Mathematical modeling of erythropoietin therapy

A simple mathematical model to describe hemoglobin (Hb) concentration response to recombinant human erythropoietin (EPO) therapy is proposed. The model is based on the assumption that Hb production increases linearly with EPO dose level. The resulting equation contains two patient parameters: 1) S, the proportionality constant between g Hb generated/L blood/wk and IU EPO administered/kg body weight/wk; and 2) tau, the patient erythrocyte lifetime in weeks. The model was applied retrospectively to 67 patients from the Canadian Erythropoietin Study, yielding an average error of 5.5 g/L between 27 measured and predicted Hb value pairs over the 27 week study. The model parameters, S (mean +/- SD = 0.015 +/- 0.005) and tau (14.0 +/- 4.1), varied over an order of magnitude. The model was also used to predict the EPO dose required to reach a target Hb of 110 g/L; the EPO requirements varied from 55 to 742 IU EPO/kg/wk (mean +/- SD = 225 +/- 124). It is recommended, based upon the model results, that EPO therapy be initiated at 3 IU EPO/kg/wk for each g/L difference between target and baseline Hb, with subsequent EPO dose adjustment guided by patient modeling.