Modeling of red blood cell life-spans in hematologically normal populations

Differential Responses of Young and Old Erythrocytes Stored with Vitamin C and Vitamin E in Additive Solution-7

Oxidative stress (OS) causes biochemical and morphological alterations in erythrocytes. The primary factors contributing to OS are aging and storage. Antioxidants significantly alleviate OS. Therefore, this study aimed to investigate the response of young and old erythrocytes to vitamin C and vitamin E during storage. Erythrocytes were separated into young and old by the Percoll method. Each erythrocyte subpopulation was categorized into the i) Control (additive solution-7 [AS-7]) and ii) vitamin C and vitamin E in AS-7 (VC+VE) groups and stored for 21 days at 4°C. OS, antioxidant, and aging markers were analyzed on days 1, 14, and 21. The activity of antioxidant enzymes was similar throughout storage in young cells. However, superoxide dismutase activity elevated in old cells (Control and VC+VE) on days 1 and 21. Catalase (CAT) activity increased on days 14 and 21, whereas glutathione peroxidase (GPX) increased on days 1 and 14 in old Controls. However, in old VC+VE, CAT increased on day 21 and GPX increased on day 1. Advanced oxidation protein products, superoxides, glutathione, and uric acid increased in old cells throughout storage. Malondialdehyde decreased in old VC+VE compared with old Control on days 14 and 21. Sialic acids and glutamate oxaloacetate transaminase activity were higher in young cells compared to old cells. Young cells exhibited lower oxidative changes throughout storage. Vitamin C and vitamin E were effective in maintaining the redox balance in old cells. These findings emphasize the need for specific approaches for different subpopulations during erythrocyte banking.

Predicting the Long-Term Effects of Therapeutic Neutralization of Oncostatin M on Human Hematopoiesis

Therapeutic neutralization of Oncostatin M (OSM) causes mechanism-driven anemia and thrombocytopenia, which narrows the therapeutic window complicating the selection of doses (and dosing intervals) that optimize efficacy and safety. We utilized clinical data from studies of an anti-OSM monoclonal antibody (GSK2330811) in healthy volunteers (n = 49) and systemic sclerosis patients (n = 35), to quantitatively determine the link between OSM and alterations in red blood cell (RBC) and platelet production. Longitudinal changes in hematopoietic variables (including RBCs, reticulocytes, platelets, erythropoietin, and thrombopoietin) were linked in a physiology-based model, to capture the long-term effects and variability of therapeutic OSM neutralization on human hematopoiesis. Free serum OSM stimulated precursor cell production through sigmoidal relations, with higher maximum suppression (Imax ) and OSM concentration for 50% suppression (IC50 ) for platelets (89.1% [95% confidence interval: 83.4-93.0], 6.03 pg/mL [4.41-8.26]) than RBCs (57.0% [49.7-64.0], 2.93 pg/mL [2.55-3.36]). Reduction in hemoglobin and platelets increased erythro- and thrombopoietin, respectively, prompting reticulocytosis and (partially) alleviating OSM-restricted hematopoiesis. The physiology-based model was substantiated by preclinical data and utilized in exploration of once-weekly or every other week dosing regimens. Predictions revealed an (for the indication) unacceptable occurrence of grade 2 (67% [58-76], 29% [20-38]) and grade 3 (17% [10-25], 3% [0-7]) anemias, with limited thrombocytopenia. Individual extent of RBC precursor modulation was moderately correlated to skin mRNA gene expression changes. The physiological basis and consideration of interplay among hematopoietic variables makes the model generalizable to other drug and nondrug scenarios, with adaptations for patient populations, diseases, and therapeutics that modulate hematopoiesis or exhibit risk of anemia and/or thrombocytopenia.

Model-based assessment of the safety of community interventions with primaquine in sub-Saharan Africa

BACKGROUND

Single low-dose primaquine (SLD-PQ) is recommended in combination with artemisinin-based combination therapy to reduce Plasmodium falciparum transmission in areas threatened by artemisinin resistance or aiming for malaria elimination. SLD-PQ may be beneficial in mass drug administration (MDA) campaigns to prevent malaria transmission but uptake is limited by concerns of hemolysis in glucose-6-phosphate dehydrogenase (G6PD)-deficient individuals. The aim of this study was to improve the evidence on the safety of MDA with SLD-PQ in a sub-Saharan African setting.

