Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer.

Brain metastases (BMs) are associated with poor prognosis in non-small cell lung cancer (NSCLC), but are only visible when large enough. Therapeutic decisions such as whole brain radiation therapy would benefit from patient-specific predictions of radiologically undetectable BMs. Here, we propose a mathematical modeling approach and use it to analyze clinical data of BM from NSCLC. Primary tumor growth was best described by a gompertzian model for the pre-diagnosis history, followed by a tumor growth inhibition model during treatment. Growth parameters were estimated only from the size at diagnosis and histology, but predicted plausible individual estimates of the tumor age (2.1-5.3 years). Multiple metastatic models were further assessed from fitting either literature data of BM probability (n = 183 patients) or longitudinal measurements of visible BMs in two patients. Among the tested models, the one featuring dormancy was best able to describe the data. It predicted latency phases of 4.4-5.7 months and onset of BMs 14-19 months before diagnosis. This quantitative model paves the way for a computational tool of potential help during therapeutic management.

Theoretical investigation of the efficacy of antiangiogenic drugs combined to chemotherapy in xenografted mice.

Antiangiogenic drugs were developed with the aim to inhibit the formation of intratumoral blood vessels and in consequence the growth of solid tumors. As these drugs are generally combined with classical cytotoxic drugs in the treatment of cancer patients, finding the optimal combinations remains a complex challenge due to possible interactions of the antiangiogenic compound with the hemodynamic property of the treated tumor. To analyze this problem, we developed a multi-scale model of vascular tumor growth combining a molecular model of VEGF signaling pathways and a tissue model of the tumor expansion including the dynamics of cellular and tissue processes of tumor growth and response to treatments. We addressed the potential impact of antiangiogenic drug by defining a new index of vasculature quality which depends on the balance between stable and unstable vessels within the tumor mass. Our goal was to investigate the interactions between a chemotherapy and a antiangiogenic treatment, and, by simulating the model, to identify the optimal delay of chemotherapy delivery after the administration of the antiangiogenic compound. This theoretical analysis could be used in the future to optimize antiangiogenic drug delivery in preclinical settings and to facilitate the translation from preclinical to clinical studies.