Modeling time variant distributions of cellular lifespans: increases in circulating reticulocyte lifespans following double phlebotomies in sheep

Abstract

Many pharmacodynamic (PD) models of cellular response assume a single and time invariant lifespan of all cells, despite the existence of a true underlying distribution of cellular lifespans and known changes in the lifespan distributions with time. To account for these features of cellular populations, a time variant cellular lifespan distribution PD model was formulated and theoretical aspects of modeling cellular populations presented. The model extends prior work assuming time variant "point distributions" of cellular lifespans (Freise et al. J Pharmacokinet Pharmacodyn 34:519-547, 2007) and models assuming a time invariant lifespan distribution (Krzyzanski et al. J Pharmacokinet Pharmacodyn 33:125-166, 2006). The formulated time variant lifespan distribution model was fitted to endogenous plasma erythropoietin (EPO), reticulocyte, and red blood cell (RBC) concentrations in sheep phlebotomized on two occasions, 8 days apart. The time variant circulating reticulocyte lifespan was modeled as a truncated and scaled Weibull distribution, with the location parameter of the distribution non-parametrically represented by an end constrained quadratic spline function. The formulated time variant lifespan distribution model was compared to the identical time invariant distribution, time variant "point distribution", and time invariant "point distribution" cellular lifespan models. Parameters of the time variant lifespan distribution model were well estimated with low standard errors. The mean circulating reticulocyte lifespan was estimated at 0.304 days, which rapidly increased over 3-fold following the first phlebotomy to a maximum of 1.03 days (P = 0.009). On average, the percentage of erythrocytes being released as reticulocytes maximally increased an estimated two-fold following the phlebotomies. The primary features of immature RBC physiology were captured by the model and gave results consistent with other estimates in sheep and humans. The comparison of the four lifespan models gave similar parameter estimates of the stimulation function and fits to the RBC data. However, the time invariant models fit the reticulocyte data poorly, while the time variant "point distribution" cellular lifespan model gave physiologically unrealistic estimates of the changes in the circulating reticulocyte lifespan under stress erythropoiesis. Thus the underlying physiology must be considered when selecting the most appropriate cellular lifespan model and not just the goodness-of-fit criteria. The proposed PD model and the numerical implementation allows for a flexible framework to incorporate time variant lifespan distributions when modeling populations of cells whose production or stimulation depends on endogenous growth factors and/or exogenous drugs.

Erythropoietic Response to Endogenous Erythropoietin in Premature Very Low Birth Weight Infants

“…Therefore, as long as T Pk Ͻ t, k is the first phlebotomy after time t Ϫ L in vivo for the f prod total (t Ϫ b) term and the first phlebotomy after time t Ϫ T i for each Hb Ti ϫ f trans (t Ϫ T Ti ) term. The presented phlebotomy correction factor after l Ϫ k ϩ 1 phlebotomies is consistent with formulas previously derived after only one or two phlebotomies (Freise et al, 2007(Freise et al, , 2008.…”

“…The PD Hb mass balance model assumed that the behavior or disposition of the Hb and RBCs in the absence of phlebotomies was life span-based (i.e., based on removal of RBCs from the circulation through cellular aging/senescence) (Landaw, 1988;Krzyzanski et al, 2006;Freise et al, 2008). A time invariant "point distribution" (i.e., no variability) of RBC life spans was assumed (Krzyzanski et al, 2006;Freise et al, 2007).…”

“…This is largely due to the complications in determining the erythropoiesis rate caused by frequent phlebotomies and RBC transfusions altering the RBC/Hb mass, and the effect of each phlebotomy on the RBC/Hb removal rate due to the life span-based disposition of RBCs (Landaw, 1988;Freise et al, 2007Freise et al, , 2008. Previous studies have demonstrated that on average 33.8 ml/kg blood is removed and 27.0 ml/kg blood is transfused during the first 4 weeks of life in infants born at a gestational age of less than 28 weeks (Madsen et al, 2000), and other studies have reported even higher phlebotomy blood loss volumes in the first 2 weeks of life alone (Lin et al, 2000;Widness et al, 2005).…”

General relationship between transit compartments and lifespan models

“…Finally, also LSMs with distributed lifespans are recently introduced and applied, see [5] or [13]. An open question is, if for such models a similar relationship to TCMs holds.…”

A Method to Evaluate Fetal Erythropoiesis from Postnatal Survival of Fetal RBCs

“…It is assumed that the disposition of Hb/RBCs was life span based (i.e., RBCs were removed from circulation through cellular aging/senescence) (14)(15)(16)(17). The model also assumed a single point distribution of RBC life spans, i.e., RBCs produced at a given time in utero have the same RBC life span.…”