A minimal mathematical model of red blood cell homeostasis in anemia

Anemias are diverse and cause significant morbidity and mortality, but their mechanisms are not fully understood. To unravel this complexity requires understanding how hemoglobin and red blood cell function is regulated, and what goes wrong in each form of anemia. Anemias present puzzling imbalance between hemoglobin (Hb) and the main regulator of red blood cells - the hormone erythropoietin (EPO). In some anemias EPO is markedly elevated relative to the degree of anemia, whereas in others it is inappropriately low. This variability suggests that the feedback between oxygen delivery and erythropoietin production involves mechanisms beyond simple oxygen sensing. We developed a minimal mechanistic model of erythropoiesis composed of four coupled differential equations representing erythroid progenitors, marrow reticulocytes, circulating RBCs, and plasma EPO. Most parameters were derived from experimental measurements and correspond to physiological quantities. Data from ~1,830 adults across 36 published studies, encompassing healthy individuals and patients with major anemia types, were used to validate the model, along with blood-donor recovery cohorts. The model reproduces the near-exponential Hb-EPO relationship observed in reference populations, the characteristic trajectory of hemoglobin recovery after blood loss, and disease-specific deviations through physiologically plausible parameter changes, without ad hoc fitting. Elevated EPO in aplastic anemia emerges from reduced erythroid mass and diminished receptor-mediated clearance; chronic kidney disease is consistent with impaired EPO synthesis and marrow suppression; anemia of chronic disease arises from reduced progenitor differentiation without requiring primary EPO failure; and shortened RBC lifespan alone does not lower steady-state EPO in hemolysis. Of potential clinical significance is that steady-state erythropoietin levels provide a noninvasive indicator of bone marrow activity, with higher levels reflecting reduced erythroid mass and diminished receptor-mediated uptake.