Modeling Fibrillation Potentials—a New Analytical Description for the Muscle Intracellular Action Potential

Masked least-squares averaging in processing of scanning-EMG recordings with multiple discharges

Removing artifacts from nearby motor units is one of the main objectives when processing scanning-EMG recordings. Methods such as median filtering or masked least-squares smoothing (MLSS) can be used to eliminate artifacts in recordings with just one discharge of the motor unit potential (MUP) at each location. However, more effective artifact removal can be achieved if several discharges per position are recorded. In this case, processing usually involves averaging the discharges available at each position and then applying a median filter in the spatial dimension. The main drawback of this approach is that the median filter tends to distort the signal waveform. In this paper, we present a new algorithm that operates on multiple discharges simultaneously and in the spatial dimension. We refer to this algorithm as the multi-masked least-squares smoothing (MMLSS) algorithm: an extension of the MLSS algorithm for the case of multiple discharges. The algorithm is tested using simulated scanning-EMG signals in different recording conditions, i.e., at different levels of muscle contraction and for different numbers of discharges per position. The results demonstrate that the algorithm eliminates artifacts more effectively than any previously available method and does so without distorting the waveform of the signal. Graphical abstract The raw scanning-EMG signal, which can be composed by several discharges of the MU, is processed by the MMLSS algorithm so as to eliminate the artifact interference. Firstly, artifacts are detected for each discharge from the raw signal, obtaining a multi-discharge validity mask that indicates the samples that have been corrupted by artifacts. Secondly, a least-squares smoothing procedure simultaneously operating in the spatial dimension and among the discharges is applied to the raw signal. This second step is performed using only the not contaminated samples according to the validity mask. The resulting MMLSS-processed scanning-EMG signal is clean of artifact interference.

A masked least-squares smoothing procedure for artifact reduction in scanning-EMG recordings

Scanning-EMG is an electrophysiological technique in which the electrical activity of the motor unit is recorded at multiple points along a corridor crossing the motor unit territory. Correct analysis of the scanning-EMG signal requires prior elimination of interference from nearby motor units. Although the traditional processing based on the median filtering is effective in removing such interference, it distorts the physiological waveform of the scanning-EMG signal. In this study, we describe a new scanning-EMG signal processing algorithm that preserves the physiological signal waveform while effectively removing interference from other motor units. To obtain a cleaned-up version of the scanning signal, the masked least-squares smoothing (MLSS) algorithm recalculates and replaces each sample value of the signal using a least-squares smoothing in the spatial dimension, taking into account the information of only those samples that are not contaminated with activity of other motor units. The performance of the new algorithm with simulated scanning-EMG signals is studied and compared with the performance of the median algorithm and tested with real scanning signals. Results show that the MLSS algorithm distorts the waveform of the scanning-EMG signal much less than the median algorithm (approximately 3.5 dB gain), being at the same time very effective at removing interference components.

Graphical Abstract

An Empirical Muscle Intracellular Action Potential Model with Multiple Erlang Probability Density Functions based on a Modified Newton Method

The convolution of the transmembrane current of an excitable cell and a weighting function generates a single fiber action potential (SFAP) model by using the volume conductor theory. Here, we propose an empirical muscle IAP model with multiple Erlang probability density functions (PDFs) based on a modified Newton method. In addition, we generate SFAPs based on our IAP model and referent sources, and use the peak-to-peak ratios (PPRs) of SFAPs for model verification. Through this verification, we find that the relation between an IAP profile and the PPR of its SFAP is consistent with some previous studies, and our IAP model shows close profiles to the referent sources. Moreover, we simulate and discuss some possible ionic activities by using the Erlang PDFs in our IAP model, which might present the underlying activities of ions or their channels during an IAP.

