Wagner diagram for modeling O<sub>2</sub> pathway—calculation and graphical display by the Helsinki O<sub>2</sub> Pathway Tool
Bibliographic record
Abstract
Abstract Objective. Maximal O 2 uptake ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mover> <mml:mtext>V</mml:mtext> <mml:mo>˙</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>2</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>max</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) reflects the individual’s maximal rate of O 2 transport and utilization through the integrated whole-body pathway composed of the lungs, heart, blood, circulation, and metabolically active tissues. As such, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mover> <mml:mtext>V</mml:mtext> <mml:mo>˙</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>2</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>max</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> is strongly associated with physical capacity as well as overall health and thus acts as one predictor of physical performance and as a vital sign in determination of status and progress of numerous clinical conditions. Quantifying the contribution of single parts of the multistep O 2 pathway to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mover> <mml:mtext>V</mml:mtext> <mml:mo>˙</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>2</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>max</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> provides mechanistic insights into exercise (in)tolerance and into therapy-, training-, or disuse-induced adaptations at individual or group levels. We developed a desktop application (Helsinki O 2 Pathway Tool—HO 2 PT) to model numerical and graphical display of the O 2 pathway based on the ‘Wagner diagram’ originally formulated by Peter D. Wagner and his colleagues. Approach. The HO 2 PT was developed and programmed in Python to integrate the Fick principle and Fick’s law of diffusion into a computational system to import, calculate, graphically display, and export variables of the Wagner diagram. Main results. The HO 2 PT models O 2 pathway both numerically and graphically according to the Wagner diagram and pertains to conditions under which the mitochondrial oxidative capacity of metabolically active tissues exceeds the capacity of the O 2 transport system to deliver O 2 to the mitochondria. The tool is based on the Python open source code and libraries and freely and publicly available online for Windows, macOS, and Linux operating systems. Significance. The HO 2 PT offers a novel functional and demonstrative platform for those interested in examining <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mover> <mml:mtext>V</mml:mtext> <mml:mo>˙</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>2</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>max</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> and its determinants by using the Wagner diagram. It will improve access to and usability of Wagner’s and his colleagues’ integrated physiological model and thereby benefit users across the wide spectrum of contexts such as scientific research, education, exercise testing, sports coaching, and clinical medicine.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".