Computer simulation study of the shape of motor unit action potential

Motor unit action potentials (MUAPs) of brachial biceps were simulated. A simulated MUAP was obtained as a sum of single fibre action potentials (SFAPs) from all the muscle fibres of a motor unit (MU). The influence of the following factors on MUAP shape for different kinds of recording electrode was studied: fibre density, neuromuscular jitter, temporal dispersion and electrode displacements. The simulation confirms that typical MUAPs recorded with needle electrodes from muscles of low fibre density such as brachial biceps are usually triphasic. Increased fibre density produces MUAPs of more complex shape and higher amplitude. Normal neuromuscular jitter is responsible for the variability of shape of subsequent potentials from the same MU as well as for electromyographic shimmer. Pathologic (increased) jitter makes the shapes of subsequent potentials unrecognizable. The influence of temporal dispersion is interconnected with other factors but rather of minor importance. The simulation shows how big changes in MUAP shape can be expected due to electrode displacements during single experiment or during estimation of MU territory.     

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.     

The morphology of single muscle fibre potentials – Part II: Experimental findings

Studies dealing with single fibre action potentials (SFAPs) have been more interested in obtaining quantitative data of certain parameters of the SFAP waveform than in the analysis of its morphologic features. The characterization of the SFAP morphology is highly valuable as it will allow to obtain information about in vivo intracellular action potentials (IAPs). However, the SFAP final portion is highly sensitive to distant electrical activity, as shown in Part I of this study. The present paper, Part II, is aimed at analysing the morphologies found in human SFAPs and deriving data of the associated IAPs. It was found that, for most SFAPs (97%), the declining negative phase starts decreasing steeply up to a certain point (slope-discontinuity point), from which it returns more slowly towards the baseline. This return may be further slowed down due to the contamination from distant potentials, but the slope-discontinuity point seems to be an intrinsic feature of human SFAPs. The third phase of SFAPs was, either absent (65%), or of rather small amplitude and prolonged duration. The slope-discontinuity point was apparent for the SFAPs of larger amplitude and vanished gradually as the SFAPs got smaller. Several lines of evidence strongly suggest that the spike duration of human IAPs should be about 1.0 ms.     

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.     

Identification procedure in a model of single fibre action potential – Part II: Global approach and experimental results

The present paper describes a global procedure for estimating all the synthesis parameters that generate a single fibre action potential (SFAP) in the Dimitrov–Dimitrova (D–D) convolutional model. We call this inverse problem Identification Procedure, and it is presented in two parts, this paper being the second. The procedure incorporates the candidate pair (CP) method developed in Part I, which provides the values of radial distance r and fibre diameter d of the simulated SFAP that best matches a potential under study. The CP-method required prior knowledge of all the excitation parameters. However, since the Identification Procedure makes no assumption about the excitation, multiple combinations of the synthesis parameters result in very similar SFAPs whose shape is close the signal under study. Analysis of the possible combinations reveals that r and d can be modelled as two jointly Gaussian random variables. The interest of the Identification Procedure is that, for a certain SFAP, it provides estimates of r and d, along with estimates of different parameters that determine the IAP waveform. Moreover, the procedure is able to determine the degree of error that accompanies the estimation of r and d.     

Extracellular potential field of excited isolated frog muscle fibres immersed in a volume conductor

The extracellular potential field of isolated frog muscle fibres immersed in a volume conductor was studied at radial distances up to 3 mm during excitation. The shape of the field distant from both the point of the origin of the excitation and the end of the fibre as well as changes in the field when depolarization wave approached the fibre end were described. Different amplitude decrease rates in individual phases of the extracellular potential and the peak-to-peak amplitude at different temperatures were found. Extracellular potentials at long radial distances were recorded using an averaging technique. The shape of the extracellular potentials at long radial distances over the fibre and beyond its end were very similar to the shape of extraterritorial potentials of a single motor unit.     

Motor unit fibre density in extremely hypertrophied skeletal muscles in man. Electrophysiological signs of muscle fibre hyperplasia

Single fibre electromyography (SFEMG) was performed on the left quadriceps, extensor digitorum communis, and biceps brachii muscles of four highly trained bodybuilders (BB). Muscle fibre areas, as assessed from biopsy samples, were similar in the BB as in age-matched habitually active male controls despite large differences in limb circumferences. This indicates a greater muscle fibre number in BB. An abnormally high muscle fibre density (FD) was recorded in two subjects exposed to extremely severe exercise for 14 years or longer, while those with normal FDs had been training extensively for a considerably shorter time (4-6 years). The abnormal FD was due either to an ephaptic transmission of action potentials between adjacent muscle fibres, or a muscle fibre hyperplasia, or most probably a combination of both, in response to a long-term functional overload. From the present results one cannot say whether the suggested muscle fibre hyperplasia had any major influence on the muscle hypertrophy per se, since all BB possessed large muscle volumes.     

