Gold standard tests for anaerobic capacity: are they so precious?

 

Recently I  started to work on an article about sport’s testing. When I came to chapter on anaerobic sport, fitness, lifestyle, technology and people concept - close up of trainer hands with clipboard writing and woman working out on exercise bike in gymcapacity, I realised that, in fact, I do not quite understand what anaerobic capacity exactly means. And it seems that I am not alone in that. Even in scientific literature there is some confusion. When I started to study this topic deeper, it became clear that material is very interesting, complex and controversial thus, probably, it deserves a separate article. In presented work, I am going to discuss anaerobic capacity through the three most popular tests which claim to be the gold standards for it.

Anaerobic capacity.

Literally anaerobic capacity means an ability to produce energy without oxygen. It possible in three ways : through the limited muscle’s ATP stores, creatine phosphate (PCr) utilisation and anaerobic glycolysis. There is small amount of oxygen in muscles in form of myoglobin, which can be used for energy production without external oxygen, but this way is not purely anaerobic. From those three anaerobic pathways, muscles ATP reserve can support just a few seconds of maximal effort, whereas PCr a few dozens of seconds. Both of these two compounds can be restored relatively quick with the presence of oxygen. The third anaerobic pathway uses the same energy compound as aerobic one – glycogen. Although the glycogen stores are comparatively large, however, when they are used anaerobically, they can be spent relatively quickly (in tens of minutes) because this way is around 9 times less efficient than aerobic.

In reality, humans don’t use particular anaerobic pathways or aerobic ways exclusively. Usually all of them are used simultaneously and in different proportions depending on many different factors. Most important of those factors are: training adaptation, exercise intensity and duration.

However, very often, sports practitioners tend to imply different meaning for anaerobic capacity. They use this term to define external work which is produced anaerobically. For example, it can be distances run or cycled. This work is not exactly the same as energy because not all energy can be transferred into external work.

And finally, frequently coaches by anaerobic capacity mean ability to produce high intensity work above so called “anaerobic threshold” because they assume that oxygen supply is inadequate there thus work has to be generated anaerobically.

All these three conceptions of anaerobic capacity are reflected in three anaerobic tests which I am going to discuss below.

Wingate test.

Wingate test is 30 seconds of maximal cycling where peak power, mean power and rate of power decline are measured. In this sense, it is rather a measure of external anaerobic work. Possibly, Wingate is the most popular anaerobic test in the world. It is conventional opinion that, due its maximal intensity and relatively shortness, aerobic contribution is insignificant thus test presents pure anaerobic capacity. It is not exactly true. Aerobic part is not so small in this test and can reach 40% (Medbo & Tabata, 1989).

However, even more interesting question is: what actually limits athlete’s performance in Wingate? More exactly, why they are unable to maintain maximum output for 30 sec? This is unlikely due to unavailability of energy substrates. Though PCr may be depleted significantly, it is still available, as well as glycogen, throughout the test. Calbet et al. proved that it is unlikely due to inability to produce energy anaerobically as well (Calbet, De Paz, Garatachea, Cabeza de Vaca, & Chavarren, 1985). More likely that rapid disturbance in homeostasis may be the main reason.

So, what do we really measure in Wingate test? It is not anaerobic energy production and it is, probably, not a measure of external anaerobic work per se. Rather it is athlete’s capacity to maintain maximal effort. This test cannot give the answer how they do this. Is it important? Well, for coaches probably not really, but for scientists – yes. At least, for the sake of science.

Maximal accumulated oxygen deficit ( MAOD).

Maximal Accumulated Oxygen Deficit is a test, which some experts consider as a gold standard for anaerobic capacity and it clams to measure what anaerobic capacity literally means – internal anaerobic energy production.

