  Prostate cancer can be lethal in advanced stages, for which chemotherapy may
become the only viable therapeutic option. While there is no clear clinical
management strategy fitting all patients, cytotoxic chemotherapy with docetaxel
is currently regarded as the gold standard. However, tumors may regain activity
after treatment conclusion and become resistant to docetaxel. This situation
calls for new delivery strategies and drug compounds enabling an improved
therapeutic outcome. Combination of docetaxel with antiangiogenic therapy has
been considered a promising strategy. Bevacizumab is the most common
antiangiogenic drug, but clinical studies have not revealed a clear benefit
from its combination with docetaxel. Here, we capitalize on our prior work on
mathematical modeling of prostate cancer growth subjected to combined cytotoxic
and antiangiogenic therapies, and propose an optimal control framework to
robustly compute the drug-independent cytotoxic and antiangiogenic effects
enabling an optimal therapeutic control of tumor dynamics. We describe the
formulation of the optimal control problem, for which we prove the existence of
at least a solution and determine the necessary first order optimality
conditions. We then present numerical algorithms based on isogeometric analysis
to run a preliminary simulation study over a single cycle of combined therapy.
Our results suggest that only cytotoxic chemotherapy is required to optimize
therapeutic performance and we show that our framework can produce superior
solutions to combined therapy with docetaxel and bevacizumab. We also
illustrate how the optimal drug-na\"{i}ve cytotoxic effects computed in these
simulations may be successfully leveraged to guide drug production and delivery
strategies by running a nonlinear least-square fit of protocols involving
docetaxel and a new design drug.
