Population Cell Life Span Models for Effects of Drugs Following Indirect Mechanisms of Action

Abstract

Pharmacokinetic/pharmacodynamic (PK/PD) models for hematological drug effects exist that assume that cells are produced by a zero- or first-order process, survive for a specific duration (cell lifespan), and then are lost. Due to the fact that delay differential equations (DDE) are needed for cell lifespan models, their software implementation is not straightforward. Our objective is to demonstrate methods to implement three different cell lifespan models for dealing with hematological drug effects and to evaluate the performance of NONMEM to estimate the model parameters. For the basic lifespan indirect response (LIDR) model, cells are produced by a zero-order process and removed due to senescence. The modified LIDR model adds a precursor pool. The LIDR model of cytotoxicity assumes a three-pool indirect model to account for the cell proliferation with capacity-limited cytotoxicity followed by maturation, and removal from the circulation. A numerical method (method of steps) implementing DDE in NONMEM was introduced. Simulation followed by estimation was used to evaluate NONMEM performance and the impact of the minimization algorithm (first-order method vs. first-order conditional estimation method) and the model for residual variability on the estimates of the population parameters. The FOCE method combined with log-transformation of data was found to be superior. This report provides methodology that will assist in application of population methods for assessing hematological responses to various types of drugs.

Pharmacodynamic Analysis of Recombinant Human Erythropoietin Effect on Reticulocyte Production Rate and Age Distribution in Healthy Subjects

“…Except for model A, these rates are similar to what has been published previously for the lifespan models. [26] The parameter estimates of the pharmacodynamic models evaluated were very similar to the median of the nonparametric bootstrap replicates, and all were contained within the 95% confidence intervals obtained from the bootstrap analyses. The precision of the NONMEM ® parameter estimates was excellent, since the relative standard error from the bootstrap analysis for the fixed and random effects was <25%, except for the variability of the lifespan of reticulocytes in models B and C and the variability of the lifespan of precursor cells in model B.…”

Comparative Performance of Cell Life Span and Cell Transit Models for Describing Erythropoietic Drug Effects

“…The transit model (Fig. 1c) consists of a series of precursor compartments (P [1][2][3][4][5] ) and RBC compartments (RBC [1][2][3][4][5] ) linked in a catenary fashion with the first-order transfer rate constants, K p (5/MTT P ) and K tr (5/MTT), respectively (15,17,23,26). The MTT P and MTT represents the mean transit time for precursors and RBC, respectively.…”

“…The alternative transit model (Fig. 1d) consists of only one series of compartments (RBC [1][2][3][4][5] ) linked in a catenary fashion to account for release and aging of RBCs in blood (25). A first-order rate constant, K tr (NRBC/MTT) was used to describe the transfer rate between the compartments.…”

“…The currently published models assume that cells are produced at a constant rate, persist for a certain time period at a maturational cell type, and are then converted to a different cell type or are lost due to natural senescence (5,10,12). The rate of cell loss is equal to their production rate but with a delay which is equal to the cell life span.…”

“…Cell life span models allow estimating the physiological or system parameters along with drug-related parameters depending on the richness of the available data. The regulatory role of hematopoietic growth factors and cytotoxic agents on cellular processes such as proliferation, differentiation, and maturation are described by modulating system parameters (5). The multicompartmental structure of the cell life span models allows inclusion of cell types at multiple defined stages of a blood cell maturation pathway in the same model structure.…”