The effect of muscle fiber length change on motor units potentials propagation velocity.

The influence of the muscle length on the propagation velocity of the extraterritorial action potentials was studied. Single low--threshold motor units (MUs) from m. biceps brachii, both with superficially and deeply situated fibers were investigated. The velocity of excitation propagation decreases with the muscle elongation. This dependence is not so prominent for MUs having more deeply situated fibers. In case of superficial MUs the experimentally obtained values are in better agreement with the core conductor model (v = k.square root of r), than with the linear dependence of the propagation velocity (v) on the muscle fiber radius (r) (v = k.r) observed by Håkansson (1957) on frog muscles. The observed difference between superficial and deep MUs was discussed. At least two factors may be responsible for greater changes of the excitation propagation velocity along the fibers of the superficially situated MUs during the muscle elongation. One possible factor is the essential change in the external resistance due to the decrease of distance from the fibers to the skin surface. The greater change of the muscle length during a passive muscle stretching might be another reason.

Relation between the motor units recruitment threshold and their potentials propagation velocity at isometric activity.

The relationship between the propagation velocity of the excitation along the muscle fibers of the motor units (MUs) and their threshold of recruitment at different level of isometric voluntary contraction was investigated. The threshold of recruitment was measured by the value of the muscle force, expressed in percents from the maximal voluntary contraction (MVC) at which the first impulse of the MU appeared. A wire subcutaneous branched electrode was used to select the potentials from a single MU. The selected in this way MU impulses were used as a trigger to average two electromyographic (EMG) signals picked up by means of two monopolar surface electrodes with small leading-off areas mounted on a common plate at a distance of 10 mm from one another. The propagation velocity of the extraterritorial potentials of the MUs increased non-linearly with the increase of the recruitment threshold. The relationship was fitted as V = square root of a+b.theta, where v is the propagation velocity, theta is the threshold of recruitment and a and b are constants. The consideration of the velocity of propagation as a "size principle parameter" was discussed and the limitations of the latter are pointed out.

Electrotonic potentials of myelinated nerve fibers.

The extracellular electrotonic potentials of a single myelinated nerve fiber in a volume conductor of infinite extent were studied. The spatial distribution of the transmembrane electrotonic potential was obtained by integrating the system of differential equations constituting the model of the activation of a myelinated nerve fiber. The stimulus was step-like. The present investigation was concerned with the steady-state conditions only. The spatial distribution of the extracellular potentials at various radial distances in the conducting medium was calculated using the line source model. Up to a certain radial distance the discontinuous structure of the myelinated fiber is reflected in the oscillatory nature of the extracellular potentials, while further in the volume conductor the potentials are smooth. The magnitude of the radial decline of the extracellular potentials were compared for myelinated fibers of various internodal distances.

Optimal interelectrode distance with the method of source density analysis.

Three error sources which contribute to the total error of the second space derivative (SSD) used with the method of current source density analysis (CSD) were examined. The approximate formula usually used with CSD was the first error source. Another error originated from the finite interelectrode distance. The measurement error of the device with which the potential was recorded was the third error source herein considered. A relative SSD error was determined to estimate the effect of the errors examined. The experimental data (a section from the three-dimensional potential profile in annuran cerebellum produced by parallel fiber activation) were fitted by polynomials, Fourier expansion and cubic splines. Then a preferable interelectrode distance was obtained corresponding to the minimal relative error.

Velocity of spreading of the excitation along the muscle fibres of human motor units measured by superficial electrodes.

It was demonstrated experimentally that the errors in measuring of the velocity of spreading of the excitations along the muscle fibres of human motor units were different when different types of surface electrodes are used. On this basis a new principle of double measurements is proposed which is applicable to all methods using surface electrodes. The principle was applied with the method for measuring velocity of the potentials of separate motor units. Correct values of velocity were obtained when v1 measured by one type of electrodes was equal to v2 measured by other type of electrodes both types abolishing to a different degree the influence of the volume conductor on the error. The mean value of velocity for m. biceps brachii using equal double measurement was 3.62 +/- 0.51 m/s.

Extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor.

The extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor were studied. The spatial distribution of the transmembrane potential was obtained by integrating the system of partial differential equations characterizing the electric processes in the active myelinated nerve fiber. The spatial distribution of the extracellular potentials at various radial distances in the volume conductor were calculated using the line source model. Up to a certain radial distance (500 microns) the discontinuity of the action potential propagation is reflected in the extracellular potentials, while further in the volume conductor the potentials are smooth. The effect of the fiber diameter and the internodal distance on the volume conductor potentials as well as the changes in the magnitude of the extracellular potential (in the time domain) between two adjacent nodes at various radial distances were studied. The radial decline of the peak-to-peak amplitude of the extracellular potential depends on the radial coordinate r of the field point and increases with the increase of r.

Comparison of the different variants of the current source density analysis methods in neurophysiological studies.

Computer calculations and theoretical studies of different variants of current-source density analysis (CSDA) for neurophysological studies were carried out. The different variants of the method are compared by estimating equiweight surfaces and equiweight lines in particular planes. The decrease in the distance between the different points of measurement has been found to result in more selective presentation of the neuronal activity. It is shown that this distance cannot be very small--50 micron seems a reasonable limit. Bidimensional and especially unidimensional CSD-analysis produces considerable volumes with negative weights, these weights being rather high in absolute value. Errors in the interpretation of the results are possible, such as incorrect calculation of the current density and even erroneous determination of its sign.

Dependence between intra- and extracellular action potentials of isolated frog muscle fibres at different temperatures.

The intra- and extracellular action potentials of isolated frog muscle fibre immersed in a volume conductor at different temperatures are described. It was found that upon increasing the temperature the amplitude of the first time derivative of the intracellular action potentials increased linearly, whereas the amplitude of the second time derivative increased nonlinearly. The duration of the separate phases of the time derivatives shortened upon heating, as the velocity of spreading of the excitation increased. The length of the separate phases of the space derivatives of the action potential shortened when increasing the temperature. The amplitudes of the space derivatives were calculated. The changes in the derivatives of the action potential were explained by the influence of the temperature on the peak inward and outward transmembrane current. The changes in the extracellular action potentials produced by the temperature near the membrane and at longer radial distance at points far and near the end of the fibre are described. They were explained by the changes in the space derivatives of the intracellular action potential as well as by the features of the distribution of the extracellular potential field in the volume conductor around the finite-in-length excitable fibre.

Application of the equiweight analysis method for the evaluation of the origin of the N1 and N2 waves of visual evoked potentials.

The applicability of the equiweight analysis method was studied with a view to evaluating the position in depth of the two dominating waves of the visual evoked potentials, recorded from the scalp of human subjects upon the appearance of a sinusoidal grating. The stimulus spatial frequency was 2, 4, 8 or 16 c/deg and its contrast was 0.2 or 0.3. The data of the topographic studies confirm earlier observations that the N1 wave with latency of about 100 ms was localized medially with maximum in Oz, while the N2 wave with latency of about 150 ms was spread over a wider area of the scalp. The results of the equiweight analysis corresponded to the evidence of cortical origin of N1. The wide propagation of the N2 wave proved to be an obstacle for the applicability of the method, although it seems promising when the source of the visual evoked potential is limited in area.

Extracellular potential field of unmyelinated active axons.

Experimental and model investigations were carried out on the extracellular action potentials and potential fields of some unmyelinated axons: the medial and the lateral giant axons of Lumbriscus terrestris and small unmyelinated axons (nerve fibres of group C). Close to the membrane the extracellular action potentials are similar in shape to the second space derivative of the intracellular action potentials--they are triphasic in case of intracellular action potential with depolarization after-potential, having four phases in case of intracellular action potentials with hyperpolarization after-potential. Upon increasing the radial distance, the amplitudes of the different phases of the extracellular action potentials decrease at a different rate, while their maxima are shifted, which results in considerable changes in their shape.

Optimization of the source derivations from the scalp surface.