The morphology of single muscle fibre potentials - Part I: simulation study of the distortion introduced by the distant-interfering potentials

Some morphologic aspects of human single fibre action potentials (SFAPs) are not sufficiently well-known. This uncertainty especially concerns the declining negative phase and the final positive phase (third phase) of SFAPs, as these parts are significantly affected by distant electrical activity. The incomplete characterisation of the SFAP shape is also explained by the limited knowledge of human intracellular action potentials (IAPs). The objectives of this study are to assess the morphologic features of human SFAPs and to derive information about the characteristics of human IAPs. To achieve this, the study has been divided into two parts. The present paper, Part I, aims to analyse the changes in the SFAP time-course introduced by distant-interfering potentials and to evaluate how these changes depend on the spike duration of the corresponding IAP. It was found that, for fibre-to-electrode distances shorter than about 0.2 mm, SFAPs generated by short-spike IAPs have a declining negative phase with a steep approximately constant slope that is largely unaffected by the potentials from distant fibres. For the same distances, SFAPs resulting from wide-spike IAPs have a declining negative phase with a slow return towards the baseline that is highly sensitive to distant-interfering potentials. The third phase of an SFAP is considerably distorted by distant potentials irrespective of the spike duration of the IAP.

Effects of changes in the shape of the intracellular action potential on the peak-to-peak ratio of single muscle fibre potentials

In situ recording of the intracellular action potential (IAP) of human muscle fibres is not yet feasible, and consequently, knowledge about certain IAP characteristics of these IAPs is still limited. The ratio between the amplitudes of the second and first phases (the so-called peak-to-peak ratio, PPR) of a single fibre action potential (SFAP) is known to be closely related to the IAP profile. The PPR of experimentally recorded SFAPs has been found to be largely independent of changes in the fibre-to-electrode (radial) distance. The main goal of this paper is to analyze the effect of changes in different aspects of the IAP spike on the relationship between PPR and radial distance. Based on this analysis, we hypothesize about the characteristics of IAPs obtained experimentally. It was found that the sensitivity of the SFAP PPR to changes in radial distance is essentially governed by the duration of the IAP spike. Assuming that, for mammals, the duration of the IAP rising phase lies within the range 0.2-0.4ms, we tentatively suggest that the duration of the IAP spike should be over approximately 0.75ms, with the shape of the spike strongly asymmetric. These IAP characteristics broadly coincide with those observed in mammal IAPs.

Estimating the duration of intracellular action potentials in muscle fibres from single-fibre extracellular potentials

In situ recording of the intracellular action potential (IAP) of human muscle fibres is not yet possible, and consequently, knowledge concerning certain IAP characteristics is still limited. According to the core-conductor theory, close to a fibre, a single fibre action potential (SFAP) can be assumed to be proportional to the IAP second derivative. Thus, we might expect to be able to derive some characteristics of the IAP, such as the duration of its spike, from the SFAP waveform. However, SFAP properties not only depend on the IAP shape but also on the fibre-to-electrode (radial) distance and other physiological properties of the fibre. In this paper we, first, propose an SFAP parameter (the negative phase duration, NPD) appropriate for estimating the IAP spike duration and, second, show that this parameter is largely independent of changes in radial distance and muscle fibre propagation velocity. Estimation of the IAP spike duration from a direct measurement taken from the SFAP waveform provides a possible way to enhance the accuracy of SFAP models. Because IAP spike duration is known to be sensitive to the effects of fatigue and calcium accumulation, the proposed SFAP parameter, the NPD, has potential value in electrodiagnosis and as an indicator of IAP profile changes due to peripheral fatigue.

Analysis of the relationship between the rise-time and the amplitude of single-fibre potentials in human muscles

Using the core-conductor theory, a single fibre action potential (SFAP) can be expressed as the convolution of a biolectrical source and a weight function. In the Dimitrov-Dimitrova (D-D) SFAP convolutional model, the first temporal derivative of the intracellular action potential (IAP) is used as the source. The present work evaluates the relationship between the SFAP peak-to-peak amplitude (V(pp)) and peak-to-peak interval (rise-time, RT) at different fibre-to-electrode distances using simulated signals obtained by the D-D model as well as real recordings. With a single fibre electrode, we recorded 63 sets of consecutive SFAPs from the m. tibialis anterior of four normal subjects. The needle was intentionally moved whilst recording each SFAP set. We used the observed changes in RT and V(pp) within each SFAP set as a point of reference with which to evaluate how closely the relationship between RT and V(pp) provided by the D-D model reflects real data. We found that half of the recorded SFAP sets had rise-times higher than those generated by the D-D model. We also showed the influence of the IAP spatial length on the sensitivity of RT and V(pp) with radial distance. The study reveals some inaccuracies in simulated SFAPs whose origin might be related to the assumptions made in the core-conductor theory.

