A computational model of direct interstitial infusion of macromolecules into the spinal cord

Abstract

Convection-enhanced interstitial infusion can deliver macromolecular drugs to large tissue volumes of the central nervous system. To characterize infusion into the spinal cord, an image-based three-dimensional finite element model of the rat spinal cord was developed. The model incorporated convection and diffusion through white and gray matter, including anisotropic transport due to alignment of white matter tracts. Spatial and temporal distribution of the marker substance albumin within the interstitial space was determined. Consistent with previous experiments, predicted distribution was highly anisotropic. Infusing into the dorsal column, albumin was primarily confined to, white matter with limited penetration into adjacent gray matter. Distribution was determined primarily by the ratio of fiber-parallel to fiber-perpendicular hydraulic conductivity tensor components (k(wm-z)/k(wm-x)), the ratio of transverse white and gray matter hydraulic conductivity (k(wm-x)/k(gm)), and tissue porosity. Fits to previous experimental measures of axial and transverse spread, distribution volume, and protein recovery yielded an optimum k(wm-z)/k(wm-x) of approximately 20 at 0.1 microl/min. k(wm-x)/k(gm) of 100 was sufficient to match experimental transverse distribution data. Best fits to data at 0.1 microl/min were achieved by porosities characteristic of moderate edema (e.g., 0.26). Distribution also varied with catheter placement with more medial placement resulting in greater distribution volumes.