The regeneration of red blood cells (RBCs) after blood loss is an individual complex process. We present a novel simple compartment model which is able to capture the most important features and can be personalized using parameter estimation. We compare predictions of the proposed and personalized model to a more sophisticated state-of-the-art model for erythropoiesis, and to clinical data from healthy subjects. We discuss the choice of model parameters with respect to identifiability. We give an outlook on how extensions of this novel mathematical model could have an important impact for personalized clinical decision support in the case of polycythemia vera (PV). PV is a slow-growing type of blood cancer, where especially the production of RBCs is increased. The principal treatment targeting the symptoms of PV is bloodletting (phlebotomy), at regular intervals that are based on personal experiences of the physicians. Model-based decision support might help to identify optimal and individualized phlebotomy schedules.

Detection thresholds for auditory stimuli, specified in terms of their -amplitude or level, depend on the stimulus temporal envelope and decrease with increasing stimulus duration. The neural mechanisms underlying these fundamental across-species observations are not fully understood. Here, we present a "continuous look" model, according to which the stimulus gives rise to stochastic neural detection events whose probability of occurrence is proportional to the 3rd power of the low-pass filtered, time-varying stimulus amplitude. Threshold is reached when a criterion number of events have occurred (probability summation). No long-term integration is required. We apply the model to an extensive set of thresholds measured in humans for tones of different envelopes and durations and find it to fit well. Subtle differences at long durations may be due to limited attention resources. We confirm the probabilistic nature of the detection events by analyses of simple reaction times and verify the exponent of 3 by validating model predictions for binaural thresholds from monaural thresholds. The exponent originates in the auditory periphery, possibly in the intrinsic Ca(2+) cooperativity of the Ca(2+) sensor involved in exocytosis from inner hair cells. It results in growth of the spike rate of auditory-nerve fibers (ANFs) with the 3rd power of the stimulus amplitude before saturating (Heil et al., J Neurosci 31:15424-15437, 2011), rather than with its square (i.e., with stimulus intensity), as is commonly assumed. Our work therefore suggests a link between detection thresholds and a key biochemical reaction in the receptor cells.

Polycythemia vera (PV) is a slow-growing type of blood cancer, where the production of red blood cells (RBCs) increase considerably. The principal treatment for targeting the symptoms of PV is bloodletting (phlebotomy) at regular intervals based on data derived from blood counts and physician assessments based on experience. Model-based decision support can help to identify optimal and individualized phlebotomy schedules to improve the treatment success and reduce the number of phlebotomies and thus negative side effects of the therapy. We present an extension of a simple compartment model of the production of RBCs in adults to capture patients suffering from PV. We analyze the model's properties to show the plausibility of its assumptions. We complement this with numerical results using exemplary PV patient data. The model is then used to simulate the dynamics of the disease and to compute optimal treatment plans. We discuss heuristics and solution approaches for different settings, which include constraints arising in real-world applications, where the scheduling of phlebotomies depends on appointments between patients and treating physicians. We expect that this research can support personalized clinical decisions in cases of PV.