Hematological Compensation During Treatment of Sickle-Cell Anemia

A Simple Mathematical Model

by Jerry Aroesty, Thomas L. Lincoln, William S. King, Paul F. Morrison

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A simplified mathematical model is proposed for describing steady-state hematologic compensation in the presence of altered red cell properties. The unique pattern of renal oxygen consumption, related to sodium reabsorption and consequently linear in blood flow, is the basis for the simplicity of the model. The model is then applied to the prediction of improvement in the chronic anemia of sickle-cell disease, when red cell life span and oxygen affinity are modified as a result of carbamylation therapy. On this basis, it is predicted that a straight-line relationship exists between hemoglobin concentration and red cell lifetime, and that the reduction in oxygen P-50, as a result of carbamylation, is secondary to red cell lifetime as a factor in determining the reduction in anemia. The predictions are compared with the limited information available from the sodium cyanate clinical trails, and the qualitative agreement between predicted and measured mean values is satisfactory.

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