New Aspects of Solution Feasibility in a Context of Personalized Therapy Optimization

In this work, the feasibility of a personalized therapy design is considered. We attempt to determine whether all of the obtained results of computer simulations should be presented to medical personnel. For this purpose, a two-drug displacement problem was used, which is the starting point of this research work. The relationships that can be used to characterize the progress as well as the efficiency of treatment in advanced cases can be modeled by a system of nonlinear dynamical equations with additional algebraic dependencies (differential-algebraic equations, DAEs). Then, to improve the efficiency of the therapy, an optimization task needs to be formulated and solved. The solution should meet all the assumed requirements and expectations. Therefore, a control vector parametrization (CVP) procedure for a DAE model is often suggested as an appropriate tool for solving the optimization-based therapy design tasks. In this work, a general iterative optimization framework is discussed in detail together with the proposed three levels of solution feasibility which try to decide if the iteratively obtained solution is trustworthy. The CVP optimization procedure with the designed levels of solution feasibility are implemented and tested. The obtained results are discussed from the perspective of their practical use in the treatment process. It is worth noting that solutions that are valuable from the perspective of creating new optimization algorithms may be rejected by the final recipient as devoid of application possibilities. Some of the presented solutions can be considered as a reference in further clinical research.