# VO2 Kinetics

A detailed introduction to my recent interest into VO2 kinetics can be found in my Current Projects section within the Topic of VO2 Kinetics to Steady State. Consequently, I will move straight into the academic and research aspects that concern me.

1. Poor Rationale For The Use of a Mono-exponential Model

Since the beginning of this field of research, there was a direction to model the VO2 response to an exercise increment to steady state based on the total data set. This is of course quite logical, as the response depicts an exponential association. To ascertain the suitability of this fit quantitatively is an appropriate research question. However, this time was pre-1980, which pre-dated the sophisticated development of mathematics software for personal computing, especially by today's standards. In addition, this early work did not compare other curve fitting models to such data, which prevents a rigorous evaluation of the suitability of the fit! For example, the initial research or commentary on VO2 kinetics data to steady state between the 1930's and 1950's was based on visual observation. This approach was made more objective by Whipp in 1971, where the mathematical nuances of a mono-exponential model were explained and applied to two exercise transitions using 8 subjects. However, at no time during this early developmental phase of the field of VO2 kinetics to steady state was any objective and empirical assessment done on different methods of data analysis and modelling. Thus, from the onset, the field of VO2 kinetics was based on an assumed superiority of a mono-exponential model, and this has been accepted without adequate empirical rigor, scrutiny and proof.

2. Poor Operational Validity Of The Term VO2 Kinetics

In the world of science, the word "kinetics" has several meanings. Strictly speaking, "kinetics" is the study of the motion of moving objects and this definition obviously is based in the physical sciences. For the biological sciences, "kinetics" has been used in context with the study of the rate of change of biological processes. The most notable fields of research are enzyme kinetics and pharmacokinetics. While both of the two biological kinetics fields of research and science mentioned prior have clear modelling of the total responses, the features of the topics that quantify kinetics are not model-based. Here, enzyme kinetics is the best example, where instantaneous kinetics is based on the initial linear increase in reaction velocity with an increase in substrate concentration(s).

The traditional features of the field of VO2 kinetics to steady state is a stand alone in being dependent on modeling the response based on the entire data set; from onset to steady state. Such a model assumes that there is nothing uniquely interesting in sub-components of the VO2 response, or the implications of deviations from the model within specific regions of the response. The model also assumes that this simplistic view is valid despite the fact that whole body VO2 responses involve a multiple systems integrated response that encompasses pulmonary gas exchange, systemic gas transport and delivery, peripheral gas diffusion, motor unit recruitment, intramuscular gas diffusion, and intramuscular metabolic oxygen consumption. Why have we always thought (and not questioned) that such a complex integrated response should always be dependent on one over-riding single function nonlinear model? I present the full complexity of the VO2 response to exercise transitions in my recent review of VO2 kinetics to steady state (Robergs RA. Sports Medicine. 2014; 44(5):641-653)

3. An Over-reliance On Tau As A Measure of Kinetics

Given the content above, the dependence of the current study of VO2 kinetics to steady state on mono-exponential modelling and the time constant, tau, could be argued to constrain future progress in understanding the physiology that governs the change in whole body VO2 during exercise increments to steady state. Such an over-emphasis of tau has caused the disastrous situation where no study in the entire history of research of VO2 kinetics to steady state has yet to quantify time to steady state based on an objectively pure method (see item 5; note that we have completed such a study but as of February, 2015, we can't get it published, so alas, it doesn't count!). Tau is not an objectively pure reflection of time to steady state, and 4 x tau (what some researchers use to estimate time to steady state) is not an objective method to measure time to steady state. I can't think of a more immediately clear example (no measure of time to steady state) of the constraint imposed on the exercise physiology of exercise increments to steady state by the strict adherence of the use of a mono-exponential model to fit and interpret such data. See item 7 for added arguments and empirical evidence to support this view.

