Sculpt & Shape^® (Sinclair, Spain) is a non-invasive RF device for skin tightening, body contouring and cellulite treatments. Among others, this device is equipped with three tips ( Figure 1 ), whose technical characteristics are detailed in Table 1 .

The RF tips include a 360˚ rotating technology to provide homogeneous heating and massage the tissue. The rotation speed for all electrodes is 40 rpm. Likewise, the target skin temperature can be configured between 39˚C and 45˚C for five treatments (wrinkles, facial skin tightening, body skin tightening, cellulite, and body shaping). A real-time temperature and impedance measurement system regulates RF power to achieve the target temperature and maintain it until the end of the treatment, or temporarily cut off the power delivery in the event of no contact between the skin and the electrode.

The RF tips were modeled, simulated and optimized using COMSOL Multiphysics^® software (version 5.4, COMSOL Inc., Burlington, MA). The tips had been designed previously with SolidWorks^® software (SolidWorks Corp., Massachusetts) and then imported to COMSOL Multiphysics. Several iterations of testing and improvement were performed. This study shows the final version of the design.

The simulations recreated the application of RF electrical currents to a specific area of the body with rotational movements.

The meshed geometrical domains consisted of the biological tissues (dermis and adipose tissue) and the RF tip in contact with the tissue ( Figure 2 ). The thickness of the skin and fat layers were 2.75 and 46.25 mm, respectively, for monopolar electrodes, and 4 and 51.5 mm for bipolar electrodes.

To present the results of the thermal maps, the XY-plane cut ( Figure 2 ) was employed to determine the depth of heat penetration into the tissue and the XZ-plane cut ( Figure 2 ) was used to show the superficial heat on the tissue.

The tips incorporate a rotating movement, which is implemented in the simulations through a deformed geometry feature. However, the translational movement that the operator would perform on the body area was not implemented.

The equations used for the numerical simulations (dynamic electric currents, electrostatics, electromagnetic heating and bioheat transfer module) are included in Section 1.1 Supplementary Information (SI). Additionally, this section incorporates tables indicating the thermal parameters of the tissues and materials ( Table S1 ), the electrical parameters of the tissues and materials ( Table S2 ), and the thermal and perfusion parameters of the blood ( Table S3 ).

All information is provided in Section 1.2 SI.

All information is provided in Section 1.3 SI.

The simulated results of heating inside the tissue (XY planes in Figure 2 ) were compared with the results obtained with pig tissue ( Figure S1 ). Pork belly pieces without the superficial skin and with an initial temperature of 15˚C to 20˚C were used.

The pieces of pig tissue were measured and cut to ensure uniform size and thickness. In addition, the pieces used with the bipolar electrode were sliced in half to compare the same plane as the simulations. A thin layer of glycerin gel¹ was spread across the surface of the tissue touching the RF tip to improve contact.

The monopolar electrodes were evaluated in rotating mode. However, the bipolar electrode was used without rotation to avoid damaging the pig tissue during the test.

Thermal measurements were taken using a Ti200 infrared thermal imaging camera (Fluke Corp, Washington). It was placed in front of the tissue that was used to obtain cross-sectional temperature maps and determine the depth of heat penetration inside tissue. The experiments were performed at room temperature and carried out by the same person to avoid variations in the force applied to the tissue. A minimum of five independent experiments were conducted.

Thermal images were analyzed using Fluke Connect software (Fluke Corp, Washington). An isotherm area of 5˚C under the maximum temperature was considered to calculate the penetration depth of the heat inside the pig tissue. ImageJ software (National Institutes of Health, Maryland) was employed to convert pixels on the thermal image into millimeters of tissue. Data analysis was performed using Microsoft Excel 365 (Microsoft, New Mexico) and data were presented as Mean ± Standard Deviation.

The simulated results for surface heating (XZ planes in Figure 2 ) were compared with the results obtained from skin heating measurements conducted on facial and corporal areas. A total of 6 facial areas were heated with the monopolar Shine tip, 9 facial areas with the monopolar Firm tip, 10 corporal areas with the Sculpt6 tip at 0.5 MHz, and 9 corporal areas with the Sculpt6 tip at 1 MHz. All subjects who participated in the study were previously briefed and signed a consent form.

