Advanced Visualization of Deformation and Stress in Porous Media for Enhanced Drug Delivery

1. Displacement and Stress Visualization in Porous Media During Convection Enhanced Drug Delivery N. Sindhwani, O. Ivanchenko and A. LinningerLaboratory for Product and Process Design, Dept. of Bioengineering University of Illinois at ChicagoChicago, IL, USA-60607 BMES Annual Meeting, Pittsburgh, PA, October 10, 2009 Goal and Approaches Motivation Goal: Experimental investigation and mathematical simulation of porous tissue deformation under infusion. • CNS Diseases: • Neurologic Disorders such as Parkinson’s, Alzheimer’s, and Brain tumors affect more than 50 million Americans each year. • Delivery of drugs to the brain is a problem due to the Blood Brain Barrier which prevents delivery of large molecules to the target site. • Convection Enhanced Delivery: • Direct infusion into the brain parenchyma bypassing the Blood-Brain-Barrier. • Bulk flow mechanism to deliver drugs to target site. • Promising tool for delivery of large molecules to the brain • Problem of Reflux: • Backflow of drug/dye along the catheter shaft. Approaches: Analysis of mathematical models for porous tissue deformation. Visualization of deformation around the catheter in brain surrogate agarose gel during infusion using Nano beads. Visualization of stress field in the porous tissue using photoelasticity experiments. Simulate deformation for better prediction of drug distribution Visualization of Deformation using Nanobeads Model for poroelastic issue • Nano bead tracking experiments • Seeding Nanobeads homogenously and at high density in the optical plane. • Images taken before and after infusion. • Cross- Correlation conducted using ISSN-DPIV software. Visualization of Stress Field using Photoelasticity • Elemental components of the deformable porous matrix model: • Incompressible solid elements. • Attached by mass less springs. • Photoelasticity Theory: • Based on the property of Birefringence, or, Double Refraction of the material. • Plane polarized light is resolved along two principle stress directions. • The stress field can be related to its index of refraction through Maxwell’s stress optic laws.  The Stress-Optic law: Solid Equations: Strain: Change in porosity: Δ= Retardation. σ1 and σ2 are principle stresses. h= Thickness of the sample λ= Wavelength of the light. Direction of infusion Seeded region Stress and strain relationship: Change in hydraulic conductivity: Catheter Fluid equations: Simulations Continuity Equation: Darcy’s Law: References Linninger A A, Somayaji M R, Zhang L, Hariharan M S, and Penn R D. Rigorous Mathematical Modeling Techniques for Optimal Delivery of Macromolecules to the Brain. IEEE Transactions on Biomedical Engineering (2008), Vol. 55, No. 9, Linninger A A, Somayaji M R, Mekarski M, Zhang L. Prediction of convection-enhanced drug delivery to the human brain. J Theor. Biol. (2008) 250, 125–138. Linninger A A, Somayaji M R, Erickson T, Guo X, Penn R D. Computational methods for predicting drug transport in anisotropic and heterogeneous brain tissue. J. Biomech. (2008) 41 2176–2187. Levine D N. The Pathogenesis of Normal Pressure Hydrocephalus: A Theoretical Analysis. Bulletin Math. Biol.(1999) 61, 875–916. Morrison P F, Chen M Y, Chadwick R S, Lonser R R and Oldfield E H. Focal delivery during direct infusion to brain: role of flow rate, catheter diameter, and tissue mechanics. Am J Physiol Regulatory Integrative Comp Physiol (1999)277:1218-1229. Conclusions • Infusion in porous agarose or brain tissue, causes deformation and stresses in the solid matrix near the infusion site. • In areas of large fluid flow, porosity and hydraulic conductivity changes. • A mathematical model that aptly predicts these changes was created. • These changes can cause backflow. Acknowledgements NSF CBET 0730048, NSF RET EEC 0743068, NSF REU EEC 0754590