Fluid infusions from catheters into elastic tissue: I. Azimuthally symmetric backflow in homogeneous media

Directly injecting therapeutics into brain tissue has been investigated both experimentally and theoretically. Paul Morrison and others from the National Institutes of Health pointed out the importance of backflow along and outside a catheter inserted into the tissue, once steady state conditions have been reached. Here we investigate and extend their model. We begin with a reformulation of their results and demonstrate an exact solution that exhibits the scaling behavior of the model where the surrounding tissue medium is homogeneous and isotropic. We report on experimental tests of our predictions in agarose gels. We describe the limitations of the assumptions used and the utility of our reformulation. Extensions of the model, including improvements on some of its crude assumptions and generalizations to inhomogeneous media, will be submitted separately.