The skin was cleaned with mild soap and water. A thin layer of glycerin gel was then applied. No topical anesthesia was applied before the treatment. The target temperature was 42˚C. During the test, the handpiece was constantly moved in a uniform pattern to achieve a homogeneous heat while remaining in full contact with the body area being treated.

All tips have an internal infrared sensor that measures the temperature in real time. The data obtained was stored in the device’s memory and later extracted for analysis.

The times taken to reach the set temperature were compared. The sets of values obtained for each case were compared with the results obtained from the corresponding simulation.

The inclusion criteria included males and females between 18 and 75 years old with concerns about skin laxity, wrinkles, cellulite, or localized fat. Specific exclusion criteria included active dermatological disease or infectious processes in the treatment area; pregnancy; breastfeeding; implanted electronic devices; blood disorders or the use of blood-thinning or antiplatelet medications; a history of active or recent neoplastic malignancy; heat-stimulated conditions and orthopedic surgery such as replacement of the hip, femur, etc.

A total of 16 subjects (14 women and 2 men) were willing to be treated for skin tightening, body shaping, wrinkles, and improvement of the appearance of cellulite in sessions performed on both sides of the face, the neck, the décolletage, the abdomen, the legs, the buttocks, and the flanks. A total of 78 areas underwent treatment. 31 areas were treated with the Sculpt6 tip to address cellulite reduction and body shaping, 25 areas were treated for skin tightening using the Firm tip, and 22 areas were treated for wrinkles with the Shine tip.

Subjects were not required to follow a special diet or exercise plan. Prior to treatment, all subjects received a detailed and clear explanation of the planned procedure and signed an informed consent form. The complete confidentiality of the subjects’ data was guaranteed throughout the entire process.

Anthropometric data (sex, age, body weight and height) were recorded. Photographs at 45˚ and 90˚ angles, as well as frontal and lateral views of the treatment area, were taken at every visit before starting the procedure.

Glycerin gel was applied to the treatment areas and no anesthesia was required. The applicator was continuously moved according to the direction of the lymphatic system to achieve homogeneous and gradual heating of the area while maintaining contact with the skin. The target temperature for the treatments was determined to be between 43˚C and 45˚C, depending on the subject’s tolerance. The device automatically regulated the RF power to maintain a constant temperature throughout the treatment.

Treatments were performed every 1 or 2 weeks. Facial sessions lasted between 12 and 40 minutes, while body sessions, depending on the areas treated, lasted between 20 and 60 minutes. Details of the clinical treatments are shown in Table S4 . All treatments were performed in accordance with the treatment tables recommended by the manufacturer.

Improvements in the appearance of skin texture and body contouring compared to baseline photographs were rated by three blinded and experienced researchers, who carried out the evaluation on each pair of pre- and post-treatment photographs. The Global Aesthetic Improvement Scale with a 0 to 4 range (0 = no improvement; 1 = mildly improved; 2 = improved; 3 = much improved; 4 = very much improved) was used. Likewise, subject satisfaction was evaluated on a 0 to 3 scale (0 = unsatisfied; 1 = low satisfaction; 2 = satisfied; 3 = very satisfied) 1 month after the last treatment.

Also, the safety was evaluated by asking the patients their perception of pain/heat during the treatment, through a scale with a 0 to 10 range (0 no pain, 1-4 mild pain, 5-7 moderate pain, 8-10 severe pain). Adverse effects are also reported during each session.

A student’s two-tailed paired t-test was applied to assess the statistical significance of the efficacy evaluation. A probability value of 95% (p < 0.05) was considered statistically significant. Data were analyzed using Microsoft Excel 365.

The thermal images taken of the skin of a subject during a real treatment were shown to be very similar to the simulation of the rotating tips. However, in the case of the Firm applicator, due to its rectangular shape, the absence of rotation generated a rectangular thermal image, which is transformed into circular heating when the tip rotates ( Figure 3 ).

The temperature scales may differ between simulation and real treatment due to the difference between the initial values of the skin and ambient temperatures.

