The modeling of tracer exchange and sequestration in the liver

Abstract

Both anatomical and physiological data have been utilized to develop a distributed-in-space mathematical model of the processes of tracer exchange and sequestration in the liver. Comparison with a vascular reference, labeled red cells, indicates that substances entering the freely accessible interstitial or Disse space do so by delayed-wave, flow-limited distribution into that space; lateral or transverse diffusional equilibration occurs virtually instantaneously at each point along the length. In contrast, axial gradients are preserved (lengthwise diffusional equilibration times are orders of magnitude larger than transit times). When a tracer pulse injection is used to explore tracer exchange with liver cells beyond this, the outflow is found to consist of an impulse that is delayed by propagation in the interstitial space and damped by cellular entry (tracer that has not entered liver cells), followed by a reduced-in-magnitude and spread out tailing (tracer that has entered and returned from liver cells). Intracellular and spread out tailing (tracer that has entered and returned from liver cells; it therefore reduces the returning part of the outflow profile. It also results in declining unlabeled substrate axial-concentration gradients in sinusoid and cell, together with a step down in concentration across the liver cell membranes.