Estimating the neural spike train from an unfused tetanic signal of low-threshold motor units using convolutive blind source separation

Abstract

Background Individual motor units have been imaged using ultrafast ultrasound based on separating ultrasound images into motor unit twitches (unfused tetanus) evoked by the motoneuronal spike train. Currently, the spike train is estimated from the unfused tetanic signal using a Haar wavelet method (HWM). Although this ultrasound technique has great potential to provide comprehensive access to the neural drive to muscles for a large population of motor units simultaneously, the method has a limited identification rate of the active motor units. The estimation of spikes partly explains the limitation. Since the HWM may be sensitive to noise and unfused tetanic signals often are noisy, we must consider alternative methods with at least similar performance and robust against noise, among other factors. Results This study aimed to estimate spike trains from simulated and experimental unfused tetani using a convolutive blind source separation (CBSS) algorithm and compare it against HWM. We evaluated the parameters of CBSS using simulations and compared the performance of CBSS against the HWM using simulated and experimental unfused tetanic signals from voluntary contractions of humans and evoked contraction of rats. We found that CBSS had a higher performance than HWM with respect to the simulated firings than HWM (97.5 ± 2.7 vs 96.9 ± 3.3, p < 0.001). In addition, we found that the estimated spike trains from CBSS and HWM highly agreed with the experimental spike trains (98.0% and 96.4%). Conclusions This result implies that CBSS can be used to estimate the spike train of an unfused tetanic signal and can be used directly within the current ultrasound-based motor unit identification pipeline. Extending this approach to decomposing ultrasound images into spike trains directly is promising. However, it remains to be investigated in future studies where spatial information is inevitable as a discriminating factor.

Accurate Identification of Motoneuron Discharges from Ultrasound Images Across the Full Muscle Cross-Section

“…In previous decompositions of US data, the RoA with respect to EMG was calculated using a window of 30 ms (± 15 ms around the EMG spike) [15], [21], which is extremely large. In contrast, we used a window of 0-5 ms following the EMG-detected spike after signal alignment.…”

“…In our case, because the sources are series of delta functions, the assumption holds as long as the maximum delay L+R is shorter than all the ISIs [16], [17]. While this is the case for the mathematically similar problem of EMG decomposition [2], [16], [17], it is not valid for US, where the velocity twitches have a large time support [7], [9], [21]. Therefore, when the sources are extended, there will be one or more delayed source with at least one discharge in common with the original source and potentially other discharges in common with other delayed versions of the same source.…”

“…Hence, we applied a further blind deconvolution step on each estimated source to identify the MU spike train times. Here, the estimated source was extended and delayed, and a second fixed-point algorithm was used to estimate the deconvolved signal, as suggested in a previous work that used linear instantaneous mixing models for ultrafast US decomposition [21]. Finally, the peaks of the estimated sources were identified using a peak-finding algorithm based on the height of the peaks and the time between them [21].…”

“…The process described in section II.A is presented in pseudocode in Table 1. The blind deconvolution peak finding algorithm is presented elsewhere [21].…”

Identification of motor unit discharges from ultrasound images: Analysis of in silico and in vivo experiments

“…This estimation was based on maximising the sparsity of the source vector using the same gradient functions as in the original work [3]. Since the estimated sources are not ideal spike trains with zeros and ones, we applied a blind deconvolution method [18] on each estimated source to identify the time instants of the spikes. For more details about the implementation including the pseudo algorithm, see the original work proposing the method [3].…”