Computationally efficient models of neuromuscular recruitment and mechanics

We have improved the stability and computational efficiency of a physiologically realistic, virtual muscle (VM 3.*) model (Cheng et al 2000 J. Neurosci. Methods 101 117-30) by a simpler structure of lumped fiber types and a novel recruitment algorithm. In the new version (VM 4.0), the mathematical equations are reformulated into state-space representation and structured into a CMEX S-function in SIMULINK. A continuous recruitment scheme approximates the discrete recruitment of slow and fast motor units under physiological conditions. This makes it possible to predict force output during smooth recruitment and derecruitment without having to simulate explicitly a large number of independently recruited units. We removed the intermediate state variable, effective length (L-eff), which had been introduced to model the delayed length dependency of the activation-frequency relationship, but which had little effect and could introduce instability under physiological conditions of use. Both of these changes greatly reduce the number of state variables with little loss of accuracy compared to the original VM. The performance of VM 4.0 was validated by comparison with VM 3.1.5 for both single-muscle force production and a multi-joint task. The improved VM 4.0 model is more suitable for the analysis of neural control of movements and for design of prosthetic systems to restore lost or impaired motor functions. VM 4.0 is available via the internet and includes options to use the original VM model, which remains useful for detailed simulations of single motor unit behavior.