Assessment of an Exponential Scaling Relationship for Backflow Length in Brain Tissue

Convection enhanced delivery is a protocol to deliver large volumes of drugs over localized zones of the brain for the treatment of diseases and tumors. Brain infusion experiments at higher flow rates showed backflow, in which an annular zone is formed outside the catheter and the infused drug preferentially flows toward the surface of the brain rather than through the tissue in the direction of the area targeted for delivery. The foundational model of Morrison et al. [1] considered the deformation of the tissue around the external boundary of the catheter, the axial flow in the annular gap formed around the cannula, and the radial flow from this annular region into the porous tissue in the development of an exponential correlation for backflow length L: where Q is the infusion flow rate, R is a tissue hydraulic resistance, r_c is the catheter radius, G is the tissue shear modulus, and μ is the fluid viscosity. However, this formula was derived under some limiting assumptions, such as considering the solid phase of the infused tissue as a linearly elastic material under infinitesimal deformations, whereas mechanical testing has shown large deformations under physiological loadings [2, 3].