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While there is a mature literature on biomathematical and biophysical modeling in cancer, many of the existing approaches are not of clinical utility, as they require input data that are extremely difficult to obtain in an intact organism, and/or require a large number of assumptions on the free parameters included in the models. Thus, there has only been very limited application of such models to solve problems of clinical import. More recently, however, there has been increased activity at the interface of quantitative, noninvasive imaging data, and tumor mathematical modeling. In addition to reporting on bulk tumor morphology and volume, emerging imaging techniques can quantitatively report on for example tumor vascularity, glucose metabolism, cell density and proliferation, and hypoxia. In this paper, we first motivate the problem of predicting therapy response by highlighting some (acknowledged) shortcomings in existing methods. We then provide introductions to a number of representative quantitative imaging methods and describe how they are currently (and potentially can be) used to initialize and constrain patient specific mathematical and biophysical models of tumor growth and treatment response, thereby increasing the clinical utility of such approaches. We conclude by highlighting some of the exciting research directions when one integrates quantitative imaging and tumor modeling.

Integrating Imaging Data into Predictive Biomathematical and Biophysical Models of Cancer