The selectivity of source derivations (SD) is computer-calucla ted using different combinations of electrodes and different interelectrode differences, with a view to the optimization of the method. For this purpose, the method described by Nunez and Katznelson (1981) is used to calculate surfaces in the brain tissue from the points of which a single current source will determine the same potential in a given point on the scalp surface. The lines of these surfaces are given for different planes. The calculations show that the selectivity increases with the decrease of the interelectrode distances, as well as when more electrodes are used. With a small number of electrodes for SD and especially when one central and two lateral electrodes are used, there exist brain areas in which the generators cause a potential with opposite sign on the scalp surface.

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.

Effect of short interstimulus intervals on the intra- and extracellular action potentials of isolated frog muscle fibres.

The changes in the time and space derivatives of the intracellular action potentials of isolated frog muscle fibers immersed in hypertonic sucrose-Ringer's solution were studied using paired stimulation with different interstimulus intervals. The peak-to-peak amplitude and the amplitudes of the separate phases of delta V/delta t and delta 2V/delta t2 decreased at intervals shorter than 10.25 ms as the duration of the phases lengthened. The velocity of spreading decreased at intervals below 7-10 ms and increased at longer intervals up to 40-100 ms. The peak-to-peak amplitude and the amplitudes of the separate phases of delta V/delta x and delta 2V/delta x2 decreased at intervals below 40-100 ms. The length of the separate phases of the space derivatives was almost constant. The extracellular action potentials near the membrane were similar to delta 2V/delta x2. When changing the interstimulus intervals the amplitude of the potentials recorded at different radial distances changed almost proportionally. In normal Ringer's solution the extracellular action potentials at different radial distances also changed almost proportionally depending on the intervals. They decreased at the shortest intervals and increased above the level measured at single stimuli for intervals longer than 7-10 ms, but shorter than 40-100 ms.

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.

Extracellular potentials of single active muscle fibres: effects of finite fibre length.

The extracellular action potentials (ECAPs) of single active muscle fibres immersed an isotropic volume conductor were investigated. The origination of excitation in the motor end-plate and its reaching the fibre end were taken into consideration. It was explained why at short radial distances the ECAPs over the fibre at points close to the end were similar in shape to the first time derivative and at points close to the motor end-plate - to the first time derivative of the intracellular action potential (ICAP) taken with minus sign. The fibre end changed the ECAP which would be recorded if the fibre was infinite and this change called pure termination potential (PTP) was a biphase positive-negative potential, proportional to the first time derivative of the ICAP at points close to the membrane and over the very end. With increasing the radial and axial distances PTP decreases in amplitude. Taking into account the PTP, the genesis of the terminal positive phase of the ECAPs (Gydikov and Kosarov 1972a, b) can be explained. The onset of the fibre or the motor end-plate also changed the potential which would be recorded if the fibre was infinite. This change was given the term of pure onset potential (POP) - a biphase negative-positive potential, proportional to the first time derivative of the ICAP taken with minus sign at a point close to the membrane and over the motor end-plate. With increasing the radial and the axial distance POP decreased in amplitude. Close to the membrane PTP and POP were commensurable with the potential of an infinite fibre only at points close to the ends or to the motor end-plate. At long radial distances they were commensurable with the potential of an infinite fibre for all axial distances.

Changes in the muscle fibre extracellular action potentials in long-lasting (fatiguing) activity.

The dependence of extracellular action potentials (ECAPs) of single frog muscle fibres on intracellular action potentials (ICAPs) was studied during long-lasting (fatiguing) activity. The conduction velocity, peak-to-peak amplitude and amplitudes of the separate phases of the first and second ICAP time derivatives decreased during long-lasting activity. The phases of the first and second ICAP space derivatives also decreased in amplitude and lengthened. ECAPs near the membrane were similar in shape and proportional in amplitude to (formula; see text) when recording at a distance from both the end of the fibre and the point of stimulation. At long radial distances, the amplitudes of the separate ECAP phases depended on the amplitude and length of the corresponding phases of (formula; see text). Thus the decrease in ECAP amplitude during long-lasting activity at long radial distances was less than at points close to the muscle fibre membrane. The consequences of these findings for the changes in electromyograms recorded by needle or superficial electrodes during long-lasting (fatiguing) activity are discussed.