TGI-Simulator: a visual tool to support the preclinical phase of the drug discovery process by assessing in silico the effect of an anticancer drug

A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions

Mathematical models used in preclinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumor volume; however, they typically have little connection with the underlying physiologic processes. This lack of a mechanistic underpinning restricts their flexibility and potentially inhibits their translation across studies including from animal to human. Here we present a mathematical model describing tumor growth for the evaluation of single-agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations and account for spatial drug distribution effects within tumors. Importantly, we demonstrate that the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for preclinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. However, in addition, the model is also able to accurately predict the observed growing fraction of tumours. Our work opens up current preclinical modeling studies to also incorporating spatially resolved and multimodal data without significant added complexity and creates the opportunity to improve translation and tumor response predictions.

Significance

This theoretical model has the same mathematical structure as that currently used for drug development. However, its mechanistic basis enables prediction of growing fraction and spatial variations in drug distribution.

A predictive pharmacokinetic-pharmacodynamic model of tumor growth kinetics in xenograft mice after administration of anticancer agents given in combination

Purpose

In clinical oncology, combination treatments are widely used and increasingly preferred over single drug administrations. A better characterization of the interaction between drug effects and the selection of synergistic combinations represent an open challenge in drug development process. To this aim, preclinical studies are routinely performed, even if they are only qualitatively analyzed due to the lack of generally applicable mathematical models.

Methods

This paper presents a new pharmacokinetic–pharmacodynamic model that, starting from the well-known single agent Simeoni TGI model, is able to describe tumor growth in xenograft mice after the co-administration of two anticancer agents. Due to the drug action, tumor cells are divided in two groups: damaged and not damaged ones. The damaging rate has two terms proportional to drug concentrations (as in the single drug administration model) and one interaction term proportional to their product. Six of the eight pharmacodynamic parameters assume the same value as in the corresponding single drug models. Only one parameter summarizes the interaction, and it can be used to compute two important indexes that are a clear way to score the synergistic/antagonistic interaction among drug effects.

Results

The model was successfully applied to four new compounds co-administered with four drugs already available on the market for the treatment of three different tumor cell lines. It also provided reliable predictions of different combination regimens in which the same drugs were administered at different doses/schedules.

Conclusions

A good and quantitative measurement of the intensity and nature of interaction between drug effects, as well as the capability to correctly predict new combination arms, suggest the use of this generally applicable model for supporting the experiment optimal design and the prioritization of different therapies.

Electronic supplementary material

The online version of this article (doi:10.1007/s00280-013-2208-8) contains supplementary material, which is available to authorized users.

Mathematical model approach to describe tumour response in mice after vaccine administration and its applicability to immune-stimulatory cytokine-based strategies

Immunotherapy is a growing therapeutic strategy in oncology based on the stimulation of innate and adaptive immune systems to induce the death of tumour cells. In this paper, we have developed a population semi-mechanistic model able to characterize the mechanisms implied in tumour growth dynamic after the administration of CyaA-E7, a vaccine able to target antigen to dendritic cells, thus triggering a potent immune response. The mathematical model developed presented the following main components: (1) tumour progression in the animals without treatment was described with a linear model, (2) vaccine effects were modelled assuming that vaccine triggers a non-instantaneous immune response inducing cell death. Delayed response was described with a series of two transit compartments, (3) a resistance effect decreasing vaccine efficiency was also incorporated through a regulator compartment dependent upon tumour size, and (4) a mixture model at the level of the elimination of the induced signal vaccine (k 2) to model tumour relapse after treatment, observed in a small percentage of animals (15.6%). The proposed model structure was successfully applied to describe antitumor effect of IL-12, suggesting its applicability to different immune-stimulatory therapies. In addition, a simulation exercise to evaluate in silico the impact on tumour size of possible combination therapies has been shown. This type of mathematical approaches may be helpful to maximize the information obtained from experiments in mice, reducing the number of animals and the cost of developing new antitumor immunotherapies.