2008 BMES Fall Annual Meeting, St. Louis, 4 th October Track: Computational Biology

1. Computational Approach for Predicting Transport of Macromolecules in the Brain Interstitium 2008 BMES Fall Annual Meeting, St. Louis, 4th October Track: Computational Biology Session: Computational Biotransport and Drug Delivery A. Linninger, M. Harihara Iyer, M. Somayaji,S. Basati, B. Sweetman and R. Penn Laboratory for Product and Process Design, Departments of Chemical and Bioengineering, University of Illinois, Chicago, IL, 60607, U.S.A. †Hamilton et al, Experimental Neurology, 168 (2001) BMES Fall 2008 1

2. Outline • Motivation for studying macromolecular transport in brain. • Methodology for predicting drug transport in patient-specific brain reconstructions. • Part I: Dye distribution experiments in brain phantoms. • Part II: MRI analysis of the macromolecular distribution. • Part III: Predicting macromolecular transport in rat brain. BMES Fall 2008 2

3. Treatment of Neurodegenerative Diseases • Diseases of central nervous system – Alzheimer’s, Parkinson’s, Multiple Sclerosis and Amyotrophic lateral sclerosis. • Slowly progressing diseases - lead to disability and premature death. • Drugs discovered for treatment – high molecular weight compounds. • Entry of these drugs into the brain is hindered by the blood-brain barrier when administered through the systemic circulation. BBB are tight junctions of the epithelium that lines capillaries in the brain. BMES Fall 2008 3

4. Drug Infusion Catheter DrugDistribution Target Site Human Brain MRI Image Coronal Slice (Level 1520)* Convection Enhanced Delivery • Direct way to circumvent blood brain barrier - invasive delivery using a catheter. • Enables targeted delivery of the drug to the site of interest. • Convection enhanced delivery creates bulk flow to achieve clinically significant distribution volumes at the target site. • Catheter size, flowrate of infusion and location of catheter. BMES Fall 2008 4

5. Brain Geometry Reconstruction Calibration of Physical Properties First Principles Computational Model MR Imaging Geometry Reconstruction Patient specific DTI data Diffusion and Hydraulic conductivity tensor field Drug Distribution Prediction using Transport Equations Grid Generation Modeling of Drug Transport in the Brain BMES Fall 2008 5

6. Part I: Dye distribution experiments in brain phantoms. BMES Fall 2008 6

7. Cannula Marker dye Backlight Digital Camera Syringe pump Computer Gel Chamber Holding frame Brain Phantoms for Infusion Experiments • 0.6% Agarose gel used as a surrogate for brain tissue. • Different catheter sizes (23 – 30 gauge) and infusion rates (0.5 – 5 µl/min) were tested in these gels. BMES Fall 2008 7

8. Cannula Dye Distribution Measurement axis Distance of Distribution Experimental Results BMES Fall 2008 8

9. 25 Gauge Cannula Flow rate 0.5 μl/min Flow rate 1.0 μl/min Experimental Results BMES Fall 2008 9

10. 27 Gauge Cannula Flow rate 0.5 μl/min Flow rate 1.0 μl/min Experimental Results BMES Fall 2008 10

11. Cannula Inlet Cannula Bulk mass balance : Bulk momentum balance : Gel Cannula Gel Interface Species Transport Equation : Gel Boundary Predicting Dye Distribution in Brain Phantoms BMES Fall 2008 11

12. 1.0 0.0 Validation of simulated results Relative Concentration Comparison of simulation result with experimental data (n=5) for 23 G cannula at 1.0 µl/min (t = 120 min ). BMES Fall 2008 12

13. Reflux of the infusate • Reflux reduces effective volume of drug distribution in the target site. • Increasing flowrate of infusion decreases drug volume in target site. • Reflux distance increases with increasing catheter diameter BMES Fall 2008 13

14. High Conc Cannula Inlet Annulus h = 0.04 r h = 0.08 r h = 0.12 r Low Conc Cannula Wall Infusate Cannula Outlet 23 Gauge Cannula Modeling Reflux of Infusate through the Annulus BMES Fall 2008 14

15. Hollow Membrane Catheter; Flow rate 5 μl/min Simulation Experimental BMES Fall 2008 15

16. Comparison of Simulation and Experimental results for Hollow Membrane Catheter Plane of reference for measuring penetration depth Experimental results are with in 15% of simulated results BMES Fall 2008 16

17. Part II: MRI analysis of the macromolecular distribution. BMES Fall 2008 17

18. Gd- labeled infusate Cannula Magnet Syringe pump Gel Chamber Image Acquisition MRI Analysis of Dye Distribution • 0.5 mM solution of Gadodiamide (Omniscan) was infused into 0.6% agarose gel brain phantom at 1 μl/min using a syringe pump. • The distribution of the Gd-dye mixture was captured using a Magnetic Resonance Imaging after 1 hr of infusion. BMES Fall 2008 18

19. Comparison of MRI data and simulation Comparison of simulation result with MRI data (n=3) for infusion of 0.5mM Gadodiamide at 1.0 µl/min (t = 60 min ). Slices of 3D simulation of Gadodiamide distribution in gel at t = 60 min BMES Fall 2008 19

20. Part III: Predicting Macromolecular Transport in Rat Brain. BMES Fall 2008 20

21. Axial section A: Corpus callosum B: Internal capsule C: Gray matter regions Coronal section Apparent water diffusion tensor in human brain from diffusion tensor imaging (DTI) Fractional anisotropy map • Apparent water diffusion tensor is anisotropic in white matter due to the directionality of the axonal fiber tracts. • Water diffusion is isotropic in gray matter. BMES Fall 2008 21

