Numerical study of high‐intensity focused ultrasound (HIFU) in fat reduction

Abstract Introduction This study aimed to investigate the effect of fat‐layer thickness and focal depth on the pressure and temperature distribution of tissue. Methods Computer simulations were performed for the skin–fat layer models during high‐intensity focused ultrasound (HIFU) treatment. The acoustic pressure field was calculated using the nonlinear Westervelt equation and coupled with the Pennes bioheat transfer equation to obtain the temperature distribution. To investigate the effect of the thickness of the fat layer on pressure and thermal distributions, the thickness of the fat layer behind the focal point (z = 13.5 mm) changed from 8 to 24 mm by 2 mm step. The pressure and temperature distribution spectra were extracted. Results The simulated results were validated using the experimental results with a 98% correlation coefficient (p < 0.05). There was a significant difference between the pressure amplitude and temperature distribution for the 8–14 mm thickness of the fat layer (p < 0.05). By changing the focal point from 11.5 to 13.5 mm, the maximum acoustic pressure at the focal point increased 66%, and the maximum temperature was 56%, respectively. Conclusion Considering the specific treatment plan for each patient, according to the skin and fat layer thicknesses, can help prevent side effects and optimize the treatment process of HIFU.


INTRODUCTION
For many years, liposuction was the only treatment for body contouring, which, like other surgical procedures, is not without its complications. As a result, the number of noninvasive methods for removing unwanted fat has increased significantly. There are several methods adjacent tissues and the concentration of heat in the focal area as well as the minimum recovery time. An imaging system could be combined with therapy, and this combination technology has made coagulation procedures more reliable and practical. Minor inflammation and bruising due to the mismatch of ultrasonic waves between the transducer and the skin are among the limitations of this method. Various fat-loss devices have been suggested, some of which like LipoSonix have been approved by the FDA. 13 There are two mechanisms for HIFU waves that lead to the destruction of adipose tissue. One is the mechanical effects that immediately disrupt cell membranes. The mechanical ultrasound wave travels through the adipocytes, creating cycles of increased and reduced pressure, which draw gas out of the solution in the form of bubbles. When these bubbles implode, they release energy, causing further mechanical damage to the targeted adipocytes. 10,11 In addition, the other is heat that destroys excess fat cells. [14][15][16] In this study, the thermal aspect of HIFU is studied.
HIFU causes rapid heating to temperatures exceeding the upper limit of protein denaturation, resulting in coagulative necrosis. As a result of heat, the temperature at the focal point reaches above 58 • C, leading to immediate cell death in the target area. This destruction occurs when adjacent tissues remain intact. Following HIFU treatment, dead cells induce wound healing and invasion of macrophages and other cells, and lipid uptake and transfer from remote areas. Most fat cell destruction occurs within the first 12 weeks after treatment and 95% localized fat cell destruction within the first 18 weeks after treatment. These changes occur without a significant increase in blood plasma lipids. The large flood of cells to heal the wound will absorb the inflammatory cells and then increase the fibroblasts. This process, by heat-denaturing collagen, generates new collagen along with skin lift. 8,9,17 HIFU is a method of noninvasive tissue heating and ablation currently used for treating a variety of disorders, including shock wave lithotripsy, uterine fibroids, and solid tumors (prostate cancer, breast cancer, pancreas, tumors Brain, etc.) has been considered. 18 Due to the widespread use of HIFU transducers in cancer treatments, numerous numerical studies have been conducted to optimize the process of HIFU treatment and to investigate the effective parameters in HIFU thermal distributions. [19][20][21] But numerical studies have not been reported for cosmetic HIFU treatment, including rejuvenation and fat reduction. In this study, due to the high nonlinear coefficient of adipose tissue and the nonlinear propagation of ultrasonic waves, by increasing the thickness of the subcutaneous fat layer, the pressure and temperature distribution in the focal area was calculated. For calculated acoustic pressure, the Westervelt equation was used. Using the Pennes bioheat transfer equation (BHTE) temperature distribution was obtained at any point. The effect of the thickness of the patient's fat layer on the selection of the focal depth and the ultrasonic transducer with the appropriate focal length was investigated. In this study, the need for a specific treatment plan for each patient according to the thickness of the fat layer was emphasized. Choosing the appropriate physical parameters of the transducer, such as input acoustic intensity, probe cross section, and sonication time for choosing optimal focal length to reduce treatment time is essential.

MATERIALS AND METHODS
The simulation was performed using the Multiphysics Simulation software (COMSOL; V. 5.3, COMSOL Co., Stockholm, Sweden).

