Population modeling of tumor size dynamics has recently emerged as an important tool in pharmacometric research. A series of new mixed-effects models have been reported recently, and we present herein a synthetic view of models with published mathematical equations aimed at describing the dynamics of tumor size in cancer patients following anticancer drug treatment. This selection of models will constitute the basis for the Drug Disease Model Resources (DDMoRe) repository for models on oncology.

Purpose: To develop a tumor growth inhibition model for adult diffuse low-grade gliomas (LGG) able to describe tumor size evolution in patients treated with chemotherapy or radiotherapy.Experimental Design: Using longitudinal mean tumor diameter (MTD) data from 21 patients treated with first-line procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea, and vincristine (PCV) chemotherapy, we formulated a model consisting of a system of differential equations, incorporating tumorspecific and treatment-related parameters that reflect the response of proliferative and quiescent tumor tissue to treatment. The model was then applied to the analysis of longitudinal tumor size data in 24 patients treated with first-line temozolomide (TMZ) chemotherapy and in 25 patients treated with first-line radiotherapy.Results: The model successfully described the MTD dynamics of LGG before, during, and after PCV chemotherapy. Using the same model structure, we were also able to successfully describe the MTD dynamics in LGG patients treated with TMZ chemotherapy or radiotherapy. Tumor-specific parameters were found to be consistent across the three treatment modalities. The model is robust to sensitivity analysis, and preliminary results suggest that it can predict treatment response on the basis of pretreatment tumor size data.Conclusions: Using MTD data, we propose a tumor growth inhibition model able to describe LGG tumor size evolution in patients treated with chemotherapy or radiotherapy. In the future, this model might be used to predict treatment efficacy in LGG patients and could constitute a rational tool to conceive more effective chemotherapy schedules.

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With the aim of inhibiting cancer growth and reducing the risk of metastasis, pharmaceutical companies in the early 1990s developed anti-metastatic agents called inhibitors of metalloproteinases (MMPi). Despite the promising results obtained in pre-clinical studies, results of Phase III trials have been somewhat disappointing for late stage cancer patients. With the aim of mathematically investigating this therapeutic failure, we developed a mechanistically based model which integrates cell cycle regulation and macroscopic tumor dynamics. By simulating the model, we evaluated the efficacy of MMPi therapy. Simulation results predict the lack of efficacy of MMPi in advanced cancer patients. The theoretical model may aid in evaluating the efficacy of anti-metastatic therapies, thus benefiting the design of prospective clinical trials.

In this paper, we present a mathematical model for avascular tumor growth and its numerical study in two and three dimensions. For this purpose, we use a multiscale model using PDEs to describe the evolution of the tumor cell densities. In our model, cell cycle regulation depends mainly on micro-environment. The cancer growth of volume induces cells motion and tumor expansion. According to biology, cells grow against a basal membrane which interacts mechanically with the tumor. We use a level set method to describe this membrane and we compute its influence on cell movement thanks to a Stokes equation. The evolution of oxygen, diffusing from blood vessel to cancer cells and used to estimate hypoxia, is given by a stationary diffusion equation solved with a penalty method. The model has been applied to investigate the therapeutic benefit of anti-invasive agents and constitutes now the basis of a numerical platform for tumor growth simulations.

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Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation.

The proposed method should be implemented to complement EBEs-based approach for increasing the performance of model diagnosis.