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. 1. Introduction The ability to identify—early in the course of therapy—patients that are not responding to a given therapeutic regimen is extraordinarily important. In addition to limiting patients’ exposure to the toxicities associated with unsuccessful therapies, it would allow patients the opportunity to switch to a potentially more efficacious approach. Unfortunately, existing methods of determining early response are inadequate. In particular, the current standard-of-care imaging assessment of tumor response to treatment is based on the Response Evaluation Criteria in Solid Tumors (RECIST, [1]). RECIST offers a simplified, practical method for extracting the basic morphological features of imaging data by assessing the overall tumor burden at baseline and comparing that measurement to subsequent measurements obtained during the course of therapy. We now present the salient features of RECIST in order to identify weaknesses that the integration of imaging and mathematical modeling can potentially address. High-resolution images (typically computed tomography (CT) or magnetic resonance imaging (MRI)) are acquired at baseline before treatment as commenced. In these
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