Simulation of fibre density in single-fibre electromyography and its relationship to macro-EMG

Marching band model for simulating a single muscle fiber action potential

OBJECTIVE

We describe a mathematical model to calculate a single muscle fiber action potential (AP). Based on a marching band pattern, it is an enhancement to our previously described "modified line source" model.

METHODS

Calculations were performed using an Excel spread sheet. AP was simulated for a 200 mm long muscle fiber with 60 µm diameter, propagation velocity of 4 m/s, and end-plate located at the center. Several different electrode locations were used to calculate the AP.

RESULTS

The AP amplitude was highest at the end-plate where the waveform was biphasic with initial negativity. When the electrode was moved towards the tendon, the amplitude decreased for the first 1.5 mm. The AP was triphasic and its waveform was relatively constant at electrode positions beyond 1.5 mm from the end-plate. It matched the calculations using the modified line source model. When the electrode was near the tendon, the AP amplitude decreased asymmetrically and waveform became biphasic resembling a positive sharp wave.

DISCUSSION

The model is conceptually and computationally simple. It simulated the expected AP shape at different electrode positions along the muscle fiber. The waveforms are similar to those obtained from mathematically complex volume conductor models.

SIGNIFICANCE

The revised model can be useful for teaching and future simulation studies.

A muscle architecture model offering control over motor unit fiber density distributions

The aim of this study was to develop a muscle architecture model able to account for the observed distributions of innervation ratios and fiber densities of different types of motor units in a muscle. A model algorithm is proposed and mathematically analyzed in order to obtain an inverse procedure that allows, by modification of input parameters, control over the output distributions of motor unit fiber densities. The model's performance was tested with independent data from a glycogen depletion study of the medial gastrocnemius of the rat. Results show that the model accurately reproduces the observed physiological distributions of innervation ratios and fiber densities and their relationships. The reliability and accuracy of the new muscle architecture model developed here can provide more accurate models for the simulation of different electromyographic signals.

Models and simulations in electromyography

In electromyography, one assesses the pathophysiology on the basis of the waveform characteristics of the recorded signal. This requires detailed knowledge of the relationship between the waveform generators and the waveform measurements. Models and computer simulations can be used to explore this relationship in an efficient manner. Combining models with experimental methods will allow us to define new measurements and new rules of interpretation. This is discussed with some of the models developed for electromyography signal analysis.

A model of the muscle action potential for describing the leading edge, terminal wave, and slow afterwave

The leading edge, terminal wave, and slow afterwave of the motor-unit action potential (MUAP) are produced by changes in the strength of electrical sources in the muscle fibers rather than by movement of sources. The latencies and shapes of these features are, therefore, determined primarily by the motor-unit (MU) architecture and the intracellular action potential (IAP), rather than by the volume-conduction characteristics of the limb. We present a simple model to explain these relationships. The MUAP is modeled as the convolution of a source function related to the IAP and a weighting function related to the MU architecture. The IAP waveform is modeled as the sum of a spike and a slow repolarization phase. The MU architecture is modeled by assuming that the individual fibers lie along a single equivalent axis but that their action potentials have dispersed initiation and termination times. The model is illustrated by simulating experimentally recorded MUAPs and compound muscle action potentials.

Motor unit sound in needle electromyography: assessing normal and neuropathic units

Motor unit action potentials (MUPs) recorded by a monopolar needle electrode in normal and neuropathic muscles were computer-simulated. Five experienced electromyographers acted as examiners and assessed the firing sounds of these MUPs without seeing them on a display monitor. They judged whether the sounds were crisp or close enough to accept for the evaluation of MUP parameters and whether, when judged acceptable, they were neuropathic-polyphasic. The examiners recognized motor unit (MU) sound as crisp or polyphasic when the MUP obtained was 0.15-0.2 mm from the edge of the MU territory. When the intensity of the sound decreased, they were unable to perceive it as crisp. When the intensity exceeded the saturation level of loudspeaker output, the sound was perceived as polyphasic, but the wave form of the MUP was not. When the frequency of the neuropathic MUP was lowered, the examiners were unable to determine whether the MUP was polyphasic. MUPs recognized as acceptable for evaluation can be distinguished by listening to MU sounds. The audio amplifier gain must be appropriately adjusted for each MUP amplitude in order to assess whether an individual MU sound is crisp or polyphasic before MUP parameters are measured on a display monitor.

