Time averaging and fitting of nonlinear metabolic changes: the issue of the time index choice applied to 31P MRS investigation of muscle energetics

We present an exact analytical method dedicated to fitting time-dependent exponential-like changes in MR spectra. As an illustration, this method has been applied to fitting metabolic changes recorded by 31P MRS in human skeletal muscle occurring during a rest-exercise-recovery protocol. When recording metabolic changes with the accumulative method, the time averaging of the MR signals implies the choice of a time index for fitting any changes in the features of the associated MR spectra. A critical examination of the different ways (constant, linear, and exponential) of choosing the time index is reported. By numerical analysis, we have calculated the errors generated by the three methods and we have compared their sensitivity to noise. In the case of skeletal muscle, both constant and linear methods introduce large and uncontrolled errors for the whole set of metabolic parameters derived from PCr] changes. In contrast, the exponential method affords a reliable estimation of critical parameters in muscle bioenergetics in both normal and pathological situations. This method is very easy to implement and provides an exact analytical solution to fitting changes in MR spectra recorded by the accumulative method.