Wagner diagram for modeling O2 pathway : calculation and graphical display by the Helsinki O2 Pathway Tool

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Wagner diagram for modeling O2 pathway : calculation and graphical display by the Helsinki O2 Pathway Tool © 2024 The Author(s). Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd. Published version Rissanen, Antti-Pekka E.; Mikkola, Tom; Gagnon, Dominique D.; Lehtonen, Elias; Lukkarinen, Sakari; Peltonen, Juha E. Rissanen, A.-P. E., Mikkola, T., Gagnon, D. D., Lehtonen, E., Lukkarinen, S., & Peltonen, J. E. (2024). Wagner diagram for modeling O2 pathway : calculation and graphical display by the Helsinki O2 Pathway Tool. Physiological Measurement, 45(5), Article 055028. https://doi.org/10.1088/1361-6579/ad4c36 2024 Physiological Measurement PAPER • OPEN ACCESS Wagner diagram for modeling O2 pathway—calculation and graphical display by the Helsinki O2 Pathway Tool To cite this article: Antti-Pekka E Rissanen et al 2024 Physiol. Meas. 45 055028 View the article online for updates and enhancements. You may also like Exploring the rubber sheet spacetime analogy by studying ball movement in a bent trampoline Pau Batlle, Adam Teixidó, Joan Llobera et al. - Accuracy and applicability of non-invasive evaluation of aortic wave intensity using only pressure waveforms in humans Arian Aghilinejad, Faisal Amlani, Jing Liu et al. - A comparison of entropy approaches for AF discrimination Chengyu Liu, Julien Oster, Erik Reinertsen et al. - This content was downloaded from IP address 130.234.242.193 on 19/06/2024 at 08:12 Physiol. 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PAPER Wagner diagram for modeling O2pathway—calculation and graphical display by the Helsinki O2Pathway Tool Antti-Pekka E Rissanen1,2,6,∗, Tom Mikkola1,3,6, Dominique D Gagnon1,2,4,5, Elias Lehtonen1,2, Sakari Lukkarinen3and Juha E Peltonen1,2 1Helsinki Sports and Exercise Medicine Clinic, Foundation for Sports and Exercise Medicine (HULA), Helsinki, Finland 2Sports and Exercise Medicine, Faculty of Medicine, University of Helsinki, Helsinki, Finland 3School of Information and Communication Technology, Metropolia University of Applied Sciences, Helsinki, Finland 4Faculty of Sports and Health Sciences, University of Jyväskylä, Jyväskylä, Finland 5School of Kinesiology and Health Sciences, Laurentian University, Sudbury, ON, Canada 6Contributed equally to the study. ∗Author to whom any correspondence should be addressed. E-mail: antti-pekka.r[email protected] Keywords: convection, diffusion, exercise, Fick, HO2PT, oxygen Supplementary material for this article is available online Abstract Objective. Maximal O2uptake ( ˙ VO2max) reflects the individual’s maximal rate of O2transport and utilization through the integrated whole-body pathway composed of the lungs, heart, blood, circulation, and metabolically active tissues. As such, ˙ VO2max 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 O2pathway to ˙ VO2max 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 O2Pathway Tool—HO2PT) to model numerical and graphical display of the O2pathway based on the ‘Wagner diagram’ originally formulated by Peter D. Wagner and his colleagues. Approach. The HO2PT 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 HO2PT models O2pathway 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 O2transport system to deliver O2 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 HO2PT offers a novel functional and demonstrative platform for those interested in examining ˙ VO2max 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. 1. Introduction Maximal O2uptake ( ˙ VO2max) is one of the most ubiquitous measures in human health and a fundamental pillar upon which the field of exercise science and medicine has evolved over the last century. The concept, according to which an individual possesses a finite rate of O2transport and utilization within an integrated pathway extending from the environment to the mitochondria to support the individual’s maximal rate of whole-body oxidative metabolism, has a central role in evolutionary history (Koch and Britton 2008). Contemporarily, well-acknowledged associations of oxidative metabolism with both physical capacity and © 2024 The Author(s). Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd Physiol. Meas. 45 (2024) 055028 A-P E Rissanen et al overall health enable the extensive use of ˙ VO2max as one predictor of physical performance and risks for morbidity and mortality in populations ranging from elite athletes to clinical patients (Levine 2008, Ross et al 2016, Millet et al 2023). Oxygen transport from the atmosphere to the mitochondria follows a well-established sequence: (i) ventilation of inspired air from the atmosphere to the pulmonary alveoli, (ii) diffusion of O2from alveolar gas into the pulmonary capillary blood, (iii) convective O2transport from the pulmonary capillary bed to the pulmonary veins, left heart, and further to the microvasculature of target tissues, and finally, (iv) unloading of O2from erythrocytes’ hemoglobin (Hb) in microvasculature and subsequent passive O2 diffusion to the mitochondria, where O2is used to produce ATP via oxidative phosphorylation (Wagner 2008,2011,2020,2023). The Fick principle equation (equation (1)) expresses parametric limits and physiological characteristics of ˙ VO2max and is historically one of the first attempts to define the O2transport cascade (Fick 1870): ˙ VO2=˙ Q×C(a-v)O2(1) where ˙ VO2=O2uptake, ˙ Q=cardiac output, and C(a-v)O2=arterial-venous O2difference. Unfortunately, the Fick principle equation fails to distinguish detailed limitations/improvements/declines in the O2cascade sequence from inspired air to the mitochondria. While the effect of ˙ Q on ˙ VO2is simplistic in nature, challenges arise when interpreting C(a-v)O2(Gifford et al 2024). This is because C(a-v)O2is affected by numerous factors such as pulmonary ventilation, matching of ventilation to ˙ Q, diffusion of O2 from the alveoli into the pulmonary circulation, affinity of Hb for O2, total Hb mass and blood volume (determining Hb concentration [Hb]), ˙ Q, systemic and local control of blood flow, number and size of capillaries, hematocrit in capillaries, diffusion of O2from the microvasculature into metabolically active cells and their mitochondria, mitochondrial density, and oxidative enzyme activity (Rowell 1986, Poole et al 2022). To overcome the obstacles of using the Fick principle equation alone, Peter D. Wagner and his colleagues presented an integrated model roughly 30 years ago to characterize how all transport steps contribute to ˙ VO2max (Roca et al 1989, Wagner 1991,1992). Their key contribution to existing knowledge was in merging Fick’s law of diffusion, presented in equation (2) and expressing peripheral O2diffusion from capillaries to mitochondria, with the Fick equation to integrate different components of the O2pathway with each other, ˙ VO2=DO2×(PcapO2−PmitoO2)(2) where DO2=diffusive O2conductance, PcapO2=partial capillary O2pressure, and PmitoO2=partial mitochondrial O2pressure. Equation (2) can be simplified by two assumptions. First, as PmitoO2is around 1–3 mmHg during (near) maximal exercise, and partial microvascular O2pressure is estimated to be between those of arteries (∼90–100 mmHg) and veins (∼20–40 mmHg), making the mean PcapO2to be commonly about 35–50 mmHg, PmitoO2is substantially lower than PcapO2and can thus be assumed to be algebraically zero (Gayeski and Honig 1986, Roca et al 1989, Richardson et al 1995). Second, PcapO2may be replaced with a constant, k, multiplied by partial venous O2pressure (PvO2). This is because PvO2is proportional to PcapO2, when DO2is assumed to be uniform along the capillaries with homogeneous blood flow distribution (Roca et al 1989). Consequently, Fick’s law of diffusion can be presented as follows (equation (3)) (Wagner 2011): ˙ VO2= DO2×k×PvO2.