Modeling convection enhanced delivery in brain with tumor: Fluid and mass transport analyses

The delivery of therapeutic agents into the brain for the treatment of malignant brain tumors is impeded by the blood-brain barrier and by elevated interstitial fluid pressure within the tumor that reduces the driving force for fluid and mass transport from the vasculature into the interstitial space. These difficulties have led to the development of the method of convection enhanced delivery as a means to deliver therapeutic agents directly into bulk brain tissue and to distribute the drugs using convective flow.; We develop a mathematical model of convection enhanced delivery that includes both the transient transport of the infused fluid and the resulting convective-diffusive transport of the therapeutic agent. We consider infusion: (1) into spherical brain tissue; (2) into the center of a spherical tumor with or without a necrotic core; (3) off-center into a spherical tumor with a necrotic core; and (4) proximal to a spherical tumor with a necrotic core. We present numerical simulations and analyses of the fluid transport resulting from both constant pressure and constant flow rate infusions in all four geometries and of the mass transport resulting from constant flow rate infusions in the first two geometries.; The numerical simulations show that the interstitial fluid pressure, the resulting convective fluid velocity, and the distribution of the therapeutic agent are highly sensitive to the applied infusion pressure or flow rate and the hydraulic and vascular conductivities of the tissues. For infusion into brain tissue, the distribution of a drug is rather uniform. In contrast, for infusion into viable tumor tissue, significant loss of fluid from the interstitial space to the vasculature causes the therapeutic agent to accumulate within a few catheter radii from the infusion site and the peak concentration to rise to many times the value at the infusion site. This suggests that it may be beneficial to target regions of the tumor with lower vascular conductivities or to place the infusion catheter closer to an artery than to a vein.