Distributed-in-space product formation in vivo: linear kinetics

Abstract

Distributed-in-space conversion of precursor substrate to product within an organ is explored when all formed product is released into the bloodstream. When precursor removal kinetics are linear (conversion occurring proportionately to concentration) and the process is uniformly distributed along the length, exponentially decreasing concentration profiles for precursor result. The vascular profile for product rises in complementary fashion; the sum of precursor and product is constant along the length. Symmetric permeability barriers are found to produce concentration stepdowns of precursor from blood to tissue and, for product, converse stepdowns from tissue to blood. Tracer precursor, introduced as an impulse input, within this steady state, is converted to product, details varying with the number of barriers. Nevertheless, a particular common feature is found in the solutions. The analytic expression for locally generated tracer product is found, in each case, to contain the impulse response to tracer product introduced at the origin. Therefore, to simplify experimental analysis and to superpose a set of constraints on computational approaches to parameter estimation, one should introduce, simultaneously with tracer precursor, tracer product labeled in an identifiably different manner.