In a previous article titled, *Critical Power: Modeling The Power-Duration Curve*, I introduced the critical power model, which aims to provide us with a useful way of modeling time to exhaustion in athletes as well as quantifying changes in both fitness characteristics and performance. One of the most fascinating things about the critical power model is that it applies across kingdoms, phylums, and classes of animal life. This suggests a highly conserved and organized physiological process, and perhaps even a unifying principle of bioenergetics. Part of my ongoing research, at the time of this article’s publication, has involved better understanding the mechanistic basis of the critical power model, which began with a paper I published titled, “*The Future Is NIRS: Muscle Oxygen Saturation As An Estimation Of The Power Duration Curve*”. At the end of that paper I made the following statement:

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It has previously been observed that as exercise increases up to a heavy exertion level, or close to a maximal power output, there is a progressive decrease in muscle oxygen saturation to a minimal point or plateau which gives rise to exhaustion. Given this information, and the relationship between oxygen delivery, critical power, and W’ it stands to reason that muscle oxygen saturation can be used as an indicator of proximity to failure. Previous investigations have shown that isometric muscle contractions result in the same muscle oxygen saturation (SmO2) value at the point of failure for individuals. These results can be further extrapolated to confirm the relationship between time to task failure and time to SmO2 minimum. Considering these findings a value as simple as SmO2min and SmO2 rate of change can be used to potentially predict failure during isometric muscle contraction and similar results were reported during sustained gripping tasks where maximum and minimum values for deoxyhemoglobin and oxyhemoglobin respectively were correlated with loss of force production. While more research into this area is needed before this concept can be extrapolated to cyclic activities such as running, it seems promising given that the hyperbolic form of the power duration relationship is rigorous and highly conserved across forms of exercise, individual muscles, and muscle groups. Additionally, experimental evidence suggests that when oxygen delivery is fixed via blood flow occlusion, regional oxygen saturation predicts time to exhaustion. This aligns with the idea that tissue oximeters provide information on the balance between oxygen supply and oxygen demand and that regional oxygenated hemoglobin saturation represents tissue reserve capacity following tissue oxygen extraction. As a result, the equation t lim= W’/P-CP can be reconceptualized as t lim= (regional O2Hb saturation)/(the balance of oxygen supply and demand). However, regional oxygenated hemoglobin saturation fails to predict time to fatigue accurately when delivery is not fixed via blood flow occlusion. As a result, more research needs to be done in order to further elucidate the incompletely understood relationship between oxygen delivery, critical power, and W’.”

Since publishing that paper this chain of research has been extended significantly, and my colleagues and I have now honed in on some novel mechanisms underpinning the critical power concept, as well as some more practical ways to model fatigue in live time using near infrared spectroscopy. In this article i’ll give you an update of our findings as well as basic applications of these techniques.

**Predicting Time to Exhaustion During Static Exercise and Dynamic Exercise With Occlusion**

In Stephane Perrey and Marco Ferrari’s 2017 systematic review titled, *Muscle Oximetry in Sports Science*, they state that tissue oximeters provide information on the balance between oxygen supply and oxygen demand in skeletal muscle and that regional oxygen saturation represents a tissue reserve capacity following oxygen extraction. In essence, the concept can be summed up with the following equation:

SmO2%= ((Oxygenated hemoglobin + myoglobin) / (total hemoglobin + myoglobin)) *100

The ‘m’ in SmO2 stands for muscle, and the ‘%’ is expressed on an a priori zero to one hundred percent scale. If we combine this the aforementioned concepts relating to regional oxygen saturation and modeling time to exhaustion with critical power, we can can hypothesize that the following statement will hold true: Time to exhaustion = SmO2% / ΔSmO2, where SmO2% represents a live muscle oxygen saturation reading and ΔSmO2 is the rate of change of muscle oxygen saturation. However, because this statement assumes that task failure will occur at 0% SmO2, it must be modified based on an individual's minimum achieved muscle oxygen saturation based on prior date. As a result, a more accurate equation describing the relationship between oxygen kinetics and task failure is as follows:

