# Experimental Analysis of Plantar Fascia Mechanical Properties in Subjects with Foot Pathologies
## 3 Results  
The typical stress-strain response of a PF sample during five loading-unloading cycles is shown in Figure 3, at 10% strain. The comparison of consecutive cycles highlights a decrease of the stress values with the increase in the number of cycles, until stabilization. From the 1 st to the 2 nd cycle, a decrease of 12% of the maximum stress is found. The percentage reduction progressively diminishes below 3% from the 4 th to the 5 th cycle; after that, the mechanical response is considered stable. The experimental results of the 5 th cycle of tensile tests at 10% strain are considered to calculate the mean values of nominal stress P for each subject (Figure 4), comparing Ledderhose disease, diabetes and healthy subjects. PF shows nonlinear stress-strain behavior with increasing stiffness at higher strain levels in both healthy and pathological conditions. Preliminary tensile tests carried out at higher strain levels showed tissue failure at about 11% strain. The elastic modulus can be evaluated at different strain levels for each subject and compared to assess possible differences in PF stiffness among samples from subjects with Ledderhose disease, diabetes and healthy subjects. In this work the secant modulus of different PF samples for each subject at 8% strain is calculated from experimental results of tensile tests and reported in Table 2.  
Figure 3: Mechanical response of a PF sample, in terms of nominal stress P vs. nominal strain \(\varepsilon\), during five loading–unloading cycles at 10% strain. Stress relaxation behavior is shown in Figure 5 for tests carried out at 8% strain, comparing PFs of patients with Ledderhose disease or diabetes and healthy subjects. The values of \(\mathrm{P_{norm}}\) at the end of the stress-relaxation test (t = 300 s) show a stress reduction ranging from 30% to 60% of the initial stress value in subjects with Ledderhose disease, from 41% to 60% in subjects with diabetes and from 33% to 46% in healthy subjects. The values of the secant modulus \(\mathrm{E_{S}}\) at 8% are compared to highlight possible differences among the three groups of involved subjects (Figure 6a). The ANOVA of the secant modulus with the Kruskal-Wallis test shows that there is a statistically significant difference among the three tested groups (\(p\)-value = 0.049). Subsequent multiple comparisons highlight that the elastic modulus of PF is significantly higher in subjects with Ledderhose disease with respect to the healthy group (\(p\)-value = 0.041). To investigate possible differences in the time-dependent mechanical behavior, normalized stress \(\mathrm{P_{norm}}\) at the end of the stress-relaxation test are compared in Figure 6b. The ANOVA with the Kruskal-Wallis test shows a statistically significant difference among different groups (\(p\)-value = 0.028). Subsequent multiple comparisons highlight that the relaxed normalized stress of PF is significantly lower in subjects with diabetes with respect to the healthy group (\(p\)-value = 0.021). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & \\ \hline
**Sample** & **L1** & **L2** & **L3** & **L4** & **L5** & **D1** & **D2** & **D3** & **D4** & **H1** & **H2** & **H3** & **H4** & **H5** \\ \hline
**\#1** & 11.04 & 30.96 & 31.40 & 11.54 & 27.43 & 7.43 & 21.83 & 14.62 & 26.37 & 11.82 & 14.02 & 8.78 & 9.87 & 6.75 \\
**\#2** & 17.04 & 17.91 & 19.75 & 19.18 & 26.32 & 16.60 & 9.05 & 8.55 & 23.73 & 10.52 & 13.85 & 14.43 & 18.70 & 9.99 \\
**\#3** & 6.79 & 25.93 & 14.11 & 13.70 & 8.79 & 11.60 & 7.75 & 25.17 & 11.93 & 10.70 & 9.72 & 8.42 & 10.28 & 13.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Secant modulus \(\mathrm{E_{S}}\) of different PF samples for each subject at 8% strain from experimental results of tensile tests. Figure 4: Results of tensile tests for PF of subjects with Ledderhose disease (**a**), diabetes (**b**) and healthy subjects (**c**). The results are reported in terms of nominal stress \(\mathrm{P}\) (mean values \(\pm\) SE) vs. nominal strain \(\varepsilon\).