# Design of HIFU Treatment Plans Using Thermodynamic Equilibrium Algorithm
## 3 Results & Discussions
### Application to HIFU
#### 3.2.2 Evaluation of the Equilibrium Process  
This section assesses the TEA's ability to determine a viable treatment plan for a specific patient. For statistical analysis, 15 separate runs were conducted with a maximum execution duration of 48 h per run. To evaluate the performance, three key metrics were looked at, including: (1) the best treatment plan's quality, (2) the amount of fitness assessments that must converge, and (3) the best system's progress over time. The capacity of the TEA to identify a suitable treatment plan is the first and most significant criterion. This was assessed with the fitness value defined in Equation (26). With the fitness value equal to zero, the ideal solution would cover the entire treated region while leaving the rest completely undamaged. Figure 11 displays the histogram of fitness values compiled from the top solutions produced in 15 distinct runs. Here, the effects of numbers of systems and sonications on the fitness value are presented. Figure 11: Histogram of the best fitness values from 15 independent runs as a function of the number of systems and the number of sonications. Figure 10: Segmented AustinWoman data with marked target area. The overall trend in Figure 11 suggests that the average quality of the treatment plan improves as the number of sonications permitted by the TEA increases. Naturally, the finer the coverage control, the more (possibly shorter or smaller) sonications are performed. However, more sonications lead to longer treatment times, patient discomfort, and heavier computational load (more thermal model runs). The best compromise between the quality of the treatment plan and the number of sonications seems to be eight sonications with 20 to 30 systems. Finally, with ten sonications and 30 systems, the best fitness value approaches zero, but most of the systems still cannot achieve the best quality. As the numbers of sonication and system increase, the evaluation time also increases and the computation time quickly reaches 48 h before convergence is reached. Since Equation (26) demonstrates that the fitness value is the product of two metrics (non-treated and mistreated), these metrics are also provided for the treatment plan's quality. Tables 3 and 4, respectively, illustrate the median and average percentages of untreated and improperly treated locations. The non-treated region denotes areas in which the treatment was unsuccessful (due to insufficient energy deposition), while the mistreated region denotes areas where the normal tissue was harmed. According to the data from both tables, the non-treated and mistreated regions make up less than 0.1 percent of the highlighted areas. This is a remarkable achievement, and is considered clinically applicable. In Table 3, given that the medians of both measures are zero for 8 and 10 sonications, regardless of the number of systems, it can be inferred that more than fifty percent of runs resulted in flawless treatment plans. The comparison between Tables 3 and 4 indicates that in most circumstances, it was easier to completely cover the treated area than to completely protect the normal tissue. Energy seeping from the focus point (heat diffusion) to the protected zone was the cause of mistreatment. Convergence speed is another crucial aspect that determines the quality of the suggested evolutionary method. Figure 12 demonstrates the number of iterations required to obtain an ideal solution, whereas Table 5 shows the wall clock time required to get a suboptimal solution to quantify this metric. As shown in Figure 12, the number of systems obviously influences the number of iterations. To achieve convergence in a population of 30 systems as opposed to a population of 20 systems, approximately 30% more TEA iterations are required. Unfortunately, the increase in evolution time due to the increase of the number of systems cannot be justified by the gain in solution quality. Increases in the number of sonications, on the other hand, have large influence on the number of iterations.