4. Poor Empirical Evidence For The Need To Interpolate And Average Multiple Trials

There seems to be a common practice to perform multiple trials of breath-by-breath VO2 data collection, then interpolate the data so that data points are aligned to the same time points, and then average the data prior to curve fitting. This procedure was first introduced by Whipp et al. in 1987. At that time, the authors argued that breath-by-breath variability in VO2 data could decrease the precision of the mono-exponential model. Actually, their rationale was even more questionable than this. For example, the authors stated that "The kinetic response to exercise (of VO2 data) can therefore be viewed as the sum of two components; 1) an underlying physiological response, and 2) 'noise', whose magnitude proves to be much greater in some subjects than others." This statement is quite inadequate as it is based on 'real' signal having no variability, where of course variability was viewed as 'noise' and therefore non-physiological. Today we know that the breath-by-breath variability in VO2 data is physiological and is caused by cyclical fluctuations in tidal volume and breathing frequency, which in turn can also cause added variability to expired gas fractions. Variability is not 'noise', and as such, is physiologically real! I explain and quantify all of this in my prior review on data processing breath-by-breath VO2 data (Robergs RA. Sports Medicine. 2010; 40(2):95-112).

The initial rationale is also interesting, because it reflected a bias in favor of the unquestioned validity of the mono-exponential model. Furthermore, the statistical analysis of the data was based on the extent of error in the mono-exponential model, and not on whether the impact of sequentially increasing the repeated trials alters each of multiple non-linear models for the VO2 response, or whether there was a superior model. Consequently, they did not design their study to quantify the decreasing variability from increments of repeated trials, nor did they approach this topic with an open mind sufficient to even question the risk for how interpolation and data averaging might over-process the data causing false data trends and subsequent misinterpretation of the results. Pertinent questions remain; Is there really a need to data average prior to non-linear curve fitting of the breath-by-breath VO2 data? If so, then how many repeat trials are needed to sufficiently decrease this variability? Should the variability be removed at all? Does interpolation and averaging force a mono-exponential profile when there is evidence that singular trial data do not conform to this model? This methodological data processing strategy lacks logic, has no empirical justification, and could be forcing a mono-exponential fit to data that has a more complex non-linear profile. Unbiased research is desperately needed on these topics.

5. Failure To Measure Time To Steady State

As previously explained, the unquestioned use of tau to quantify the kinetic response of VO2 in an exercise transition to steady state has prevented the measurement of time to steady state. I have developed a methodology to measure time to steady state, and it has shown trends against relative intensities (%VT) that differ to tau. Let me first explain the method.

Logically, steady state means that the VO2 response over time has plateaued. Thus, the last minutes of a steady state bout can be extrapolated backwards using linear regression. The initial segment of the VO2 response to the transition can be non-linearly fit (2nd order polynomial , and where these two lines (2nd order polynomial for the initial segment vs. the linear zero slope steady state value) intersect is time to steady state. We use Prism (GraphPad Software, Ventura, CA, USA) and my own custom software (LabVIEW, National Instruments, Austin, TX, USA) to process our data. The LabVIEW program allows the user to extend the time range of the 2nd order polynomial fit, and computes the residual to the regression of the steady state plateau. As the time range is increased for the polynomial fit to the initial segment, where this residual is smallest (closest to zero) is the intersect, and the time from test start to this intersect is time to steady state.

Our data is quite impressive for our recent study, and I cannot show you this for our mean data without compromising our future submissions of our manuscript. Nevertheless, the image provided here is an example of the method that clearly shows the improved modelling of the 2nd order polynomial + linear steady state segment vs. the complete monoexponential model.

6. The Need to Study Onset Kinetics

I term the study of the immediate VO2 response to an exercise transition, VO2 Onset Kinetics. There may be a better term to label this component of the VO2 response to a transition, and future research will hopefully critically evaluate this field of research and assign an appropriate label. I view this area to have tremendous potential to further research and gain knowledge of the physiological determinants to exercise to steady state. As evidence of this, I processed the data differently for two subjects from our recent research on VO2 kinetics to steady state (the one we are having difficulty publishing). The data look interesting, and for those with an inquisitive mind raise many questions that require research clarification, and I will pursue these with one of my PhD students over the next two years.

In the figure below, I present data for the linear regression of the initial VO2 response to 5 different exercise increments (30, 45, 60, 75 and 90% VT-Watts). Subject 1 is a relatively untrained individual, and subject 2 is a highly endurance trained cyclist.

