## 3 Results
### Evaluation of MLP-Based Model Fitting Reliability  
The second phase of experiments consisted of using the trained MLP network to estimate 2 CFM model parameters, as well as the GFR values for the 20 DCE-MRI examinations available in this study. The statistics of the parameter estimates are summarized in Table 3, whereas the calculated GFR values are collected in Table 4. The reliability of GFR estimation was also evaluated against the ground-truth using the Bland-Altman plot, shown in Figure 11. When compared to Figure 5b, it emerges that the mean biases from the reference values are similar for both optimization methods--MLP and NLLS curve-fitting. However, the limits of agreement \(\kappa\) and confidence intervals are narrower for the neural network. Moreover, our ANNs ensure the better balance of the estimated values around the mean. The NLLS method, on the other hand, tends to overestimate the measured quantity, especially in the lower range of values. On the other hand, in the case of ANN, GFR was estimated without explicit determination of AIF for a given subject. It proves that the designed network was capable of extracting the general characteristics of the underlying perfusion process. From the analysis of Table 3, it emerges that MLP determined \(K^{tmus}\) and \(v_{p}\) parameter values close to those of the reference method. The box plots presented in Figure 12a,b visually illustrate that the ranges of estimated \(K^{tmus}\) and \(v_{p}\) values partially overlap, and their medians are similar. The result of the \(t\)-test gives evidence that the \(v_{p}\) results, as estimated by MLP and NLLS, are not statistically different (\(p\)-value \(>0.3\)), which effectively shows that both methods can be used interchangeably for blood volume fraction assessment. In the case of \(K^{tmus}\), the difference in parameter estimates becomes statistically significant (\(p\)-value \(<10^{-3}\)), although the medians remain relatively close with respect to the overall data variability. Estimates of \(T_{g}\) and \(\Delta\) vary more significantly (cf. Figure 12c,d). The evidence against the null hypothesis of there being equal means in the MLP- and NLLS-based calculations is even stronger than for the \(K^{tmus}\) parameter (\(p\)-value \(<10^{-6}\)). Apparently, the variation in the vascular impulse response function manifests itself in the CA concentration time courses in a way which is less evident in comparison to the other two PK model parameters. As such, the neural network could not precisely infer the relationship between the concentration time curves and the expected \(T_{g}\) and \(\Delta\) values. This effect is consistent with the observed \(R^{2}\) scores calculated on the test set upon MLP training. The VIRF timing factors are remarkably lower than the blood volume fraction and transfer constant. Figure 10: Determination coefficients for two-compartment filtration model (2 CFM) model parameters obtained for various network configurations (test set). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{MLP Estimates} & \multicolumn{6}{c}{NLLS Estimates} & \multirow{2}{*}{ \begin{tabular}{c} **Ground-** \\ **Truth** \\ **(Total)** \\ \end{tabular}