Description and Validation of a Finite Element Model of Backflow During Infusion Into a Brain Tissue Phantom

Abstract

An axisymmetric biphasic finite element model is proposed to simulate the backflow that develops around the external boundary of the catheter during flowcontrolled infusions. The model includes both material and geometric nonlinearities and special treatments for the nonlinear boundary conditions used to represent the forward flow from the catheter tip and the axial backflow that occurs in the annular gap that develops as the porous medium detaches from the catheter. Specifically, a layer of elements with high hydraulic conductivity and low Young’s modulus was used to represent the nonlinear boundary condition for the forward flow, and another layer of elements with axial hydraulic conductivity consistent with Poiseuille flow was used to represent the backflow. Validation of the model was performed by modifying the elastic properties of the latter layer to fit published experimental values for the backflow length and maximum fluid pressure obtained during infusions into agarose gels undertaken with a 0.98mmradius catheter. Next, the finite element model predictions showed good agreement with independent experimental data obtained for 0.5mmradius and 0.33mmradius catheters. Compared to analytical models developed by others, this finite element model predicts a smaller backflow length, a larger fluid pressure, and a substantially larger percentage of forward flow. This latter difference can be explained by the important axial flow in the tissue that is not considered in the analytical models. These results may provide valuable guidelines to optimize protocols during future clinical studies. The model can be extended to describe infusions in brain tissue and in patientspecific geometries.