(3) As originally presented by Wagner and his colleagues, the Fick principle and the presented form of Fick’s law of diffusion (i.e. equations (1) and (3), respectively) can be graphically displayed as a relationship between ˙ VO2and PvO2(figure 1). While the described system and equations (1) and (2) apply equally from rest to maximal exercise, it is only from near-maximal to maximal exercise that the graphical display is appropriate for the necessary assumptions to apply. This particularly means that PmitoO2must be low enough to have a negligible influence on the calculations (Gayeski and Honig 1986, Richardson et al 1995), which enables the use of equation (3). In other words, the approach presented here and the graphical display pertain only to conditions under which the oxidative capacity of the metabolically active tissues’ mitochondria exceeds the capacity of the O2transport system to deliver O2to the mitochondria. Wagner’s and his colleagues’ conflation of the Fick principle and Fick’s law of diffusion to the ‘Wagner diagram’ exemplifies whole-body cooperativity between perfusive (Fick principle) and diffusive (Fick’s law) processes from pulmonary ventilation to skeletal muscles (Wagner 2008,2011,2020,2023, Esposito et al 2010). To understand O2transport, every step of the pathway must be considered simultaneously instead of approaching them separately, and no single step can solely be the factor limiting ˙ VO2max. Mathematically, 2 Physiol. Meas. 45 (2024) 055028 A-P E Rissanen et al Figure 1. Schematic graphical display of the relationship between O2uptake ( ˙ VO2) and partial venous O2pressure (PvO2). The Fick principle, represented by the curved line, and Fick’s law of diffusion, represented by the straight line, are conflated to yield a given maximal ˙ VO2(˙ VO2max) for the given conditions at the intersection of the two lines. See text for details and table 1for the abbreviations. conservation of O2mass is maintained at every step, and the two conservation of mass equations (i.e. Fick principle and Fick’s law of diffusion) can be solved simultaneously to provide a quantitative understanding of how the transport processes function together, how each step affects overall transport, and in particular, how O2transport and utilization eventually reach their limits so that the conservation of O2mass equations eventually result in the same ˙ VO2at the same PvO2(Wagner 2020,2023). This model can be and has been utilized in health and disease and its underlying physiology has been extensively clarified (Poole and Richardson 1997, Poole and Musch 2008, Hirai et al 2015, Poole et al 2021,2022). Although ˙ VO2measurements along with development and validation of invasive and noninvasive ˙ Q measurements have provided an access to the Wagner diagram for decades, an easy access to quantify all key variables of the O2pathway has been a challenge. Recently, however, both Houstis et al (2018) and Legendre et al (2021) have provided detailed steps for O2pathway calculation. Similarly, a web-based calculator (https://bakersportscardiology.shinyapps.io/fitoxy/) presented by Howden et al (2021) allows independent calculation of O2pathway steps. Furthermore, Pilotto et al (2022) and Manferdelli et al (2023) have very recently presented near-infrared spectroscopy-based methods providing functional estimates of muscle DO2 in exercising humans. However, to our knowledge, these advances have yet to be integrated into a comprehensive system, or tool, providing simultaneous calculation of the Wagner diagram’s variables and their graphical display. The purpose of this paper is to present a newly-developed publicly and freely available application, the Helsinki O2Pathway Tool (HO2PT), to import, calculate, graphically display, and export variables of the Wagner diagram. We believe this tool will advance the use of Wagner’s and his colleagues’ model and thereby the understanding of the physiological basis, limitations, and trainingor disuse-induced adaptations of ˙ VO2max and its components. For a more comprehensive and detailed physiological background of the current work, we encourage the reader to refer to the presented (e.g. Wagner 2008,2011,2020,2023) and other related literature. 