Relating prostate-specific antigen leakage with vascular tumor growth in a mathematical model of prostate cancer response to androgen deprivation

Abstract

The use of prostate-specific antigen (PSA) as a prognostic indicator for prostate cancer (PCa) patients is controversial, especially since it has been shown to correlate poorly with tumor burden. The poor quality of PSA as a biomarker could be explained by current guidelines not accounting for the mechanism by which it enters circulation. Given that mature blood vessels are relatively impermeable to it, we hypothesize that immature and leaky blood vessels, formed under angiogenic cues in a hypoxic tumor, facilitate PSA extravasation into circulation. To explore our hypothesis, we develop a nonlinear dynamical systems model describing the vascular growth of PCa, that explicitly links PSA leakage into circulation with changes in intra-tumoral oxygen tension and vessel permeability. The model is calibrated versus serum PSA and tumor burden time-courses from a mouse xenograft model of castration resistant PCa response to androgen deprivation. The model recapitulates the experimentally observed and – counterintuitive – phenomenon of increasing tumor burden despite decreasing serum PSA levels. The validated model is then extended to the human scale by incorporating patient-specific parameters and fitting individual PSA time-courses from patients with biochemically failing PCa. Our results highlight the limitations of using time to PSA failure as a clinical indicator of androgen deprivation efficacy. We propose an alternative indicator, namely a treatment efficacy index, for patients with castration resistant disease, to identify who would benefit most from enhanced androgen deprivation. A critical challenge in PCa therapeutics is quantifying the relationship between serum PSA and tumor burden. Our results underscore the potential of mathematical modeling in understanding the limitations of serum PSA as a prognostic indicator. Finally, we provide a means of augmenting PSA time-courses in the diagnostic process, with changes in intra-tumoral vascularity and vascular architecture.