A study of the motor unit action potential by means of computer simulation

In order to study the motor unit action potential a computer simulation model was developed. It is based on the superposition of single muscle fibre potentials of the fibres belonging to the motor unit. The parameters which characterize each fibre (spatial position, diameter, and a dispersion of arrival time of the potential at the electrode) are chosen from statistical distributions which can be derived from anatomical and physiological data. The electrode type, position and dimensions can be specified. Simulated motor unit action potentials are presented in the time and frequency domain. The simulation results refer to (1) the influence of the electrode position and dimensions with respect to the motor unit territory, (2) the meaning of this model for the study of pathological phenomena, (3) the variability of some parameters characterizing the motor unit, (4) the selectivity of uni- and bipolar electrodes and finally (5) the influence of the geometrical situation of the motor end-plates within the muscle, on the shape of motor unit action potentials.     

Estimation of monopolar signals from sphincter muscles and removal of common mode interference

The detection of surface electromyogram (EMG) by multi-electrode systems is applied in many research studies. The signal is usually recorded by means of spatial filters (linear combination of the potential under at least two electrodes) with vanishing sum of weights. Nevertheless, more information could be extracted from monopolar signals measured with respect to a reference electrode away from the muscle. Under certain conditions, surface EMG signal along a curve parallel to the fibre path has zero mean (property approximately satisfied when EMG is sampled by an array of electrodes that covers the entire support of the signal in space). This property allows estimating monopolar from single differential (SD) signals by pseudoinversion of the matrix relating monopolar to SD signals. The method applies to EMG signals from the external anal sphincter muscle, recorded using a specific cylindrical probe with an array of electrodes located along the circular path of the fibres. The performance of the algorithm for the estimation of monopolar from SD signals is tested on simulated signals. The estimation error of monopolar signals decreases by increasing the number of channels. Using at least 12 electrodes, the estimation error is negligible. The method applies to single fibre action potentials, single motor unit action potentials, and interference signals.The same method can also be applied to reduce common mode interference from SD signals from muscles with rectilinear fibres. In this case, the last SD channel defined as the difference between the potentials of the last and the first electrodes must be recorded, so that the sum of all the SD signals vanishes. The SD signals estimated from the double differential signals by pseudoinvertion are free of common mode.     

Local development of action potentials in slow muscle fibres after complete or partial denervation.

Pyriformis muscles of Rana temporaria were completely or partially denervated by cutting the sciatic nerve or some of the small nerve branches entering the muscle. One stimulating and one to three recording microelectrodes were inserted along the fibres in order to compare the electrical activity at these points. In an early period following denervation action potentials of variable size and shape could be observed; these action potentials were often composed of two, sometimes of three or four, components. The size of individual components depended on the position of the recording microelectrode. Individual components could occasionally be triggered separately by adjusting the strength of the stimulating current pulse; propagation of these "all or none" responses was absent. In other fibres one component of the action potential could trigger another one several millimetres apart, thus indicating propagation. Conduction velocities were approximately 0.4 m/s. In partially denervated slow fibres, endplate potentials were confined to one lateral segment of the fibres, while the action potential occupied the denervated part of the membrane. The amplitudes of endplate and action potentials varied inversely with distance. Rough estimates of the length constant of the slow fibre membrane were calculated from the spatial decay of action potentials, endplate potentials and hyperpolarizing electrotonic potentials; mean values obtained were 2.5, 4.8 and 7.7 mm respectively. The results suggest that following denervation Na channels are built into discrete areas of the slow fibre membrane and that this process depends on the amount of denervation in individual fibres.     

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.     

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 0.2-0.4 ms, we tentatively suggest that the duration of the IAP spike should be over approximately 0.75 ms, with the shape of the spike strongly asymmetric. These IAP characteristics broadly coincide with those observed in mammal IAPs.     

A fibre optic catheter for simultaneous measurement of longitudinal and circumferential muscular activity in the gastrointestinal tract

Diagnostic catheters based on fibre Bragg gratings (FBG's) are proving to be highly effective for measurement of the muscular activity associated with motility in the human gut. While the primary muscular contractions that generate peristalsis are circumferential in nature, it has long been known that there is also a component of longitudinal contractility present, acting in harmony with the circumferential component to improve the overall efficiency of material movement. We report the detection of longitudinal motion in mammalian intestine using an FBG technique that should be viable for similar detection in humans. The longitudinal sensors have been combined with our previously reported FBG pressure sensing elements to form a composite catheter that allows the relative phase between the two components to be detected. The catheter output has been validated using video mapping in an ex‐vivo rabbit ileum preparation. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the muscle fibre end geometry on the extracellular potentials