2. Methods 2.1. HO2PT—aim, technical development, and functionalities The HO2PT is based on the integrated O2pathway model originally presented by Peter D. Wagner and his colleagues (Roca et al 1989, Wagner 1991,1992,2008,2011,2020, Esposito et al 2010). The model combines the Fick principle equation and Fick’s law of diffusion to illustrate an integrated approach of convective and diffusive components of O2delivery, known as the Wagner diagram. The HO2PT is intended to be used as a tool by anyone measuring ˙ VO2and its components across the wide spectrum of contexts including scientific research, education, exercise testing, coaching, or clinical medicine. Technical development of the HO2PT was done as part of a Bachelor of Engineering thesis in cooperation between Helsinki Sports and Exercise Medicine Clinic (HULA), Sports and Exercise Medicine, Faculty of Medicine, University of Helsinki, and the School of Information and Communication Technology of Metropolia University of Applied Sciences in Helsinki, Finland (Mikkola 2022). The tool has been programmed in Python (www.python.org/) programming language and bundled to a cross-platform 3 Physiol. Meas. 45 (2024) 055028 A-P E Rissanen et al software application with PyInstaller (https://pyinstaller.org/en/stable/), which makes running the HO2PT possible in Windows, macOS, and Linux operating systems. The graphical user interface was developed using Python’s Tkinter (https://docs.python.org/3/library/tkinter.html) interface for Tk graphical user interface toolkit. Other library dependencies the HO2PT has are Numpy (https://numpy.org/) and Matplotlib (https:// matplotlib.org/), that are used for the modeling, in addition to Pandas (https://pandas.pydata.org/) and Pandastable (https://pandastable.readthedocs.io/en/latest/description.html), that are used for data importing and exporting. Delivery of the HO2PT, its source code, and user instructions (i.e. a detailed Operation Manual), are shared via GitHub (https://github.com/HO2PT/Helsinki-O2-Pathway-Tool/releases), which is a free online platform, and available also via the website of HULA (https://hula.fi/EP2/HO2PT). The HO2PT can be used to model O2pathway according to the Wagner diagram both quantitatively and graphically. Both user input data and data imported from a file with a data importer tool, specifically created for the application, can be used for modeling. In addition, the tool contains functionalities to modify and analyze the graphical results. For example, at an individual level, comparisons of individual’s responses to exercise tests before and after any intervention can be made. At a group level, where utilizing the Wagner model and diagram has previously provided mechanistic insights into the determinants and adaptations of ˙ VO2max in both health and disease (Esposito et al 2010,2011, Wagner 2015, Houstis et al 2018, Broxterman et al 2020,2021,2024, Howden et al 2021, Legendre et al 2021, Manferdelli et al 2023), responses of one group can be modeled and illustrated, or responses of one group before and after any intervention or responses of two or several groups can be compared with each other. Basic statistical parameters (mean ±standard deviation or mean with 95% confidence intervals for normally distributed data; median with interquartile range for nonnormally distributed data) can be calculated for group-level data. Results of the modeling can be exported as image or spreadsheet files. Currently, there is no technical support for the source code. However, the source code of this tool is free to use and modifiable to fit one’s individual needs and preferences. 2.2. HO2PT—calculation Variables and equations used in the HO2PT are based on the original Wagner diagram and presented in table 1. Figure 2illustrates a step-by-step flow chart for how the HO2PT calculates its outputs. Regarding table 1, figure 2, and the equation of DO2, while the original data of Roca et al (1989) show the constant k may slightly vary both intraand interindividually along with prevailing circumstances, the same data also suggest it to be quite close to 2, and this is why the HO2PT multiplies PvO2by 2 when the default setting is used. However, a user can instead input another individual value for kto be used for the calculation if one has experimentally determined such value. To complement further the information in table 1and figure 2, the equations used for calculating PvO2, corrected for venous blood temperature and pH, are based on Severinghaus’s modified Hill equation (1979) and its direct solution for partial O2pressure (Ellis 1989) and are detailed in supplementary material 1. 