| In this work, we present a rigorous mathematical framework for the usage of multiple patient-specific molecular images to enable model-based precision medicine, a paradigm of medical decision making defined by the employment of mathematical models of treatment efficacy to direct optimized treatment decisions for individual patients. We address the question of how to define and compute patient-specific probability of treatment success, using random field theory to define the notion of in silico virtual patient ensembles and patient-specific virtual clinical trials. We then provide a novel and rigorous deterministic and statistical analysis of photon-processing Emission Computed Tomography (ECT) data, highlighting the importance of null functions and Poisson statistics in defining the virtual patient ensemble and probability of treatment success. We discuss novel high-performance parallel numerical methods to simulate virtual patient ensembles and photon processing ECT systems; these simulations will advance our understanding of the uncertainties inherent in imaging-based precision medicine. Finally, we present a spatially resolved model for chemotherapy efficacy that employs ECT data, and demonstrate how our framework can be used to define, compute and optimize patient-specific probability of treatment success in this setting. |
