  In this paper, a new framework for obtaining personalized optimal treatment
strategies in colon cancer-induced angiogenesis is presented. The dynamics of
colon cancer is given by a It\'o stochastic process, which helps in modeling
the randomness present in the system. The stochastic dynamics is then
represented by the Fokker-Planck (FP) partial differential equation (PDE) that
governs the evolution of the associated probability density function. The
optimal therapies are obtained using a three step procedure. First, a finite
dimensional FP-constrained optimization problem is formulated that takes input
individual noisy patient data, and is solved to obtain the unknown parameters
corresponding to the individual tumor characteristics. Next, a sensitivity
analysis of the optimal parameter set is used to determine the parameters to be
controlled, thus, helping in assessing the types of treatment therapies.
Finally, a feedback FP control problem is solved to determine the optimal
combination therapies. Numerical results with the combination drug, comprising
of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed
framework.