2.3. HO2PT—graphical display For graphical display, the ˙ VO2formulae need to be presented as a function of PvO2. In terms of Fick’s law of diffusion, PvO2is available in the formula. This is not the case, however, for the Fick principle, where C(a-v)O2must be split into its contributory factors. Consequently, the following formulae are used for the graphical display: ˙ VO2=DO2×k×PvO2(4) ˙ VO2=˙ Q×((1.34×[Hb]×SaO2+0.03×PaO2)−1.34×[Hb]×SvO2)(5) where SaO2=arterial O2saturation, PaO2=partial arterial O2pressure, and SvO2=venous O2saturation. In terms of PaO2, a user of the HO2PT can choose from the tool’s settings whether one includes PaO2in the equation (5) or not; in other words, the HO2PT can also be used without data on PaO2, and arterial O2 content is in such case calculated as 1.34 ×[Hb] ×SaO2. In addition, the coefficient of PaO2in equation (5) is either 0.03 or 0.003 and depends on whether one uses ml O2/l blood or ml O2/dl blood, respectively, as a unit of arterial O2content. Figure 1illustrates a schematic graphical display of the relationship between ˙ VO2and PvO2. The curved Fick principle line in figure 1plots ˙ VO2as a function of PvO2and takes the shape of the oxyhemoglobin dissociation curve, albeit inverted; ˙ VO2and PvO2must lie on this curved line as the Fick principle conveys the conservation of O2mass. In figure 1, the straight line, which illustrates Fick’s law of diffusion and the slope of which represents DO2, shows what ˙ VO2(y-axis) should be in order that O2mass be conserved if 4 Physiol. Meas. 45 (2024) 055028 A-P E Rissanen et al Table 1. Variables in the Helsinki O2Pathway Tool: abbreviations, units, procurement methods, and equations. Variable Abbreviation UnitaMethodbEquationc Pulmonary O2 uptake ˙ VO2 •l/min •ml/min •Measured •Calculated •˙ Q×C(a-v)O2 Hemoglobin concentration [Hb] •g/l •g/dl •Measured Arterial O2 saturation SaO2•%•Measured Arterial O2 content CaO2 •ml O2/l blood •ml O2/dl blood •Measured •Calculated d •1.34×[Hb]×SaO2+ 0.03 ×PaO2 •C(a-v)O2+ CvO2 Partial arterial O2 pressure PaO2•mmHg •Measurede Heart rate HR •bpm •Measured Stroke volume SV •ml •Measured •Calculated •˙ VO2 HR×C(a-v)O2 Cardiac output ˙ Q•l/min •Measured •Calculated •SV ×HR •˙ VO2 C(a-v)O2 Convective O2 delivery ˙ QaO2•ml/min •Calculated •˙ Q×CaO2 Arterial-venous O2difference C(a-v)O2 •ml O2/l blood •ml O2/dl blood •Calculated •CaO2−CvO2 •˙ VO2 ˙ Q Diffusive O2 conductance DO2•ml/min/mmHg •Calculatedf•˙ VO2 2×PvO2 Venous O2 saturation SvO2•%•Measured •Calculated •CaO2−C(a-v)O2 1.34×[Hb] Venous O2content CvO2 •ml O2/l blood •ml O2/dl blood •Measured •Calculated •1.34×[Hb]×SvO2 •CaO2−C(a-v)O2 Partial venous O2 pressure PvO2•mmHg •Measured •Calculated See supplementary material 1 (Venous) blood temperature T •◦C •F •K •Measured •Estimated (Venous) blood pH pH •Measured •Estimated aVariable-specific alternatives of units that can be used when using the Helsinki O2pathway tool (HO2PT). bVariable-specific alternatives of methods that can be used to procure needed data for using the HO2PT. cVariable-specific and method-dependent alternatives of equations that are used to quantify needed data when using the HO2PT. See also figure 2for the flow chart for how the HO2PT step by step calculates its outputs. dThe HO2PT can alternatively calculate CaO2without PaO2(i.e. 1.34 ×[Hb] ×SaO2). The coefficient of PaO2, used by the HO2PT, is either 0.03 or 0.003 and depends on whether one uses ml O2/l blood or ml O2/dl blood, respectively, as a unit of CaO2. eThe HO2PT can be used without any measured data on PaO2(see dabove). fThe default equation to calculate DO2uses 2 for the constant k(i.e. the nominator in the default equation of DO2is: 2 ×PvO2), but a user can instead input another individual value for kto be used for the calculation if one has experimentally determined such value. See also text for details. PvO2(x-axis) took any value between its lower