METHODS

A nonlinear mixed-effects model describing the pharmacokinetics and treatment-induced hemolysis of primaquine was developed using data from an adult (n = 16, G6PD deficient) and pediatric study (n = 38, G6PD normal). The relationship between primaquine pharmacokinetics and hemolysis was modeled using an established erythrocyte lifespan model. The safety of MDA with SLD-PQ was explored through Monte Carlo simulations for SLD-PQ at 0.25 or 0.4 mg/kg using baseline data from a Tanzanian setting with detailed information on hemoglobin concentrations and G6PD status.

RESULTS

The predicted reduction in hemoglobin levels following SLD-PQ was small and returned to pre-treatment levels after 25 days. G6PD deficiency (African A- variant) was associated with a 2.5-fold (95% CI 1.2-8.2) larger reduction in hemoglobin levels. In the Tanzanian setting where 43% of the population had at least mild anemia (hemoglobin < 11-13 g/dl depending on age and sex) and 2.73% had severe anemia (hemoglobin < 7-8 g/dl depending on age and sex), an additional 3.7% and 6.0% of the population were predicted to develop at least mild anemia and 0.25% and 0.41% to develop severe anemia after 0.25 and 0.4 mg/kg SLD-PQ, respectively. Children < 5 years of age and women ≥ 15 years of age were found to have a higher chance to have low pre-treatment hemoglobin.

CONCLUSIONS

This study supports the feasibility of MDA with SLD-PQ in a sub-Saharan African setting by predicting small and transient reductions in hemoglobin levels. In a setting where a substantial proportion of the population had low hemoglobin concentrations, our simulations suggest treatment with SLD-PQ would result in small increases in the prevalence of anemia which would most likely be transient.

Unraveling Disease Pathophysiology with Mathematical Modeling

Modeling has enabled fundamental advances in our understanding of the mechanisms of health and disease for centuries, since at least the time of William Harvey almost 500 years ago. Recent technological advances in molecular methods, computation, and imaging generate optimism that mathematical modeling will enable the biomedical research community to accelerate its efforts in unraveling the molecular, cellular, tissue-, and organ-level processes that maintain health, predispose to disease, and determine response to treatment. In this review, we discuss some of the roles of mathematical modeling in the study of human physiology and pathophysiology and some challenges and opportunities in general and in two specific areas: in vivo modeling of pulmonary function and in vitro modeling of blood cell populations.

Ribavirin does not potentiate favipiravir antiviral activity against Ebola virus in non-human primates

BACKGROUND

In spite of recurrent and dramatic outbreaks, there are no therapeutics approved against Ebola virus disease. Favipiravir, a RNA polymerase inhibitor active against several RNA viruses, recently demonstrated significant but not complete protection in a non-human primate model of Ebola virus disease. In this study, we assessed the benefit of the combination of favipiravir and ribavirin, another broad spectrum antiviral agent, in the same model.

METHODS

15 female cynomolgus macaques were challenged intramuscularly with 1,000 FFU of Ebola virus Gabon 2001 strain and followed for 21 days. All animals received favipiravir 180 mg/kg twice a day (BID), either as monotherapy (n = 5) or in combination with ribavirin (n = 10). Ribavirin was given either at the dose 10 mg/kg BID (n = 5) or 5 mg/kg BID (n = 5). Favipiravir and ribavirin were initiated two and one days before viral challenge respectively and treatment were continued for 14 days. Treatment effects on viral and hematological markers were assessed using a mathematical model. Survival rate of 0% and 20% were obtained in macaques receiving favipiravir plus ribavirin 10 and 5 mg/kg BID, respectively, compared to 40% in the favipiravir monotherapy group (P = 0.061 when comparing monotherapy and bitherapy, log rank). Viral dynamic modeling analysis did not identify an association between plasma concentrations of ribavirin and viral load levels. Using a model of erythropoiesis, plasma concentrations of ribavirin were strongly associated with a hemoglobin drop (p = 0.0015).

