## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Wearable Device**} & \multicolumn{3}{c}{**Reference Instrumentation**} \\ \hline
**Subject** & **TV (L)** & \(\widehat{\mathbf{TV}_{\text{WD}}}\) **(L)** & \(R^{2}\) **(adi)** & \(\rho\) **(adi)** & \(\widehat{\mathbf{TV}_{\text{REF}}}\) **(L)** & \(R^{2}\) **(adi)** & \(\rho\) **(adi)** \\ \hline
1 & 2.5 \(\pm\) 0.8 & 2.6 \(\pm\) 0.4 \({}^{*}\) & 0.66 & 0.91 \({}^{\lx@sectionsign}\) & 2.6 \(\pm\) 0.5 \({}^{*}\) & 0.66 & 0.94 \({}^{\lx@sectionsign}\) \\ \hline
2 & 2.9 \(\pm\) 0.7 & 2.4 \(\pm\) 0.3 \({}^{*}\) & 0.75 & 0.75 \({}^{\lx@sectionsign}\) & 2.2 \(\pm\) 0.4 \({}^{*}\) & 0.78 & 0.83 \({}^{\lx@sectionsign}\) \\ \hline
3 & 2.7 \(\pm\) 0.6 & 3.0 \(\pm\) 0.6 \({}^{*}\) & 0.65 & 0.97 \({}^{\lx@sectionsign}\) & 3.1 \(\pm\) 0.6 \({}^{*}\) & 0.68 & 0.98 \({}^{\lx@sectionsign}\) \\ \hline
4 & 2.8 \(\pm\) 0.5 & 3.0 \(\pm\) 0.4 \({}^{*}\) & 0.69 & 0.69 \({}^{\lx@sectionsign}\) & 3.0 \(\pm\) 0.4 \({}^{*}\) & 0.69 & 0.76 \({}^{\lx@sectionsign}\) \\ \hline
5 & 2.4 \(\pm\) 0.5 & 2.4 \(\pm\) 0.5 \({}^{*}\) & 0.65 & 0.93 \({}^{\lx@sectionsign}\) & 2.2 \(\pm\) 0.5 \({}^{*}\) & 0.66 & 0.95 \({}^{\lx@sectionsign}\) \\ \hline
6 & 3.1 \(\pm\) 0.6 & 2.7 \(\pm\) 0.7 \({}^{*}\) & 0.70 & 0.68 \({}^{\lx@sectionsign}\) & 2.8 \(\pm\) 0.7 \({}^{*}\) & 0.70 & 0.73 \({}^{\lx@sectionsign}\) \\ \hline
7 & 2.5 \(\pm\) 0.5 & 2.8 \(\pm\) 0.4 \({}^{*}\) & 0.66 & 0.93 \({}^{\lx@sectionsign}\) & 2.8 \(\pm\) 0.4 \({}^{*}\) & 0.68 & 0.94 \({}^{\lx@sectionsign}\) \\ \hline
8 & 2.2 \(\pm\) 0.4 & 3.2 \(\pm\) 0.5 \({}^{*}\) & 0.72 & 0.93 \({}^{\lx@sectionsign}\) & 3.2 \(\pm\) 0.6 \({}^{*}\) & 0.75 & 0.93 \({}^{\lx@sectionsign}\) \\ \hline
9 & 2.4 \(\pm\) 0.6 & 1.7 \(\pm\) 0.8 \({}^{*}\) & 0.69 & 0.96 \({}^{\lx@sectionsign}\) & 1.8 \(\pm\) 0.7 \({}^{*}\) & 0.69 & 0.95 \({}^{\lx@sectionsign}\) \\ \hline \hline \end{tabular}  
* TV: breath-by-breath tidal volume (L); \(\widehat{\mathbf{TV}_{\text{WD}}}\): prediction of tidal volume using wearable-device data (L); \(\widehat{\mathbf{TV}_{\text{REF}}}\): prediction of tidal volume using reference instrumentation data (L); \(R^{2}\): explained variance. Data of all subjects are reported as mean \(\pm\) standard deviation. \({}^{*}\)\(p\)-value \(<\) 0.05 assuming limits of equivalence equal to 70% of standard deviation. \({}^{\lx@sectionsign}\)\(p\)-value \(<\) 0.05 for Pearson’s correlation analysis.  
\end{table} 
Table 5: Distribution estimations and gold standard of the cross-validation. volume [21; 22]. Of note, body composition may be estimated by several indexes, such as body mass index or body surface area. In the proposed approach, body mass index was selected as the clinical index of body composition, considering its wide diffusion and easy estimation. The body surface area is a measurement of the same physiological structure; it is thus highly correlated with body mass index [23] and was not included among the predictors. Gender is also known to affect tidal volume [21; 22], but it was not possible to assess its effect in the present study since all the volunteers were males. Moreover, tidal volume has been shown to continuously adjust on the basis of breathing rate, but not vice versa [4; 24]. Furthermore, despite intra-subject differences, tidal volume variations are also correlated with heart rate [25; 26]. However, we cannot exclude the possibility that other factors not considered in this study may affect the ability of our model to estimate tidal volume. For instance, between-subject differences in exercise capacity may lead to different values of tidal volume that are not captured by age, body mass index, or breathing-rate or heart-rate values. In addition, our results may not necessarily be extended to other exercise protocols or modalities. Since the number of subjects included in the present study is quite limited--although still comparable with similar studies [17; 18]--and their characteristics do not cover all the possible variety of conditions, further studies are needed to address these issues.