A model for the distribution and clearance of inert substances in subcutaneous tissue

The subcutaneous space has received attention in recent years as a route for the continuous administration of drugs and implantation of drug delivery systems. Yet little work has been devoted to an examination of the mass transport (distribution) of drugs in the subcutaneous space and the factors that influence their rate of clearance. A mathematical model is developed to describe the spreading and resorption of substances infused into the subcutaneous space. It simulates radial diffusion and flow in the direction of spreading as well as lateral convection into the systemic circulation. An analytic solution is obtained for the distribution of the substance as a function of time and position in the subcutaneous space. Two independent parameters, v (Péclét no.) and H (generalized Biot no.), are found to control the transport. Examples are presented to illustrate the effects of these parameters on the distribution of substances in the subcutaneous space.