A mathematical model of erythropoiesis in mice and rats. Part 1: Structure of the model

Abstract

A mathematical model has been developed which describes the regulation of erythropoiesis in mice and rats. The main model assumptions are: (1) Regulation is mediated by erythropoietin (EPO). (2) The production of EPO depends exponentially on the tissue oxygen pressure (e.g. in the renal production sites). (3) There are sigmoidal dose-response curves relating the EPO concentration in the plasma to the mitotic activity of CFU-E and proliferative erythropoietic precursors. For maximum stimulation two to four additional mitoses may occur, while for an absent stimulus three to five mitoses may be omitted. (4) The normal precursor transit time of three to four days may be shortened by more than 50% during maximum stimulation. (5) The erythrocytes have a normal lifespan of 42-56 days, which may be reduced to 15-20 days under erythropoietic stimulation. Among these assumptions, the dose-response relationships between EPO and the mitotic activity of CFU-E and the proliferative erythropoietic precursors are the most important hypotheses of the model. This is the first of a series of three papers and gives a description of the mathematical formalism and the parameters used. In the subsequent papers computer simulations on erythropoietic stimulation and suppression are presented.