Pharmacodynamic models of age-structured cell populations

Pharmacodynamic Age Structured Population Model For Cell Trafficking

OBJECTIVES

Cell trafficking encompasses movement of the immune system cells (e.g., granulocytes, lymphocytes) between the blood and the extravascular tissues (e.g., lymph nodes). Corticosteroids are known to suppress cell trafficking. The age-structured cell population models introduce the transit time as a structure that allows one to quantify the distribution of times the immune cells spend in the blood and the extravascular tissues. The objective of this work is to develop an age-structured cell population model describing drug effects on cell trafficking and to implement the model in pharmacometric software to enable parameter estimation and simulations.

METHODS

We adopted the well-known McKendrick age-structured population model to describe the age distributions in two cell populations: blood cells and cells in the extravascular space. The hazard of cell recirculation from the extravascular tissues was age dependent and described by the Weibull function with the shape ν and scale β parameters. The drug effect on cell trafficking was modeled as the product of the Emax function of the drug plasma concentration and the Weibull hazard. The model was implemented in NONMEM 7.5.1. The model was applied to the basophil data in 34 healthy subjects who received a single intramuscular or oral dose of 6 mg dexamethasone (DEX). A recently published pharmacokinetic model was applied to describe DEX plasma concentration. Typical values of parameter estimates were further used to simulate the DEX effect of the basophil mean transit time in the extravascular tissues.

RESULTS

Simulations of basophil time courses for varying ν demonstrated that the rebound in the blood count data following drug administration is only possible for ν >1. The estimates of model parameters were ν = 3.02, β = 0.00863 1/h, and IC50 = 7.47 ng/mL. The calculated baseline mean transit times of basophils in the blood 7.2 h and extravascular tissues 104.9 h agree with the values reported in the literature.

CONCLUSIONS

We introduced an age-structured population model to describe cell trafficking between the blood and extravascular tissues. The model was adopted to account for the inhibitory drug effect on the cell recirculation. We showed that the age structure is essential to explain the rebound observed in the blood count response to a single dose drug administration. The model was validated using the basophil responses to DEX treatment in healthy subjects.

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics

Stability analysis of an autonomous epidemic model of an age-structured sub-populations of susceptible, infected, precancerous and cancer cells and unstructured sub-population of human papilloma virus (HPV) (SIPCV epidemic model) aims to gain an insight into the features of cervical cancer disease. The model considers the immune functional response of organism to the virus population growing by the HPV-density dependent death rate, while the death rates of infected, precancerous and cancerous cells do not depend on the HPV quantity because the immune system of organism does not respond to its own cells. Interaction between susceptible cells and HPV is described by the Lotka-Voltera incidence rate and leads to the growth of infected cells. Some of infected cells become precancerous cells, and the other apoptosis when viruses leave infected cells and are ready to infect new susceptible cells. Precancerous cells partially become cancer cells with the density-dependent saturated rate. Conditions of existence of the endemic equilibrium of system were obtained. It was proved that this equilibrium is always locally asymptotically stable whenever it exists. We obtained: (i) the conditions of cancer tumor localization (asymptotically stable dynamical regimes), (ii) outbreak of cancer cell population (that may correspond to metastasis), (iii) outbreak of dysplasia (precancerous cells) which induces the outbreak of cancer cells (that may correspond to metastasis). In cases (ii), (iii) the conditions of existence of endemic equilibrium do not hold. All cases are illustrated by numerical experiments.

Recent advances in physiologically based pharmacokinetic and pharmacodynamic models for anticancer nanomedicines

Nanoparticles (NPs) have distinct pharmacokinetic (PK) properties and can potentially improve the absorption, distribution, metabolism, and elimination (ADME) of small-molecule drugs loaded therein. Owing to the unwanted toxicities of anticancer agents in healthy organs and tissues, their precise delivery to the tumor is an essential requirement. There have been numerous advancements in the development of nanomedicines for cancer therapy. Physiologically based PK (PBPK) models serve as excellent tools for describing and predicting the ADME properties and the efficacy and toxicity of drugs, in combination with pharmacodynamic (PD) models. The recent preliminary application of these modeling approaches to NPs demonstrated their potential benefits in research and development processes relevant to the ADME and pharmacodynamics of NPs and nanomedicines. Here, we comprehensively review the pharmacokinetics of NPs, the developed PBPK models for anticancer NPs, and the developed PD model for anticancer agents.

Age-structured population model of cell survival

Age-structured cell population model was introduced to describe cell survival. The impact of the environment on the cell population is represented by drug plasma concentration. A key model variable is the hazard of cell removal that is a subject to the environment effect. The model is capable of describing cohort and random labeling cell survival data. In addition, it accounts for cell loss due to labeling of cell sample, but it lacks ability to describe the effect of label elution on the survival data. The model was applied to red blood cell (RBC) survival data in two groups of Wistar rats obtained by two techniques: cohort labeling using ¹⁴C-glycine (N = 4) and random labeling using biotin (N = 8). The Weibull probability density function was selected for the RBC lifespan distribution. The data were simultaneously fitted by the mixed effects model implemented in Monolix 4.3.3. The estimated typical values of RBC lifespan and age were 53.7 and 27.8 days, respectively. A noticeable effect of biotinylation on RBC survival was observed that resulted in a significant difference between the means of individual RBC lifespan for two groups. The model provides a mechanistic framework flexible enough to account for various experimental designs to generate the cell survival data. Despite model qualification using animal data, the model has the same potential to be applied to cell survival data analysis in humans.