A model of EMG generation

Simulation models are unavoidable in experimental research when the point is to develop new processing algorithms to be applied on real signals in order to extract specific parameter values. Such algorithms have generally to be optimized by comparing true parameter values to those deduced from the algorithm. Only a simulation model can allow the user to access and control the actual process parameter values. This constraint is especially true when dealing with biomedical signals like surface electromyogram (SEMG). This work is an attempt to produce an efficient SEMG simulation model as a help for assessing algorithms related to SEMG features description. It takes into account the most important parameters which could influence these characteristics. This model includes all transformations from intracellular potential to surface recordings as well as a fast implementation of the extracellular potential computation. In addition, this model allows multiple graphically-programmable electrode-set configurations and SEMG simulation in both voluntary and elicited contractions.

The size index as a motor unit identifier in electromyography examined by numerical calculation

A computer simulation was performed to investigate the size index as a motor unit identifier in electromyography. The size index calculated from the amplitude and area of the simulated motor unit action potential (MUP) was plotted against the distance between the needle electrode and current source to show how the index changes as a function of the distance. The index of the MUP also was plotted against the number of muscle fibers belonging to a single motor unit, the size of the motor unit territory, and the diameter of the muscle fibers in order to establish the major determinants of the index. The index was relatively constant for the distance less than 2 mm between the needle electrode and closest edge of the current source. It changed logarithmically with the number of muscle fibers and with the diameter of the fibers.

[Value of a rapid method to determine muscle fiber density in amyotrophic lateral sclerosis]

We shortened single fiber electromyography examination by evaluating fiber density, jitter and block numbers in the 10th and the 20th different needle positions in the extensor digitorum communis. The results obtained in 15 normal subjects and 12 amyotrophic lateral sclerosis patients were comparated. There were no significant differences with the 10th and 20th needle positions in normal subjects or in patients. This method diminished patient discomfort and shortened the examination time.

Innervation patterns in the cat tibialis anterior six months after self-reinnervation

The spatial distribution of fibers belonging to a single motor unit was analyzed in 10 motor units from the tibialis anterior of the cat 6 months after denervation and self-reinnervation of the anterior (superficial) compartment of the muscle. After self-reinnervation, the distribution patterns of the fibers in the fast motor units were significantly different than control, whereas the fiber distribution in the slow unit was similar to control. Reinnervated fast units had a significant increase in the number of adjacencies among motor unit fibers, and there were often distinct "clusters or groups" of fibers distributed within the motor unit territory. Clustering or grouping of fibers was evident within the motor unit, even though fiber type grouping was not evident within the muscle. The differences in distribution patterns between control and reinnervated units may be related to variations in the branching pattern of axons during reinnervation compared to the process that occurs during development.

An augmented computer model of motor unit reorganization in neurogenic diseases of skeletal muscle

A computer model of denervation and complete reinnervation in skeletal muscle was originally developed for the purpose of furthering an understanding of the underlying mechanisms of motor unit reorganization in neurogenic diseases. We now describe its successor, a computer model for investigating different rates of denervation and reinnervation, as well as incomplete reinnervation. The new model introduces the concept of permanent denervation and features enhanced interactive control over the distribution of motor unit centers and additional measures of dispersion and co-dispersion of muscle fibers. The use of this model for investigating pathophysiologically significant issues in denervating diseases is illustrated with five different sets of parameters. These simulate some of the processes that may be operational in chronic spinal muscular atrophy, amyotrophic lateral sclerosis, and progressive postpolio muscular dystrophy. The enhanced model will allow in-depth analysis of the influence of hypothesized pathophysiological processes on clinical, electrophysiological and pathological outcomes in human disease.

Nerve-muscle involvement in a large family with mitochondrial cytopathy: electrophysiological studies

Thirteen patients with mitochondrial cytopathy were investigated. They represent different generations, ages, stages, and severities of the disease. All were assumed to have the same metabolic defect. The disease is a multisystem disorder with a metabolic defect located at complex 1 in the respiratory chain. Clinically, the disorder gives symptoms such as hearing loss, retinal pigmental degeneration, ataxia, cardiomyopathy, muscular fatiguability and neuropathy. The patients were investigated with nerve conduction studies, concentric needle EMG, SFEMG, and macro EMG examinations. Neurophysiologic studies revealed signs of myopathy in both the younger members and in those with slight muscular symptoms. In the more advanced stages, neuropathic changes of the axonal type were seen as well. Macro EMG was interpreted as indicating muscle fiber membrane abnormalities in the early stages. Single fiber EMG studies indicate that this metabolic defect does not disturb neuromuscular transmission.

