A theoretical model of circulatory interstitial fluid flow and species transport within porous cortical bone

A three-dimensional model of interstitial fluid flow and passive species transport within mineralized regions surrounding cross-cortical vessel canals is developed. In contrast to earlier studies, the present model applies to circulatory, non-stress-induced interstitial flow in porous cortical bone. Based on previous experimental observations, the canals are modeled as line sources that pass at an oblique angle through the cortex. Cross-cortical interstitial flow from the endosteal surface to the periosteal surface is also taken into account. It is found that model transport characteristics are qualitatively consistent with reported observations. In addition, parametric studies reveal the following: (1) Solute contact with the matrix is maximized when the ratio of canal radius to cortex thickness (R) is near physiological R values. (2) Solute-matrix contact falls to low levels when R falls below the physiological range. (3) Solute-matrix contact is maximized when the cross-cortical velocity is approximately an order of magnitude smaller than the canal outflow velocity. The first and second findings suggest that within porous bone physiological ranges of R promote near optimal species contact with the mineralized matrix. The third finding suggests that relatively impermeable layers of bone within the cortex can effectively promote solute-matrix contact by limiting cross-cortical flow. Finally, the model suggests that intra-canal resorption associated with reduced external loading may effectively compensate for reduced stress-induced interstitial flow by enhancing circulatory interstitial flow and species transport.