between subjects. Overall similar infusate distributions were observed for five different DTI data sets with some variations. For the infusion between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus, infusate was predicted to distribute preferentially along the

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113 white matter region, most likely along the mossy fibers in the molecular layer of the dentate gyrus. It was also predicted to occupy interspersed gray matter in the hippocampus. A significant amount of the infusate was also pre dicted in CSF spaces for all subjects. However, distribution shape s were not identical for each simulation Tissue structure variation between subjects could be the reason for these differences. Another possibility is variation of the infusion site for e ach subject. The infusion site was determined from experimental data and using a rat atlas the same coordinate was implemented in the computational model for different subjects. However, there is some error associated with determining the experimental inf usion site due to limitations in MR resolution as well as in assigning the same infusion site in a different animal. Predicted d istribution volumes in each structure were reasonably similar between subjects. It was noted that subject two exhibited a diff erent distribution volume trend for white matter and gray matter when compared to the remaining four subjects. This difference may be a result of local tissue structure variations. In this data set, an unusual ly high FA value region was observed in the ventral hippocampus, which was not shown in the other four DTI data sets. For alveus/corpus callosum infusion, a similar preferential distribution pattern along the white matter tracts in the corpus callosum was predicted for each subject. Infusate was also predicted to occupy the hippocampal fimbr ia (white matter) for all subjects. The p redicted total distribution volume s for each subject were almost identical (standard deviation less than 1 mm3) For all cases, less than 3 mm3 of the distribution volume w as predicted to be confined in the CSF space. This was expected due to the infusion site location with respect to the CSF space. H owever, the degree of the preferential distribution along the fiber tracts was not the same for each subject In s ubject 3, a significant amount of the infusate seem ed to occupy the adjacent pyramidal cell layer of the CA1 in the ventral hippocampus I n this region, axons emerge from

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114 the pyramidal ce ll lay of the CA1 usually resulting in a structure that is a combination of white and gray matter. As a result, in some subjects this region may be characterized as white matter and in others it may be characterized as gray matter based on the segmentation scheme The individual variation s in this region a ccount f or the observed differences in infusate distribution. P redicted tracer distributions were found to be comparable with experimental measures ( Astary et al. 2010) for 5 L infusion volume with two different infusion sites. Three dimensional volumes of predicted and measured final distribution s were qualitatively similar to each other for both infusion sites. Infusate was predicted to primarily occupy the same structures as those observed in the experiment. It should be noted that the total infusion volume for alveus/CC infusions were over predicted since more infusate occupied the hippocampal fimbria. In the experiment, little infusate was observed in the fimbria of the hippocampus. Perhaps the segmentation does not accurately characterize the connectivity between the fimbria of the hippocampus and the corpus callosum ; resulting, in an over prediction of the total infusate distribution volume up to 20.7 %. The simulated and experimental transient distribution s for the ventral hippocampus infusion exhibited similar preferential distribution patterns and leakage in to CSF space which wa s observed in the experimental results in Chapter 5. Although simulation results and experimental results showed similar distribution patterns in the landmark structures of the hippocampus, the shape of the infusate distribution and volume for each experiment trial and each simulation trial also have some un ique pattern due to variation of individual tissue structure, potential difference of the infusion site and unpredictable factors such as backflow and cannula clogging in the experiment. It should be mentioned that the predicted and measured distribution pattern s for each time frame did not matched up with each other I n the experiment s infusate

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115 was not released (up to ~10 min) from the infusion system at the start of infusion. However, in the simulation s the infusion site was modeled as an ideal cubic source in the middle of the tissue without considering backflow and delay of infusion due to a cannula clogging. Predicted total distribution volume s between subjects were almost identical up to approximately 5 L due to constant porosity assumption in tissue regions, after which variation was noted. Distribut ion vol ume s in the CSF space differed for each subject and this appeared to be the greatest contributing factor in the variation of the distribution volume after infusion of 5 L It should be noted that Darcys law, instead of the Navier Stokes equation, was applied to the CSF space with for rapid modeling. Further studies are needed to validate this assumption for the case of significant leakage in the CSF space. The CED experiment s performed in Chapter 5 and the developed computational model demonstrated the significance of accounting for leakage of infusate into the CSF space. Only t he ventral hippocampus infusions were s imulated and compared to experimental results. Although the average diffusivity thresholds delineated major CSF spaces, it was unable to detect thin CSF spaces such as the hippocampal fissure and the velum interpostum between the dorsal hippocampus and the thalamus. The s imulation for the dorsal hippocampus infusion showed that significant infusate traveled into the thalamus, which has not seen in the experiments. I t is likely due to the absence of thes e CSF spaces in the model segmentation map More proper segmentation for these regions would be needed to improve the computational model, especially for infusions near these regions. White matter in the brain has an anisotropic structure. DTI data provide d the principle direction of the water diffusion in each voxel and this information was utilized to obtain anisotropic transport properties For transport modeling, two different hydraulic conductivities

