Fig 1.
General features of ESA therapy and hemoglobin cycling.
(A) Simplified representation of the treatment loop involved in erythropoiesis-stimulating agent (ESA) therapy: An anemic patient’s hemoglobin levels are measured on a regular basis and inform ESA dose adjustments via a dosing algorithm and/or an anemia manager’s decision. The given ESA dose, in turn, affects the patient’s hemoglobin levels. (B) Historical record of hemoglobin (Hb) cycling in an anemic hemodialysis patient showing Hb measurements (dots) and ESA administrations (bars). Dashed lines indicate mean values for the respective quantities on the shown time horizon. (C) Schematic depiction of the biomedical model with three variables (Hb levels, current ESA dose prescription and systemic ESA levels) capturing the key features of the feedbacks shown in panel A. The model is described in detail in the Methods section.
Fig 2.
Decision tree used in the biomedical model that represents the prototypical features ESA dosing schemes based on a patient’s current hemoglobin measurement.
Fig 3.
Simulated hemoglobin dynamics display a steady or cycling behavior, respectively, depending on physiological and treatment parameters.
Plots show simulated ground-truth hemoglobin levels (gray curves), hemoglobin levels including simulated measurement errors (dots) and ESA administrations (bars). (A) Simulations with a reference parameter set (selected parameters shown above the plot, all other parameters given in Table 1). (B–D) Simulations with parameters varied with respect to the reference parameter set as indicated. In all panels, the shaded region indicates the hemoglobin target window that dose adjustments aim to reach. Initial conditions were drawn from the distribution of equilibrated states. See Methods for simulation details.
Fig 4.
Statistical indicators of self-sustained hemoglobin (Hb) cycling in simulations and in clinical data.
(A) The long-term Hb standard deviation (solid curve) serves as a proxy for the amplitude of Hb cycles, shown here as a function of ESA responsiveness in model simulations. The associated ESA standard deviation (blue curve) is displayed for reference. The gray arrow marks the onset of cycling as predicted by the inequality (25). Here, all other model parameters describing patient physiology and treatment modalities, including the dosing interval, are fixed to reference values (1). (B) The Pearson correlation coefficient of Hb levels and ESA doses quantifies the offset (or ‘phase shift’) between bursts of ESA administrations and subsequent Hb cycles and vice versa, see Methods. The correlation coefficient is shown for the same set of simulations as in panel A. (C) Distribution of Hb-ESA correlation coefficients across clinical data, pooled by number of Hb cycles in a patient’s dataset, see Methods. Bars indicate the total range of values, with the center horizontal bar indicating the mean. Numbers in parentheses indicate the number of datasets within the respective group. Pairs of groups were compared using the Anderson–Darling test as indicated (**, p < 0.01; *, p < 0.05; n.s., p > 0.05). (D, E) Pairs of Hb-ESA cross correlation coefficients and Hb standard deviation from (D) model simulations and (E) clinical data (same dataset as in panel C).
Fig 5.
Variability in hemoglobin and ESA administration dynamics for a simulated example patient and treatment setting, where individual physiological and treatment parameters are varied.
(A) Mean distance of the ground-truth Hb levels to the specified Hb target range (10–11 g/dL) if RBC lifespan is varied and all other physiological, treatment and ESA parameters are fixed. (A’) Fraction of time the patients spends with Hb levels below the target window and (A”) above the target window as a function of RBC lifespan. In panels A–A”, the red shaded region indicates where RBC lifespan is so small that even repeated administration of the maximum ESA dose cannot achieve Hb target levels, see Eq (15); in the green shaded region, RBC lifespan is high enough to maintain Hb target levels even without ESA therapy, see Eq (16). (B–D”) Contour plots show the indicated quantities if two parameters are varied simultaneously. Columns are organized by quantity displayed and rows are organized by pair of parameters varied. The white line in panels B–B” indicates the cross section of the plot that is displayed in panels A–A”, respectively. Parameters not indicated are fixed to the values provided in Table 1.
Fig 6.
Variability in hemoglobin and ESA administration dynamics for a simulated example patient and treatment setting, where individual physiological and treatment parameters are varied (continued).
All conventions identical to Fig 5. (A) Standard deviation of Hb levels, (A’) Correlation coefficient between simulated Hb measurements and ESA doses and (A”) mean ESA dose as a function of RBC lifespan. (B–D”) Contour plots show the indicated quantities if two parameters are varied simultaneously. Columns are organized by quantity displayed and rows are organized by pair of parameters varied. Hatched regions in panels B’ and C’ indicate parameter regions where the Hb-ESA correlation coefficient is not defined. Parameters not indicated are fixed to the values provided in Table 1.
Fig 7.
Transient cycling can be induced by events unrelated to treatment such as sudden blood loss.
(A–C) Simulated bleeding scenarios where hemoglobin levels have been instantly reduced by 4 g/dL at 12 months (gray arrow). Parameter values for the reference scenario (panel A) are provided in Table 1. Parameter changes in panels B and C as indicated in the plot. All display conventions as in Fig 3.
Table 1.
List of reference model parameters.