Backflow length predictions during flow-controlled infusions using a nonlinear biphasic finite element model

A previously proposed finite element model that considers geometric and material nonlinearities and the free boundary problems that occur at the catheter tip and in the annular zone around the lateral surface of the catheter was revised and was used to fit a power-law formula to predict backflow length during infusions into brain tissue. Compared to a closed-form solution based on linear elasticity, the power-law formula for compliant materials predicted a substantial lower influence of the shear modulus and catheter radius on the backflow length, whereas the corresponding influence for stiffer materials was more consistent with the closed-form solution. The finite element model predicted decreases of the backflow length for reduction of the shear modulus for highly compliant materials (shear modulus less than 500 Pa) due to the increased area of infusion and the high fluid fraction near the infusion cavity that greatly increased the surface area available for fluid transfer and reduced the hydraulic resistance toward the tissue. These results show the importance of taking into account the material and geometrical nonlinearities that arise near the infusion surface as well as the change of hydraulic conductivity with strain for a proper characterization of backflow length during flow-controlled infusions into the brain.