# New Aspects of Solution Feasibility in a Context of Personalized Therapy Optimization
###### Abstract  
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. In general, an application of new computational methods gives a hope for a significant increase in the quality of a life in various areas. The ability to simulate and optimize even complex phenomena can result in better and more accessible solutions [1]. The development of new, computer-aided design methods can be observed in social life, where optimization-based approaches can be efficiently applied to solve general and specialized problems. In particular, the application of computer programs built of specialized numerical procedures can have a positive impact on the treatment process design. This is especially true in a context of individual healing therapies, where unique individual solutions can be applied. Computer-assisted medicine has many specific applications. Some of the examples of applications include:  
* Designing three-dimensional models of bones and joints [2],
* Precise additive tissue production [3],
* Scheduling activities during complex, multi-team surgical operations [4],
* Planning the course of operations in a dedicated simulation environment [5],
* Improvement of selected activities using physical simulators [6],
* An attempt at algorithmization of activities and a numerical evaluation of the quality of their execution [7]. Moreover, depending on the available mathematical models and data, the observed phenomena can be personalized. Then, the obtained results, conclusions and observations can be generalized and extrapolated to other therapeutic processes. Therefore, all research in computationally personalized therapy design, such as conceptual considerations, experimental research and computer-based simulations, have an extremely important application potential. The positive effects of the work in this area, undertaken by numerous researchers, have been presented in recent literature. In particular, [PERSON] et al. [8] presented a new approach to optimize a thiazole series of novel small molecule Abelson kinase activators. They proposed and tested a new methodology to increase a number of circulating neutrophils in order to improve treatment for chemotherapy-induced neutropenia. [PERSON] et al. [9] considered a method for optimization of a structure-guided design and water displacement strategy. Moreover, they indicated JAK inhibitors as a major therapeutic advancement in treating autoimmune disease. As a result, a discovered JAK inhibitor BMS-986165 (11) has been advanced as a pseudokinase-directed therapeutic in clinical development. Recently, [PERSON] et al. [10] tested a cholinergic hypothesis of [PERSON]'s disease as a tool for drug development.