limit (i.e. 0 mmHg) and upper limit of PaO2. The straight line also defines the complete range of possible ˙ VO2values across the range of possible PvO2values. In consequence, ˙ VO2must lie somewhere on the straight line to maintain the conservation of O2mass, and 5 Physiol. Meas. 45 (2024) 055028 A-P E Rissanen et al Figure 2. Flow chart illustrating how the Helsinki O2Pathway Tool (HO2PT) performs its calculations from inputs to outputs. Example values of each variable of one individual’s maximal exercise data are written in brackets. The boxes with dashed edges include either the note that a user inputs a value for a variable located in the adjacent box with solid edges or the equation(s) used for calculating each variable located in the adjacent box with solid edges. See text, table 1, and supplementary material 1 for details and the abbreviations. ∗7.2 and 39 ◦C are examples of pH and temperature (T), for which partial venous O2pressure (PvO2) can be corrected. eventually, the two mass conservation equations (i.e. the Fick principle and Fick’s law of diffusion) must result in the same ˙ VO2at the same PvO2, which is demonstrated by the intersection point of the curved and straight lines (Wagner 2008,2011,2020). Figure 2illustrates how the HO2PT proceeds from receiving inputs to the calculation of the particular intersection point and the graphical display. 2.4. HO2PT—methods and data used during development Data used during development of the tool have been collected at HULA and Sports and Exercise Medicine, Faculty of Medicine, University of Helsinki, Helsinki, Finland. To model and illustrate group-level data of healthy, normally-to-highly active men, we retrospectively used previously published data (Peltonen et al 2013). For individual-level analyses, we retrospectively used subjects ranging from clinical patients to elite athletes who have undergone comprehensive exercise testing described below. These subjects included but were not limited to individuals from our previously published studies (Peltonen et al 2013, Rissanen et al 2015,2016,2023), in which the individuals have represented both sexes, have been 19–46 year-old, have been either healthy or had disturbances in glucose-insulin homeostasis (i.e. type 1 diabetes, insulin resistance with no diabetes, polycystic ovary syndrome), and have had body mass index between 19 to 38 kg/m2and ˙ VO2max between 16 to 61 ml/min/kg body mass. To demonstrate the effect of varying value of kon DO2during maximal cycling exercise at both group and individual levels, we used previously published data on premenopausal women with no diseases, medications, or other factors possibly affecting ˙ VO2max (Rissanen et al 2023). Two methods provided data for ˙ VO2measurements: (i) ventilation measurements by a low-resistance volume turbine (Triple V, Jaeger Mijnhardt, Bunnik, The Netherlands) and inspired and expired gases by mass spectrometry (AMIS 2000, Innovision A/S, Odense, Denmark), and (ii) a low-resistance volume 6 Physiol. Meas. 45 (2024) 055028 A-P E Rissanen et al turbine combined with an electrochemical fuel cell method to determine O2concentrations (Vyntus CPX, CareFusion, Hoechberg, Germany). Two versions of an impedance cardiography method were used to obtain stroke volume and ˙ Q: (i) PhysioFlow PF-05 Lab1 (Manatec Biomedical, Paris, France), and (ii) PhysioFlow PF-07 Enduro (Manatec Biomedical, Paris, France). SaO2was monitored by pulse oximetry (Nonin 9600, Nonin Medical, Inc., Plymouth, MN) either from a fingertip or an earlobe. Measures for capillary blood [Hb] and pH were provided by blood gas analyzers (ABL725, Radiometer, Copenhagen, Denmark; ABL90 FLEX PLUS, Radiometer, Copenhagen, Denmark). Hb samples collected from the antecubital vein were analyzed in two local accredited laboratories (www.synlab.fi;https://huslab.fi). In our laboratory, we have measured ˙ VO2and ˙ Q, and calculated C(a-v)O2according to the Fick principle. However, the HO2PT can be used by providing measured values for any two of these variables to calculate the third one, and of course, all three variables can also be used as measured values (table 1). In addition, SaO2and [Hb] are needed for the calculations (table 1). In terms of venous blood temperature and pH, the values reflecting the existing venous conditions can be either directly measured or approximated according to the literature (e.g. Arngrimsson et al 2004, Mortensen et al 2005, González-Alonso et al 2015, Trangmar et al 2017). Regarding standard physiological conditions at rest, we have used T=37.0 ◦C and pH =7.4 in our example calculations. 