# Design of HIFU Treatment Plans Using Thermodynamic Equilibrium Algorithm
## 4 Conclusions  
High-Intensity Focused Ultrasound (HIFU) is a state-of-the-art, minimally invasive method of cancer treatment. However, significant preoperative treatment planning is necessary to accurately aim the ultrasonic beam and ablate only the tumor without damaging healthy tissue. Manual and semi-automated planning are time consuming and computationally complex tasks. As a result, new techniques for fully automated treatment planning are of great interest.  
In this paper, an optimization algorithm based on the behavior of the thermodynamic systems, called the thermodynamic equilibrium algorithm (TEA), was proposed. In TEA, each individual of the population was modeled as a gas container. The global minimum of the function was defined as the thermodynamic equilibrium state. Changes in thermodynamic states of the systems toward the equilibrium direction, in which the temperature  
Figure 15: Comparison of the numerical simulation with the experimental treatment plan composed of 5 sonications.  
difference is reduced, formed the core of this algorithm. The proposed approach showed good performance in the convergence of systems to the global minimum of the problem. While the thermodynamic states were changing, most of the systems could reach the global minimum through thermodynamic equilibrium process. The TEA was tested with 25 benchmark functions, and the results confirmed that the algorithm was able to find the global minimum of these functions successfully. Additionally, the algorithm was evaluated by comparing its performance with PSO and GA for three of the benchmark functions, which showed that the convergence rate was faster and the global minimum was reached sooner with the TEA than with PSO or GA.  
The TEA was applied to HIFU planning and produced excellent outputs with mis-treated and undertreated areas on the order of 0.1 percent. These results shows that TEA can be utilized to create treatment plans that are close to ideal. The major benefit of the proposed method is that it just needs a map of the patient's anatomy and the corresponding target and prohibited areas. Evolution will take care of the rest.  
The proposed method, on the other hand, has a few drawbacks. First, even when no acoustic model was used and just 2D thermal simulations were performed, it took anywhere between 36 and 48 h to construct a good treatment plan. This will be addressed in the next phase of the study, which entails rewriting the whole algorithm in high-performance languages such as parallel C/C++ with the aim of achieving at least a five-fold reduction in computation time. Second, owing to computational complexity, it is only able to operate in two dimensions. Third, it requires a numerical model that accounts for acoustic heterogeneities in treatment plans by linking the ultrasonic and temperature modes.  
Conceptualization, S.L. and H.J.K.; methodology, S.W.H.; software, S.L.; validation, S.L. and S.W.H.; formal analysis, H.J.K.; investigation, S.L.; resources, S.W.H. and J.U.K.; writing--original draft preparation, S.L.; writing--review and editing, J.U.K. and H.J.K.; visualization, S.L. and S.W.H.; supervision, H.J.K. and J.U.K.; project administration, J.U.K.; funding acquisition, H.J.K. and J.U.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Korea Electrotechnology Research Institute (KERI) grant number 22A03009.  
Not applicable.  
This research was supported by Changwon-city, Republic of Korea through Korea-Canada Joint AI Research Program.  
The authors declare no conflict of interest.