Fluid Flows through Anisotropic, Poroelastic Bone Models in the opposite Direction to That through Analogous Isotropic Models

INTRODUCTION Biot’s theory of poroelastic solids [1] describes the behavior of fluids in porous materials and provides the biophysical basis for loadinduced fluid flow in bone. Applying this theory to bone, compression of the matrix causes an instantaneous increase in pore pressure within the matrix; to equilibrate this pore pressure gradient, fluid moves out of the pore spaces of the matrix under compression and back into the matrix upon subsequent load relaxation. Hence, bone essentially acts as a stiff, fluid-filled sponge. We developed a three-dimensional (3D) transversely isotropic, poroelastic finite element (FE) model of the rat tibia to predict fluid movements induced by different mechanical loading regimes [2-4]. Both elastic properties and permeability were assumed to be transversely isotropic. Cortical bone stiffness is approximately 50 percent higher in the longitudinal direction than in the transverse direction [2]. Permeability of the fluid filled pericellular space, i.e. the lacunocanalicular system (LCS), is approximately one order of magnitude higher in the transverse direction than in the longitudinal direction [2]. In applying four-point bending loads to this transversely isotropic model tibia load-induced fluid movement occurs in a direction opposite to that described in the “bone sponge” analogy above; namely, interstitial fluid flow flows from the tensile toward the compressive aspect of the bone during load application, and vice versa during the load relaxation. Reverting to isotropic material parameters causes fluid to flow again as expected. After insuring that this unexpected effect was not due to a bug or modeling fluke, we embarked on a study to elucidate its cause and to understand its implications for convection-enhanced transport in bone.