Intra- and extracellular action potentials of isolated frog muscle fibres were recorded at different distances to the end of the fibre. The first and second time derivatives of the intracellular action potentials were also recorded. The intracellular action potentials and their first and second time derivatives were almost the same regardless of the place of recording. With the decrease in the axial distance to the end the extracellular action potentials changed gradually in a complicated manner from a shape similar to the second time derivative into a shape similar to the first time derivative. Extracellular potentials, having two negative maxima, were recorded over the terminal taper part of the fibres.These alterations were simulated by a mathematical model. It was shown that the changes in the shape of the extracellular action potentials around the end of the fibres were mainly due to the existence of the fibre end though a better correspondence of the experimentally recorded and the calculated extracellular action potentials was obtained when the morphology of the fibre end was taken into consideration.     

Dendritic backpropagation and synaptic plasticity in the mormyrid electrosensory lobe

This study is concerned with the origin of backpropagating action potentials in GABAergic, medium ganglionic layer neurones (MG-cells) of the mormyrid electrosensory lobe (ELL). The characteristically broad action potentials of these neurones are required for the expression of spike timing dependent plasticity (STDP) at afferent parallel fibre synapses. It has been suggested that this involves active conductances in MG-cell apical dendrites, which constitute a major component of the ELL molecular layer. Immunohistochemistry showed dense labelling of voltage gated sodium channels (VGSC) throughout the molecular layer, as well as in the ganglionic layer containing MG somata, and in the plexiform and upper granule cell layers of ELL. Potassium channel labelling was sparse, being most abundant in the deep fibre layer and the nucleus of the electrosensory lobe.Intracellular recordings from MG-cells in vitro, made in conjunction with voltage sensitive dye measurements, confirmed that dendritic backpropagation is active over at least the inner half of the molecular layer. Focal TTX applications demonstrated that in most case the origin of the backpropagating action potentials is in the proximal dendrites, whereas the small narrow spikes also seen in these neurones most likely originate in the axon. It had been speculated that the slow time course of membrane repolarisation following the broad action potentials was due to a poor expression of potassium channels in the dendritic compartments, or to their voltage- or calcium-sensitive inactivation. However application of TEA and 4AP confirmed that both A-type and delayed rectifying potassium channels normally contribute to membrane repolarisation following dendritic and axonal spikes. An alternative explanation for the shape of MG action potentials is that they represent the summation of active events occurring more or less synchronously in distal dendrites.Coincidence of backpropagating action potentials with parallel fibre input produces a strong local depolarisation that could be sufficient to cause local secretion of GABA, which might then cause plastic change through an action on presynaptic GABA_B receptors. However, STP depression remained robust in the presence of GABAB receptor antagonists.     

Induction of action potentials in fish red muscle by denervation

The effects of denervation on the electrical membrane properties of fish red muscle were investigated. Forty to fifty hours after denervation, miniature endplate potentials disappeared abruptly and field stimulation of the nerve within the muscle failed to evoke endplate potentials, indicating that transmission failure occurred at this time. The membrane resistance of the red muscle fibre increased after denervation. Normally innervated fish red muscles do not generate action potentials in response to either nerve or direct muscle stimulation. However, approximately 3 weeks after nerve sectioning, action potentials could be induced in the muscles. The action potential was sodium-dependent, and was sensitive to tetrodotoxin. Actinomycin D injected in the early phase after operation suppressed the induction of the action potential. These results indicate that RNA synthesis is preliminary to the induction of the action potential mechanism, and that this mechanism is under neural control.     

The Genesis and Transmission of Epidermal Potentials of Newt Embryonic Cells in Vivo and in Vitro

The genesis and transmission of action potentials in epidermal cells of a newt ( Cynops pyrrhogaster ) embryo were investigated quantitatively in vivo during development and in vitro in the absence of nerve cells. Typical action potentials, composed of a fast spike followed by a slow action potential, can be recorded from any of the epidermal cells from Stage 24/25 to 35/36. The potential is graded with current intensity, and only the slow component induces transmission to other epidermal cells. The fast spike is found in all epidermal cells from Stage 24/25 to Stage 50; it is abolished by Stage 52. The slow potential disappears at Stage 38 just before or after hatching. The cultured epithelioid explants (epithelioid aggregate) and cultured monolayer cells taken from the presumptive epidermal tissue of the ectoderm of the pregastrula, indicate that sequential changes in the genesis of the dual action potentials are similar to those of the intact embryo. In monolayer cell culture devoid of nerve cells, the epidermal cells, also generate a two-step action potential. Such two-step potentials are characteristic of both ciliated and non-ciliated epidermal cells and occur even during mitotic activity. In contrast, cultured neural plate cells isolated from the neurula generate typical spike-like action potentials.