Is the motor unit mean firing rate versus recruitment threshold relationship linear?

Advances in surface electromyographic (EMG) signal decomposition allow researchers to analyze data for 20-50 motor units per contraction. To simplify interpretation, some investigators rely on group mean analysis of the mean firing rate versus recruitment threshold relationship, but it is unclear if this association is linear. Objective: To determine whether this relationship is strongest when analyzed via linear, quadratic, or cubic regression. Approach: Twenty-one men (mean +/- SD age = 24 +/- 4 years) and 16 women (21 +/- 2 years) performed isometric contractions of the knee extensors at 50% of maximal force while bipolar surface EMG signals were recorded from the vastus lateralis. A decomposition algorithm was used to calculate the mean firing rate and recruitment threshold of each motor unit at accuracy levels ranging from 90.0%- 93.0%. Polynominal regression was used to determine if each relationship was best fit with a linear, quadratic, or cubic model. We examined individual contractions and grouped data. Main results: Overall, 80% of the relationships were best fit with a linear model. Quadratic and cubic relationships were more appropriate for 16% and 2% of the contractions, respectively. Selecting varying accuracy levels within a range of 90.0%-93.0% had little influence on whether a given dataset was best fit with a linear, quadratic, or cubic model. Grouping of data provided different relationships than otherwise found on a contraction-by-contraction basis. Significance: The mean firing rate versus recruitment threshold relationship is typically best fit with a linear model. These relationships should be examined on an individual contraction basis.