The heating inside the tissue has also been found to be very similar between the tests carried out with pig tissue and the simulations ( Figure 4 ). An isotherm of 5˚C, from 44˚C to 39˚C (thin black line in the simulations) was drawn to calculate the heat penetration depth ( Table 2 ).

The effect of rotation is more notable in the case of the bipolar tip. Without rotation, all the heat is concentrated under the electrodes, while rotation homogenizes the heat under the tip ( Figure 5 ).

The effect of frequency with the bipolar applicator is shown in Figure 6 . The penetration depth simulated for 0.5 MHz was 25.00 mm, and for 1 MHz it was 20.15 mm.

Ex-vivo tests with pig tissue could not be performed with rotation because the tissue was damaged and did not allow for reliable results. Without rotation, heating was concentrated under the electrode ( Figure 7 ), as shown by the tests conducted on the surface ( Figure 5 ). Qualitatively, a greater penetration depth was also observed with the lowest frequency of 0.5 MHz.

Figure 8 compares the times required by each tip to reach the set temperature (42˚C for these tests), which were obtained from the simulations and in tests with subjects. For each tip, a set of in-vivo tests was

performed to provide a statistic which is compared with the single value obtained in the simulation. Monopolar electrodes took around 30 s to reach 42˚C, and about 100 s for bipolar one.

All subjects completed at least 7 sessions of RF treatments, with an average treatment time of 18 minutes for facial treatments and 40 minutes for body treatments; the treatment temperature range was 42 to 44˚C. Information related to the treatments and the characteristics of the subjects is presented in Table S4 . Before and after images of representative treatments are shown in Figure 9 .

The clinical investigators’ assessment using the GAIS resulted in a score of 1.83 out of 4, which is a 25% - 49% improvement over baseline. Moreover, subject satisfaction after 1 month was evaluated through personal questionnaires, which reported a value of 2.50 out of 3 (between satisfied and very satisfied). No side or adverse effects were reported.

The subjects rated the heat/pain experienced from the heating during the treatment at 6.6 ± 1.1 on a scale of 1 to 10. Minor adverse effects were observed, such as mild superficial first-degree burns (which disappeared within a few days) resulting from sparks due to the tip losing contact with the skin during treatment sessions. No major adverse effects were reported.

As previously mentioned, COMSOL Multiphysics^® Software was used to solve both the heat transfer and electrical equations employed in these models. To study the interaction between the currents produced by RF and the tissue (dermis and adipose tissue), four physics are used: dynamics of electric currents, electrostatics, electromagnetic heating, and heat transfer in biomaterials.

1) Equations for Dynamic Electric Currents

In the frequency domain (AC current mode) and time dependent study types, dynamic formulas accounting for both conduction and displacement currents are used.

Combining the time-harmonic equation of continuity (1) with Equation (2) and generalizing to handle current sources, yields the following Equation (3):

$\nabla \cdot J=\nabla \cdot \left(\sigma E+J_e\right)=-j\omega \rho$ (1)

$\nabla \cdot D=\rho$ (2)

$-\nabla \cdot \left(\left(\sigma +j\omega {\epsilon }_0\right)\nabla V-\left(J_e+j\omega P\right)\right)=Q_j$ (3)

where J is the current density, σ is the electrical conductivity, E is the electrical field, J_e is the external current density, j is the imaginary number, ω is the frequency used, ρ is the charge density, D is the electric flux density, ε₀ is the vacuum permittivity, V is the electric potential, Q is the charge and P is the electric polarization vector.

For the transient case, using the transient equation of continuity (4) and generalizing to handle current sources, the resulting equation becomes (5):

$\nabla \cdot J=\nabla \cdot \left(\sigma E+J_e\right)=\frac{\partial \rho }{\partial t}$ (4)

$-\nabla \cdot \frac{\partial }{\partial t}\left({\epsilon }_0\nabla V-P\right)-\nabla \cdot \left(\sigma \nabla V-J_e\right)=Q_j$ (5)

2) Electrostatics Equations

Under static conditions, the electric potential, V, is defined by Equation (6). By combining this equation with the constitutive relationship (7) between the electric displacement D and the electric field E, it is possible to represent Gauss’ law as the following Equation (8):

$E=-\nabla V$ (6)

$D={\epsilon }_{0}E+P=\epsilon E={\epsilon }_0{\epsilon }_{r}E$ (7)

$-\nabla \cdot \left({\epsilon }_0\nabla V-P\right)=\rho$ (8)

This equation describes the electrostatic field in dielectric materials.

