STATISTICAL-MECHANICS OF HEPATIC ELIMINATION

Enzymatic elimination of substrates carried by the blood through the liver occurs in a large ensemble of anatomically defined elements arranged in parallel. A common measured input concentration of the substrate is changed by elimination into an output concentration with values distributed over the elements, of which only the flow-weighted mean is measured. The output concentration from each element is determined in the steady state by the input concentration, the blood flow and the kinetic parameters of the enzymatic reaction according to a previously established model based on Michaelis-Menten kinetics. Assuming a distribution of blood flow and of the enzymatic elimination capacity over the elements, the problem is formulated of determining the density function of the distribution from the input-output relation observed over a large range of concentrations. The density function satisfies an integral equation of the first kind, with a kernel given by a transcendental equation. Results are obtained on the uniqueness and existence of the density function, on its determination in closed form and from a series expansion, and on the relation of the problem to the problem of moments. © 1979.