CONCLUSION

Ribavirin plus favipiravir did not extend survival rates and did not lower viral replication rate compared to favipiravir monotherapy in this animal model. Patients receiving this combination in other indications, such as Lassa fever, should be closely monitored to prevent potential toxicity associated with anemia.

Comparison of Power, Prognosis, and Extrapolation Properties of Four Population Pharmacodynamic Models of HbA1c for Type 2 Diabetes

Reusing published models saves time; time to be used for informing decisions in drug development. In antihyperglycemic drug development, several published HbA1c models are available but selecting the appropriate model for a particular purpose is challenging. This study aims at helping selection by investigating four HbA1c models, specifically the ability to identify drug effects (shape, site of action, and power) and simulation properties. All models could identify glucose effect nonlinearities, although for detecting the site of action, a mechanistic glucose model was needed. Power was highest for models using mean plasma glucose to drive HbA1c formation. Insulin contribution to power varied greatly depending on the drug target; it was beneficial only if the drug target was insulin secretion. All investigated models showed good simulation properties. However, extrapolation with the mechanistic model beyond 12 weeks resulted in drug effect overprediction. This investigation aids drug development in decisions regarding model choice if reusing published HbA1c models.

Age-structured population model of cell survival

Age-structured cell population model was introduced to describe cell survival. The impact of the environment on the cell population is represented by drug plasma concentration. A key model variable is the hazard of cell removal that is a subject to the environment effect. The model is capable of describing cohort and random labeling cell survival data. In addition, it accounts for cell loss due to labeling of cell sample, but it lacks ability to describe the effect of label elution on the survival data. The model was applied to red blood cell (RBC) survival data in two groups of Wistar rats obtained by two techniques: cohort labeling using ¹⁴C-glycine (N = 4) and random labeling using biotin (N = 8). The Weibull probability density function was selected for the RBC lifespan distribution. The data were simultaneously fitted by the mixed effects model implemented in Monolix 4.3.3. The estimated typical values of RBC lifespan and age were 53.7 and 27.8 days, respectively. A noticeable effect of biotinylation on RBC survival was observed that resulted in a significant difference between the means of individual RBC lifespan for two groups. The model provides a mechanistic framework flexible enough to account for various experimental designs to generate the cell survival data. Despite model qualification using animal data, the model has the same potential to be applied to cell survival data analysis in humans.

Population pharmacokinetics and pharmacodynamics of IONIS-GCGRRx, an antisense oligonucleotide for type 2 diabetes mellitus: a red blood cell lifespan model

IONIS-GCGR_Rx (ISIS 449884) is an antisense oligonucleotide inhibitor of the glucagon receptor (GCGR). The objective of this study was to evaluate the pharmacokinetics (PK) and pharmacodynamics (PD) of IONIS-GCGR_Rx via population-based modeling. The observed data were obtained from a Phase 1 (50, 100, 200, 300 and 400 mg) single- and multiple-dose study in healthy volunteers and a Phase 2 (100 and 200 mg) multiple-dose study in T2DM patients. The PK of IONIS GCGR_Rx was characterized by two primary systemic compartments and three absorption transit compartments with elimination out of the peripheral compartment. The fasting plasma glucose (FPG) PD was an indirect-response model (inhibition of FPG production) linked to the HbA1c PD model which was a semi-mechanistic model capturing RBC maturation dynamics. Stepwise covariate modeling was performed to identify relevant covariates. In the PK model, bodyweight (BW) was the only significant covariate influencing tissue clearance, tissue volume and plasma volume. Plots of parameter-covariate relations indicate the influence of BW is clinically relevant. In the PD models, baseline HbA1c had a positive correlation with I _max and baseline FPG had a negative correlation with the glycosylation rate (k _gl ). Simulations from the final model showed that the doses tested in the Phase 2 were at or close to the maximum of the dose-response curve and that dose reduction down to 50 mg resulted in minimal effect to efficacy. The model was useful in supporting the decision for dose reduction in a subsequent trial.

Glycated Hemoglobin, Plasma Glucose, and Erythrocyte Aging

BACKGROUND

The relationship between HbA1c and blood glucose averages has been characterized many times, yet, a unifying, mechanistic description is still lacking.

