Predictive Pharmacokinetic-Pharmacodynamic Modeling of Tumor Growth Kinetics in Xenograft Models after Administration of Anticancer Agents

Abstract

The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.

Preclinical Modeling of Tumor Growth and Angiogenesis Inhibition to Describe Pazopanib Clinical Effects in Renal Cell Carcinoma

“…The term representing drug‐induced decay can be constant or exponential, driven by drug exposure, and it can incorporate a resistance term or a delay term to accommodate a wide range of tumor response shapes (see refs. 8, 9, 19, 20, 21, 22, 23, 24 for reviews).…”

Assessing Similarity Among Individual Tumor Size Lesion Dynamics: The CICIL Methodology

“…Added benefits have been gained from mathematical models of tumor size (TS) dynamics4, 5, 6 and tumor growth inhibition,7, 8, 9 which can characterize anticancer drug effects over time and provide improved predictors of long‐term clinical outcomes 10, 11…”

Modeling Tumor Growth for Kidney Cancer Based on Nuclei Clusters of Pathology Slides

“…Exponential-linear model [1], [10], [11] is an empirical method to analyze the tumor cell proliferation quantitatively based on parameters defined for exponential and linear phases of tumor growth. We build artificial intelligence based mathematical models to compute tumor growth and related parameters including exponential-linear model parameters.…”

“…Empirical models describe tumor growth using mathematical equations without in-depth analysis of basal processes, whereas functional models concentrate on physiological hypotheses and biochemical processes [1], [2]. Exponential-linear tumor growth model [1] built based on experimental observations is a well-accepted empirical model. Tumor mass grows exponentially until it reaches a certain weight and volume, at which increase in tumor size becomes linear due to nutritional and oxygen limitations [3].…”

“…Tumor mass grows exponentially until it reaches a certain weight and volume, at which increase in tumor size becomes linear due to nutritional and oxygen limitations [3]. In exponential-linear model, tumor growth is expressed as a function of rate constants and tumor weight or volume when no drug is administered [1]. In our previous work [4], we computed tumor growth curves using genetic information from breast cancer patients in our artificial intelligence based methods.…”