The peak-to-peak ratio of single-fibre potentials is little influenced by changes in the electrode positions close to the muscle fibre

In a series of previous works we studied the ratio between the amplitudes of the second and first phases (the peak-to-peak ratio) of single fibre action potential (SFAPs) using the Dimitrov-Dimitrova SFAP convolutional model as a reference. From experimental potentials extracted from both healthy and diseased muscles, we determined typical peak-to-peak ratio (PPR) values and ranges for both normal and pathological conditions. In addition, we investigated the changes observed in the PPR of consecutive potentials recorded at different fibre-to-electrode distances. However, our results were not conclusive due to insufficient data. The objective of the present work was to obtain a more concrete description of the relation between PPR and radial distance. To this end, we recorded 135 sets of consecutive SFAPs from the m. tibialis anterior of four normal subjects. The needle was intentionally moved whilst recording each SFAP set. We found that PPR was largely independent of small changes in electrode position when the electrode was close to the fibre and sufficiently far from the neuromuscular and/or fibre-tendon junctions. In the discussion, we provide evidence that this result is in agreement with the generation of extracellular potentials considering the spatial extension of the intracellular action potential (IAP) along the fibre.

Analysis of the peak-to-peak ratio of extracellular potentials in the proximity of excitable fibres

In a previous work we studied the ratio between the amplitudes of the second and first phases (which we call PPR, after peak-to-peak ratio) of the single fibre action potential (SFAP) for a collection of fibrillation potentials (FPs) extracted from two pathological muscles. These FPs showed a wider PPR range than the Dimitrov-Dimitrova (D-D) convolutional model could provide. We proposed a modification of the D-D intracellular action potential (IAP) in order to obtain a range of PPRs comparable to that observed in our FPs. This paper extends that study to a large number of SFAPs extracted from the tibialis anterior muscle of normal subjects. The estimation of the average PPR range of non-diseased muscles in non-fatigued conditions is important since it can be used as a reference to establish a comparison with PPR ranges from muscles suffering some disorder or from fibres that are fatigued. Other aspects of the PPR, as its sensitivity with volume conductor parameters or to what extent changes in the SFAP PPR reflects changes in IAP spatial profile are also examined. We found that the PPR of experimental SFAPs ranges from 0.3 to 2.5 in all subjects and that all PPR histograms contain a well-defined single peak around the PPR value 1.0.

Effects of changes in intracellular action potential on potentials recorded by single-fiber, macro, and belly-tendon electrodes

Some myopathies are accompanied by abnormal calcium homeostasis. Electromyography (EMG) in such patients shows signs of normal or myopathic EMG when detected by a single-fiber electrode and abnormally increased values in macro EMG. As calcium accumulation might be accompanied by changes in intracellular action potential (IAP) and muscle-fiber propagation velocity, we simulated the effects of such changes on motor unit potentials (MUPs) recorded by different kinds of electrodes. We found that: (1) the requirements for what potential can be accepted as a single-fiber action potential (SFAP) are too rigorous; (2) macro MUP amplitude can increase while SFAP amplitude can decrease when there is an increase in the spatial length of IAP spike; and (3) changes in the second phase of a belly-tendon-detected MUP or M wave could be used for noninvasive detection of increased IAP depolarizing (negative) after-potential.

Modelling fibrillation potentials--analysis of time parameters in the muscle intracellular action potential

A single fiber action potential (SFAP) can be modelled as the convolution of a biolectrical source and a filter impulse response. In the Dimitrov-Dimitrova (D-D) convolutional model, the first temporal derivative of the intracellular action potential (IAP) is used as the source, and Tspl is a time parameter related to the duration of the IAP waveform. This paper is centred on the relation between Tspl and the main spike duration (MSD), defined as the time interval between the first and third phases of the SFAP. We show that Tspl essentially determines the MSD parameter. As experimental data, we used fibrillation potentials (FPs) of two different muscles to study the D-D model. We found that Tspl should have a certain statistical variability in order to explain the variability in the MSD of our FPs. In addition, we present a method to estimate the Tspl values corresponding to a given SFAP from its measured MSD.