Physics theory
In this study, an acoustic module was used to calculate acoustic pressure. To obtain the acoustic pressure, the nonlinear propagation equation (Westervelt) of the ultrasonic waves is used. The following full-wave Westervelt equation, which is based on the effects of diffraction, absorption, and nonlinear propagation, is used [19][20][21][22][23][24][25] : where p, c, ρ, and δ are the acoustic pressure, speed of the sound propagation in the medium, density, and the diffusivity of sound (Equa- where indices t and b are tissue and blood parameters, respectively.
w b and Q are the blood perfusion rate and external heat source, respectively. Q represents the volumetric heat generation due to the absorption of acoustic intensity in the tissue domain and can be calculated by the following equation: where α and P rms are the absorption coefficient of tissue and root mean square (rms) of acoustical pressure. 27

Model geometry
The where Z mat is the medium impedance, in which the boundary condition is imposed on the boundary of that medium. ⃗ n is a normal vector of a surface. The initial conditions for the acoustic equations are p = 0 and TA B L E 1 Physical properties of the two layers of skin, fat, and also, water as matching layers 29 = 0, and the initial condition for solving the heat transfer is defined as T = T 0 = 310 K.

Meshing
Mesh size, in which the equation is solved, should be small enough to take into account the peak and subdivisions of the wave to accurately calculate the propagation of a wave during the medium.
Therefore, an ultrasonic transducer has to be divided into several elements. The longer the transducer area is divided into more elements, the better the wavelength resolution would be. Here, the elements are considered to be smaller than one fourth of the wavelength (λ/4), and the focal size is also considered to be λ/ 8 Figure 1C.
The numerical solution method in this study was validated using experimental results obtained from Kim et al. 38 An HIFU probe was placed in a chamber filled with water (18 • C) that can move by a stepping motor. The irradiation time was less than 40 ms with a 3 s total time. The probe stops at given intervals and emits a 4 MHz focused ultrasound and a 9 mm focal length. The tissue-mimicking phantom was fabricated using 10% carrageenan gel, which has ultrasonic characteristics similar to human tissue. The temperature distribution in the phantom was observed using thermochromic films.
In the experimental study conditions (9 mm focal length, 21 W input power, 4 MHz frequency, and the same phantom's physical parameter), modeling is done. The results of temperature changes in terms of the depth of the simulation and experimental data were analyzed by Pearson's correlation analysis and estimated at a 95% confidence level (p < 0.05).  Table 2. The maximum pressure and temperature occurred at the focal point.

Increasing the fat thickness
An increase in fat thickness has no effect on the focal point location

Pressure and temperature distributions with changing the focal length
At constant physical conditions (30 W/cm 2 intensity, 16 mm aperture diameter) and 8 mm fat thickness, the focal length was changed. By changing the focal length from 13.5 to 11.5 mm, the acoustic pressure (MPa) contours, rms pressure (MPa) on (z-r) plane, are plotted in temperature ( • C) contour at 1 ms sonication time (for ROC = 11.5, 13.5 mm) is plotted in Figure 8. With decreasing focal length and the ROC from 13.5 to 11.5 mm (8 mm fat thickness), the maximum temperature at the focal point has increased from 40.2 to 62.9 • C ( Figure 8A,B).
The temperature on the skin has also risen (from 39.2 to 57.0 • C) ( Figure 8C,D). This result emphasizes the need to be careful in choosing the type of treatment plan and the focal length to prevent skin burns.  Park et al. 13 discussed the impact of treatment parameters on outcomes and side effects. The target depth is defined as 4.5 and 6 mm, which is equal to that of the thermal coagulation point (TCP) depth.

DISCUSSION
Exposures of HIFU were performed at the same power settings (35 W) and 90 ms exposure times. Porcine tissues were examined. They also observed coagulated tissue and measured the width, height, and depth of the TCP. In porcine muscle, TCP was measured 130% deeper compared with the preselected penetration depth. The thermally injured Acoustic pressure (MPa) contour in (r-z) plane (mm) with a radius of the curvature of (A) 13.5 mm and (B) 11.5 mm; acoustic pressure (MPa) in axial direction (z) (mm) with a radius of the curvature of (C) 13.5 mm and (D) 11.5 mm; root mean square of pressure (MPa) contour in (r-z) plane (mm) with a radius of the curvature of (E) 13.5 mm and (F) 11.5 mm area in the fat layer was approximately six times larger with 4.5 mm HPs compared to the skin exposed to 6.0 mm HPs under the same con-

CONCLUSION
HIFU is a modern, nonsurgical alternative to operative facial rejuvenation and body contouring. HIFU treatment has shown statistically significant effects on removing unwanted fat and cellulite.
The results in our simulation showed a change in the focal length of the transducer and thickness of a fat layer of the patient; it can be very effective in treating the output. Therefore, it is necessary to provide a treatment plan. Thus, HIFU parameters should be optimized to reduce the treatment time, damage to the surrounding normal structures, and to ensure the safety and efficacy of this modality. Our numerical model can simulate the acoustic and thermal field of HIFU waves with high computational accuracy. Optimization of HIFU treatment planning is feasible to enhance efficacy and safety. Experimental results confirmed this numerical model.

ACKNOWLEDGMENT
This study was approved by the Faculty of Medical Sciences, Tarbiat Modares University.