A geometric approach to quantifying the neuromodulatory effects of persistent inward currents on individual motor unit discharge patterns

Objective. All motor commands flow through motoneurons, which entrain control of their innervated muscle fibers, forming a motor unit (MU). Owing to the high fidelity of action potentials within MUs, their discharge profiles detail the organization of ionotropic excitatory/inhibitory as well as metabotropic neuromodulatory commands to motoneurons. Neuromodulatory inputs (e.g. norepinephrine, serotonin) enhance motoneuron excitability and facilitate persistent inward currents (PICs). PICs introduce quantifiable properties in MU discharge profiles by augmenting depolarizing currents upon activation (i.e. PIC amplification) and facilitating discharge at lower levels of excitatory input than required for recruitment (i.e. PIC prolongation). Approach. Here, we introduce a novel geometric approach to estimate neuromodulatory and inhibitory contributions to MU discharge by exploiting discharge non-linearities introduced by PIC amplification during time-varying linear tasks. In specific, we quantify the deviation from linear discharge (‘brace height’) and the rate of change in discharge (i.e. acceleration slope, attenuation slope, angle). We further characterize these metrics on a simulated motoneuron pool with known excitatory, inhibitory, and neuromodulatory inputs and on human MUs (number of MUs; Tibialis Anterior: 1448, Medial Gastrocnemius: 2100, Soleus: 1062, First Dorsal Interosseus: 2296). Main results. In the simulated motor pool, we found brace height and attenuation slope to consistently indicate changes in neuromodulation and the pattern of inhibition (excitation–inhibition coupling), respectively, whereas the paired MU analysis (ΔF) was dependent on both neuromodulation and inhibition pattern. Furthermore, we provide estimates of these metrics in human MUs and show comparable variability in ΔF and brace height measures for MUs matched across multiple trials. Significance. Spanning both datasets, we found brace height quantification to provide an intuitive method for achieving graded estimates of neuromodulatory and inhibitory drive to individual MUs. This complements common techniques and provides an avenue for decoupling changes in the level of neuromodulatory and pattern of inhibitory motor commands.