## 3 Results and Discussions
### Implant Materials  
Since the influences of implants on the temperature distribution during ultrasound diathermy can be studied from analytical solutions, another important issue for implants in clinical applications is the selection of implant materials. In recent years, the list of potential materials for surgical implants has been notably expanded. However, the effects of these new implant materials on ultrasound diathermy are still unknown. To enhance the safety in clinical applications, it is important to get more understanding of the responses of ultrasound thermal therapies using new implant materials.  
Five metals (Stainless steel, Tantalum, Titanium alloys, Co-Cr-Mn Alloy, Niobium), one plastic (Polyethylene), and one ceramic implant (Zirconia Oxide), for which material properties are listed in Tables 2 and 3, were selected. These seven implant materials are denoted as 'STE', 'TAN', 'TIT', 'CCM', 'NiO', 'POL', and 'ZO' for short. Typical simulation results for the temperature distribution within the composite specimen, obtained from the analytical solution, are presented in Figures 10 and 11, which correspond to 1 MHz and 3 MHz ultrasound operation frequency, respectively. The duration of the heating process was 30 s. The location of the implant is indicated by dashed gray lines in Figures 10 and 11.  
As observed in Figures 10 and 11, the obtained results show a rising trend when the value of x ranged between 0 and 8 mm. As opposed to the polymer implant, the temperature responses of the metal and ceramic implants were very close when x \(<\) 10 mm. In the case of Polyethylene (POL), the temperature rose considerably in the implant and bone region. The peak temperature of the POL case was above 65 \({}^{\circ}\)C and 125 \({}^{\circ}\)C for 1 MHz and 3 MHz, respectively, at 30 s. Therefore, ultrasound should avoid near polymer implants. Alternatively, the average temperature of the Tantalum (TAN) was under 25 \({}^{\circ}\)C in the bone region, while in the tissue region it was also the minimum. As a result, the use of Tantalum in implants is preferred with regard to ultrasound diathermy. It is worth emphasizing that only thermal responses were considered in this study. One may consider mechanical properties, surface properties, and biocompatibility in clinical performances to determine the optimal implant material.  
Furthermore, to determine which material property has the most influence on the temperature distribution, sensitivity analyses were performed to investigate the effects of five material properties of the stainless steel--density, specific heat, sound velocity, thermal conductivity, and attenuation coefficient--on the temperature distribution during the ultrasound diathermy. Figures 12 and 13 show the temperature distribution along the acoustic axis at 30 s during the ultrasound diathermy, corresponding to 1 MHz and 3 MHz, respectively. Each temperature curve represents an increase of a specific material property to two times that of the stainless steel while keeping other material properties the same as those of the stainless steel. Figures 12 and 13 show that an increase in the attenuation coefficient increases the temperature in the composite system during the ultrasound diathermy. However, the increases in the density and specific heat cause the temperature in the composite system to decrease during the ultrasound diathermy. Finally, the increase of the thermal conductivity seems not to affect the temperature in the composite system during the ultrasound diathermy. The increase of the sound velocity may increase or decrease the temperature in the composite system depending on the ultrasound operation frequency.  
Figure 11: Temperature distribution within the three-layer composite bio-system for various implants at 30 s using 3 MHz ultrasound.  
Figure 10: Temperature distribution within the three-layer composite bio-system for various implants at 30 s using 1 MHz ultrasound.