Prompted by the observation that the slope of the relationship between average rectified electromyography (EMG) and the ensemble activation rate of a pool of motor units progressively decreased (showing a downward nonlinearity), an experimental study was carried out to test the widely held notion that the EMG is the simple algebraic sum of motor-unit action-potential trains. The experiments were performed on the cat soleus muscle under isometric conditions, using electrical stimulation of alpha-motor axons isolated in ventral root filaments. The EMG signals were simulated experimentally under conditions where the activation of nearly the entire pool of motor units or of subsets of motor units was completely controlled by the experimenter. Sets of individual motor units or of small groups of motor units were stimulated independently, using stimulation profiles that were strictly repeatable between trials. This permitted a rigorous quantitative comparison of EMGs that were recorded during combined activation of multiple motor filaments with EMGs that were synthesized from the algebraic summation of motor unit action potential trains generated by individual nerve filaments. These were recorded separately by individually stimulating the same filaments with the same activation profiles that were employed during combined stimulation. During combined activation of up to 10 motor filaments, experimentally recorded and computationally synthesized EMGs were virtually identical. This indicates that EMG signals indeed are the outcome of the simple algebraic summation of motor-unit action-potential trains generated by concurrently active motor units. For both recorded and synthesized EMGs, it was confirmed that EMG magnitude increased nonlinearly with the ensemble activation rate of a pool of motor units. The nonlinearity was largely abolished when EMG magnitude was estimated as the sum of rectified, instead of raw, motor-unit action-potential trains. This suggests that the downward nonlinearity in the EMG-ensemble activation rate relation is due to signal cancellation arising from the perfectly linear summation of positive and negative components of action-potential waveforms. The findings provide a much needed post hoc validation of the concept of EMG generation by strict algebraic summation of motor unit action potentials that is generally relied on in theoretical modeling studies of EMG and in EMG decomposition algorithms.

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Nearly all muscle models and most motor control concepts assume that forces from individual muscle fibers and motor units sum in an additive manner once effects of in-series tendon compliance are taken into account. Due to the numerous mechanical linkages between individual fibers, though, it is unclear whether this assumption is warranted. This work examined motor unit force summation over a wide range of muscle forces in the cat soleus. Nonadditive summation implies a nonlinear summation of motor unit forces. Summation nonlinearities were quantified during interactions of 10 individual motor units and 4 motor unit bundles containing approximately 10 units each. These protocols allowed motor unit force summation to be examined from approximately 0 to 25% of tetanic muscle force. Nonlinear summation was assessed by comparing the actual forces to the algebraic sum of individual units and bundles stimulated in isolation. Superadditive summation meant that the actual force exceeded the algebraic sum, whereas subadditive summation meant that the actual force was smaller than the algebraic sum. Experiments tested the hypothesis that superadditive summation occurs at low force levels when few motor units are recruited, whereas subadditive summation prevails above 10% of tetanic force. Results were consistent with this hypothesis. As in previous studies, nonlinear summation in the soleus was modest, but a clear transition from predominately superadditive to predominantly subadditive summation occurred in the range of 6–8% of tetanic force. The largest nonlinearities were transient and appeared at the onset of recruitment and derecruitment of groups of motor units. The results are discussed in terms of the mechanical properties of the connective tissue forming the tendon and linking muscle fibers.