Optimizing breast cancer treatment using hyperthermia: A single and multi-objective optimal control approach

In recent decades, the study and development of numerical strategies for cancer treatment have become increasingly feasible, thanks to the advancement of numerical techniques and the increased availability of higher-performance computers. This has enabled researchers to tackle more complex and realistic problems associated with cancer treatment. Among the deadliest types of carcinomas, breast cancer is one of the most extensively studied, primarily due to its high annual incidence and mortality rate. From a medical standpoint, hyperthermia has emerged as one of the most promising treatment modalities. In general, this procedure involves applying heat to the tumor using an applicator over a period of time in order to destroy pathological cells. The applicator provides a source of energy that is used to raise the temperature inside the tumor. Traditionally, a constant heat source has been utilized during the treatment period. This article proposes single and multi-objective optimal control problems for breast cancer treatment by hyperthermia, and solutions for these problems are provided. In this instance, the heat source is treated as a control variable considering two types of strategies: ������) increasing monotone control and ������������) non-monotone control. For this purpose, the extent of tissue damage is considered a constraint in each application to ensure the degree of tissue damage. As expected, the findings demonstrate that the best result was achieved when employing a strategy that considers only the lateral limits, without any additional constraints. In addition, for every case study, a more appropriate optimal strategy can be employed for cancer treatment. Moreover, for the multi objective optimal control problem, a satisfactory balance between the objectives can be selected such that a specific optimal strategy can be established for each patient.