Evaluation of an automatic method of measuring features of motor unit action potentials

This study was performed to evaluate an automatic method of motor unit action potential (MUAP) analysis developed in our laboratory. MUAPs were recorded from the biceps brachii muscle of 68 normal subjects and 122 patients with nerve or muscle disease. The values of mean MUAP durations from normal subjects obtained by automatic analysis were similar to those reported in the literature. However, the normal range of MUAP amplitude and the incidence of polyphasic MUAPs were much higher. Normal ranges of mean MUAP area, area/amplitude ratio, and the number of turns were also defined. Automatic analysis demonstrated an abnormality of at least one MUAP feature in 70% of patients. There was concordance between automated analysis and visual assessment of MUAPs in 76% of patients with neuropathy but in only 50% of patients with myopathy. The relationships between different MUAP features seen in neuropathy and myopathy are explained in physiologic terms.

EMG of reinnervated motor units: a simulation study

Using computer simulation techniques, reinnervation of motor units (MUs) was studied by increasing the number of muscle fibers in the MU without changing the MU territory. The fiber density (FD) measured by single fiber EMG electrodes, the amplitude, area and number of turns of concentric needle (CN) EMG motor unit action potentials (MUAPs) and the amplitude of macro EMG MUAPs were most affected by partial reinnervation changes. The values of these features increased during simulated advanced reinnervation, as did the number of CNEMG MUAPs that had increased numbers of phases or turns and the mean CNEMG MUAP duration. The increase in macro EMG MUAP amplitude, FD and CNEMG MUAP area were proportional to the increase in the number of muscle fibers in the MU. When loss of muscle fibers due to so-called MU fractionation was simulated, values of all EMG features fell, but were still increased compared to normal. Two patterns of change in SFEMG and macro EMG values were identified that may distinguish between recordings made from reinnervated low force threshold MUs and those from higher force threshold MUs.

Simulation of concentric needle EMG motor unit action potentials

Computer simulations of motor unit action potentials (MUAPs) as measured by a concentric needle (CN) electromyography (EMG) electrode in normal motor units (MUs) indicated that the MUAP amplitude is determined mainly by the proximity of the electrode to the closest muscle fiber. The area and duration of the simulated MUAPs were affected by all muscle fibers in front of the active recording surface but mainly by those that were less than 2 and 2.5 mm, respectively, from the active recording surface. The MUAP area was also affected by the proximity of the electrode to the closest muscle fiber. The number of phases of the simulated MUAPs increased when the dispersion of the arrival times of individual muscle fiber APs at the electrode was increased. Increased temporal dispersion of APs decreased the MUAP amplitude and area slightly but did not affect the MUAP duration. It is inferred that different features of the CN MUAP are determined by the distribution of muscle fibers within different portions of the MU territory and thus provide complementary information about the MU architecture.

Electrophysiological study of size and fibre distribution of motor units in the human masseter and temporal muscles

Probably related to their unique function, human jaw muscles have a specialized muscle-fibre composition different from that of limb and trunk muscles. In jaw muscle from healthy young adults, there were large groups of densely-packed fibres of the same histochemical type, a finding which indicates re-innervation when seen in limb muscles. The number of muscle fibres per motor unit, the local distribution of muscle fibres within motor units and the neuromuscular transmission in human masseter and temporal muscles were examined by single-fibre EMG and macro EMG. One hundred and forty-seven low-threshold motor units in four healthy subjects were recorded. The first dorsal interosseus muscle of the hand was similarly measured. In the jaw and hand muscles the low-threshold motor units were slightly smaller, than in large arm and leg muscles. The temporal muscle differed from the masseter in having significantly-higher fibre density, which may be explained by the higher frequency of small type-II fibres in the temporal causing closer packing of the type-I, low-threshold motor units. The fibre concentration within motor units was similar to that of normal limb muscles without any sign of grouping of fibres from the same motor unit. Normal motor end-plate transmission was another argument against re-innervation.