Second-order modeling for the pulmonary oxygen uptake on-kinetics: a comprehensive solution for overshooting and nonovershooting responses to exercise
Bibliographic record
Abstract
The human oxygen uptake (V̇o2) response to step-like increases in work rate is currently modeled by a First Order System Multi-Exponential (FOME) arrangement. Because of their first-order nature, none of FOME model’s exponentials is able to model an overshoot in the oxygen uptake kinetics (OV̇o2K). Nevertheless, OV̇o2K phenomena are observed in the fundamental component of trained individuals’ step responses. We hypothesized that a Mixed Multi-Exponential (MiME) model, where the fundamental component is modeled with a second- instead of a first-order system, would present a better overall performance than that of the traditional FOME model in fitting V̇o2 on-kinetics at all work rates, either presenting or not OV̇o2K. Fourteen well-trained male cyclists performed three step on-transitions at each of three work rates below their individual lactate thresholds’ work rate (WRLT), and two step on-transitions at each of two exercise intensities above WRLT. Averaged responses for each work rate were fitted with MiME and FOME models. Root mean standard errors were used for comparisons between fitting performances. Additionally, a methodology for detecting and quantifying OV̇o2K phenomena is proposed. Second order solutions performed better ( P < 0.000) than the first-order exponential when the OV̇o2K was present, and did not differ statistically ( P = 0.973) in its absence. OV̇o2K occurrences were observed below and, for the first time, above WRLT (88 and 7%, respectively). We concluded that the MiME model is more adequate and comprehensive than the FOME model in explaining V̇o2 step on-transient responses, considering cases with or without OV̇o2K altogether. NEW & NOTEWORTHY To our knowledge, this is the first study applying second-order system equations to model V̇o2 on-kinetics, which is useful for both mathematical representation and physiological understanding of the overshoot phenomenon manifesting in the fundamental components of some step responses. Moreover, an objective methodology for detecting and quantifying this overshoot that considers data from the whole response is proposed. Finally, this is the first work detecting overshoot occurrences outside the moderate domain of exercise.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".