Time to exhaustion = (SmO2min - SmO2max) / ΔSmO2

There is evidence showing that the above equation accurately predicts time to exhaustion during static exercise. In figure I we have an individual's muscle oxygen saturation plotted against time during three load conditions performing an isometric split squat hold to exhaustion. Using the above formula, applied to these data sets we get the following results for the three load conditions:

Heavy load condition; (22%-70%)/66s = -0.73 %/s

Moderate load condition; (23%-71%)/141s = -0.34 %/s

Light load condition; (26%-76%)/236s = -0.21%

As you can see from the calculations above, the heavier the load condition the more negative ΔSmO2 becomes, indicating that oxygen utilization outstrips oxygen supply at a faster rate. Interestingly, this formula also holds accurate during dynamic exercise with occlusion, because like static exercise SmO2min is relatively fixed. However, during dynamic exercise without occlusion SmO2min is too variable for this to be accurate, as you can see in figure II comparing muscle oxygen saturation trends during heavy, moderate, and light bicep curls with and without occlusion. As a result, more accurate means are needed to predictive model dynamic exercise without occlusion. One such method is using critical energetic rate.

**Predicting Time to Task Failure During Dynamic Exercise With Critical Energetic Rate**

Whereas critical power represents the higher power-output that can be sustained indefinitely, critical energetic rate represents the highest rate of steady state oxygen supply and demand. In essence both critical power and critical energetic rate can modulate intensity independent of one another. Demonstrating this concept is a case study from a high level post collegiate rower I coached through his 2019 season. Over three separate days this athlete completed time to exhaustion trials on an erg where they held 350, 375, and 400 watts until failure. For each test I recorded his average power output, time to task failure, and his rate of change of muscle oxygen saturation, termed ΔSmO2. Based on his average power output and time to task failure data points I calculated his critical power to be 322 watts. I also calculated his critical energetic rate using his ΔSmO2 and time to task failure data points. The hyperbolic equation which describes the relationship between the balance of oxygen supply and oxygen utilization and exercise tolerance within the severe exercise intensity domain is as follows:

Time to Exhaustion = (M’) / (ΔSmO2 - Critical Energetic Rate)

Using this formula I calculated this athlete's critical energetic rate to be -0.05 %/ second, which represents the rate of change of muscle oxygen saturation that can be sustained indefinitely before oxygen utilization outstrips oxygen supply. One week after completing the three aforementioned tests I had this athlete do one final trial where they were asked to hold 365 watts on the erg until task failure ensued. Based on this individual's critical power and critical energetic rate curves I predicted they would fail in twenty two minutes and thirty eight seconds with a ΔSmO2 of -0.29 %/second. In actuality they sustained this power output for twenty two minutes and forty six seconds with a ΔSmO2 of -0.28 %/second. This demonstrates the fact that both critical power and critical energetic rate can predict time to exhaustion independent of one another. However, critical energetic rate makes up for many of critical power’s shortcomings. For example, critical energetic rate predicts exercise intensity and an athlete's current proximity to task failure in constant fixed power output, constant mixed power output, and intermittent activities. Additionally, critical energetic rate removes the need for individualized W’ recharge rates and it lessens the testing burden required to create accurate predictions compared to critical power. Finally, the critical energetic rate demonstrates a clear intensity duration relationship.

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**As always, if you enjoyed this article please share it with a friend. Additionally, if there are specific topics you’d like to see my write about in the upcoming weeks you can shoot me an email at EvanPeikon@gmail.com**

This one is brutal, thank you again !

Great content, Evan. A couple of questions:

1) Does critical energetic rate overcome the low reliability of time to exhaustion trials? - https://pubmed.ncbi.nlm.nih.gov/18348590/

2) Could critical energetic rate be determined via 3-minute critical power test?