Design of HIFU Treatment Plans Using Thermodynamic Equilibrium Algorithm

High-intensity focused ultrasound (HIFU) is a non-invasive medical procedure, which is mainly used to ablate tumors externally by focusing on them with high-frequency ultrasound. Because a single ablation can process only a small volume of tissue, a succession of ablations is required to treat a large volume of cancerous tissue. In order to maximize the therapeutic effect and reduce side effects such as skin burns, careful preoperative treatment planning must be performed to determine the focal location and sonication time for each ablation. This paper proposes a novel optimization algorithm, called the thermodynamic equilibrium algorithm (TEA), inspired by the behavior of thermodynamic systems reaching their equilibrium states. Like other evolutionary algorithms, TEA starts with an initial population. Gas chambers at various thermodynamic states are employed as representatives of the population individuals, and the equilibrium state is regarded as the global minimum. The movement of thermodynamic parameters in the direction of reducing the temperature gradient forms the basis of the proposed evolutionary algorithm. During this movement, the second law of thermodynamics is checked to ensure that entropy will increase in each process. This movement leads to the state where most of the systems are at equilibrium. In this state, the systems are localized at the same position and have the same cost as the global minimum. The TEA was applied to several well-known unconstrained and constrained benchmark cost functions, and the performance was compared with other well-known optimization algorithms. The results showed that the TEA has high potential to handle various types of optimization problems with a good convergence rate and high precision. Finally, the suggested evolutionary approach is applied to HIFU treatment regimens adopting a map of patient-specific material properties and an accurate thermal model. High-quality treatment plans could be created using the suggested method, and the average amount of tissue that is over- or under-treated was less than 0.08 percent.