Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects

Chemotherapy is a common treatment for advanced prostate cancer. The standard approach relies on cytotoxic drugs, which aim at inhibiting proliferation and promoting cell death. Advanced prostatic tumors are known to rely on angiogenesis, i.e. the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or in combination with standard cytotoxic protocols. However, the complex genetic alterations that originate and sustain prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient's tumor. Here, we present a mathematical model of prostate cancer growth and chemotherapy that may enable physicians to test and design personalized chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction-diffusion dynamics. Tumor proliferation and apoptosis (i.e. programmed cell death) can be parameterized with experimentally-determined values. Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples the tumor phase field with the production of prostate-specific antigen, which is a prostate cancer biomarker that is extensively used in the clinical management of the disease. We prove the well posedness of our model and we run a series of representative simulations leveraging an isogeometric method to explore untreated tumor growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well as common outcomes of cytotoxic and antiangiogenic mono therapy and combined therapy. Additionally, our model also reproduces the usual temporal trends in tumor volume and prostate-specific antigen evolution observed in experimental and clinical studies.