The lifespan of red blood cells (RBCs) plays an important role in the study and interpretation of various clinical conditions. Yet, confusion about the meanings of fundamental terms related to cell survival and their quantification still exists in the literature. To address these issues, we started from a compartmental model of RBC populations based on an arbitrary full lifespan distribution, carefully defined the residual lifespan, current age, and excess lifespan of the RBC population, and then derived the distributions of these parameters. For a set of residual survival data from biotin-labeled RBCs, we fit models based on Weibull, gamma, and lognormal distributions, using nonlinear mixed effects (NLME) modeling and parametric bootstrapping. From the estimated Weibull, gamma, and lognormal parameters we computed the respective population mean full lifespans (95% confidence interval): 115.60 (109.17–121.66), 116.71 (110.81–122.51), and 116.79 (111.23–122.75) days together with the standard deviations of the full lifespans: 24.77 (20.82–28.81), 24.30 (20.53–28.33), and 24.19 (20.43–27.73). We then estimated the 95th percentiles of the lifespan distributions (a surrogate for the maximum lifespan): 153.95 (150.02–158.36), 159.51 (155.09–164.00), and 160.40 (156.00–165.58) days, the mean current ages (or the mean residual lifespans): 60.45 (58.18–62.85), 60.82 (58.77–63.33), and 57.26 (54.33–60.61) days, and the residual half-lives: 57.97 (54.96–60.90), 58.36 (55.45–61.26), and 58.40 (55.62–61.37) days, for the Weibull, gamma, and lognormal models respectively. Corresponding estimates were obtained for the individual subjects. The three models provide equally excellent goodness-of-fit, reliable estimation, and physiologically plausible values of the directly interpretable RBC survival parameters.

Anemia is prevalent in end-stage renal disease (ESRD). The discovery of recombinant human erythropoietin (rHuEPO) over 30 years ago has shifted the treatment of anemia for patients on dialysis from blood transfusions to rHuEPO therapy. Many anemia management protocols (AMPs) used by clinicians comprise a set of experience-based rules for weekly-to-monthly titration of rHuEPO doses based on hemoglobin (Hb) measurements. In order to facilitate the design of an AMP using model-based feedback control theory, we present a physiologically relevant erythropoiesis model and demonstrate its applicability using clinical data.

A complex bio-mechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the short-term dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a two-pool, linear, time-varying model to describe the dynamics of this calcium homeostasis subsystem, the Ca-PTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a two-pool, linear, time-varying model with an asymmetric reverse sigmoid relation characterizes the short-term dynamics of the Ca-PTH axis.

A complex bio-mechanism, referred to as calcium homeostasis, regulates plasma ionized calcium (Ca++) concentration in the human body to within a narrow physiologic range which is crucial for maintaining normal physiology and metabolism. In this paper we present a qualitative model of the calcium homeostatic system and then focus on a particular sub-system, termed Ca-PTH axis. We consider the dynamics of the axis involving the response of the parathyroid glands to acute changes in plasma Ca++ concentration. We use a two-pool, linear time-varying model to describe the Ca-PTH axis. We show that this model, parameterized using a guided iterative parametrization scheme and induced hypocalcemic clamp test data, successfully predicts dynamics observed in clinical tests of induced hypercalcemia in normal humans.

JTT-305/MK-5442 is a calcium-sensing receptor (CaSR) allosteric antagonist being investigated for the treatment of osteoporosis. JTT-305/MK-5442 binds to CaSRs, thus preventing receptor activation by Ca 2þ . In the parathyroid gland, this results in the release of parathyroid hormone (PTH). Sharp spikes in PTH secretion followed by rapid returns to baseline are associated with bone formation, whereas sustained elevation in PTH is associated with bone resorption. We have developed a semimechanistic, nonpopulation model of the time-course relationship between JTT-305/MK-5442 and whole plasma PTH concentrations to describe both the secretion of PTH and the kinetics of its return to baseline levels. We obtained mean concentration data for JTT-305/MK-5442 and whole PTH from a multiple dose study in U.S. postmenopausal women at doses of 5, 10, 15, and 20 mg. We hypothesized that PTH is released from two separate sources: a reservoir that is released rapidly (within minutes) in response to reduction in Ca 2þ binding, and a second source released more slowly following hours of reduced Ca 2þ binding. We modeled the release rates of these reservoirs as maximum pharmacologic effect (E max ) functions of JTT-305/MK-5442 concentration. Our model describes both the dose-dependence of PTH time of occurrence for maximum drug concentration (T max ) and maximum concentration of drug (C max ), and the extent and duration of the observed nonmonotonic return of PTH to baseline levels following JTT-305/MK-5442 administration.