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\begin{document}

\title{Relating Prostate Specific-Antigen leakage with vascular tumor growth in
a mathematical model of prostate cancer response to androgen deprivation}



\author[1]{Johnna Barnaby}%
\author[2]{Inmaculada Sorribes}%
\author[3]{Harsh Jain}%
\affil[1]{Shippensburg University of Pennsylvania}%
\affil[2]{Duke University}%
\affil[3]{University of Minnesota Duluth}%


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  \date{June 18, 2024}


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\begin{abstract}
Introduction: 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. Methods: To explore our hypotheses, 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. Results: The model recapitulates the experimentally
observed -- and counter-intuitive -- 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. Conclusions: A critical
challenge in prostate cancer 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 .%
\end{abstract}%



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