METHODS

We calculated the level of HbA1c from plasma glucose averages based solely on the in vivo rate of hemoglobin glycation, and the different turnover rates for erythrocytes of different ages. These calculations were then compared to the measured change of HbA1c due to changes in mean blood glucose (MBG), to complex models in the literature, and our own experiments.

RESULTS

Analysis of data on erythrocyte ageing patterns revealed that 2 separate RBC turnover mechanisms seem to be present. We calculated the mean red blood cell (RBC) life span within individuals to lie between 60 and 95 days. Comparison of expected HbA1c levels to data taken from continuous glucose monitors and finger-stick MBG yielded good agreement (r = .87, P < .0001). Experiments on the change with time of HbA1c induced by a change of MBG were in excellent agreement with our calculations (r = .98, P < .0001).

CONCLUSIONS

RBC turnover seems to be dominated by a constant rate of cell loss, and a mechanism that targets cells of a specific age. Average RBC life span is 80 ± 10.9 days. Of HbA1c change toward treatment goal value, 50% is reached in about 30 days. Many factors contribute to the ratio of glycated hemoglobin, yet we can make accurate estimations considering only the in vivo glycation constant, MBG, and the age distribution of erythrocytes.

Models for the red blood cell lifespan

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 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.

Weight-HbA1c-insulin-glucose model for describing disease progression of type 2 diabetes

A previous semi‐mechanistic model described changes in fasting serum insulin (FSI), fasting plasma glucose (FPG), and glycated hemoglobin (HbA1c) in patients with type 2 diabetic mellitus (T2DM) by modeling insulin sensitivity and β‐cell function. It was later suggested that change in body weight could affect insulin sensitivity, which this study evaluated in a population model to describe the disease progression of T2DM. Nonlinear mixed effects modeling was performed on data from 181 obese patients with newly diagnosed T2DM managed with diet and exercise for 67 weeks. Baseline β‐cell function and insulin sensitivity were 61% and 25% of normal, respectively. Management with diet and exercise (mean change in body weight = −4.1 kg) was associated with an increase of insulin sensitivity (30.1%) at the end of the study. Changes in insulin sensitivity were associated with a decrease of FPG (range, 7.8–7.3 mmol/L) and HbA1c (6.7–6.4%). Weight change as an effector on insulin sensitivity was successfully evaluated in a semi‐mechanistic population model.

Distributed transit compartments for arbitrary lifespan distributions in aging populations

Transit compartment models (TCM) are often used to describe aging populations where every individual has its own lifespan. However, in the TCM approach these lifespans are gamma-distributed which is a serious limitation because often the Weibull or more complex distributions are realistic. Therefore, we extend the TCM concept to approximately describe any lifespan distribution and call this generalized concept distributed transit compartment models (DTCMs). The validity of DTCMs is obtained by convergence investigations. From the mechanistic perspective the transit rates are directly controlled by the lifespan distribution. Further, DTCMs could be used to approximate the convolution of a signal with a probability density function. As example a stimulatory effect of a drug in an aging population with a Weibull-distributed lifespan is presented where distribution and model parameters are estimated based on simulated data.

Use of an oral stable isotope label to confirm variation in red blood cell mean age that influences HbA1c interpretation

HbA1c is commonly used to monitor glycemic control. However, there is growing evidence that the relationship between HbA1c and mean blood glucose (MBG) is influenced by variation in red blood cell (RBC) lifespan in hematologically normal individuals. Correction of HbA1c for mean RBC age (MRBC ) requires a noninvasive, accurate, and affordable method to measure RBC survival. In this study, we evaluated whether a stable isotope approach would satisfy these requirements. RBC lifespan and MRBC were determined in a group of nine hematologically normal diabetic and nondiabetic subjects using oral (15) N-glycine to label heme in an age cohort of RBC. The MRBC was 58.7 ± 9.1 (2SD) days and RBC lifespan was 106 ± 21 (2SD) days. This degree of variation (±15-20%) is consistent with previous studies using other techniques. In a subset of seven subjects, MRBC determined with the biotin label technique were available from approximately five years prior, and strongly correlated with the stable isotope values (R(2) = 0.79). This study suggests that the MRBC is stable over time but varies substantially among individuals, and supports the importance of its variation in HbA1c interpretation. The characteristics of the stable isotope method support its suitability for studies to directly evaluate the impact of variation in MRBC on the interpretation of HbA1c.

