Molecular imaging of physiological random processes for in silico prediction of treatment efficacy

In silico prediction of cancer treatment efficacy for individual patients is a promising direction towards achieving the goal of personalized oncology through mathematical modeling, patient-specific data collection and simulation. While such strategies have begun to gain traction in a limited number of cases, the approach overall continues to face several challenges. First, the inherent physiological and genetic complexity of the disease and the presence of multiple spatial and time scales has led to a lack of sufficiently validated mathematical efficacy models for many treatments. Additionally, while mathematical and computational models are theoretically capable of resolving behavior across a continuum of spatial and time scales, the data available to the clinician has finite spatiotemporal resolution and is furthermore noisy, incomplete, and usually only indirectly related to the parameters which would otherwise be necessary to constrain a highly resolved in silico model. Thus for the in silico paradigm to become clinically relevant across oncology, uncertainty must be addressed in a fundamental way. It is our view that any figure of merit, such as log cell kill, which is used to predict patient-specific treatment efficacy and hence optimize treatment parameters, should be considered as a random quantity so that confidence can be provided. Because both spatiotemporal heterogeneity and uncertainty play key roles, we make the fundamental mathematical modeling assumption that all physiological processes relevant to cancer modeling are spatiotemporal random processes. Furthermore, because multiple interacting physiological processes, such as normal and neoplastic cell density, vasculature, oxygen saturation and drug concentration are required to fully describe the dynamics of treatment delivery, response and ultimately efficacy, we consider coupled physiological random processes. Using the tools of probability and stochastic process theory, we have derived mathematical expressions relating patient-specific parameters to simple, interpretable quantities of interest which can be used to make patient-specific treatment decisions while seamlessly providing quantification of uncertainty. In this work, we discuss specifically how molecular imaging will play a unique role in measuring the spatiotemporal behavior of coupled physiological random processes both in vitro and in vivo, allowing many of the patientspecific parameters necessary to perform in silico predic