Motivation

1. A Poroelastic-Fluid Interaction Model to Quantify Human Brain Intracranial DynamicsBrian Sweetman, Sukhraaj Basati, Madhu Smitha Harihara Iyer, Andreas A. LinningerLaboratory for Product and Process Design Department of Bioengineering, University of Illinois at Chicago Motivation Intracranial Dynamics • Millions of people suffer from brain related diseases • Hydrocephalus Alzheimer's Parkinson's • Improvements in current treatments for hydrocephalus needed • Dangers of treatment • Expense • Unpredictability of treatment • High rate of shunt failure • How to improve treatment for hydrocephalus patients • Advance the current understanding of central nervous system (CNS) mechanics • Investigate the mechanical properties of brain tissue, cerebral vasculature, and cerebral spinal fluid (CSF) • Investigate the complex mechanical interaction between all components of the CNS • Definition: Quantification of how the brain, blood, and CSF interact (in mechanical terms) under normal and diseased conditions • How do we observe the brain/CNS and understand how it works? • Phase-contrast-magnetic resonance imaging (PC-MRI) measures CSF velocities and flow rates • Computed tomography (CT) imaging allows delineation of fluid and solid regions of the CNS; needed for building computational models • Goals • Validate CSF flow field of computational model with PC-MRI measurements • Compute the dynamic pressure field required to produce measured flow field • Determine changes in system compliance that lead to hydrocephalus MR image of implanted shunt Schematic of shunt implantation PC-MRI: CSF flow field Child with hydrocephalus CSF flow over 1 Car. Cycle Arterial vasculature Fluid-Tissue Interaction Computational Model Poroelasticity • Definition: The quantification of force balances between fluid and tissues in the body • We seek to determine • Fluid flow dictated by moving solid boundaries • Solid displacements, stresses, and strains due to moving fluid and fluid pressures • Definition: A mathematical description of how a poroelastic material behaves • Poroelastic materials • Return to original configuration after removal of applied mechanical stress (no loss of energy) • Contain pores through which fluid may flow; diffusivity dependent on material’s porosity • Flow through Porous Media • Governed by Darcy’s Law • Fluid velocity: average velocity through the pores Governing Equations for Fluids and Solids Boundary Conditions for Model • Momentum • Continuity • Darcy’s Law • Brain movement dictated by blood flow • CSF outflow at the sagittal sinus • Constant CSF production from choroid plexus • Distensible spinal canal • Material properties of fluid/solid specified • Stress-Strain Relationships Continuity for extracellular (EC) fluid Continuity for Solid Matrix Fluid flow in EC Newtonian Fluids Elastic Solids • FTI Constraints Dynamic Kinematic Force balance for solid phase Model Validation ICP and Ventricular Enlargement Computational results were compared to PC-MRI flow measurements to confirm validity of model Model found to be accurate in predicting Velocities Flow rates Pressures Question: Does an increase in CSF outflow resistance lead to an increase an intracranial pressure (ICP)? Velocity in Lower Aqueduct; Normal Case Flow field through cerebrum under conditions of high ICP Velocity in Lower Aqueduct; Hydrocephalic Case LV Surface Area [cm2] Intraventricular Pressure [Pa] Compressive stresses: mid lateral ventricle Tensile stresses: anterior & posterior horns TPG: Transmantle Pressure Gradient Conclusions and Significance References Bathe, K.: Finite Element Procedures. New Jersey, Prentice-Hall, Inc., 1996. Greitz, D. Neurosurgical Review. 27:145-165. 2004. Linninger, A.A., Xenos, M., Zhu, D.C., Somayaji, M.B., Penn, R. IEEE TBME. 54(2):291-302, 2007. Zhu, D., Xenos, M., Linninger, A., Penn, R., MD. Jnl of MRI. 24:756-770. 2006. • The proposed computational model accurately predicts the CSF flow field for both a normal subject and a patient with communicating hydrocephalus • Aqueductal flow rate higher (pontine cistern velocity decreased) in the hydrocephalic patient compared to normal subjects • An increase in CSF outflow resistance results in higher intracranial (consequently intraventricular) pressure which acts to deform the cerebrum and displace extracellular fluid • The transmantle pressure gradient remains small, even during the transitional phase from normal to hydrocephalic conditions Acknowledgments • Dr. Richard Penn, University of Chicago Hospitals • ADINA, Watertown, MA • NIH, Grant 5R21EB4956-2