Tissue-scale, patient-specific modeling and simulation of prostate cancer growth

Abstract

Prostate cancer is a major health problem among aging men worldwide. This pathology is easier to cure in its early stages, when it is still organ-confined. However, it hardly ever produces any symptom until it becomes excessively large or has invaded other tissues. Hence, the current approach to combat prostate cancer is a combination of prevention and regular screening for early detection. Indeed, most cases of prostate cancer are diagnosed and treated when it is localized within the organ. Despite the wealth of accumulated knowledge on the biological basis and clinical management of the disease, we lack a comprehensive theoretical model into which we can organize and understand the abundance of data on prostate cancer. Additionally, the standard clinical practice in oncology is largely based on statistical patterns, which is not sufficiently accurate to individualize the diagnosis, prediction of prognosis, treatment, and follow-up. Recently, mathematical modeling and simulation of cancer and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a patient-specific basis. This new trend in medical research has been termed mathematical oncology. Prostate cancer is an ideal candidate to benefit from this technology for several reasons. First, patient-specific clinical approaches may contribute to reduce the rates of overtreatment and undertreatment of prostate cancer. Multiparametric magnetic resonance is increasingly used to monitor and diagnose this disease. This imaging technology can provide abundant information to build a patient-specific mathematical model of prostate cancer growth. Moreover, the prostate is a sufficiently small organ to pursue tissue-scale predictive simulations. Prostate cancer growth can also be estimated using the serum concentration of a biomarker known as the prostate specific antigen. Additionally, some prostate cancer patients do not receive any treatment but are clinically monitored and periodically imaged, which opens the door to in vivo model validation. The advent of versatile and powerful technologies in computational mechanics permits to address the challenges posed by the prostate anatomy and the resolution of the mathematical models. Finally, mathematical oncology technologies can guide the future research on prostate cancer, e.g., proposing new treatment strategies or unveiling mechanisms involved in tumor growth. Therefore, the aim of this thesis is to provide a computational framework for the tissuescale, patient-specific modeling and simulation of organ-confined PCa growth within the context of mathematical oncology. We present a model for localized prostate cancer growth that reproduces the growth patterns of the disease observed in experimental and clinical studies. To capture the coupled dynamics of healthy and tumoral tissue, we use the phase-field method together with reaction-diffusion equations for nutrient consumption and prostate specific antigen production. We leverage this model to run the first tissue-scale, patient-specific simulations of prostate cancer growth over the organ anatomy extracted from medical images. Our results show similar tumor progression as observed in clinical practice. We leverage isogeometric analysis to handle the nonlinearity of our set of equations, as well as the complex anatomy of the prostate and the intricate tumoral morphologies. We further advocate dynamical mesh adaptivity to speed up calculations, rationalize computational resources, and facilitate simulation in a clinically relevant time. We present a set of efficient algorithms to accommodate local h-refinement and h-coarsening of hierarchical splines in isogeometric analysis. Our methods are based on Bézier projection, which we extend to hierarchical spline spaces. We also introduce a balance parameter to control the overlapping of basis functions across the levels of the hierarchy, leading to improved numerical conditioning. Our simulations of cancer growth show remarkable accuracy with very few degrees of freedom in comparison to the uniform mesh that the same simulation would require. Finally, we study the interaction between prostate cancer and benign prostatic hyperplasia, another common prostate pathology that causes the organ to gradually enlarge. In particular, we investigate why tumors originating in larger prostates present favorable pathological features. We perform a qualitative simulation study by extending our mathematical model of prostate cancer growth to include the equations of mechanical equilibrium and the coupling terms between them and tumor dynamics. We assume that the deformation of the prostate is a quasistatic phenomenon and we model prostatic tissue as a linear elastic, heterogeneous, isotropic material. This model is calibrated by studying the deformation caused by either disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that hamper prostatic tumor growth and limit its invasiveness.