Generally, the idea is following. During a few constant-speed submaximal runs, when oxygen consumption reaches plateau, relationship between oxygen consumption and running intensity is established. So now researchers know “cost” of running in oxygen units and can plot VO2 against running speed  (picture 1). Then athlete performs supramaximal constant-speed effort to exhaustion at speed correspondent to 120% of speed at VO2 max (this leads to test termination approximately after 2-3 min). During this bout, real oxygen consumption is measured and subtracted from theoretically predicted oxygen cost of work produced. The difference is supposed to be covered by anaerobic energy production thus is the measure of anaerobic capacity (though in oxygen units). Typical values may range from 33 ml/kg in prepubescent males to 80-85 ml/ kg in sprint athletes (D. Noordhof, de Koning, & Foster, 2010).

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Picture 1. MAOD test.  

Participant made 4 sub-maximal constant bouts below VO2 max ( lower dashed line). Best fitted  line was built and prediction for VO2 at speed corresponding to 120 % of VO2 max was made (upper dashed line).

This seems logical. However there are a few issues with this test. First of all, the real cost of work depends not only on aerobic production. Some part of energy is produced anaerobically even during sub-maximal bouts. Second is assumption of linearity in work-oxygen relation at higher intensities. Oxygen consumption rises non- proportionally to work rate there, thus real oxygen cost of supramaximal bout may be underestimated. There are arguments about test design , for example, how many sub-maximal bouts are needed for establishing reliable oxygen cost of work. Interested reader may find detailed review on MAOD in Noordhof et al. paper. Their conclusion is that: “…the MAOD method may have limitations as a valid and reliable measure of anaerobic capacity and needs to be further improved”(D. Noordhof, et al., 2010).

However, for me, the strangest thing in this test is that usually oxygen deficit not only tends to higher values for sprinters, which is expected, but often is the same for endurance athletes and for non-athletic population (Green & Dawson, 1993). Indeed, sprinters usually have higher proportion of fast-twitch fibres thus may produce more energy anaerobically than endurance athletes; however, I cannot believe that endurance athlete has the same anaerobic capacity as untrained person. So, why they may have close values in MAOD test?

Well, possibly, we need to come back to the question how we define anaerobic capacity. If the only criterion is the amount of energy which is produced anaerobically, then, probably, endurance athletes and non-athletes exhibit close values during 2-3 min of maximal work. However, it would be worth to note that athletes, in this test, make much more overall work than non-athlete. They just cover most of it aerobically. Aerobic and anaerobic ways of energy production are not something fixed. They change, interact and add each other in dependence of intensity, availability of oxygen and fuel reserves as well as of athlete’s training status and sport’s specialisation. Thus, probably, endurance athletes, with their great aerobic capacity, just don’t need to produce a lot of energy anaerobically.

I have found support for my opinion in Calbet’s study (Calbet, et al., 1985). They measured performance and MAOD in elite sprinters and endurance cyclists during Wingate test. They did that in normoxia and acute hypoxia conditions (equivalent of 5300 m altitude). Of course, sprinters  showed greater MAOD. However, interestingly, endurance athletes maintained their performance during hypoxia by increasing their MAOD. So, they can produce more energy anaerobically when it is needed! Authors concluded that: “In contrast to the prevailing paradigm, this study shows for the first time that performance during the traditional Wingate test is not limited by anaerobic energy supply in endurance cyclists”. I think the same may be true for 2-3 min exhaustive effort in MAOD test.

What may be the reason for fatigue then? Well, what we should consider, in my opinion, is that ability to perform high intensity exercise (in this case running/cycling at 120% of speed at VO2max), depends not only on ability to produce energy but on capacity to clean and tolerate metabolites. Production of metabolites rises together with exercise intensity, even if work is performed in “aerobic range”, below VO2 max. Especially rapidly, it may rise after so called anaerobic threshold (other names are: maximal lactate steady state, lactate turn point and critical power). While endurance athletes and non-athletes can produce the same amount of anaerobic energy during the supramaximal test, athletes, nevertheless, purify significantly more metabolites than non-athletes because their absolute intensity and overall workload are much higher. Thus, possibly, the over-taxation of the clearance/buffering system, which is not measured during MAOD test, makes athletes to terminate supramaximal exercise, not inability to produce energy anaerobically per se.

