Modelling red blood cell data

Background & Objectives: The survival time of red blood cells (RBCs) is commonly determined based on labelling experiments, where the obtained data is either analysed based on the assumption of a finite and fixed lifespan for all cells, random destruction irrespective of age, or sometimes a combination of both (1). However, it would be desirable to obtain a better insight into the processes of RBC destruction, especially in pathological states such as anaemia of chronic kidney disease (CKD). We have previously developed a theoretical model for the survival time of RBCs that accounts for plausible processes of RBC destruction, and that can be used to describe RBC survival studies using different types of labelling methods (2). It was shown that parameter estimation for this model would be possible under ideal labelling conditions as well as in a hypothetical well controlled study based on optimal design theory (3). The aim of the current work is to evaluate this model when applied to clinical data.

Materials & Methods: RBC survival data was available from 14 CKD patients receiving haemodialysis and 14 healthy controls by using radioactive chromium as a random labelling method. Each subject provided 10 to 13 blood samples between day 1 and day 40 after labelling. Modelling of RBC survival was considered in 2 stages: 1.) where predictions from the current model and parameter values were overlaid on the study data and 2.) where the main likely destruction processes were considered (random or senescence) to assess a plausible of RBC survival differences caused by CKD and haemodialysis. Random effects were not considered.
Additionally, blood haemoglobin concentrations were available for two patients with CKD before and under treatment with erythropoietin (EPO). It was investigated whether this data supported an alteration in RBC lifespan caused by EPO treatment and if so what the mechanism might be.

Results: The RBC model and parameter values provided a good description of the RBC data arising from the controls. A slight improvement can be gained by, estimation of the senescence component which resulted in a lifespan distribution with a maximum at 100 days, whereas for the patients undergoing haemodialysis the maximum lifespan was located at 69 days. These results are in accordance with observed literature values for healthy individuals and patients with CKD (4,5). The data did not support a change in random destruction as the primary mechanism for different life spans between controls and patients. Results for the patients receiving EPO treatment are pending at the moment.

Discussion: Due to the complexity of the model, complete parameter estimation on real data is currently not possible. The available clinical data is not powered sufficiently to support estimation under the full model. Nevertheless, individual components of the model can be estimated in a naïve pooled analysis, and the obtained RBC survival time agrees with literature. Future work with the model will focus on estimation of between subject variability by applying a full population approach.


  1. International Committee for Standardization in Haematology. Recommended method for radioisotope red-cell survival studies. Br J Haematol. 1980;45(4):659-66.
  2. Korell J, Coulter C, Duffull S. A statistical model for red blood cell survival. J Theor Biol. 2011;268(1):39-49. doi:10.1016/j.jtbi.2010.10.010.
  3. Korell J, Coulter C, Duffull S. Design of survival studies for red blood cells. PAGE 19 (2010) Abstr 1701 []; Berlin, Germany 2010.
  4. Loge J, Lange R, Moore C. Characterization of the anemia associated with chronic renal insufficiency. Am J Med. 1958;24:4-18.
  5. Greer J, Foerster J, Lukens J, Rodgers G, Paraskevas F, Glader B, editors. Wintrobe’s Clinical Hematology. 11th ed. Philadelphia, USA: Lippincott Williams & Wilkins; 2004.