## 5 Poromechanics Test Results and Fittings
### Creep Test Results--Fractional Porelastic Model  
Focusing on confined compression tests, we specifically measured the decrease in weight of the cylinder during the tests and correlate this data to the amount of fluid discharged by the samples \(j_{f}\) during the test. We now illustrate the best-fitting procedure performed between the proposed model in Equation (26) and the experimental results as shown in Figure 4a-f for a few samples taken from one of the three lateral menisci.  
In particular, three free parameters are considered: \(\beta,\tilde{\lambda}\), and \(\lambda_{\beta}\). We perform the best-fitting procedure for a time window extended from t 0 to 450 s. \(\gamma=0.695\) was fixed by considering specific mechanical parameters, which are summarized in Table 4.  
\begin{table}
\begin{tabular}{l l} \hline Bulk modulus & K = 1.6 \(\times\) 10\({}^{5}\) Pa \\ \hline shear modulus & G = 76,923 Pa (\(E=0.2\times 10^{6}\) Pa, \(\
u=0.3\)) \\ \hline Skempton coefficient & B = 0.88 \\ \hline Biot coefficient & \(\alpha=0.65\) \\ \hline Undrained bulk modulus & \(K_{u}=\) K/1 \(-\alpha\) B \\ \hline \end{tabular}
\end{table}
Table 4: Material parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Ramp Amplitude**} \\ \hline
**Sample** & **Step** & **(\% Height)** & **H\({}_{\mathbf{A}}\) (MPa)** & **k (m\({}^{4}\)/s \(\times\) N)** & **RMSE** \\ \hline \multirow{6}{*}{TK11-CB-Circ} & 1 & 2 & 0.180 & \(0.858\times 10^{-12}\) & 0.0003 \\  & 2 & 4 & 0.135 & \(2.803\times 10^{-12}\) & 0.0002 \\  & 3 & 6 & 0.032 & \(0.410\times 10^{-12}\) & 0.0011 \\  & 4 & 8 & 0.122 & \(0.953\times 10^{-12}\) & 0.0004 \\  & 5 & 10 & 0.058 & \(1.714\times 10^{-12}\) & 0.0004 \\ \hline \multirow{6}{*}{TK11-CB-Rad} & 1 & 2 & - & - & - \\  & 2 & 4 & 0.044 & \(1.572\times 10^{-12}\) & 0.0005 \\  & 3 & 6 & 0.007 & \(3.383\times 10^{-12}\) & 0.1533 \\  & 4 & 8 & 0.037 & \(0.870\times 10^{-12}\) & 0.0003 \\  & 5 & 10 & 0.030 & \(0.525\times 10^{-12}\) & 0.0008 \\ \hline \multirow{6}{*}{TK11-CB-Vert} & 1 & 2 & 0.0173 & \(1.0190\times 10^{-12}\) & 0.0023 \\  & 2 & 4 & 0.0116 & \(0.9400\times 10^{-12}\) & 0.0100 \\ \cline{1-1}  & 3 & 6 & 0.0126 & \(0.8100\times 10^{-12}\) & 0.0120 \\ \cline{1-1}  & 4 & 8 & 0.0230 & \(0.4760\times 10^{-12}\) & 0.0025 \\ \cline{1-1}  & 5 & 10 & 0.0173 & \(0.4850\times 10^{-12}\) & 0.0080 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Complete set of the five-step test results of the central portion of the medial meniscus shown in Figure 3 for the three directions (vertical, radial and circumferential). Note that the expected trend of decreasing permeability with increasing strain was visible only for the vertical direction (TK11-CB-Vert). The root mean square error (RMSE) values are high in some cases showing that the model does not always fit the experimental behaviour.  
The values of the parameters obtained through the fittings are reported in Table 5. For samples extracted in the anterior/central/posterior and in vertical, radial and circumferential direction as shown in Figure 5.  
Figure 4: Evolution of the decrease in weight during the confined compression test, which was correlated with the amount of the fluid discharged upon compression of the tissue. The fittings relation is given in Equation (26). The graphs shown are related to samples extracted from a lateral meniscus (tk16). (**a**) Sample from the central body (B) and along the circumferential direction (C). (**b**) Sample from the posterior horn (P) and along the radial direction (R). (**c**) Sample from the central body (B) and along the vertical direction (V). (**d**) Sample from the posterior horn (P) and along the vertical direction (V). (**e**) Sample from the central body (B) and along the radial direction (R). (**f**) Sample from the anterior horn (A) and along the radial direction (R).