Your athlete shows low values in MAOD test? No need to be worried if his/her overall performance is fine.

CP-W’ concept.

There is another method to quantify anaerobic capacity – the CP-W’ concept. CP (critical power) represents the highest constant work rate that can be sustained without a progressive loss of homeostasis (D. A. Noordhof, Skiba, & de Koning, 2013). W’ is work that can be done above CP. In running CP and W’ can be substituted by critical speed (CS) and distance (D) run above critical speed. For convenience, I will continue to use CP and W’ in this article.

From physiological perspective, CP represents a border between two intensity domains – heavy and severe. In former some homeostasis parameters such as: VO2, blood lactate, pH, etc. stabilise and exercise can be sustain relatively long. In latter, they continue to shift towards their extreme values until exercise cannot be tolerated.

Though most of the professionals continue to call W’ “anaerobic capacity”, according to my rough calculations aerobic pathway may account for 30-40% of W ‘in 2-3 min exhaustive run. However, this theory, actually doesn’t claim that W’ should be done anaerobically or aerobically. Some researches, in my opinion correctly, point out that W’ is rather capacity to tolerate disturbance in homeostasis which is rapidly develops above CP (Burnley & Jones, 2016).

Adherents of this theory claim that  W’ is limited and its amount is fixed. The rate of its depletion may be different in dependence of intensity. The further you go above CP, the faster you will spend your W’. It worth to note that CP- W’ is a purely mathematical concepts and it doesn’t describe physiological mechanism of W’.

To find athlete’s CP and W’, he/she needs to make 4-5 exhaustive bouts lasting from 2 to 15 minutes. Alternatively, you can take athlete’s results for 800 – 5000 meters runs. Then you can plot P (speed/power) against time which this speed can be sustained (T). It will be inverse curve where constant (asymptote) represents CP and coefficient is equal W’ (picture 2).

P=W’/T +CPGreen2

Picture 2. Speed – Time inverse curve

Another way is to plot linear regression – distance against time (picture 3). Best fitted line for 4-5 time trials (e.g. 800 – 5000 meters for running) gives you W’ which is a constant (intercept with axis Distance ) and CP is a coefficient (slope of the line).

D= W’+ CP x T

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Picture 3. Distance – Time linear regression

These bouts should be not less than 2 min, otherwise factors different from CP and W’, such as absolute speed, can play a significant role. We are interested mostly in endurance, thus possibly too short distances are not suitable in this case. They should not be longer than 15 min, because this may overlap lower intensity’s range – heavy domain. The causes of fatigue may be significantly different in heavy and severe domains. In former VO2 and homeostasis indicators can temporally stabilise and fatigue may be largely due to the depletion of glycogen in certain muscle’s fibres and sites, muscles damage, rising core temperature and the inhibitory effect of the central nervous system.

Relatively recently, 3-min all-and out test was suggested as more economical alternative to mentioned above procedures (Vanhatalo, Doust, & Burnley, 2007). Athlete cycles or runs with maximum effort, and as his/her power or speed declines it should achieve stable value in the final 30 sec. This value is  CP. W’ may be easily calculated by extracting CP x 180 sec from the overall work/distance. In my opinion, besides the theoretical issues, this test presents a practical problem – pacing. It is very difficult to motivate athletes to give maximum from the start when they know that they should last 3 min.

Practical and theoretical issues may cause problems in calculating CP and W’. For example, Jones with colleagues presented their calculation of CP and W’ for elite runners (Jones & Vanhatalo, 2017). Mean CP was 5.84 m/sec and W’ 320 m. My expectation is that CP should be significantly higher and W’ significantly lower for this group of athletes. I checked my doubts by calculating of CP and W’ for Haile Gebrselassie, Mo Farah and Keneise Bekele . My results (6.43-125.31; 6.26-162.76; 6.41-119.35) respectively, were quite different from Jones et al.

