Erythropoietin production-oxyhemoglobin concentration

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. 

Figure 1. Block diagram of a model for the control of erythropoiesis (HbO), oxyhemoglobin concentration Vi, viscosity factor (HbO), effective oxyhemoglobin concentration R, rate of erythropoietin release (E), plasma erythropoietin concentration E0, normal plasma erythropoietin concentration V , distribution volume for erythropoietin P, rate of hemoglobin production MT, erythrocyte maturation time L, rate of hemoglobin loss TH, total circulating hemoglobin (Hb), blood hemoglobin concentration Vb, blood volume Vp, plasma volume Vp0, normal plasma volume Vpf, steady-state hypoxic plasma volume MCV, mean corpuscular volume MCH, mean corpuscular hemoglobin k, constant...

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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