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Despite recent advances in deciphering cancer drug resistance mechanisms, relapse is a widely observed phenomenon in advanced cancers, mainly due to intratumor clonal heterogeneity. How tumor clones progress and impact each other remains elusive. In this study, we developed 2D and 3D non-small cell lung cancer co-culture systems and defined a phenomenological mathematical model to better understand clone dynamics. Our results demonstrated that the drug-sensitive clones inhibit the proliferation of the drug-resistant ones under untreated conditions. Model predictions and their experimental in vitro and in vivo validations indicated that a metronomic schedule leads to a better regulation of tumor cell heterogeneity over time than a maximum-tolerated dose schedule, while achieving control of tumor progression. We finally showed that drug-sensitive and -resistant clones exhibited different metabolic statuses that could be involved in controlling the intratumor heterogeneity dynamics. Our data suggested that the glycolytic activity of drug-sensitive clones could play a major role in inhibiting the drug-resistant clone proliferation. Altogether, these computational and experimental approaches provide foundations for using metronomic therapy to control drug-sensitive and -resistant clone balance and highlight the potential of targeting cell metabolism to manage intratumor heterogeneity.

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Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidγ mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were [Formula: see text] for primary tumor growth and [Formula: see text] for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading during the earliest stages of cancer.

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Ischemic stroke involves numerous and complex pathophysiological mechanisms including blood flow reduction, ionic exchanges, spreading depressions and cell death through necrosis or apoptosis. We used a mathematical model based on these phenomena to study the influences of intensity and duration of ischemia on the final size of the infarcted area. This model relies on a set of ordinary and partial differential equations. After a sensibility study, the model was used to carry out in silico experiments in various ischemic conditions. The simulation results show that the proportion of apoptotic cells increases when the intensity of ischemia decreases, which contributes to the model validation. The simulation results also show that the influence of ischemia duration on the infarct size is more complicated. They suggest that reperfusion is beneficial when performed in the early stroke but may be either inefficacious or even deleterious when performed later after the stroke onset. This aggravation could be explained by the depolarisation waves which might continue to spread ischemic damage and by the speeding up of the apoptotic process leading to cell death. The effect of reperfusion on cell death through these two phenomena needs to be further studied in order to develop new therapeutic strategies for stroke patients.

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The inflammatory process during stroke consists of activation of resident brain microglia and recruitment of leucocytes, namely neutrophils and monocytes/macrophages. During inflammation, microglial cells, neutrophils and macrophages secrete inflammatory cytokines and chemokines, and phagocytize dead cells. The recruitment of blood cells (neutrophils and macrophages) is mediated by the leucocyte-endothelium interactions and more specifically by cell adhesion molecules. A mathematical model is proposed to represent the dynamics of various brain cells and of immune cells (neutrophils and macrophages). This model is based on a set of six ordinary differential equations and explores the beneficial and deleterious effects of inflammation, respectively phagocytosis by immune cells and the release of pro-inflammatory mediators and nitric oxide (NO). The results of our simulations are qualitatively consistent with those observed in experiments in vivo and would suggest that the increase of phagocytosis could contribute to the increase of the percentage of living cells. The inhibition of the production of cytokines and NO and the blocking of neutrophil and macrophage infiltration into the brain parenchyma led also to the improvement of brain cell survival. This approach may help to explore the respective contributions of the beneficial and deleterious roles of the inflammatory process in stroke, and to study various therapeutic strategies in order to reduce stroke damage.

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Diseases are complex systems. Modelling them, i.e. systems physiopathology, is a quite demanding, complicated, multidimensional, multiscale process. As such, in order to achieve the goal of the model and further to optimise a rather-time and resource-consuming process, a relevant and easy to practice methodology is required. It includes guidance for validation. Also, the model development should be managed as a complicated process, along a strategy which has been elaborated in the beginning. It should be flexible enough to meet every case. A model is a representation of the available knowledge. All available knowledge does not have the same level of evidence and, further, there is a large variability of the values of all parameters (e.g. affinity constant or ionic current) across the literature. In addition, in a complex biological system there are always values lacking for a few or sometimes many parameters. All these three aspects are sources of uncertainty on the range of validity of the models and raise unsolved problems for designing a relevant model. Tools and techniques for integrating the parameter range of experimental values, level of evidence and missing data are needed.

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Ischemic stroke is the third cause of death in industrialised countries, but no satisfactory treatment is currently available. The hundreds of neuroprotective drugs developed to block the ischemic cascade gave very promising results in animal models but the clinical trials performed with these drugs showed no beneficial effects in stroke patients. Many hypotheses were advanced to explain this discrepancy, among which the morphological and functional differences between human and rodent brains. This discrepancy could be partly due to the differences in white matter and glial cell proportions between human and rodent brains. In order to test this hypothesis, we built a mathematical model of the main early pathophysiological mechanisms of stroke in rodent and in human brains. This model is a two-scale model and relies on a set of ordinary differential equations. We built two versions of this model (for human and rodent brains) differing in their white matter and glial cell proportions. Then, we carried out in silico experiments with various neuroprotective drugs. The simulation results obtained with a sodium channel blocker show that the proportion of penumbra recovery is much higher in rodent than in human brain and the results are similar with some other neuroprotective drugs tested during phase III trials. This in silico investigation suggests that the proportions of glial cells and white matter have an influence on neuroprotective drug efficacy. It reinforces the hypothesis that histological and morphological differences between rodent and human brains can partly explain the failure of these agents in clinical trials.

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