It seems that a problem is that authors included distances from 1.5 kilometres up to 15 kilometres in their calculation, though they acknowledged in their article that trials should be 2-15 min. In addition, they possibly included road and indoor results in calculations (these are usually slower than track). This led to relatively low CP which is very close to marathon speed for these runners. My calculations are based on personal bests up to 5000 m and only track events were included. CPs, which I’ve got, are very close to 10000 personal best for these athletes, and that is in agreement with Billat (Billat, Sirvent, Py, Koralsztein, & Mercier, 2003) and some other authors.

Although CP is theoretical concept, by its nature it should be close to MLSS (maximal lactate steady state) which can be measured physiologically. Nevertheless usually, when CP is calculated on basis of 2-15 min trials, MLSS is lower than CP.  In my opinion, coaches have to choose one of them in accordance with their preferences and options and follow it consistently in their exercises prescriptions and evaluations.

Another issue with CP-W’ is that researchers make their measurements in particular conditions or take athlete’s results on particular days and then assume that their calculation will be valid in all different circumstances. It is not always correct.

Recently CP and W’ concept was extended to intermittent activities (Skiba, Chidnok, Vanhatalo, & Jones, 2012). Scientists tried to quantify ability to perform high-intensity work during exercises when intensity spontaneously switches between below and above CP. There are many example of this type of activity in sport games, and even races usually have such periods, as well. At intensities above CP W’ is depleted and, when intensity is below CP, it is restored. The rates of depletion and restoration are determined by proximity of depletion and recovery intensities from CP. Perhaps coaches intuitively knew this long ago, however scientists now put this in relatively complicated equation:

Wbal=W -∫ (Wex) e(-(t-u)/ Tw’))

Where W is subject’s W’; Wbal is W’ remaining at particular moment; Wex is W’ already spent ; (t-u) is a rest period and Tw’ is time-constant for W’ recovery (time needed for 63.2% recovery).

In simple words, the amount of W’ remaining at any time is equal to the difference between the overall W’ and the total sum of the W’ expended and exponentially recovered in different work-rest intervals before this time.

In spite of its complexity, this formula, again, expresses logical and, probably intuitively already known notion that athletes spend and are able to recover their high-intensity work capacity. How fast they can recover depends on intensity of the rest period. Authors attempted to find exact formula for time-constant :

Tw’=546 e(-0.01Dcp) + 316

Where Dcp is a distance between rest intensity and CP.

So how they found this exact equation? Seven subjects performed multiple cycle-ergometer tests. Work intervals were fixed at the same relative fraction of VO2 max in severe-intensity-work domain. However rest intensity varied between tests. It was at different proximities from the work intensity. Researchers measured how rest intensity influenced test duration (before W’ was depleted) and found the best fitted equation describing the rate of W’ recovery.

Is there any practical implication?

Perhaps, it will be risky to rely on this equation. Seven recreational athletes are not enough for deriving exact formula. Moreover, participants showed significant variability in speed of W’ recovery even when relative rest intensity was the same. Especially this was noticeable when rest intensity was in heavy domain. Range of T w’ in that occasion was 377-719 sec. Importantly, there was just weak correlation between CP and Tw’, which means that subjects with the better CP did not always recover faster, although logically they were supposed to. Authors acknowledged complexity of the recovery process and possible limitations of CP-W’ theory application.

Of course, we can find out specific Tw’ equation for every athlete. I suppose it would be possible to integrate calculation programme into the sports watches’ software or bicycle powermeter thus athlete can get online information how much W’ he/she has left during the race. Does this really help? Possibly not so much. All measures, used for calculations, were made in particular conditions and in particular athlete’s physical and mental state, however now he/she may be running in completely different environmental, psychological and physical conditions. In addition,W’ itself may be hugely different ( up to 3 times!) depending on how you calculate it. Instead of trusting their experience and feelings, athletes start to look at their watches and worried about numbers they see. These numbers are, actually, far from being reliable. Don’t worry. Keep running.

