## 4 Results
### Parameter Estimation  
The parameter estimation was performed by exploiting the SAEM algorithm. To ensure convergence towards a global optimum, an initial exploration phase was carried out using the simulated annealing algorithm: decreasing by 5% the variance of the random effects, and of the residual error parameter between two iterations, guarantees the exploration of a larger parameter space for a reasonable number of iterations. In such a manner, we can explore a larger space by improving the choice of the best starting point for subsequent parameter estimation [36]. The empirical and theoretical distributions of the obtained parameters estimate are reported in Figure 5 for all the parameters of model (6). All the empirical parameter distributions are nicely fitted through log-normal density functions, except for parameter \(b\): in this case, the theoretical distribution exhibits a bimodal trend, which is interpolated by the mixture of two log-normal distributions (dyslipidemic and no-dyslipidemic groups). This bimodality was confirmed by means of [PERSON]'s bimodality coefficient (BC), [40], which resulted as equal to 0.7.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Dyslipidemia Yes** & **Dyslipidemia No** \\ \hline mean & 1.5 & 4.1 \\ \hline std & 2.4 & 5.7 \\ \hline median & 0.62 & 1.8 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean, std, and median of cTnT concentration over the observation interval, for dyslipidemic and non-dyslipidemic patients.  
Figure 4: Time course of the concentration levels of cTnT into the plasma of the 27 STEMI patients, with and without dyslipidemia. Each color is associated with the time series of a different patient.  
Information about the estimated parameters is shown in Table 3, which reports the typical value for the fixed effects, and the standard deviation of the random effects, explicable as the inter-individual variability. The standard error (SE) and the percentage relative standard error (RSE%) are quite limited, implying that the variability in the estimator remains low.  
Such low variability in fixed- and random-effects coefficients, along with the good agreement between experimental measurements and model output (see Figure 6), let us conclude that the proposed mixed-effect model effectively describes the observed inter-individual variability in cTnT release. Figure 6 shows the results of the individual fitting  
Figure 5: Empirical and theoretical distribution of the estimated values for each parameter of the model (6). The distribution for parameter \(b\) clearly exhibits a bimodal trend, confirmed by evaluating [PERSON]’s bimodality coefficient (BC) which for the distribution of the estimated values for parameter b is \(>\)0.5 (0.7).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{Fixed Effects} \\ \hline Parameter & Value & S.E. & R.S.E(\%) \\ \hline \(a_{pop}\) & 0.0361 & 0.00675 & 18.7 \\ \hline \(b_{pop}\) & 0.0986 & 0.0144 & 14.6 \\ \hline \(\beta b_{Dyslip.}\) & 1.16 & 0.241 & 20.9 \\ \hline \(T_{d_{pop}}\) & 193 & 17.9 & 9.26 \\ \hline \(C_{s0_{pop}}\) & 15.1 & 4.3 & 28.4 \\ \hline C\(\alpha_{pop}\) & 23.5 & 7.34 & 31.2 \\ \hline \multicolumn{3}{c}{Standard Deviation of the Random Effect} \\ \hline Parameter & Value & S.E. & R.S.E(\%) \\ \hline \(\omega_{a}\) & 0.682 & 0.165 & 24.2 \\ \hline \(\omega_{b}\) & 0.329 & 0.109 & 33.2 \\ \hline \(\omega_{T_{d}}\) & 0.221 & 0.0611 & 27.7 \\ \hline \(\omega_{C_{s0}}\) & 1.4 & 0.188 & 13.5 \\ \hline \(\omega_{C_{s0}}\) & 1.47 & 0.204 & 13.8 \\ \hline \end{tabular}
\end{table}
Table 3: Fixed and random effects estimated for each parameter. S.E. and R.S.E (%) are reported for both effects.  
for some patients: the reconstructed curves for every single patient are reported in comparison to the population model (red line). The results for all the 27 analyzed patients are shown in Figure S1 in the Supplementary Materials.