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LETTER TO THE EDITOR
This study examined neurohumoral alterations during prolonged exercise with and without hyperthermia. The cerebral oxygen-to-carbohydrate uptake ratio (O2/CHO = arteriovenous oxygen difference divided by arteriovenous glucose difference plus one-half lactate), the cerebral balances of dopamine, and the metabolic precursor of serotonin, tryptophan, were evaluated in eight endurance-trained subjects during exercise randomized to be with or without hyperthermia. The core temperature stabilized at 37.9 ± 0.1°C (mean ± SE) in the control trial, whereas it increased to 39.7 ± 0.2°C in the hyperthermic trial, with a concomitant increase in perceived exertion (P < 0.05). At rest, the brain had a small release of tryptophan (arteriovenous difference of –1.2 ± 0.3 µmol/l), whereas a net balance was obtained during the two exercise trials. Both the arterial and jugular venous dopamine levels became elevated during the hyperthermic trial, but the net release from the brain was unchanged. During exercise, the O2/CHO was similar across trials, but, during recovery from the hyperthermic trial, the ratio decreased to 3.8 ± 0.3 (P < 0.05), whereas it returned to the baseline level of 
6 within 5 min after the control trial. The lowering of O2/CHO was established by an increased arteriovenous glucose difference (1.1 ± 0.1 mmol/l during recovery from hyperthermia vs. 0.7 ± 0.1 mmol/l in control; P < 0.05). The present findings indicate that the brain has an increased need for carbohydrates during recovery from strenuous exercise, whereas enhanced perception of effort as observed during exercise with hyperthermia was not related to alterations in the cerebral balances of dopamine or tryptophan.
A spurious correlation
To the Editor: Nybo et al. (3) examined the relationship between the arterial concentration of free tryptophan (TRP) and the arteriovenous concentration difference of free TRP across the brain. The correlation coefficient between these two variables was reported to be 0.54 (P < 0.05). Nybo et al. proposed that this significant relationship supported their main research hypothesis that "serotonin levels in the brain could increase when exercise elevates the plasma concentration of free TRP." Although we do not necessarily disagree with the possibility that this hypothesis is true, we maintain that the correlation analysis, which was employed to arrive at this conclusion, is spurious.
A spurious correlation between two variables is defined as one that could occur in the absence of any real organic link between the variables (4). There may be a real physiological relationship between the variables of interest, but a mathematical process may also mediate the relationship. The variables that were correlated by Nybo et al. (3) are not independent, irrespective of any physiological mechanisms that are hypothesized to link them together. Arterial free TRP was one variable in the analysis, but it was also involved in the calculation of the other variable to be correlated against it (arteriovenous concentration difference of free TRP). Therefore, the two variables that were correlated are already linked mathematically, and a significant moderate-to-high correlation between these two variables would be expected with any values of arterial and venous free TRP. This artifact has been known for many years (4) and was recently shown to be present by Atkinson et al. (1) in some research studies on cycling efficiency. We can prove the relevancy of this artifact to the data of Nybo et al. (3) with the aid of a data simulation.
We generated two sets of random data (n = 40) representing arterial and venous free TRP concentrations within the same physiological ranges as reported by Nybo et al. (3). Both sets of data were normally distributed and completely unrelated (the correlation coefficient between our hypothetical arterial and venous free TRP concentrations was 0.02). We then calculated the arteriovenous concentration difference of free TRP and plotted these data against our arterial free TRP data (Fig. 1). It can be seen that a moderate-to-strong positive relationship results (r = 0.74), which is statistically significant (P < 0.0005).
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REFERENCES
Alan M. Nevill
School of Sport, Performing Arts and Leisure, University of Wolverhampton, Walsall WS1 3BD, United Kingdom
First of all, Atkinson et al. state that we use the positive correlation between arterial TRP and the arteriovenous concentration difference of TRP to support our main research hypothesis (which they cite as "serotonin levels in the brain could increase when exercise elevates the plasma concentration of free TRP"). However, this is not correct. With respect to TRP, our hypothesis was that the cerebral balance would change during prolonged exercise and especially so when hyperthermia was superimposed, if this neurohumoral factor (TRP) was linked with central fatigue. In the discussion, we concluded that "the cerebral TRP uptake was not affected by hyperthermia" (nor by 2 h of exercise) and that the "serotonin central fatigue hypothesis" cannot explain the fatigue that develops with hyperthermia. However, the present results do not exclude a role for TRP in central fatigue (during other exercise conditions), as there is a positive correlation between the arterial availability and the arteriovenous concentration difference across the brain.
Regarding the so-called spurious correlation, it is statistically trivial that a randomly generated data set of unrelated arterial and venous values (without any model restrictions) yields a positive correlation between the arteriovenous concentration difference and the arterial concentration. However, that does not mean that experimental data automatically will turn out with a positive correlation because, in physiological systems, the venous values are usually not independent of the arterial concentrations. For example, during prolonged exercise, the arterial concentration of free fatty acid (FFA) also increases (2), but a positive correlation between the arteriovenous concentration difference of FFA and arterial FFA is not observed because the blood-brain barrier (BBB) is almost impermeable to FFA (see Fig. 2). IL-6 is another example of a substance that becomes elevated in the arterial blood during exercise without yielding a positive correlation between the arteriovenous concentration difference and the arterial concentration. IL-6 is released rather than taken up by the brain during prolonged exercise (4). However, for substances where the cerebral uptake may be influenced by the concentration gradient across the BBB, as expected for the mediated transport of TRP (1), it is physiologically reasonable that the arteriovenous concentration difference will increase as the arterial availability increases. This was the model or hypothesis tested by the linear regression in our original article (Fig. 2 in Ref. 3), and the results from such correlation analysis are not comparable with and not negated by the correlation coefficient presented by Atkinson et al. Thus their statistical model ignores any relation between the arterial and venous values, and consequently it does not consider that, in real biological systems, the difference between factor A and factor V may be unrelated to factor A, although they mathematically have a common component.
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REFERENCES
Eva Blomstrand
University College of Physical Education and Sports and Department of Physiology and Pharmacology, Karolinska Institute, SE-17177 Stockholm, Sweden.
Kirsten Møller
Niels Secher
Departments of Infection Diseases and Anesthesia, Rigshospitalet, The Copenhagen Muscle Research Center, University of Copenhagen, DK-2100 Copenhagen, Denmark.
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