However, my fundamental concern about CP-W’ concept is a connection between its mathematics and real life. Possibly logic here is not perfect. If athlete runs particular distance with the speed P (above CP) then, from CP-W’ theory, this speed can be expressed as: P= CP+ W’/T, where T is time over this distance. How it can be applied in real life? Well, if one athlete beats another on 10000 meters and loses him on 1500, from CP-W’ theory, we can conclude that, albeit first athlete has better CP, nevertheless his overall P (speed) on 1500 meters is lower due to inferior W’. In simple words first athlete has superior aerobic abilities whereas second one – anaerobic. Fair enough.

However, let’s take another example when athlete increased his critical speed by 1 km/h. This can be an average speed over 10 km race or a marathon, depending on what you consider to be a critical speed. Imagine that this athlete competes on 1500 as well, and he has not improved there. Now his W’ actually decreased because new equation for 1500 meters now is: P= (CP+1) + W’/T. This situation is not rare for CP-W’ theory. Often researchers find in their experiments that improvement in CP is associated with decrements in W’.

Basically, this means that, despite a progress on 10000 meters and consistency on 1500 meters, we have to inform our athlete that something wrong with him and his ability to perform high-intensity work impairs. Do you think he will agree? Essentially, CP-W’ concept demands that improvements over longer distances (5000-10000 meters) should follow by improvements in shorter (800-1500) and vice-versa, otherwise we have to conclude that one of the parameters impairs. In reality, however, it is often when athletes improve on their favourite distances without improvements on others.

Logically, improved CP should not impair athlete’s capacity to perform high intensity work. And, in my opinion, this does not really happen! This ability impairs only mathematically. Mathematically W’ is work performed above CP hence, when CP becomes higher, it may “eat” part of W’. In reality however, athletes just cover greater part of high-intensity with his/her CP and less with W’. We can say that he/she now covers more high intensity work “aerobically” and he/she doesn’t need the same W’. In study, when CP was increased in group of athletes by hyperoxia condition, their W’ decreased though overall amount of high intensity work was increased (Vanhatalo, Fulford, DiMenna, & Jones, 2010). Does this remind you something? Yes, (Calbet, et al., 1985) experiment . Only then oxygen availability was decreased by hypoxia and athletes switched to “anaerobic mode”. Probably CP and W’ are not so firmly fixed and independent indexes, as CP-W theory suggests, rather they are inseparable parts of one, complexly regulated process.

Actually, I am not saying something revolutionary. Some experts in this field expressed the same idea (Poole, Burnley, Vanhatalo, Rossiter, & Jones, 2016). However, they defend the notion about fixed thresholds in human sports physiology. In opposite, I rather agree with Tim Noakes (Noakes, 2003)  that there are no precise and fixed cliff edges. Rather, there is tendency, for the rate of metabolites accumulation to accelerate towards higher intensity spectrum. This non-linear curve is specific for every athlete. It is not correct that below CP athletes do not spend their homeostasis maintaining capacity and then, when they go over CP, they suddenly start to spend it. Look at the picture 4.Green11

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Picture 4. Incremental step cycle ergometer test.

Graph above represents blood lactate accumulation during test when intensity was increased by 50 W every 3 min. Lactate turn point (rapid acceleration in lactate accumulation) probably may be identified around 19-th minute. However respiratory  compensation point (line starts to curve up) for the same subject on the graph below is not  easy to define. 

Probably, you may identify lactate turn point (anaerobic threshold) at upper graph, where resolution (sampling intervals) was 3 min, however it will be much more difficult to define another threshold – respiratory compensation point (another way to define anaerobic threshold), when gas exchange graph for the same test is presented with resolution of 10 sec (lower graph). Nevertheless curvature of the line, thus acceleration of changes, is clear.

