# New Aspects of Solution Feasibility in a Context of Personalized Therapy Optimization
## 3 Three Levels of Feasibility  
Research experience can suggest that a feasible solution may be understood from at least several perspectives. Therefore, it is worth considering in detail what restrictions are actually met, what conditions have been set and, finally, what the main expectations are. For these reasons, the feasibility of a given solution can be presented on various levels. * **Level 1. A mathematical feasibility** The first perspective taken into account is to view the considered model or set of constraints as a pure mathematical construct, such as, e.g., (28). Such systems of equations can only be considered in clearly defined sets or their indicated subsets. However, the very origin of the model under consideration and the way it was constructed can be completely arbitrary and may not reflect the full physics of the phenomenon. Definition 1: The mathematical feasibility denotes whether the problem constraints (28) have been met. Proposition 1: If the constraints (28) are not met, then the constraints' violation can be measured as  
\[\|c(\mathbf{U}^{\star})\|\to[0,\quad+\inf). \tag{30}\]  
Remark 1: Fulfillment of the constraints (28), understood as the pure mathematical relations, does not guarantee that the obtained solution is of an application nature. * **Level 2. A physical rationality** In practice, such limitations are difficult to grasp because they are taken for granted, and therefore, often not even symbolic attention is paid to them. For example, surface area and volume are evidently considered as positive values from the set of real numbers. Likewise, the concentration of a substance cannot be expressed as a negative number. In addition, the temperature, expressed in degrees Celsius, is greater than or equal to \(-273.15^{\circ}\). Definition 2: The physical rationality indicates whether the constraints that were used to determine the physical feasibility of the proposed solution are met. Remark 2: A computational experience can suggest that taking the above physical properties as granted and not expressed explicitly in the model may lead to results which, despite the mathematical correctness, will not meet the most obvious expectations. Such a phenomenon can be observed at the beginning of the iterative calculations when the starting point may differ significantly from the final solution. Then, the intermediate results do not have any reasonable interpretation even though the dynamical equations of the model were resolved correctly. However, deficiencies of this type result in a significant distrust of the applied computing procedure, which allows for an intermediate solution that does not comply with the fundamental laws of physics and expectation of common sense. For the same reason, the received final solution, although factually correct and valuable, may be disqualified. * **Level 3. A technological applicability** Specifying this area causes the main goal of the performed computer simulations to increase the numerical accuracy of the proposed solution, which is approximately known a priori. Definition 3: The technological applicability denotes the highest level of details in the constraints that reflect real technological expectations and possibilities. Remark 3: The technological applicability's constraints reflect the experiences of practitioners, technologists and experimenters that must be met and may not result explicitly from the model equations. This can be the narrowest area of the solution feasibility. Developing a new approach in computer simulations, the results of which could be used to design dedicated therapies, require consideration of the various constraints and their impact on the computation, as well as the confidence of those who will benefit from these results. The experience so far shows that the final results of the simulation are characterized by trust and approval, especially when the subsequent calculation steps are accessible to understand and an aura of secrecy and inaccessibility is not created.