Modeling red blood cell survival data

Reduced erythrocyte lifespan measured by chromium-51 in patients with type 2 diabetes undergoing long-term hemodialysis

INTRODUCTION

A reduced erythrocyte lifespan potentially explains the low hemoglobin A1c values found in hemodialysis patients. However, data supporting this notion in patients with type 2 diabetes is unclear. We evaluated the erythrocyte lifespan in patients with type 2 diabetes undergoing long-term hemodialysis and investigated potential predictors of erythrocyte lifespan.

METHODS

Long-term hemodialysis patients with type 2 diabetes and type 2 diabetes patients without nephropathy (estimated glomerular filtration rate > 60 mL/min/1.73 m² ) were included. The erythrocyte lifespan was measured using chromium-51 (⁵¹ Cr)-labeled erythrocytes. Blood radiotracer activity was measured six to nine times over a period of 3-5 weeks to determine the erythrocyte lifespan of each patient. Biochemical markers were obtained five times over 16 weeks and associated with the erythrocyte lifespan.

FINDINGS

Type 2 diabetes patients undergoing hemodialysis (N = 13) had a significantly shorter median erythrocyte lifespan of 49.7 (interquartile range [IQR] = 44.1-58.6) days compared with 64.2 (IQR = 62.6-83.5) days in the control group (N = 10) (P ˂ 0.001) with a difference between medians of 14.5 (95% confidence interval = 8.1-38.8) days. In the hemodialysis group, no association could be detected between the erythrocyte lifespan and markers of hemolysis, level of inflammation, or urea.

DISCUSSION

A reduced erythrocyte lifespan was detected in type 2 diabetes patients undergoing long-term hemodialysis. This may contribute to the reduced hemoglobin A1c values observed in the type 2 diabetic hemodialysis population. An association could not be detected between the erythrocyte lifespan and biochemical markers of hemolysis or inflammation.

Population Pharmacodynamic Modeling of Epoetin Alfa in End-Stage Renal Disease Patients Receiving Maintenance Treatment Using Bayesian Approach

The ability to control dosage regimens of erythropoiesis-stimulating agents (ESAs) to maintain a desired hemoglobin (HGB) target is still elusive. We utilized a Bayesian approach and informative priors to characterize HGB profiles, using simulated drug concentrations, in patients with end-stage renal disease receiving maintenance doses of epoetin alfa. We also demonstrated an adaptive Bayesian method, applied to individual patients, to improve the accuracy of HGB predictions over time. The results showed that sparse HGB data from daily clinical practice were characterized successfully. The adaptive Bayesian method effectively improved the accuracy of HGB predictions by updating the individual model with new data accounting for within-subject changes over time. The Bayesian approach presented leverages existing knowledge of the model parameters and has a potential utility in clinical practice to individualize dosage regimens of epoetin alfa and ESAs to achieve target HGB. Further studies are warranted to develop an application for practical use.

Application of Reticulocyte-Based Estimation of Red Blood Cell Lifespan in Anemia Management of End-Stage Renal Disease Patients

Shortened red blood cell (RBC) lifespan is one of the major factors contributing to anemia in end-stage renal disease (ESRD) patients and should be taken into account in anemia management protocols. In this study, we aimed to estimate RBC lifespan and the source of between-subject variability in ESRD patients. The resulting individual parameters (empirical Bayes estimates) were used to predict hemoglobin concentrations 2 weeks in advance. The reticulocyte-based estimation of RBC lifespan (REBEL) and the population modeling of RBC count data were used. A total of 120 blood samples collected biweekly over 10 weeks in 24 patients receiving maintenance doses of recombinant human erythropoietin (rHuEPO) subcutaneously were included in this analysis. Typical RBC lifespan was estimated to be 63.3 days. RBC lifespan was found to increase with erythroferrone, a recently identified hormone participating in iron metabolism. Approximately, a 10% increase in plasma erythroferrone was associated with a 5% increase in RBC lifespan. In addition, RBC lifespan was 18.7% shorter in females compared with males. Out of 24 subjects, 16 had hemoglobin concentrations predicted within 95% prediction intervals. The median absolute prediction error was 15.9% (interquartile range, 9.5 to 24.7%). We demonstrated that REBEL coupled with the population modeling technique can be used effectively to estimate RBC lifespan. Then, individual parameters can be used to predict future hemoglobin concentrations in ESRD patients.

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.

Characterization of Anti-Dal Alloantibodies Following Sensitization of Two Dal-Negative Dogs

Since its discovery, the immunogenicity of the Dal blood type has not been further investigated. The aim of this study was to better characterize anti- Dal alloantibodies produced following sensitization of Dal-negative dogs, notably their rate of appearance, the agglutination titer over time, and their immunoglobulin class. A secondary objective was to obtain polyclonal anti- Dal alloantibodies to increase the availability of Dal blood typing. Of 100 healthy laboratory Beagles tested, 2 Dal-negative dogs were identified as recipients. Ten healthy Dal-positive dogs were investigated as potential blood donors. All dogs were extensively blood typed for DEA 1, 3, 4, 5, and 7, as well as for Dal. Then, the recipients were transfused uneventfully with 10 ml/kg of Dal-positive but otherwise compatible packed red blood cells. Posttransfusion blood samples were collected routinely over a minimum of 1 year. Using a gel column technology, anti- Dal alloantibodies were detected as early as 4 days posttransfusion and remained detectable 2 years posttransfusion, with maximum agglutination titers reached at 1 and 2 months posttransfusion. The immunoglobulin class was IgG. The immunogenicity and clinical significance of the Dal blood type were confirmed. The results support the recommendations that previously transfused dogs be crossmatched starting 4 days posttransfusion and for the animal’s lifetime. The polyclonal anti- Dal antibodies produced will allow blood typing of a significant number of dogs, especially transfused dogs facing blood incompatibilities and canine blood donors.

