Effects of saturating metabolic uptake on space profiles and tracer kinetics

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Abstract
Vascular and steady-state lengthwise concentrations evolving in tissue as a consequence of saturable uptake processes are explored when there is no effective barrier between blood and tissue, when there is one effective barrier (the liver), and when barriers are present at both capillary and cell membrane. Falling exponential profiles develop at low-input concentrations and grade over into much smaller linear decreases at high concentrations. Uptake behind an effective barrier produces a step-down in concentration. With no effective barriers, a tracer impulse propagates to the outflow in a delayed fashion, reversible binding to the enzymic removal mechanism increasing its space of distribution and delaying it further and irreversible uptake diminishing its area. As bulk concentration is increased, proportional tracer uptake diminishes and ultimately approaches zero. With barriers in the system, tracer output consists of an impulse damped by cell entry, followed by outflow recovery of material that has escaped cell uptake. Increase in bulk concentration is found to saturate the uptake mechanism, with a proportionate increase in the returning material.