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116 and diffusivities were assigned to each voxel for white matter; one in the direction parallel to the fiber tract and the other for the direction perpendicular to the fiber tract. However, to simplify computational modeling, white ma tter could be modeled as isotropic media characterized by transport property values larger than those of gray matter. T he result s shown in Figure 613 demonstrated the possibility of using the isotropic assumption for white matter. Two different isotropic values for white matter were assigned and predicted infusate distribution s for two infusion site s were found. The isotropic modeling with assigned tissue properties in accordance with values for perpendicular white matter properties showed a similar fin al distribution as the experimental results for both infusion sites More studies are needed to determine the accuracy of this assumption using various input parameters (infusion rate, infusion site, etc.) as well as tissue properties (hydraulic conductivity and diffusivity). 6. 5 Conclusions In this study, voxelized models with more realistic structural information provided by an improved segmentation scheme were used to predict infusate distribution for direct infusions. The developed model and s egmentation scheme were used to predict CED transport in the ventral hippocampus and compared with experimental studies. The following aspects were highlighted in this chapter: Average diffusivity values of DTI were employed to provide more realistic characterization of CSF s paces in the brain and predict infusate distribution in these regions. Modeling infusions in five subjects using the same infusion sites and obtaining similar distribution patterns demonstrated the reliability and repeat ability of this modeling scheme Qualitative comparisons between predicted and measured distribution patterns, volumes and shapes demonstrated the models proficiency. The model can be used to vary infusion parameters to optimize drug delivery in the brain and reduce experimental time/cost. The parameter analysis for assuming isotropic tissue properties in white matter demonstrated the possibility of obtaining useful predictions when appropriate values are selected for tissue

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117 properties. Using isotropic assumptions would simplify the model and reduce computational time. Table 6 1. FA and AD ranges used in segmentation of the rat brain. Subject Region Fractional Anisotropy (FA) Normalized average diffusivity (AD) Subject 1 White matter 0.22 ~ 1 .0 NA Gray matter 0 ~ 0.22 NA Non tissue(free water region) NA 0.16 ~ 1.0 Subject 2 White matter 0.26 ~ 1.0 NA Gray matter 0 ~0.26 NA Non tissue (free water region) NA 0.25 ~ 1.0 Subject 3 White matter 0.244 ~ 1 .0 NA Gray matter 0 ~ 0.244 NA Non tissue (free water region) NA 0.26 ~ 1.0 Subject 4 White matter 0.225 ~ 1.0 NA Gray matter 0 ~ 0.225 NA Non tissue (free water region) NA 0.29 ~ 1.0 Subject 5 White matter 0.22 ~ 1.0 NA Gray matter 0 ~ 0.22 NA Non tissue (free water region) NA 0.26 ~ 1.0 Mean Standard deviation FA threshold (white matter, gray matter) 0.233 0.0158 AD threshold (tissue, nontissue) 0.244 0.0452

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118 Figure 61. Schematic diagram of the one side of the rat brain used in the computational model for direct infusion Figure 62. Modeled infusion site s in the ventral hippocampus using a rat brain atlas ( red dot: AP = 5.88mm, ML = 5.1 mm, DV = 5.2 mm, blue dot: AP = 5.04 mm, ML = 5.6 mm, DV = 5.2 mm ) ( Paxinos G., 2007)

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119 Figure 63. A) T he segmentation map using FA threshold from the previous model where CSF regions and the skull were not accurately characterized B) I mproved segmentation map using F A and AD thresholds, blue = white matter, green = gray matter, yellow = free water regions ( CSF spaces, subarachnoid space) red = non permeability region ( skull region), C) A rat atlas ( Paxinos G., 2007 ) Figure 64. Volume percentage of each brain region segmented for each subject 0 10 20 30 40 50 60 70 subject 1 subject 2 subject 3 subject 4 subject 5Tissue percentage (%) WM GM CSF A B C CSF spaces

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120 Figure 65. Predicted distribution pattern for direct infusion between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus for each subject. Predicted n ormalized concentration contours were overlaid on the FA map on coronal, horizontal and sagittal plane images near the infusion site. Total infusion volume wa s 5 L.

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121 Figure 66. Predicted distribution pattern for direct infusion in alveus/CC. Predicted normalized concentration contours were overlaid on the FA map of coronal, horizontal and sagittal plane images near the infusion site. Total infusion volume wa s 5 L.

