Collaborative Research: A New Multiscale Methodology and Application to Tumor Growth modeling

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The complexity of tumor growth, which involves interactions within cells, among cells, and between cells and their environment, calls for development of mathematical and computational models that can connect processes from the cell, and sub-cell scales, to tissue level scales. These methods are needed to help tumor biologists gain further insight into the underlying mechanisms of the processes (e.g., proliferation, differentiation, and migration) involved in tumor development, at the scales which influence their behavior. Because of this complexity, it has been challenging to functionally link cell and tissue scale processes, the knowledge of which is key to development of predictive multiscale tumor models. However, current models typically use ad-hoc rules to bridge between scales, which limits their predictive capability. This project will address this challenge by developing a new multiscale method where directly measurable quantities at the cell-scale inform the model parameters at the continuum tissue scale through rigorous, mathematical upscaling techniques. The multiscale model will be tested and validated by comparing simulation results against experimentally obtained information about the overall growth rates and spatiotemporal behaviors of the different cells and tumors. The new multiscale method will be used to study pancreatic tumors to elucidate the transition of pancreatic lesions into invasive pancreatic ductal adenocarcinoma (PDAC). By integrating patient data analysis with quantitative tumor modeling, the project will develop reliable methods that can predict the likelihood of pancreatic cyst progression to PDAC using relatively non-invasive approaches. The project team will develop a new class of multiscale models that bridge these scales non-phenomenologically through application of rigorous upscaling techniques in order to close the continuum equations at the tissue scale and provide an accurate description of the processes across both cell and tissue scales. Specifically, stochastic agent-based models at the cell-scale and continuum partial differential equation models at the tissue-scale will be developed. Consistent functional relationships between the variables at the tissue-scale and measurements at the cell-scale will be found by upscaling the discrete models by using and extending the framework of dynamic density functional theory (DDFT) to obtain multi-cell scale continuum equations that account for correlations among cells as well as biological processes such cell birth and death. Further upscaling to the tissue scale will be done by identifying and deriving equations for slowly varying variables. The consistency of the different models in domains where the scales overlap will be tested and validated. The new multiscale method will be applied to model the progression of pancreatic neoplasms into invasive carcinomas in order to estimate the probability of this progression. Large-scale human patient datasets of pancreatic lesions, provided by our consultants through a separately funded project, will be used to validate and refine the models. The project will enhance the cross disciplinary training of students.