Elevating core temperature at rest causes increases in minute ventilation (V̇e), which lead to reductions in both arterial CO partial pressure (hypocapnia) and cerebral blood flow. We tested the hypothesis that in resting heated humans this hypocapnia diminishes the ventilatory sensitivity to rising core temperature but does not explain a large portion of the decrease in cerebral blood flow. Fourteen healthy men were passively heated using hot-water immersion (41°C) combined with a water-perfused suit, which caused esophageal temperature (T) to reach 39°C. During heating in two separate trials, end-tidal CO partial pressure decreased from the level before heating (39.4 ± 2.0 mmHg) to the end of heating (30.5 ± 6.3 mmHg) ( P = 0.005) in the Control trial. This decrease was prevented by breathing CO-enriched air throughout the heating such that end-tidal CO partial pressure did not differ between the beginning (39.8 ± 1.5 mmHg) and end (40.9 ± 2.7 mmHg) of heating ( P = 1.00). The sensitivity to rising T (i.e., slope of the T - V̇ relation) did not differ between the Control and CO-breathing trials (37.1 ± 43.1 vs. 16.5 ± 11.1 l·min·°C, P = 0.31). In both trials, middle cerebral artery blood velocity (MCAV) decreased early during heating (all P < 0.01), despite the absence of hyperventilation-induced hypocapnia. CO breathing increased MCAV relative to Control at the end of heating ( P = 0.005) and explained 36.6% of the heat-induced reduction in MCAV. These results indicate that during passive heating at rest ventilatory sensitivity to rising core temperature is not suppressed by hypocapnia and that most of the decrease in cerebral blood flow occurs independently of hypocapnia. NEW & NOTEWORTHY Hyperthermia causes hyperventilation and concomitant hypocapnia and cerebral hypoperfusion. The last may underlie central fatigue. We are the first to demonstrate that hyperthermia-induced hyperventilation is not suppressed by the resultant hypocapnia and that hypocapnia explains only 36% of cerebral hypoperfusion elicited by hyperthermia. These new findings advance our understanding of the mechanisms controlling ventilation and cerebral blood flow during heat stress, which may be useful for developing interventions aimed at preventing central fatigue during hyperthermia.

An approximate analytical approach using complex fractional moments (CFMs) is developed for determining the transient response　probability density of nonlinear oscillators with fractional derivative elements under Gaussian white noise. The CFM is defined as the Mellin transform of a probability density function. The system response is represented in the form of a pseudo-harmonic oscillation with amplitude and phase slowly varying with time. Equivalent linearization is first implemented to obtain an equivalent natural frequency and an equivalent damping coefficient of the oscillator. In this regard, simple formulas for determining them are proposed, in which both the nonlinear elements and the elastic and viscous contributions of the fractional elements are taken into account. Next, applying stochastic averaging, the response amplitude is described by a one-dimensional stochastic differential equation, and the corresponding Fokker-Planck equation is derived. The Mellin transform then converts the Fokker-Planck equation into coupled linear ordinary differential equations governing the evolution of amplitude CFMs, which are solved with a constraint corresponding to the normalization condition for a probability density. Finally, the inverse Mellin transform of the CFMs yields the amplitude probability density. The joint probability density of displacement and velocity is also obtained from the amplitude probability density in conjunction with the Jacobian of the pseudo-harmonic variable transformation for the response. Three linear and nonlinear oscillators with fractional derivatives are considered in numerical examples. For all cases, the analytical results obtained by the proposed method are in good agreement with the results of the pertinent Monte Carlo simulation.

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