22. Tensor calibration for transport properties Proposition 1. Apparent water diffusion tensor represents tissue anisotropy & heterogeneity 2. All transport tensors share the same eigenvectors 3. Maximum transport corresponds to the direction of major eigenvector †Linninger, A.A., et al., Computational methods for predicting drug transport in anisotropic and heterogeneousbrain tissue, Journal of Biomechanics (2008), doi:10.1016/j.jniomech.2008.04.025 BMES Fall 2008 22

23. Brain Geometry Reconstruction Calibration of Physical Properties Computational Model Grid Generation T2 Weighted Image Functional Anisotropy Map Prediction of dye distribution Reconstruction of 2D Rat Brain Slice BMES Fall 2008 23

24. High Conc Low Conc Prediction of dye distribution in Rat Brain Slice BMES Fall 2008 24

25. Summary • Gel experiments validate computer predictions of convection enhanced delivery technique. • Quantify the fundamental transport phenomena. • Understanding problems of CED technique – reflux, help in catheter designing. • Computational tool for predicting macromolecular transport helps designing in-vivo animal experiments. BMES Fall 2008 25

26. Acknowledgements • Dr. David Wright, University of Chicago • Dr. Xiaodong Guo, University of Chicago • Komal Prem, NSF-REU 2008 Fellow, Laboratory of Product and Process Design. • Erum Ahmed and Rashi Bamzai, NSF-REU 2007 Fellow, Laboratory of Product and Process Design. • Robert Dawe and Terri Erickson, NSF-REU 2006 Fellow, Laboratory of Product and Process Design. BMES Fall 2008 26

27. References • Z. J. Chen, G. T. Gillies, W. C. Broaddus, S. S. Prabhu, H. Fillmore, R. M. Mitchell, F. D. Corwin, and P. P. Fatouros, “A realistic brain tissue phantom for intraparenchymal infusion studies,” J. Neurosurg., vol. 101, no. 2, pp. 314–322, 2004. • M. Y. Chen, R. R. Lonser, P. F. Morrison, L. S. Governale, and E. H. Oldfield, “Variables affecting convection- enhanced delivery to the striatum: A systematic examination of rate of infusion, cannula size, infusate concentration, and tissue-cannula sealing time,” J. Neurosurg., vol. 90, no. 2, pp. 315–320, 1999. • A. A. Linninger, M. R. Somayaji, M. Mekarski, and L. Zhang, “Prediction of convection-enhanced drug delivery to the human brain,” J. Theoret. Biol., vol. 250, pp. 125–138, 2008. • M. R. Somayaji, M. Xenos, L. Zhang, M. Mekarski, and A. A. Linninger, “Systematic design of drug delivery therapies,” Comput. Chem. Eng., vol. 32, pp. 89–98, 2008. • D. A. Nield and A. Bejan, Convection in Porous Media. NewYork: Springer-Verlag, 1998, pp. 1–50. • J. R. Wujek and D. R. Hafemann, “Quantitative study of bromophenol blue diffusion in the rabbit brain,” Exp. Neurol., vol. 53, pp. 166–177, 1976. • L. Zhang, K. Kulkarni, M. R. Somayaji, M. Xenos, and A. A. Linninger,“Discovery of transport and reaction properties by problem inversion,” AIChE J., vol. 53, no. 2, pp. 381–396, 2007. • Fluent Inc. (2007). Fluent and Gambit [Online]. Available: www.fluent.com. • R. Raghavan, M. L. Brady, M. I. Rodriguez-Ponce, A. Hartlep, C. Ped´ıan and J. H. Sampson, “Convection enhanced delivery of therapeutics for brain disease, and its optimization,” Neurosurg. Focus, vol. 20, pp. 1–13, 2006. • P. F. Morrison, M. Y. Chen, R. S. Chadwick, R. R. Lonser, and E.H. Oldfield, “Focal delivery during direct infusion to brain: Role of flow rate, catheter diameter, and tissue mechanics,” Amer. J. Physiol. Regul. Integr. Comp. Physiol., vol. 277, no. 4, pp. R1218–R1229, 1999. • M. T. Krauze, R. Saito, C. Noble, M. Tamas, J. Bringas, J. W. Park, M. S. Berger, and K. Bankiewicz, “Reflux-free cannula for convection enhanced high-speed delivery of therapeutic agents,” J. Neurosurg., vol. 103, pp. 923–929, 2005. • A. Polson, “Some aspects of diffusion in solution and a definition of a colloidal particle,” J. Phys. Chem., vol. 54, pp. 649–652, 1950. • P. J. Basser and D. K. Jones, “Diffusion-tensorMRI: Theory, experimental design and data analysis—A technical review,” NMR Biomed., vol. 15, pp. 456–467, 2002. • M. Sarntinoranont, X. Chen, J. Zhao, and T. H. Mareci, “Computational model of interstitial transport in the spinal cord using diffusion tensor imaging,” Ann. Biomed. Eng., vol. 34, no. 8, pp. 1304–1321, 2006. • X. Chen, G Astary, T. Mareci and M. Sarntinoranont, “Determination of Macromolecular Concentration Following Direct Infusio into Hydrogel using Contrast-Enhnaced MRI”, Proceedings of IEEE EMBS, August 23-26, 2007. • Gordon MJ, Chu KC, Margaritis A, Martin AJ, Ethier CR, Rutt BK, “Measurement of Gd-DTPA diffusion through PVA hydrogel using a novel magnetic resonance imaging method.”, Biotechnol Bioeng., vol. 65, no.4, pp. 459-67, 1999. BMES Fall 2008 27