## 4 Discussion
Based on these elements, BJ-TF models are believed to be more reliable than exponential method C for the determination of kinetic feature values. MRT varied less than TC over the different modelling methods for quantifying the speed of the primary VO\({}_{2}\) response (Figure 5). This confirms the findings from test-retest reliability studies that determine VO\({}_{2}\) kinetics from healthy subjects using a treadmill [27] or step test [28]. Inaccurate TD estimates will directly affect TC estimates in the opposite direction. These opposing effects are balanced in the calculation of MRT, making MRT more robust towards inaccurate TD estimations. This study also confirms earlier findings that not all CWRT datasets of COPD patients are well-suited for kinetic analyses [29]. One patient showed no meaningful VO\({}_{2}\) response due to a very low cycling load (22 W). More interestingly, another patient had an almost linear primary VO\({}_{2}\) response that was not due to a low cycling load. The airway and alveolar abnormalities in COPD patients, which can limit the oxygen delivery to the working muscles [4], might have led to this alteration of the VO\({}_{2}\) response. Analyses of larger COPD populations will be required to confirm this hypothesis. In addition to the more reliable determination of kinetic feature values compared to exponential methods, A and B, BJ-TF models can also be applied more broadly than exponential models. Exponential models do not explicitly include an input variable in their model, limiting their use to experiments with a single input transition (e.g., non-active to active or unloaded to loaded cycling). BJ-TF, however, are able to estimate kinetic feature values with multiple input transitions, e.g., for time-domain analyses of pseudo-random binary sequences of the cycling load [30], or during unsupervised physical activities. As physical activity and VO\({}_{2}\) can nowadays be measured with wearable devices [31; 32], combining these measurements with BJ-TF modelling can produce frequent estimates of kinetic feature values during standard unsupervised training sessions, without the need for elaborate testing procedures. Similar models have already been successfully used to model heart rate responses during road cycling [33]. Although this study showed the advantages of applying BJ-TF models, some considerations should be taken into account. We only examined a specific population, which exhibits a reduced signal to noise ratio (due to the reduced VO\({}_{2}\) response amplitudes [3]) and phase I contribution [5]. It would thus be interesting to test the performance of BJ-TF models in other population types (e.g., athletes or other disease states). Furthermore, other exercise modalities (e.g., treadmill walking) and exercise intensities should be examined to test the general applicability of BJ-TF models for analysing VO\({}_{2}\) kinetics. In conclusion, low residual values showed that BJ-TF models accurately model the VO\({}_{2}\) response of COPD patients during a CWRT. These models, in contrast to the typically used exponential models, were able to account for unwanted noise contributions (e.g., the phase I contribution), leading to more reliable determinations of kinetic feature values compared to methods A and B. Only exponential modelling method C, which excludes the data during the cardiodynamic phase, led to comparable kinetic feature values as extracted from BJ-TF models. Based on theoretical considerations, we recommend using BJ-TF, rather than exponential models, for reliable determinations of VO\({}_{2}\) kinetics. Conceptualization, J.B., J.T., M.A.S., P.D.B. and J.-M.A. ; methodology, [PERSON], [PERSON] and [PERSON]-M.A. ; formal analysis, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON], A.P.F., [PERSON], M.A.S., P.D.B. and [PERSON]-M.A. ; visualization, [PERSON]; supervision, [PERSON], M.A.S., P.D.B. and [PERSON]-M.A. This research received no external funding.