A Novel Physiology-Based Mathematical Model to Estimate Red Blood Cell Lifespan in Different Human Age Groups

Direct measurement of red blood cell (RBC) survival in humans has improved from the original accurate but limited differential agglutination technique to the current reliable, safe, and accurate biotin method. Despite this, all of these methods are time consuming and require blood sampling over several months to determine the RBC lifespan. For situations in which RBC survival information must be obtained quickly, these methods are not suitable. With the exception of adults and infants, RBC survival has not been extensively investigated in other age groups. To address this need, we developed a novel, physiology-based mathematical model that quickly estimates RBC lifespan in healthy individuals at any age. The model is based on the assumption that the total number of RBC recirculations during the lifespan of each RBC (denoted by N max) is relatively constant for all age groups. The model was initially validated using the data from our prior infant and adult biotin-labeled red blood cell studies and then extended to the other age groups. The model generated the following estimated RBC lifespans in 2-year-old, 5-year-old, 8-year-old, and 10-year-old children: 62, 74, 82, and 86 days, respectively. We speculate that this model has useful clinical applications. For example, HbA1c testing is not reliable in identifying children with diabetes because HbA1c is directly affected by RBC lifespan. Because our model can estimate RBC lifespan in children at any age, corrections to HbA1c values based on the model-generated RBC lifespan could improve diabetes diagnosis as well as therapy in children.

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.

Erythropoietin reduces storage lesions and decreases apoptosis indices in blood bank red blood cells

Background

Recent evidence shows a selective destruction of the youngest circulating red blood cells (neocytolysis) trigged by a drop in erythropoietin levels.

Objective

The aim of this study was to evaluate the effect of recombinant human erythropoietin beta on the red blood cell storage lesion and apoptosis indices under blood bank conditions.

Methods

Each one of ten red blood cell units preserved in additive solution 5 was divided in two volumes of 100 mL and assigned to one of two groups: erythropoietin (addition of 665 IU of recombinant human erythropoietin) and control (isotonic buffer solution was added). The pharmacokinetic parameters of erythropoietin were estimated and the following parameters were measured weekly, for six weeks: Immunoreactive erythropoietin, hemolysis, percentage of non-discocytes, adenosine triphosphate, glucose, lactate, lactate dehydrogenase, and annexin-V/esterase activity. The t-test or Wilcoxon's test was used for statistical analysis with significance being set for a p-value <0.05.

Results

Erythropoietin, when added to red blood cell units, has a half-life >6 weeks under blood bank conditions, with persistent supernatant concentrations of erythropoietin during the entire storage period. Adenosine triphosphate was higher in the Erythropoietin Group in Week 6 (4.19 ± 0.05 μmol/L vs. 3.53 ± 0.02 μmol/L; p-value = 0.009). The number of viable cells in the Erythropoietin Group was higher than in the Control Group (77% ± 3.8% vs. 71% ± 2.3%; p-value <0.05), while the number of apoptotic cells was lower (9.4% ± 0.3% vs. 22% ± 0.8%; p-value <0.05).

Conclusions

Under standard blood bank conditions, an important proportion of red blood cells satisfy the criteria of apoptosis. Recombinant human erythropoietin beta seems to improve storage lesion parameters and mitigate apoptosis.

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.

Reticulocyte-based estimation of red blood cell lifespan

We introduce a new, minimally invasive laboratory technique called reticulocyte-based estimation of lifespan (REBEL) of erythrocytes in humans. Its major advantage over existing techniques is its applicability to patients with both changing and steady-state erythropoiesis status. The feasibility of REBEL was tested in five patients with hemodialysis-dependent end-stage renal disease. The RNA degradation half-life was first determined for each subject on day 1 by flow cytometry measurement of the decay rate of thiazole orange stain. Reticulocyte age distribution was then measured from residual RNA content weekly for 2 months to estimate the RBC production rate time course. Mean RBC lifespan per subject was estimated by fitting the integrated RBC production rate over time to the measured RBC count and optimizing the integration limits. The mean reticulocyte RNA half-life was 0.71 ± 0.11 days. The small coefficient of variation (15.6%) indicated that the degradation rate of RNA did not vary substantially between subjects. The mean RBC lifespan (TRBC = 76.6 ± 23.8 days) was comparable to the reported values for this patient population.

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

Despite the impact of red blood cell (RBC) Life-spans in some disease areas such as diabetes or anemia of chronic kidney disease, there is no consensus on how to quantitatively best describe the process. Several models have been proposed to explain the elimination process of RBCs: random destruction process, homogeneous life-span model, or a series of 4-transit compartment model. The aim of this work was to explore the different models that have been proposed in literature, and modifications to those. The impact of choosing the right model on future outcomes prediction--in the above mentioned areas--was also investigated. Both data from indirect (clinical data) and direct life-span measurement (biotin-labeled data) methods were analyzed using non-linear mixed effects models. Analysis showed that: (1) predictions from non-steady state data will depend on the RBC model chosen; (2) the transit compartment model, which considers variation in life-span in the RBC population, better describes RBC survival data than the random destruction or homogenous life-span models; and (3) the additional incorporation of random destruction patterns, although improving the description of the RBC survival data, does not appear to provide a marked improvement when describing clinical data.