Oxyhemoglobin relationship, erythropoietin

A mathematical model of the control system for erythropoiesis is presented. It is postulated that the rate of erythropoiesis is controlled by a hormone, erythropoietin, which is released from the kidney in response to reduced renal oxygen supply. Equations are developed relating erythropoietin release to arterial oxyhemoglobin concentration, and hemoglobin production to plasma erythropoietin concentration, with appropriate time delays. Effects of plasma volume changes during hypoxia are included. The model simulates the dynamic response of the erythropoietic system to a step decrease in the pOt of inspired air. Contributions of the parameters and relationships to the predicted response are analyzed. The model response compares favorably with experimental data obtained from mice subjected to different degrees of hypoxia. 

Major components of the model are shown in Figure 1. In the model the controlled variable is oxyhemoglobin concentration (the product of hemoglobin concentration and percent oxygen saturation). Erythropoietin is released from the kidney according to an exponential relationship (Equation 1) relating oxyhemoglobin concentration to the rate of erythropoietin release. 

A delay of 4 hours (Ti) was incorporated into the model between changes in oxyhemoglobin concentration and subsequent erythropoietin release to account for the time required from release of the renal erythropoietic factor to the development of active erythroproietin in the blood stream (3). Values for Ki and K2 were estimated for the mouse by scaling a relationship derived from data in rats, relating oxyhemoglobin concentration to erythropoietin release (I). It was assumed that the released erythroproietin mixes instantly in a volume equal to twice the plasma volume and that the disappearance rate of erythropoietin is proportional to the plasma erythropoietin concentration with a disappearance constant of. 130 day (4). 

With the relationship between oxyhemoglobin concentration and erythropoietin production selected to provide good agreement of erythropoietin concentration changes and experimental data, the constants in Equation 2 (hemoglobin production) were modified to produce a better total hemoglobin response. The conditions were that (1) normal plasma... 

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