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122 Figure 67. Predicted v olume distributions in each structure for direct infusion between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus (A) and direct infusion alveus/CC for each subject (B) Total infusion volume wa s 5 L 0 5 10 15 20 25 30 35 subject 1 subject 2 subject 3 subject 4 subject 5Distribution volume (mm^3) WM GM CSF TOTAL 0 5 10 15 20 25 30 35 40 45 subject 1 subject 2 subject 3 subject 4 subject 5Distribution volume (mm^3) WM GM CSF TOTAL A B

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123 Figure 68. P redicted excised (A) and m easured in vivo (B) final distribution patterns ( Astary et al., 2010) i n five consecutive coronal slices for infusion in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus (yellow dots = the leakage in to the CSF space, blue dots = the molecular layer of the dentate gyrus, green dots: CA1 sub field of the ventral hippocampus, dashed orange circle: infusate in the dorsal hippocampus), In ( C) t hree dimensional contour s of the predicted (left in red) and measured (green in right) final distribution are shown Total infusion volume wa s 5 L

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124 Figure 69. P redicted excised (A) and measured in vivo (B) final distribution patterns ( Astary et al., 2010) i n five consecutive coronal slices for infusion in alveus/CC (yellow dots: fimbria of the hippocampus) In ( C) t hree dimensional contour s of the predicted (left in red) and measured (green in right) final distributions are shown Total infusion volume wa s 5 L

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125 Figure 610. P redicted (A) and measured (B) transient infusate distribution patterns in three coronal slices for 10 L infusions between the molecular layer of the dentate gyrus and CA1 subfield of the ventral hippocampus. The r ed region in ( A) represents the region in which normalized concentration of the infusate was higher than 5%.

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126 Figure 611. Predicted total distribution volumes (A) and predicted distribution volumes in white matter (B) gray matter (C) and CSF regions (D) for 10 L for direct infusion in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus (n=5) 0 10 20 30 40 50 60 70 0 2 4 6 8 10Distribution volume (mm^3) Infusion volume ( L) subject 1 subject 2 subject 3 subject 4 subject 5 0 5 10 15 20 25 30 35 0 2 4 6 8 10Distribution volume (mm^3) Infusion volume ( L) 0 5 10 15 20 25 0 2 4 6 8 10Distribution volume (mm^3) Infusion volume ( L) 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10Distribution volume (mm^3) Infusion volume ( L) A B C D

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127 Figure 612. Percentage of infusate in the tissue and CSF space at various time frames for 10 L infusions in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus. 0 20 40 60 80 100 120 0 2 4 6 8 10 12Perceentage (%) Infusion volume ( L) subject1 tissue subject1 CSF subject2 tissue subject2 CSF subject3 tissue subject3 CSF subject4 tissue subject4 CSF subject5 tissue subject5 CSF

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128 Figure 613. T1 weighed MR images of final distributions in the molecular layer of the dentate gyrus/CA1 subfield of the ventral hippocampus ( A) and alveus/CC (E ) ( Astary et al. 2010) in vivo t he predicted infusate distributions using anisot ropic white matter tissue properties (B and F ) from the excised brain t he predicted distributions for isotropic white matter using values for tissue properties perpendicular (C and G) and parallel (D and H) to the fiber tracts

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129 CHAPTER 7 CONCLUSIONS AND FUTURE WORKS 7.1 Summary and Conclusions The developed voxelized transport model provided practical insights to understand the effect of embedded tissue structure on local convection enhanced drug delivery. The in vivo infusion experiments demonstrated how infusate distributed through convoluted structures in the hippocampus and entered into CSF regions which has not been shown in previous studies. Also, t he experimental result s indicated that more realistic CSF regions should be included to improve the computational model The infusate distribution was predicted in the landmark structures of the hippocampus and occupied the entire hippocampus toward the end of infusion, which was observed in the experiments. T he developed mo deling schem e is able to estimate optimal infusion parameters such as infusion rate, infusion volume and infusion site for the desired drug delivery at the targeted region of the brain. Ultimately t he developed 3D porous media transport models for CED in the brain m ay be a useful tool for surgical planning and may lead to improve treatment of neurological brain diseases by maximizing drug delivery to targeted regions and minimizing syste mic and neurologic toxicities. Detail ed aspects highlighted in each chapter are s ummarized below In C hapter 3, a new computational modeling methodology was developed for CED transport that use d a semi automatic voxelized approach to account for anisotropic transport and complex underlying tissue structures. In vivo and excised d iffusion tensor imaging of the rat spinal cord were employed to provide preferential transport directions and anatomical boundaries on a voxel by voxel basis. The semi automatic segmentation schemes expedited building of the computational models and provi de d a means for rapid prediction of interstitial flow and tracer

