M. Rocchetti

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

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.

Testing additivity of anticancer agents in pre-clinical studies: A PK/PD modelling approach

In clinical oncology, combination regimens may result in a synergistic, additive or antagonistic interaction (i.e. the effect of the combination is greater, similar or smaller than the sum of the effects of the individual compounds). For this reason, during the drug development process, in vivo pre-clinical studies are performed to assess the interaction of anticancer agents given in combination. Starting from a widely used single compound PK/PD model, a new additivity model able to predict the tumour growth inhibition in xenografted mice after the administration of compounds in combination was developed, under the assumption of a pharmacodynamic null interaction. By comparing the predicted curves with actual tumour weight data, possible departures from additivity can be immediately ascertained by visual inspection; a statistical procedure based on a chi(2) test has also been developed for this aim. The advantages of the proposed approach in comparison to other modelling methodologies are discussed and its application to four combination studies is presented.

A Minimal Model of Tumor Growth Inhibition

The preclinical development of antitumor drugs greatly benefits from the availability of models capable of predicting tumor growth as a function of the drug administration schedule. For being of practical use, such models should be simple enough to be identifiable from standard experiments conducted on animals. In the present paper, a stochastic model is derived from a set of minimal assumptions formulated at cellular level. Tumor cells are divided in two groups: proliferating and nonproliferating. The probability that a proliferating cell generates a new cell is a function of the tumor weight. The probability that a proliferating cell becomes nonproliferating is a function of the plasma drug concentration. The time-to-death of a nonproliferating cell is a random variable whose distribution reflects the nondeterministic delay between drug action and cell death. The evolution of the expected value of tumor weight obeys two differential equations (an ordinary and a partial differential one), whereas the variance is negligible. Therefore, the tumor growth dynamics can be well approximated by the deterministic evolution of its expected value. The tumor growth inhibition model, which is a lumped parameter model that in the last few years has been successfully applied to several antitumor drugs, is shown to be a special case of the minimal model presented here.

Nonparametric AUC Estimation in Population Studies with Incomplete Sampling: A Bayesian Approach

The estimation of the AUC in a population without frequent and/or fixed individual samplings is of interest because the number of plasma samples can often be limited due to technical, ethical and cost reasons. Non-linear mixed effect models can provide both population and individual estimates of AUC based on sparse sampling protocols; however, appropriate structural models for the description of the pharmacokinetics are required. Nonparametric solutions have also been proposed to estimate the population AUC and the associated error when particular sampling protocols are adopted. However, they do not estimate the individual AUCs and lack flexibility. Also a semiparametric method has been proposed for addressing the problem of sparse sampling in reasonably well designed studies. In this work, we propose and evaluate a nonparametric Bayesian scheme for AUC estimation in population studies with arbitrary sampling protocols. In the stochastic model representing the whole population, the individual plasma concentration curves and the “mean” population curve are described by random walk processes, allowing the application of the method to the reconstruction of any kind of “regular” curves. Population and individual AUC estimation are performed by numerically computing the posterior expectation through a Markov chain Monte Carlo algorithm.

A minimal model describing the effect of drug administration on tumor growth dynamics

The preclinical development of antitumor drugs would greatly benefit from the availability of models capable of predicting tumor growth as a function of the drug administration schedule. For being of practical use such models should be simple enough to be identifiable from standard experiments conducted on animals. In the present paper, a simple mathematical model of tumor dynamics is derived from a set of minimal assumptions formulated at cellular level. In the model there are two classes of tumor cells: proliferating and non-proliferating. Assuming independence between the cells, the mean tumor mass obeys two differential equations: an ordinary and a partial differential one. It is shown that, due to the large number of cells in measured tumor masses, the variance of the mass tumor is negligible compared to its expected value so that the stochastic model can be replaced by a deterministic one. For suitable choice of the model parameters, the proposed minimal model yields the so-called TGI (tumor growth inhibition) model. This is a lumped parameter model, based on only five parameters, that in the last few years has been successfully used to fit and predict the effect of several antitumor drugs

A Versatile Simulator for Validation of Hormone Pulse Detection Algorithms

Abstract A stochastic model for the simulation of pulsatile hormone secretion is presented. By properly adjusting the model parameters it is possible to reproduce typical observed patterns of hormone time series. By means of simulated data, an evaluation of the rate of false-positive and false-negative errors produced by a computerized pulse detection algorithm is provided. Finally, the stochastic model is used to develop a smoothing technique based on Kalman filtering theory.