## 4 Discussion  
This is the first study to apply BJ-TF models to determine VO\({}_{2}\) kinetics during a CWRT. BJ-TF models provided better fits than the typically applied exponential models and were able to account for unwanted contributions (e.g., phase I contribution or measurement noise). When applying exponential models, method C succeeded best at surpassing the phase I contribution and most closely resembled the \"noise-free\" system model of BJ-TF models. Exponential models are most commonly used to examine VO\({}_{2}\) kinetics [4]. However, none of the applied exponential modelling methods were able to account for the noise components in the VO\({}_{2}\) time series, as could be seen in the VO\({}_{2}\) time series, residual and autocorrelation plots (Figures 2 and 3). NRMSE values showed that the residuals acted on a magnitude of 10-12% of the total response amplitude, indicating that these noise components should not be neglected. Methods B and C had higher NRMSE values because they tried to surpass the contribution of the cardiodynamic phase (phase I), leading to higher residual values at the start of the test when the cardiodynamic phase plays an important role (Figures 2 and 3). However, method A is mechanistically unrealistic, as it does not assume any transit delays between muscle oxygen uptake and oxygen uptake at the mouth [19]. Only method C was able to fully discard the phase I contribution by removing the first 20 s of data. The ability to (partly) surpass the cardiodynamic phase was mainly reflected in the TD values, which in turn greatly affected all other feature values (Figure 5). This shows that for COPD patients, similar to healthy subjects [19; 20], the applied exponential modelling method had a significant effect on the kinetic feature values. Another strategy to exclude the phase I contribution might be applying a second-order exponential model, which aims to separately model the phase I and phase II contributions [4; 20]. However, a second-order exponential model is based on the unproven assumption that the phase I response is exponential of nature [20]. Furthermore, the phase I contribution was not the only unwanted noise component in the data, as can be seen in Figure 3a. These other noise contributions acted at a similar level as phase I, making it difficult to distinguish phase I from other noise contributions (Figure 3a). The relatively small phase I contributions, compared to the other noise contributions, might be a result  
Figure 5: NRMSE and kinetic feature values summarised as median (bar) and interquartile range (line) for exponential modelling methods A, B, C and the BJ-TF model with noise model order [2 0]. of the patients suffering from COPD [5] or because the test was preceded by unloaded cycling [19]. Averaging the VO\({}_{2}\) response of several repetitions of the same exercise can cancel out the noise contributions that are not related to the phase I contribution [21; 22], but this requires unnecessarily strenuous exercise sessions. Therefore, BJ-TF models were preferred because of their ability to account for all unwanted components at once. A [20] noise model structure was considered the most suitable for BJ-TF modelling. When considering all second order noise models, NRMSE values were all at the same magnitude, and a [20] structure had the best YIC values. This indicates that increasing the order of C(z\({}^{-1}\)) above zero induced unnecessary complexity. Some structure remained in the residuals when applying a second order noise model, but at a very low magnitude (Figure 3b and Table 2). When increasing the noise model dynamics to order three, this low-magnitude structure in the residuals disappeared in most patients (Figure 3c) and NRMSE values became slightly lower, but were still at a similar magnitude as second order models (Table 2).