Lifespan based indirect response models

Abstract

In the field of hematology, several mechanism-based pharmacokinetic-pharmacodynamic models have been developed to understand the dynamics of several blood cell populations under different clinical conditions while accounting for the essential underlying principles of pharmacology, physiology and pathology. In general, a population of blood cells is basically controlled by two processes: the cell production and cell loss. The assumption that each cell exits the population when its lifespan expires implies that the cell loss rate is equal to the cell production rate delayed by the lifespan and justifies the use of delayed differential equations for compartmental modeling. This review is focused on lifespan models based on delayed differential equations and presents the structure and properties of the basic lifespan indirect response (LIDR) models for drugs affecting cell production or cell lifespan distribution. The LIDR models for drugs affecting the precursor cell production or decreasing the precursor cell population are also presented and their properties are discussed. The interpretation of transit compartment models as LIDR models is reviewed as the basis for introducing a new LIDR for drugs affecting the cell lifespan distribution. Finally, the applications and limitations of the LIDR models are discussed.

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.…”

“…Lifespan models (LSM) are important tools to describe the development of a population y(t) controlled by birth (input) and death (output) of their individuals. For an overview of LSMs in the context of indirect response models see [5]. LSMs have the general form y 0 ðtÞ ¼ k in ðtÞ À k out ðtÞ; yð0Þ ¼ y 0…”

Clinical Pharmacokinetics and Pharmacodynamics of Monoclonal Antibodies Approved to Treat Rheumatoid Arthritis

“…Indeed, the IL-6 pathway is involved in T-cell activation and stimulation of hematopoiesis: the blockade of IL-6 receptor triggers not only a reduction in systemic inflammation, but also mechanism-related adverse effects, including a decrease in neutrophil and platelet counts. A mechanistic model, which included TMDD and lifespan models [114], showed that the decrease in neutrophil and platelet counts were concentration dependent and was reversible when tocilizumab was withdrawn [35]. To date, no concentration-adverse effect relationship was reported for anti-TNF-a biopharmaceuticals.…”

Models for the red blood cell lifespan

“…Indirect models are lifespan-based compartmental PK/PD models (e.g., lifespan-based indirect response or LIDR models [38]), of which transit compartment (TC) models are a special case [37]. A series of transit compartments, each compartment with a PDF representing the lifespan distribution of the cells in that compartment [30, 37, 45] is a hallmark of TC models.…”

“…A new lifespan based compartmental PK/PD model paved the way to an indirect and compartmental approach to quantify RBC/reticulocyte mean lifespan [39]. Earlier works based on this approach assumed that all cells in a compartment survived for a fixed time, which introduced a time-delay in the input/output models thus representing the lifespan of the cells in a compartment by a point distribution [1, 38, 39, 41, 57, 59]. The theory was expanded later to represent the RBC lifespan distribution by possibly time-varying continuous PDF [21–23, 40, 61].…”