Effects of IL-1β-Blocking Therapies in Type 2 Diabetes Mellitus: A Quantitative Systems Pharmacology Modeling Approach to Explore Underlying Mechanisms

Recent clinical studies suggest sustained treatment effects of interleukin-1β (IL-1β)–blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1β effects on β-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and β-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in β-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin–insulin ratio, and a small increase in β-cell mass. We propose that improved β-cell function, rather than mass, is likely to explain the main IL-1β–blocking effects seen in current clinical data, but that improved β-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

Longitudinal Modeling of the Relationship Between Mean Plasma Glucose and HbA1c Following Antidiabetic Treatments

Late-phase clinical trials within diabetes generally have a duration of 12–24 weeks, where 12 weeks may be too short to reach steady-state glycated hemoglobin (HbA1c). The main determinant for HbA1c is blood glucose, which reaches steady state much sooner. In spite of this, few publications have used individual data to assess the time course of both glucose and HbA1c, for predicting HbA1c. In this paper, we present an approach for predicting HbA1c at end-of-trial (24–28 weeks) using glucose and HbA1c measurements up to 12 weeks. The approach was evaluated using data from 4 trials covering 12 treatment arms (oral antidiabetic drug, glucagon-like peptide-1, and insulin treatment) with measurements at 24–28 weeks to evaluate predictions vs. observations. HbA1c percentage was predicted for each arm at end-of-trial with a mean prediction error of 0.14% [0.01;0.24]. Furthermore, end points in terms of HbA1c reductions relative to comparator were accurately predicted. The proposed model provides a good basis to optimize late-stage clinical development within diabetes.

A semi-mechanistic red blood cell survival model provides some insight into red blood cell destruction mechanisms

Most mathematical models developed for the survival of haematological cell populations, in particular red blood cells (RBCs), follow the principle of parsimony. They focus on the predominant destruction mechanism of age-related cell death (senescence) and do not account for within subject variability in the RBC lifespan. However, assessment of the underlying physiological destruction mechanisms can be of interest in pathological conditions that affect RBC survival, for example sickle cell anaemia or anaemia of chronic kidney disease. We have previously proposed a semi-mechanistic RBC survival model which accounts for four different types of RBC destruction mechanisms. In this work, it is shown that the proposed model in combination with informative RBC survival data is able to provide a deeper insight into RBC destruction mechanisms. The proposed model was applied in a non-linear mixed effect modelling framework to biotin derived RBC survival data available from literature. Three mechanisms were estimable based on the available data of twelve subjects, including random destruction, senescence and destruction due to delayed failure. It was possible to identify three subjects with a decreased RBC survival in the study population. These three subjects all showed differences in the contribution of the estimated destruction mechanisms: an increased random destruction, versus an accelerated senescence, versus a combination of both.

A semi-mechanistic model of the relationship between average glucose and HbA1c in healthy and diabetic subjects

HbA1c is the most commonly used biomarker for the adequacy of glycemic management in diabetic patients and a surrogate endpoint for anti-diabetic drug approval. In spite of an empirical description for the relationship between average glucose (AG) and HbA1c concentrations, obtained from the A1c-derived average glucose (ADAG) study by Nathan et al., a model for the non-steady-state relationship is still lacking. Using data from the ADAG study, we here develop such models that utilize literature information on (patho)physiological processes and assay characteristics. The model incorporates the red blood cell (RBC) aging description, and uses prior values of the glycosylation rate constant (KG), mean RBC life-span (LS) and mean RBC precursor LS obtained from the literature. Different hypothesis were tested to explain the observed non-proportional relationship between AG and HbA1c. Both an inverse dependence of LS on AG and a non-specificity of the National Glycohemoglobin Standardization Program assay used could well describe the data. Both explanations have mechanistic support and could be incorporated, alone or in combination, in models allowing prediction of the time-course of HbA1c changes associated with changes in AG from, for example dietary or therapeutic interventions, and vice versa, to infer changes in AG from observed changes in HbA1c. The selection between the alternative mechanistic models require gathering of new information.