3) Electromagnetic Heating

The Electromagnetic Heating represents the electromagnetic losses, Q_e. This electromagnetic heat will be the heat source used in the heat transfer equation, coupling the electric equations with heat transfer in biomaterials. It is determined by (9):

$Q_e=Q_{rh}+Q_{ml}$ (9)

where the resistive losses Q_rh are defined as (10) and, in this case, magnetic losses Q_ml are equal to zero.

$Q_{rh}=\frac{1}{2}Re\left(J\cdot E^{*}\right)$ (10)

where J is the current density and E is the electrical field.

4) Bioheat transfer module

The heat transfer equation for biomaterials is defined as (13) using (11) and (12):

$\rho C_p\frac{\partial T}{\partial t}+\nabla \cdot q=Q_e+Q_{bio}$ (11)

$q=-k\nabla T$ (12)

$Q_{bio}={\rho }_b{C}_{pb}{\omega }_b\left(T_b-T\right)+Q_{met}$ (13)

where ρ is the density of the tissue, C_p is the specific heat capacity of the tissue at constant pressure, k is the thermal conductivity of the tissue, T is the absolute temperature of the tissue, q is the heat flux by conduction in the tissue, ρ_b is the blood density, C_p,b is the blood-specific heat capacity at constant pressure, ω_b is the blood perfusion rate, T_b is the arterial blood temperature, Q_met is the metabolic heat source and Q_e is the heat source provided by the electromagnetic heating.

To solve the equations, the thermal and electrical parameters of each of the tissues that make up the area to be treated must be known, as well as those of the materials used to manufacture the RF tips. The monopolar tips are capacitive electrodes fabricated from a resistive material (Aluminum 6082) but covered with a thin layer of an insulating material (Anodized Aluminum), thus, in addition to electrical resistance they also have a high electrical capacity. The bipolar tips are resistive electrodes made of a material that only has electrical resistance (Steel AISI 4340).

The thermal ( Table S1 ) and electrical ( Table S2 ) parameters of the tissues and materials used are shown, in addition to the thermal and perfusion parameters of the blood in the tissues ( Table S3 ).

Thermal and electrical boundary conditions were established.

With regard to the electrical boundary conditions, first, the surfaces of application of an electric potential (electrodes) and the return surface (V = 0) can be distinguished. For a monopolar tip, the electrical potential application surface is the electrode surface, and the return surface is through a passive plate (for simplicity, a plane at infinity has been considered). In the case of the bipolar tip, the electrical potential application surface is the surface of one electrode row, and the return surface is the other row of electrodes. As an electric current source, a potential is applied. The equipment does not apply a specific power, but a potential difference, which, depending on factors such as the impedance adaptation or the electrical impedance of the tissue to be treated delivers a specific electrical power. The electrical power delivered heats the tissue depending on its electrical characteristics. Secondly, it is necessary to simulate the tissue edges. In this case, they are approximated by an infinite distance (infinite domains) to simulate that an electric current is applied to a tissue of dimensions much larger than the dimensions of the applicator. Lastly, all other external surfaces involved in the simulation are considered isolated from the outside, since in principle they are in contact with the air. The electrical initial conditions are 0 V in all the studied materials.

Regarding the thermal boundary conditions, the initial temperature for biological tissue was set at 36˚C (body temperature) and the surface of the electrode at a temperature between 27˚C and 29˚C, taken from the experiments carried out with the different electrodes. All other exterior surfaces are considered thermally insulated, which means that there is no heat flow in their contours. The heat source is the electric current that flows through the tissue. Therefore, it is a source of heat by volume, and is the result of the application of the electrical module on the biological tissue.

Four mesh structures were used: extra fine for the contact surface between the dermis and electrodes, very fine for the dermis, fine for the electrodes and coarse for the adipose tissue.