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I quote the following from one of the book written by one of these authors to see if my students can see the flaws in this explanation:
".... your marathon pace is very close to your lactate threshold pace, which is determined by your oxygen consumption at your lactate threshold and your running economy. If you run faster than your lactate threshold pace, then lactate accumulates in your muscles and blood; this occurrence deactivates the enzymes for energy production and makes you slow down".
If this explanation is correct, then there is only one competitive pace - that at which the poisonous lactate reaches the threshold at which it begins to "deactivate" the enzymes for energy production. But how would this same mechanism explain your different paces at other distances - 1 mile; 21 km; 100 miles?
Next, if this explanation is correct, then muscles would run out of energy and go into rigor as a result of the "deactivation of the enzymes for energy production" which would cause muscle ATP concentrations to become depleted. That is how metabolic poisons work. Unless there is another control available this would be the outcome - athletes would not slow down; their muscles would simply go into rigor.
Finally there would be an easy way for the body to allow you to run faster. All it need do is increase your cardiac output which is submaximal during marathon running. This would increase the oxygenation of the muscles, reverse the anerobiosis and lactate production, causing the lactate concentrations to go down and the energy producing enzymes to be re-activated allowing you to speed up. Only when the maximal cardiac output was reached would this mechanism then explain why you slow down.
The same paradox occurs when we try to explain why some forms of altitude training improve performance or why EPO use increases submaximal exercise performance more than it does the VO2max. The moment you say that either intervention improves exercise performance by increasing oxygen delivery to
muscle, then you have to answer the question: Well why in the control state did the heart not simply pump harder and so send more blood to the muscles and so allow the exercise to be performed at a higher intensity (up to the point at which the cardiac output is maximal)? Why in the absence of altitude training or EPO treatment is the heart not pumping optimally to maximize oxygen delivery to the muscles?
These are fundamental questions that in my view cannot be answered by the HIll model.
If however the regulated variable is the mass of muscle that is being activated which then sets the pace and consequently the demand for oxygen and cardiac output, then the explanation is easier. It would then be hypothesized that altitude training and EPO use improve submaximal exercise performance by allowing the recruitment of a larger muscle mass during exercise allowing an increased running speed to be achieved.
Changes in which sensed variables allow this to happen, is the mystery inviting answers.