Parameter estimation in modeling phosphocreatine recovery in human skeletal muscle

Commonly, muscle phosphocreatine (PCr) recovery from exercise has been fitted to a monoexponential function. However, a number of experiments indicate that at low muscle pH, a monoexponential fit is not suitable. We have performed in vivo 31P-MRS measurements of PCr during recovery from high-intensity intermittent exercise where muscle pH dropped below 6.5 (35 out of 40 cases). Results of a statistical analysis showed that monoexponentiality should be rejected in 32 out of 40 cases. Therefore, a Monte Carlo simulation was carried out to test the quality of competing models used in the literature at low pH: monoexponential, biexponential and changing rate utilization resource (CRUR). For each model, random Gaussian-distributed errors were imposed on simulated PCr recovery before performing the fits. A monoexponential function (three estimated parameters) provided a correct estimation of parameters (unbiased, normally distributed, poorly correlated estimates) and, therefore, should be preferred. When alternative functions are required, as in 32 cases out of 40 in the present study, it is demonstrated that a biexponential function (five estimated parameters) is not well suited (estimates were correlated), whereas a CRUR function (four estimated parameters) provides correct estimation of the parameters. It is concluded that a biexponential fit to PCr recovery is too sensitive to experimental errors to be practicable. Statistical and physiological relevance of CRUR are discussed.