Non-linearity in motor unit velocity twitch dynamics: Implications for ultrafast ultrasound source separation

Abstract

Ultrasound (US) muscle image series can be used for peripheral human-machine interfacing based on global features, or even on the decomposition of US images into the contributions of individual motor units (MUs). With respect to state-of-the-art surface electromyography (sEMG), US provides higher spatial resolution and deeper penetration depth. However, the accuracy of current methods for direct US decomposition, even at low forces, is relatively poor. These methods are based on linear mathematical models of the contributions of MUs to US images. Here, we test the hypothesis of linearity by comparing the average velocity twitch profiles of MUs when varying the number of other concomitantly active units. We observe that the velocity twitch profile has a decreasing peak-to-peak amplitude when tracking the same target motor unit at progressively increasing contraction force levels, thus with an increasing number of concomitantly active units. This observation indicates non-linear factors in the generation model. Furthermore, we directly studied the impact of one MU on a neighboring MU, finding that the effect of one source on the other is not symmetrical and may be related to unit size. We conclude that a linear approximation is limiting the decomposition methods to decompose full velocity twitch trains from velocity images, highlighting the need for more advanced models and methods for US decomposition than those currently employed.

Spatial decomposition of ultrafast ultrasound images to identify motor unit activity – A validation study using intramuscular and surface EMG

“…Third, the BSS method can identify MUs at 30% MVC. This is the first study showing that MUs at 30% MVC can be identified using UUS, as previous studies have been constrained to very low force levels with single MU feedback (Lubel et al, 2022;Rohlén et al, 2020a) and from 2% up to 20% MVC (Carbonaro et al, 2022;Lubel et al, 2023). We expect declining performance at the higher force levels due to inherent non-linearities complicating the velocity field (Lubel et al, 2023) and violating the linear mixture assumption in both the BSS and STA methods.…”

“…This is the first study showing that MUs at 30% MVC can be identified using UUS, as previous studies have been constrained to very low force levels with single MU feedback (Lubel et al, 2022;Rohlén et al, 2020a) and from 2% up to 20% MVC (Carbonaro et al, 2022;Lubel et al, 2023). We expect declining performance at the higher force levels due to inherent non-linearities complicating the velocity field (Lubel et al, 2023) and violating the linear mixture assumption in both the BSS and STA methods. Going from a linear to a nonlinear BSS model (Hyvärinen et al, 2023b(Hyvärinen et al, , 2023a may possibly overcome this limitation by integrating prior velocity field information and, as discussed above, it is also important to estimate all the spikes accurately.…”

“…2). The reason for this relatively low accuracy may partly be related to the non-linear summation of MU twitch velocities (displacements) in UUS, as recently shown (Lubel et al, 2023). Specifically, Lubel et al (2023) observed that the peak-to-peak STA twitch amplitude was suppressed with increasing MU activity (force level), although the twitch waveform shape was maintained.…”

“…The reason for this relatively low accuracy may partly be related to the non-linear summation of MU twitch velocities (displacements) in UUS, as recently shown (Lubel et al, 2023). Specifically, Lubel et al (2023) observed that the peak-to-peak STA twitch amplitude was suppressed with increasing MU activity (force level), although the twitch waveform shape was maintained. In this study, we also found a high rate of falsely identified spikes (58%), which can be explained by additional oscillatory peaks, not in response to the spikes of the reference MU but possibly due to nearby MUs and high-amplitude noise.…”

“…The velocity field associated with individual MUs can be extracted by spike-triggered averaging (STA) of the ultrasound images using the time instants of activation of MUs identified with concurrently recorded EMG (Lubel et al, 2023(Lubel et al, , 2022. Alternatively, the velocity images associated with muscle contractions can be directly decoded into contributions of individual MUs (Rohlén et al, 2020b(Rohlén et al, , 2020a.…”