If W’ is ability to maintain homeostasis, which is probably more genuine physiological definition rather than pure mathematical – “work capacity above CP”, then different factors have unequal contributions to its depletion throughout intensity’s spectrum. All of them may have different thresholds. At one intensity, some factors play a predominant role, and at the other – others (Burnley & Jones, 2016). Their influences overlap and interact with each other, causing non-linear acceleration in fatigue development rather than discrete quantum jump.

From my point of view, CP-W’ model tries to squeeze fundamentally uncertain, multifactorial sports performance into rigid mathematical model with fixed thresholds and exact numbers. However, its predictions are not always reliable.

What really determinates high-intensity work capacity?

Athletes may cover high-intensity work aerobically and anaerobically. Nevertheless this does not define unreservedly work’s tolerance. Ability to perform intense exercise depends mostly on ability to maintain homeostasis. In its turn that depends on many internal (e.g. training adaptation) and external (e.g. intensity’s magnitude and duration) factors as well as on their interactions. We can test this ability for different classes of challenges but it is not easy to quantify it in one universal value. MAOD and CP-W’ concept doesn’t describe comprehensively all complexity of high-intensity exercise.

When coaches talk about anaerobic capacity they are interested in ability to perform, or rather maintain, high-intensity work. It may be single bout longer than 10 sec or it may be multiple high-intensity bouts with incomplete recovery between them. They (coaches) expect that tests for anaerobic capacity provide them necessary information.

The problem is that it looks like anaerobic energy production and work that can be done using this energy are not the decisive factors which limit high-intensity performance. Most likely, aerobic and buffering /clearing capacities are more important elements. For example, when Olsen et al. compared competitive and recreational runners on traditionally “anaerobic” distances 400 and 800 m they found that competitive runners were much more superior thanks to their more advanced aerobic qualities whereas MAOD was not different between two groups (Olesen, Raabo, Bangsbo, & Secher, 1994). Other researchers found that 400 m and long-distance runners attained the same result during incremental test. However, former achieved that using more their buffering capacity whereas latter exploited their superior aerobic qualities (Rocker, Striegel, Freund, & Dickhuth, 1994). Aerobic fitness and buffering/clearance capacity were shown as important factors in repeated sprint tests (Bishop, Hill-Haas, Dawson, & Goodman, 2006; McGawley & Bishop, 2015).

Keeping this in mind, what three anaerobic tests can tell us?

Well, in my opinion, Wingate test can give information about rate of power decline. This may be useful for evaluating ability to maintain maximal effort inside single, relatively short bout. To some extant this is evaluation of buffering/clearing capacities. CP-W’ technique may be useful for CP estimation. In spite that CP is probably not a “true threshold” we need it as a reference point for exercise prescription and assessment of aerobic abilities. From this point of view CP may be a useful alternative to MLSS. However, I don’t advice to use W’  for training guidance and evaluation. MAOD test, though may reflect anaerobic energy production in particular settings (2-3 min exhaustive run), has little practical significance.

Defending homeostasis.

Imagine fortress which represents our ability to defend homeostasis. During exercise this fort is under siege of the enemies – bad guys who want to destroy homeostasis. Intensity of the fight depends on intensity of exercise. Height and thickness of fortress’s walls reflect our aerobic capacity. However, walls are not the only defence of our fort. There are some special guys who can deal with the enemies if they manage to break over or through the walls. These guards represent our buffering/ clearing capacity. Our guards can temporally isolate some bad guys, throw back outside the fort others and kill thirds. Their capacity is not endless however. How long they can last depends on how many enemies brake through and how long siege continues and, of course, how good are our guards and how many we have. Endurance athletes may have very high and thick walls but relatively mediocre guards. Sprint athletes may have lower walls but very strong guards. However, any attempt to accurately assess our defensive capabilities runs into some difficult problems.