3. Results Based on the Python open source code and libraries, the HO2PT was developed to model O2transport pathway both numerically and graphically according to the Wagner diagram. Figure 3illustrates the data structure of the HO2PT. The core of the HO2PT is the App object acting as an interface between other objects. It contains information on the current status of the tool including an active project, subject, and exercise test. The App object also communicates with the Settings object that governs default settings. The most visible objects for the user are Project, Subject, and Test objects, that a user can create manually or import from an existing data file. Division of current data into three main categories is based on the nature of the research material: Each data set, which is modeled and analyzed, may contain various subjects with results from several exercise tests. Each test (Test) may have individual environmental conditions (EnvDetails) and subject’s background information (SubjectDetails). In addition to data on maximal exercise, several workloads (Load) with individually measured and/or calculated values (WorkLoadDetails) can also be processed, although it deserves to be repeated here that it is only from near-maximal to maximal exercise when the graphical display is appropriate for the necessary assumptions to apply, as previously justified (see Introduction). Figure 4provides an overall user view of the HO2PT. The left panel (panel 1) in figure 4contains information on available project(s), subject(s), and exercise test(s). The panel’s tools enable the user to create, edit, delete, and import data as well as add data to the graph. These functionalities enable the user to construct and analyze data freely from different sources. The top panel (panel 2) in figure 4presents detailed information on active project(s) and test(s) and allows user to modify settings for graphical display. The modeling is based on the information provided in the top panel and its graphical and numerical results are provided in a tab in the bottom panel (panel 3). The bottom panel is divided into the graphical results and its tools and the numerical values. The panel presents data according to the Wagner diagram and the corresponding numerical values are visible on a separate tab next to the graph. The user can separately edit the appearance of the diagrams by controlling their visibility, line type, and line color. The user can also modify the graph title, numbers of ticks, and scales of axes, and when finished, save the graphical result as an image file (.png). The numerical results provide an option for the user to edit the units and information about the method (i.e. measured or calculated) used for data collection. Both the graphical and numerical results can be exported into a spreadsheet file. Figures 5and 6demonstrate examples of groupand individual-level data. Figure 5provides an example of group-level data (medians) on healthy, normally-to-highly active men during maximal cycling exercise. Figure 6provides an example of maximal exercise responses of a male cross-country skier before and after a 4-week ‘Living High-Training High and Low’ camp. Supplementary material 2 demonstrates the effect of varying value of kon DO2during maximal exercise at both group and individual levels. At group level, DO2during maximal exercise does not differ between a situation where kconstantly equals 2 and a situation where krandomly varies from 1.8 to 2.2. At individual level, compared to a situation where kequals 2, DO2during maximal exercise is 11% higher, 5% higher, 5% lower, or 9% lower if kequals 1.8, 1.9, 2.1, or 2.2, respectively. 7