Note the ordered change in the linear slope of the data from lowest to highest intensities. Also note the very different sequence of tau for subject 1 vs. 2. Sorry about the different start times for the data of subject 1, as this was caused by the need to remove the phase-I component if it existed. Also understand that the linear fit of the VO2 data segment was always superior to the mono-exponential fit for both subjects, with this fact being more apparent the higher the exercise intensity. The ordered nature of the change in the slope data interested me. How does this response compare between the trained and untrained subject? Do the slopes appear on different regions of a Watts vs. VO2 slope graph? If so, what does this mean? If not, what does this mean? How do we interpret the varied response of tau vs. the similar response of the VO2 slope? To assist in answering these questions, at least on a speculative basis for now, I graphed the slope and tau data against Watts, and present this below.

I am very excited by this figure on the left. As explained above, the slope and tau responses differ considerably. The VO2:time slope data appear to closely align to a similar total slope (slope:Watts) value, regardless of the subjects being at near opposite ends of the training and endurance fitness spectrum. The trained subject's responses were more rapid, but it appears that this was not due to training-induced adaptation aiding more rapid VO2 onset kinetics, but simply because of a higher wattage on the ergometer. Perhaps this means similar oxygen delivery and consumption capabilities for steady state intensities during this onset phase. In other words, no functional limitation differences seem to exist between these two very different subjects. Perhaps for healthy humans in normoxia there is no limitation to oxygen delivery and extraction during this onset phase of cycling transitions. Further inquiry is tempting. How does the time segment that follows differ at different exercise intensities? Is there a consistent model for this response? What does it reveal or how can it be interpreted? What would happen if you compared different inspired PO2 conditions? Would the linear onset lines no longer overlay close to each other? What would happen during partial blood flow occlusion? Or what happens after chronic exposure to hypoxia? When does older age become a problem, or is it ever a problem? Is the problem muscle wasting not aging? For all these conditions, are changes more noticeable for the data segment that follows? Yes, many of these questions have been addressed in research based on quantifying tau, but there are so many studies to redo based on this new data processing strategy.

The responses of tau are also very interesting. In being different does this mean the physiology as data approaches steady state is very different to the onset kinetic data? It appears so to me. This would mean that the latter VO2 kinetic response to steady state increments is influenced by factors additional to the onset phase. What is/are this/these factor(s)? How do they change with changing inspired PO2? Or are these responses more reflective of muscle metabolic capacities? The important fact to ram home here is that when you adopt a total data set mono-exponential model, you place a blindfold over your face and you are unable to study sub-components to the total VO2 response to steady state. Surely this presentation of data and all the doors of scientific inquiry that it opens, reveals the errors of current mono-exponential modelling practice!

7. The Need to Improve Our Understanding and Cause of Prolonged Kinetics (onset and mono-exponential) at the Upper End of Steady State

The thorough background to this topic is found in my recent review of VO2 kinetics to steady state. I will keep this brief. We now know that the response of tau does not adhere to linear first order kinetics (i.e, it is not invariant across all magnitudes of exercise increments when starting with unloaded cycling, or when commencing from a higher baseline intensity). We show in our recent work, that tau increases to previously unreported higher values the higher the baseline intensity is. As such, the factors governing VO2 kinetics at the higher end of the steady state domain are far more complex than initially thought and portrayed by the "experts" of the field through to ~2006, even though evidence against linear first order kinetics was apparent as early as the 1980's.

Surprisingly, this area of research has largely been overlooked, and we argue, has yet to be researched adequately. For example, we studied the near complete range of steady state exercise transitions (20 - 90 %VT), with baseline intensities ranging from unloaded cycling as well as 10 Watt increments from 20 to 60 %VT. Our data reveal the highest values ever reported for tau, as we are seeing that steady state may not be a totally absolute entity. For example, an exercise transition from prior work to a higher intensity below the VT is more difficult than the same transition end-point when starting from unloaded cycling. We are eager to further study the kinetic responses of VO2 to the higher end of the steady state domain in subjects of different fitness levels, apply our new data processing strategies, and submit our results to peer review.