We don’t really have comprehensive understanding about who our enemies are, how they interact with each other and how they may change their tactics in dependence of duration and intensity of the siege. In relation to our defence force, we are relatively good only in measuring walls (oxygen capacity) but we don’t know well our guards. The problem of their study is aggravated by our current technological inability to measure exercising humans “online”, comprehensively, at the deepest, cellular level.

Thus, at the moment, we can assess our defensive capabilities mostly indirectly – how long we can withstand different types of sieges and storms. We cannot completely separate and quantify how many enemies were not allowed through the walls and how many were neutralised by the guards. We cannot say that all our enemies have “anaerobic nature”, and that our guards start to fight only after some “anaerobic threshold”. Nevertheless we can make some assumptions, generalisations and predictions. From this point of view such variables as VO2 max, running economy, Wingate fatigue index and thresholds values (MLSS, gas exchange, CP, etc.) may provide us with useful information which may help to improve training and performance. However, attempts to universally express our ability to withstand high intensity exercises in exact and fixed numbers of “anaerobic capacity”, whether it is purely mathematically concept ( W’), theoretical extrapolation (MAOD) and even more practical Wingate test, cannot overcome all difficulties that presents a multifactorial, changeable and very complex nature of the sports exercise. At least for now.

Reference

Billat, V. L., Sirvent, P., Py, G., Koralsztein, J.-P., & Mercier, J. (2003). The concept of maximal lactate steady state. Sports Medicine, 33(6), 407-426.

Bishop, D., Hill-Haas, S., Dawson, B., & Goodman, C. (2006). Comparison of muscle buffer capacity and repeated-sprint ability of untrained, endurance-trained and team-sport athletes. European Journal of Applied Physiology, 96(3), 225-234.

Burnley, M., & Jones, A. M. (2016). Power-duration relationship: Physiology, fatigue, and the limits of human performance. European journal of sport science, 1-12.

Calbet, J. A., De Paz, J. A., Garatachea, N., Cabeza de Vaca, S., & Chavarren, J. (1985). Anaerobic energy provision does not limit Wingate exercise performance in endurance-trained cyclists. J Appl Physiol, 94(2), 668-676.

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McGawley, K., & Bishop, D. J. (2015). Oxygen uptake during repeated-sprint exercise. Journal of Science and Medicine in Sport, 18(2), 214-218.

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Noordhof, D., de Koning, J., & Foster, C. (2010). The maximal accumulated oxygen deficit method: a valid and reliable measure of anaerobic capacity? Sports medicine (Auckland, NZ), 40(4), 285-302.

Noordhof, D. A., Skiba, P. F., & de Koning, J. J. (2013). Determining anaerobic capacity in sporting activities. International Journal of Sports Physiology and Performance, 8(5), 475-482.

Olesen, H. L., Raabo, E., Bangsbo, J., & Secher, N. H. (1994). Maximal oxygen deficit of sprint and middle distance runners. European Journal of Applied Physiology and Occupational Physiology, 69(2), 140-146.                                                                 Poole, D. C., Burnley, M., Vanhatalo, A., Rossiter, H. B., & Jones, A. M. (2016). Critical power: an important fatigue threshold in exercise physiology. Med Sci Sports Exerc, 48(11), 2320-2334.

Rocker, K., Striegel, H., Freund, T., & Dickhuth, H. (1994). Relative functional buffering capacity in 400-meter runners, long-distance runners and untrained individuals. European Journal of Applied Physiology and Occupational Physiology, 68(5), 430-434.

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Vanhatalo, A., Fulford, J., DiMenna, F. J., & Jones, A. M. (2010). Influence of hyperoxia on muscle metabolic responses and the power-duration relationship during severe-intensity exercise in humans: a 31P magnetic resonance spectroscopy study. Exp Physiol, 95(4), 528-540.