# Extacorporeal Shockwave Applicator for Spinal Pain and Muscular Contractive: A New Design Approach
## 2 Methodology for the Statistical Data Interpretation and Finite Element Analysis
### Predesign of the Applicator and Finite Element Analysis Methodology  
This challenge implied undergoing an investigation of the mechanics of the shockwave process, skin mechanical reaction, applicator design, and process parameters. Understanding the full extent of the process allowed us to perform a finite element analysis (FEA) by using various process conditions. The results were analyzed statistically and consequently, the conclusions were drawn regarding the efficiency of the new applicator and the possibility of machining it by metal cutting techniques. The starting point of this experimental study was a conventional shockwave applicator, made out of stainless steel (SAE 316). In Figure 5a, it can be noted that the applicator has three distinct zones: the impact of the projectile takes place in zone I; zone II is designed for fixture purposes, while zone III is designed as a 15 mm diameter cylinder having a convex or concave 55 [mm] radius. This part comes in direct contact with the skin. Before performing any experimental study, we had proven, based on practical experience, that this part has to be perpendicular to the skin, for maximum treatment efficiency. This assumption was necessary for simulation orientation and final design purposes. Figure 3: Schematic representation of a ballistic shockwave source, adapted from “Extracorporeal Shockwave Therapy” by [PERSON] & [PERSON], 2007 [21]. Figure 2: Dual-tip shockwave applicator design steps. Computer-aided design and FEA were made using the SolidWorks 2019. A total number of six concave and convex applicators had been conceived. The predesign of the dual-tip applicator is shown in Figure 5b and was used for the finite element analysis. The distance between the applicator tips was the essential part of this study as it had to satisfy the distance between the spinal muscles, which varies by gender, age, and body fat [25], therefore, this distance was set between 40 and 80 [mm]. The tip flatness was designed either concave or convex, as this feature may influence the wave dissipation (radial or focused). Since they are known to be widely used in the medical equipment industry, three common materials were analyzed: stainless steel SAE 316, titanium alloy Ti6 Al4V, and cobalt-chrome alloy R30075. The alloys' mechanical data used within the finite element analysis are shown in Table 1.  
Figure 4: Shockwave propagation through the soft tissue to the spinal cord; simulation using finite element analysis; (**a**) indicates the location where the analysis was performed; (**b**) indicates the area of interest of the spinal cord; (**c**) shows a conventional applicator in direct contact with soft tissue and the induced shockwaves propagation [23]. Figure 5: Conventional (**a**) and predesigned dual-tip (**b**) shockwave applicator schematic representation and dimensions in milimiters. Taking into consideration the technical data in the field of human skin mechanical properties, the soft tissue thickness was set to 5 mm [26; 27]. This was necessary to understand how the soft tissue reacts and how the applicator shape influences the shockwave propagation. Thus, for the applicator, a linear elastic isotropic model was applied, as highlighted in Table 1, while for the soft tissue, a hyperplastic material that imitates human skin was defined using the Mooney-Rivlin model, with the constants C\({}_{01}\) = C\({}_{10}\) = 0.1 MPa, Poisson's coefficient \(\
u\) = 0.48, and density \(\rho\) = 1020 kg/m\({}^{3}\)[26; 27; 28; 29]. The assembly of the applicator and soft tissue implied placing them in direct contact, tangent by the tip radius, as shown in the left side of Figure 6. The soft tissue was fully fixed, while the applicator could move only in the vertical direction. The finite element simulation was performed by using a nonlinear dynamic 2D analysis. The connection between the applicator and the soft tissue had been defined by two contact sets, with no penetration conditions.