# Design of HIFU Treatment Plans Using Thermodynamic Equilibrium Algorithm
## 3 Results & Discussions
### Application to HIFU
#### 3.2.1 HIFU Treatment Setup  
For the application of TEA to HIFU treatment, realistic parameters and situations were employed. The material properties were established using data from real patients, and the transducer parameters were created using data from a true-to-life HIFU transducer. Simulation parameters were selected using numerical analysis.  
Maps of the material characteristics of the human body were needed to illustrate the suggested algorithm's capacity to develop appropriate treatment regimens. AustinWoman, an open-source voxel model, was used in this case [55]. This is a segmentation of a digital image dataset obtained as a result of the Visible Human Project run by the US National Library of Medicine. The original dataset consists of digital cryosection images with a 0.33 mm pixel spacing of a 59-year-old female corpse taken at 0.33 mm intervals along the axial direction. There are also radiological imaging (CT and MRI) accessible. The AustinWoman segmentation divides the digital image data into 58 material labels, each of which stands for one of the main tissue types in the human body. The distribution of tissue density, specific heat, and thermal conductivity was obtained using the ITIS tissue property database V3.0 [56]. Capillary blood perfusion was solely considered throughout this examination for the purpose of simplicity.  
One thorax target inside the left lobule was utilized for the case study of HIFU therapy planning. The divided section of the body used for treatment planning is shown in Figure 10. The target location is near the center of the breast. \(D\) (target map) at this area is equal to 1 (\(D_{x,y}=1\)) and elsewhere equals to zero (\(D_{x,y}=0\)).  
The HAIFU JC-200's nominal characteristics and a single-element transducer were used to size the heat source [57]. The focusing beam has an oval shape with a diameter of around 19 \(\times\) 2.5 mm, a radius of curvature of 145 mm, an aperture diameter of 200 mm, and a frequency of 0.95 MHz. This dimension was used to calculate the half-maximum full-width ellipsoidal heat source term. The peak rate of heat deposition in space was set to 100 W/cm\({}^{2}\), which is close to the values used in clinical treatments.  
Following the results of numerical convergence testing, the following parameters were included into the numerical thermal model:  
* 495 \(\times\) 495 grid points, discretized simulation domain; periodic boundary condition.
* 0.2 mm of spatial resolution. Linear interpolation was used to upsample the original AustinWoman data.
* 0.1 s temporal resolution.
* The total length of the simulation \(\sum_{i=0}^{N}(t_{on,i}+t_{off,i})\).
* Positions of the ultrasound focus center are limited to the bounding box at grid positions [270, 230] \(\times\)[345, 295].
* Maximum sonication and cooling periods \(t_{on}\) = [0, 5 s], \(t_{off}\) = [0, 20 s].
* Number of sonications considered \(N\in\mathbb{Z}^{+}\).  
The numerical model and the TEA were run in Matlab 2021b. The Matlab Parallel Computing Toolbox was used to parallelize the execution over 16 processor cores.