The convergence of a neuromuscular impulse response towards a lognormal, from theory to practice

Lognormal functions have been found among the best descriptors of the impulse response of neuromuscular systems under various experimental conditions. This arises from the fact that lognormal patterns automatically emerge when a large number of coupled systems interact to produce a response. This paper evaluates the error of convergence towards a lognormal. Under the umbrella of the Central Limit Theorem, the error functions for lognormal and delta-lognormal equations are derived and analyzed. It is shown that these errors can be computed from the estimated values of the lognormal parameters, without any explicit reference to the number of subsystems involved. The resulting theoretical framework is then exploited in three applications: the comparative benchmarking of parameter extraction algorithms, the validation of the results in analysis-by-synthesis experiments and the estimation of the range of acceptable movement times in tests involving rapid movements.