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

Abstract

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.

Appendix

Model for random labelling using biotin

Based on Eq. 1 and a constant RBC production rate p on any day τ, the survival of multiple RBC cohorts is given based on Eq. 6. Here, a cohort of RBCs refers to a group of RBCs born on the same day, and N(t) is the total number of RBCs present at day t.

$$ N\left( t \right) = \int\limits_{0}^{t} {p\left( \tau \right) \cdot S\left( {t - \tau } \right) \, d\tau } $$

(6)

The solution of Eq. 6 was approximated as:

$$ N\left( t \right) = \sum\limits_{\tau = 0}^{t} {p\left( \tau \right) \cdot S\left( {t - \tau } \right) \, } $$

(7)

As random loss of the biotin label from viable RBCs is considered to be minimal [10], no adjustment of the proposed RBC survival model to account for flaws associated with the labelling method was required for this study. We have previously described that such an ideal random labelling method can be simulated based on Eq. 6 by stopping the production of RBCs (equivalent to the day of labelling), provided that N(t) has reached steady state before the production is stopped [8]. Observing the disappearance of the cells is then equivalent to the disappearance of the label over time after labelling under the assumption that 1 unit RBCs equals 1 unit label. The constant production rate p can be chosen arbitrarily as only the relative fraction of label left in the circulation is of interest. This relative survival fraction is calculated as N(t)/N(t _L ), where t _L is the time of labelling.