Optimization of Fuzzy Model of High Dose Brachytherapy Problem for the Treatment of Prostate Cancer Using Evolutionary Algorithms

Cancer is one of the great human challenges in all countries, both advanced and developing. Cancer treatment management can include surgery, chemotherapy, or radiation therapy (1). Radiation therapy is done in two ways: Teletherapy and Brachytherapy. Brachytherapy involves the use of radiation sources to treat cancer by irradiating cancerous tissue from within the patient’s body (2). But the dose and how to use this method has always been questionable for researchers. Therefore, this study creates a new fuzzy approach to high-dose brachytherapy by optimizing the distribution of double roughness based on dosimetric criteria. The use of fuzzy logic itself has increased the accuracy of the mathematical model of the problem. This fuzzy model is a new study and innovation used in this paper. Due to the fuzzy nature of this method and its limitations, it is considered fuzzy. This makes the method more accurate and includes parameters such as the patient’s physical ability and age in the problem, which in itself increases the accuracy of the method for each patient. As a result, the obtained answer is improved and the executive program of brachytherapy method is more accurate.

In the present study, the dose prescribed for an organ was evaluated by dosimetric indices listed in Table 1 (18). For the present study, data from 20 patients in the age range of 50 to 74 and mean age 62 years with a wide range of prostate volume between 23 and 103 cubic centimeters, and for the treatment of prostate cancer by brachytherapy from the Academic Medical Center (AMC, Amsterdam, the Netherlands) had participated. To compare brachytherapy programs with high interstitial dose, the dose rate was calculated with 192Ir beam with a radiation dose of 13 Gy, according to the standard protocol TG-43.
To begin with, computed tomography (CT) scans or magnetic resonance imaging (MRI) were taken from the patients pelvis, and entered into the treatment planning software for use in treatment planning sessions. BT treatment planners and specialists then determined the input catheters, target volumes, and OARs obtained from the medical images. Depending on the size and exact location of the target volumes, between 14 and 20 catheters entered the patient’s body, reaching the target volumes. After designing and approving an acceptable treatment plan, the catheters inserted into the patient’s body were connected to a retractor 4 that controls the movement of the radiation source. After the treatment program, the source was returned to the retractor (8, 14). Then, an integer program model with fuzzy constraints was proposed for programming on high-dose brachytherapy. The description of infrastructures, parameters and variables in this model are in Table 2 (15). Finally, the dosimeter index is equal to the sum of all the index variables, as it turned out: The proposed model is a correct programming model called IP.
In general, three evolutionary algorithms (EP), (GA) and (ES) were used in this research. The algorithms stopped after creating 20 generations of desirable answers and the best answer of each generation was determined on the chart as a point. The resulting set of answers were connected in the form of graphs, which are used to analyze the results. Each point on the graph identifies the best answer from each of the generations generated by the respective algorithms. These three algorithms were performed independently for each patient and the obtained answers were identified as dots on the chart. The graph obtained for each patient indicates the capability of each of these algorithms.

According to this study, each of the three algorithms (EP), (GA) and (ES) are each run independently for each of the patients with prostate cancer. At first, the genetic algorithm showed the ability to get closer to the desired answer sooner, but as the optimization process continues, the rate of convergence to the desired answer decreases, so if the time parameter is very important, the genetic algorithm can be useful. Especially for patients whose prostate volume was larger than other patients. In patients 15, 12, 8 and 9, due to their younger age than other patients and better physical condition, as well as prostate volume less than 80 ml, they had much more promising results than other patients. In contrast, for patients 4 and 19 with an age of over 70, the results were not as favorable as for other patients. The * sign in the table indicates that there is no answer through that patient-specific algorithm that covers 95 or even more of the tumor volume. Therefore, according to Table 2, it can be concluded that the best algorithm that can be considered for the case where the shortest time to reach the target coverage above 95% is the genetic algorithm. According to Table 2, it can be concluded that the best algorithm that can be considered for the case where the shortest time to reach the target coverage above 95% is the genetic algorithm. Therefore, according to Table 3, the ES algorithm has better answers than the other two algorithms for the case in which the largest volume of the tumor is covered. According to the results, the ES algorithm has obtained the best results for patients under 60 years of age and normal prostate volume.

According to the obtained results, it can be stated that whether the main goal is the maximum coverage or the goal is the shortest possible time to reach the coverage above 95%, the best algorithm that can get a good answer for each patient is the evolutionary strategy algorithm.