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130 distributions that a voided the time consuming and labor intensive geometric volume reconstructions required in previous computational models In C hapter 4, the developed modeling methodology in Chapter 3, was adopted for 3D computational transport model of CED in the rat brain. Interstitial pressure, interstitial velocity fields and tracer transport were predicted for CED in the ventral hippocampus and the corpus callosum of the rat brain. I n parametric analys i s, predicted CED tracer transport was stable over the variable ranges tested, and CED tracer distributions were most sensitive to changes in FA thresholds used for segmentation, DTI voxel resolution, tissue porosity and the selected inf usion site. To a lesser extent, predicted distributions were also sensitive to relative differences in gray matter and white matter transport properties. In C hapter 5, i n vivo direct infusion experiments with MR imaging were performed to investigate tran sient infusate distribution patterns in complex tissue structures for local drug delivery in the rat brain Dynamic contrast MR images provided insights into transport phenomena in complex structures in the rat brain. Significant leakage from the hippocampus into adjacent CSF spaces was observed toward the end of infusion with total infusion volume s of 8 L and 10 L in the dorsal and ventral hippocampus respectively. A cannula retraction method to reduce administration of a bolus injection due to cannula clogging was proposed. The feasibility of monitoring direct infusion using inline pressure measurement was demonstrated. In C hapter 6 simulations for direct infusion in the ventral hippocampus of the rat brain were performed with more realisti c structural information provided by an improved segmentation scheme. Modeling infusions in five subjects using the same infusion sites and obtaining similar distribution patterns demonstrated the reliability and repeatability of the voxelized modeling sc heme. Qualitative comparisons between predicted and measured

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131 distribution patterns, volumes and shapes demonstrated the models proficiency for these infusion sites Only t he ventral hippocampus infusions were simulated and compared to experimental resul ts. For dorsal infusion, t he applied segmentation technique was unable to detect thin CSF spaces such as the hippocampal fissure and the velum interpostum between the dorsal hippocampus and the thalamus. Variations between simulated and experimental resul ts are likely due to the absence of these CSF spaces in the model segmentation map. Improved segmentation of these regions is needed to accurately predict infusion in the dorsal hippocampus. The parameter analysis for assuming isotropic tissue properties in white matter also demonstrated the possibility of obtaining useful predictions when appropriate values are selected for tissue properties. This provides an opportunity for simpler modeling schemes in the future. 7.2 Future Work The developed computational models and in vivo experiments provide useful insight into the effects of underlying transport forces and tissue structure on local CED transport. With further understanding of transport phenomena for CED gained via this study, e xperimental and modeling improvements are needed to further validate this computational modeling technique. Ideally the same brain would be used in modeled and experiment al infusion for direct comparison. In orde r to do this, in vivo DWI scans before infusion would allow for the segmentation of the individual anatomy of the animal under experimental testing. Larger animals, i.e. nonhuman primates, could also be used to model brain infusions eliminating the resol ution issue associated with the MR imaging of small structures. T he following aspects should be highlighted in future studies: Further improve surgical procedure for in vivo infusion studies to prevent cannula clogging and backflow t o obtain more accurate infusate distribution s Obtain T2weighted and/or DWI scans before infusion to provide more detail ed anatomical information allowing for better quantification of infusion volume.

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132 Advance segmentation scheme to obtain more detail brain structure such as thin CSF spaces and fissures. Improved segmentation of these regions would provide more accurate predictions of infusions in the brain, i.e. dorsal hippocampus Perform computational modeling with pre infusion in vivo DTI at high resolution to obt ain detail ed structural information (i.e. CED in nonhuman primat e) and validate predicted infusate distribution volume with experimental results during and after infusion within the same animal

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140 BIOGRAPHICAL SKETCH Jung Hwan Kim was born in Seoul, South Korea. He grew up mostly in Seoul. He earned his Bachelor of Science in m echanical e ngineering from Kyung Hee University in 2002 after finishing his two years and two months military service duty. He also earned an Master of Science in m echanical e ngineering from Kyung Hee University in 2004. He worked on designing heat exchanger for H2o/Libr absorptio n chiller to improve system performance. In 2005, he started the Ph.D. program in the Department of Mechanical and Aerospace Engineering of the University of Florida. He joined Dr. Malisa Sarntinoranont s research group in f all semester of 2006, and has worked on 3D porous media computationa l modeling in biological tissue.