# Extacorporeal Shockwave Applicator for Spinal Pain and Muscular Contractive: A New Design Approach
## 3 Results  
The results were analyzed from two perspectives. The first one refers to the numeric values obtained from the FEA and the second one refers to the data obtained from the statistical analysis. Stress developed in the soft tissue, when using the lowest dual-tip applicator, ranged between 0.108 and 0.527 MPa. When using the conventional applicator, stress increased by more than 310%, at a maximum value of 1.654 MPa. The same pattern was observed when comparing the contact pressure obtained by the two applicators. The measurements ranged from 2.8 and 9.92 MPa for the conventional applicator to 1.22 and 2.76 MPa for the dual-tip type, thus, the soft tissue recorded lower contact pressures, as much as 580% when using the new applicator. The total strain energy J/m\({}^{3}\) represents the energy that was needed to deform the soft tissue. Due to its nature, which is easily deformable, the values obtained were between 10\({}^{-4}\) and 10\({}^{-5}\) J/m\({}^{3}\). As in the previous cases, higher values corresponded to the conventional applicator, while the lower ones to the dual-tip applicator. The pressure wave propagation velocity followed the same tendency; it was shown that slower propagation velocities resulted when using a large tip distance. The experimental data indicate that the dual-tip design provided up to 130% slower pressure wave propagation velocity, with values in the range of 1.53 and 6.96 mm/s, while the conventional applicator induced speeds up to 15.92 mm/s. Table 3 shows the ANOVA results for each model. Taking into consideration that the p-values for each model were below 0.0001 and that coefficients of determination were above 0.89, we concluded that the model was significant, meaning that the input factors had a strong impact on the responses. For each of the input factors, a Box-Cox analysis was performed and a transformation was recommended \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Name** & **Units** & **Type** & **Levels** & **Level 1** & **Level 2** & **Level 3** \\ \hline Frequency & Hz & Continuous & - & 2 & 14 & - \\ Pressure & bar & Continuous & - & 1 & 6 & - \\ Tip distance & mm & Discrete & 3 & 0 & 40 & 80 \\ Tip shape & - & Nominal & 2 & conventional & dual-tip & - \\ Tip flatness & - & Nominal & 2 & concave & convex & - \\ Material & - & Nominal & 3 & SAE 316 & TifeAl4V & R30075 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Response surface method optimal design matrix. (sst-natural logarithm, cp-inverse square root, tse and wv-square root). Therefore, the equations for each mathematical model are highlighted below in Equations (1)-(4) and expressed accordingly. \[\ln(st_{s})=c_{1}+0.056P-0.0309T_{d} \tag{1}\]  
\[1/\sqrt{c_{p}}=c_{2}+0.0151f-0.0011P+0.0014T_{d} \tag{2}\]  
\[\sqrt{ts_{e}}=c_{3}+0.0004P \tag{3}\]  
\[\sqrt{w_{v}}=c_{4}+0.0076f+0.0194P-0.0296T_{d} \tag{4}\]  
The input factors had a variable influence on the responses. The analysis was orientated through developing a new dual-tip applicator by analyzing the effects this tool had on the soft tissue. Therefore, the graphs from Figure 7; Figure 8 highlight the relevant factors for this design process. High amounts of stresses induced in the soft tissue are specific to low tip distances. Figure 7a indicates that a larger tip distance induced considerably less stress. The optimal tip distance was above 40 mm and the estimated stress was lower than 0.5 MPa. The contact pressure, as shown in Figure 7b, was slightly influenced by the tip distance, however, a contact pressure of 3 MPa was estimated. Figure 8a offers the same positive tendency for the dual-tip applicator, but in this case, the required strain energy was insignificantly small. The velocity of the pressure wave through the soft tissue had average values when using a dual-tip design, with a distance between 40 and 60 mm, as it can be seen in Figure 8b.