The purpose of this study was to use 31P-nuclear magnetic resonance spectroscopy to examine changes in wrist flexor muscle metabolism during the transitions from rest to steady-state exercise (on-transient) and back to rest (off-transient). Five healthy young males (mean age 25 +/- 2 yr) performed a series of square-wave exercise tests, each consisting of 5 min of moderate-intensity work followed by a 5-min recovery period. The subjects repeated this protocol six times, and each individual's results were pooled before analysis. ATP and intracellular pH did not change significantly during exercise or recovery. Phosphocreatine (PCr) declined progressively at the onset of exercise, reaching a plateau after approximately 2 min. A reciprocal increase in Pi occurred during the onset of exercise. During the recovery period PCr was resynthesized, whereas Pi returned to resting levels. The data were plotted as a function of time and fit with both first- and second-order exponential growth or decay models; however, the second-order model did not significantly improve the fit of the data. Time constants for the first-order model of the on- and off-transient responses for both PCr and Pi were approximately 30 s. These values are nearly identical to the time constants for oxygen consumption during submaximal exercise that have been reported previously by several authors. The results of this study show that the metabolism of muscle PCr during steady-state exercise and recovery can be accurately described by a monoexponential model and, further, suggest that a first-order proportionality exists between metabolic substrate utilization and oxygen consumption.
A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness
