A mathematical model of erythropoiesis in mice and rats Part 2: Stimulated erythropoiesis

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Abstract
A mathematical model of erythropoietic cell production and its regulation process has been proposed in a preceding paper. It is primarily based on the assumption that the number of cell divisions taking place in the CFU‐E and erythropoietic precursor stages is regulated depending on the oxygen supply of the tissue. Quantitative dose‐response relationships for in vivo erythropoiesis are suggested. Here, we demonstrate that this model adequately reproduces data obtained in situations of stimulated erythropoiesis in mice and rats. In detail, this implies a quantitative description of the following processes: (1) Changes in tissue oxygen tension (PtO2) following removal of red cells (bleeding, haemolytic anaemia) or increase in plasma volume (dilution anaemia) or decrease in atmospheric oxygen pressure (hypoxia). (2) PtO2 dependent erythropoietin (EPO) production. (3) Dose‐response of EPO on erythropoietic amplification (up to two to four additional mitoses). (4) The changes of the marrow transit time. Model simulations are compared with experimental data for changes of erythropoiesis during hypoxia, EPO‐injection, and different forms of anaemia. A satisfactory agreement suggests that the model adequately describes and correlates different direct and indirect ways to stimulate erythropoiesis. It quantifies the role and relative contribution of the haematocrit, haemoglobin concentration, atmospheric oxygen pressure, tissue oxygen pressure, and plasma volume as triggers in erythropoietic stimulation under various conditions. Furthermore, the model may allow to optimize the scheme of EPO‐administration and to find the maximum increase of erythropoiesis for a given amount of erythropoietin.