Our understanding of the firing behaviour of motoneuron (MN) pools during human voluntary muscle contractions is currently limited to electrophysiological findings from animal experiments extrapolated to humans, mathematical models of MN pools not validated for human data, and experimental results obtained from decomposition of electromyographical (EMG) signals. These approaches are limited in accuracy or provide information on only small partitions of the MN population. Here, we propose a method based on the combination of high-density EMG (HDEMG) data and realistic modelling for predicting the behaviour of entire pools of motoneurons in humans. The method builds on a physiologically realistic model of a MN pool which predicts, from the experimental spike trains of a smaller number of individual MNs identified from decomposed HDEMG signals, the unknown recruitment and firing activity of the remaining unidentified MNs in the complete MN pool. The MN pool model is described as a cohort of single-compartment leaky fire-and-integrate (LIF) models of MNs scaled by a physiologically realistic distribution of MN electrophysiological properties and driven by a spinal synaptic input, both derived from decomposed HDEMG data. The MN spike trains and effective neural drive to muscle, predicted with this method, have been successfully validated experimentally. A representative application of the method in MN-driven neuromuscular modelling is also presented. The proposed approach provides a validated tool for neuroscientists, experimentalists, and modelers to infer the firing activity of MNs that cannot be observed experimentally, investigate the neuromechanics of human MN pools, support future experimental investigations, and advance neuromuscular modelling for investigating the neural strategies controlling human voluntary contractions.

Our understanding of the behaviour of spinal alpha-motoneurons (MNs) in mammals partly relies on our knowledge of the relationships between MN membrane properties, such as MN size, resistance, rheobase, capacitance, time constant, axonal conduction velocity and afterhyperpolarization period. We reprocessed the data from 40 experimental studies in adult cat, rat and mouse MN preparations, to empirically derive a set of quantitative mathematical relationships between these MN electrophysiological and anatomical properties. This validated mathematical framework, which supports past findings that the MN membrane properties are all related to each other and clarifies the nature of their associations, is besides consistent with the Henneman's size principle and Rall's cable theory. The derived mathematical relationships provide a convenient tool for neuroscientists and experimenters to complete experimental datasets, to explore relationships between pairs of MN properties never concurrently observed in previous experiments, or to investigate inter-mammalian-species variations in MN membrane properties. Using this mathematical framework, modelers can build profiles of inter-consistent MN-specific properties to scale pools of MN models, with consequences on the accuracy and the interpretability of the simulations.

Backed by a century of research and development, Hill-type muscle-tendon models are extensively used for countless applications. Lacking recent reviews, the field of Hill-type modelling is however dense and hard-to-explore, with detrimental consequences on knowledge transmission, inter-study consistency, and innovation. Here we present the first systematic review of the field of Hill-type muscle-tendon modelling. It aims to clarify the literature by detailing its contents and proposing updated terminology and definitions, and discussing the state-of-the-art by identifying the latest advances, current gaps, and potential improvements in modelling muscle properties. To achieve this aim, fifty-five criteria-abiding studies were extracted using a systematic search and their Hill-type models assessed according to a completeness evaluation, which identified the modelled muscle-tendon properties, and a modelling evaluation, which considered the level of validation and reusability of the model, and attention given to its modelling strategy and calibration. It is concluded that most models (1) do not significantly advance the dated gold standards in muscle modelling and do not build upon more recent advances, (2) overlook the importance of parameter identification and tuning, (3) are not strongly validated, and (4) are not reusable in other studies. Besides providing a convenient tool supported by extensive supplementary material for understanding the literature, the results of this review open a discussion on the necessity for global recommendations in Hill-type modelling and more frequent reviews to optimize inter-study consistency, knowledge transmission and model reusability.

Our understanding of the behaviour of motoneurons (MNs) in mammals partly relies on our knowledge of the relationships between MN membrane properties, such as MN size, resistance, rheobase, capacitance, time constant, axonal conduction velocity and afterhyperpolarization period. Based on scattered but converging evidence, current experimental studies and review papers qualitatively assumed that some of these MN properties are related. Here, we reprocessed the data from 27 experimental studies in cat and rat MN preparations to empirically demonstrate that all experimentally measured MN properties are associated to MN size. Moreover, we expanded this finding by deriving mathematical relationships between each pair of MN properties. These relationships were validated against independent experimental results not used to derive them. The obtained relationships support the classic description of a MN as a membrane equivalent electrical circuit and describe for the first time the association between MN size and MN membrane capacitance and time constant. The obtained relations indicate that motor units are recruited in order of increasing MN size, muscle unit size, MN rheobase, unit force recruitment thresholds and tetanic forces, but underlines that MN size and recruitment order may not be related to motor unit type.

The spinal motor neurons are the only neural cells whose individual activity can be non-invasively identified using grids of electromyographic (EMG) electrodes and source separation methods, i.e., EMG decomposition. In this study, we combined computational and experimental approaches to assess how the design parameters of grids of electrodes influence the number and characteristics of the motor units identified. We first computed the percentage of unique motor unit action potentials that could be theoretically discriminated in a pool of 200 simulated motor units when recorded with grids of various sizes and interelectrode distances (IED). We then identified motor units from experimental EMG signals recorded in six participants with grids of various sizes (range: 2-36 cm2) and IED (range: 4-16 mm). Increasing both the density and the number of electrodes, as well as the size of the grids, increased the number of motor units that the EMG decomposition could theoretically discriminate, i.e., up to 82.5% of the simulated pool (range: 30.5-82.5%). Experimentally, the configuration with the largest number of electrodes and the shortest IED maximized the number of motor units identified (56 +/- 14; range: 39-79) and the percentage of low-threshold motor units identified (29 +/- 14%). Finally, we showed with a prototyped grid of 400 electrodes (IED: 2 mm) that the number of identified motor units plateaus beyond an IED of 2-4 mm. These results showed that larger and denser surface grids of electrodes help to identify a larger and more representative pool of motor units than currently reported in experimental studies.