Научная статья на тему 'Human motoneurone firing characteristics: model and experiment'

Human motoneurone firing characteristics: model and experiment Текст научной статьи по специальности «Биологические науки»

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Текст научной работы на тему «Human motoneurone firing characteristics: model and experiment»

на длительные или медленно развивающиеся во времени стимулы. Автор предполагает, что эти изменения можно объяснить нарушением способности клеточной мембраны отвечать на раздражение избирательным повышением к ионам натрия, . . . -верхности клеточной мембраны наступает фиксация молекул наркотика, вследствие чего происходит блокирование натриевых каналов мембраны.

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УДК 617.58.

M. Piotrkiewicz1, L. Kudina2, J. Mierzejewska1, N. Zhoukovskaya2

HUMAN MOTONEURONE FIRING CHARACTERISTICS: MODEL AND

EXPERIMENT

INTRODUCTION. In a few past decades a lot of information on the function of mammalian motoneurones (MNs) has been derived from intracellular recordings gathered in acute animal experiments. This kind of direct recording from MN of course cannot be applied in humans. However, indirect information on human MNs can be deduced from statistical characteristics of MN rhythmic firing. This is possible by studying motor unit (MU) activity, since there is one-to-one relation between MN and MU discharges. Computer simulations are commonly applied to allow for the proper interpretation of these results.

The special attention has been brought to the relationship between standard deviation of interspike interval (ISI) and their mean value, (Tm). The shape of this characte-

1 Bionics Department, Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland

2 Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

ristic is different for the short- and long-interval range of ISI. It has already been shown (Piotrkiewicz, 1999) that its position with respect to the mean ISI axis is related to the duration of MN afterhyperpolarisation (AHP) and that the synaptic inflow, or rather its variable component (synaptic noise), determines absolute values of SD. In the present paper, more attention has been paid to the other properties of MNs, which may be reflected by the shape of (Tm) relationship.

METHODS. Modelling. Motoneuronal firing was simulated according to a simple model. The interspike voltage trajectory was obtained by summing up the AHP curve and the steady level of synaptic inflow with a variable component. Whenever the trajectory crossed the threshold, the time of spike generation was recorded and the whole process was reset.

Two different AHP curves, A1 and A2, were used (see Fig. 1) with the following basic parameters: threshold, 0 mV, the resting level, -10 mV, amplitude, -10 mV; duration, 120 ms; joint level (the voltage level at which the straight line was substituted by the exponential in version A2), -2 mV or -1 mV.

Experiments: the potentials of single motor units (MUs) were picked up from nine healthy volunteers aged 22-58 years by bipolar needle electrodes. The rhythmic firing of voluntarily activated single MUs was recorded during weak and moderate voluntary muscle contractions. Muscles investigated: biceps brachii (BB) and soleus (SOL).

The amplified MU potentials were transferred to a PC computer with the sampling rate of 15 kHz for computer-assisted analysis. After decomposing the recordings into single MU potential trains, the distribution of ISI, their mean value and standard deviation were determined for stationary fragments of experimental MU potential trains and the results of simulation. Whenever possible, the break point of the relationship delimiting short-and long-interval ranges was estimated as an intersection of two straight lines fitted to the initial and final portions of the data by means of the least-squares method.

In addition, for 6 SOL MNs AHP duration was estimated according to the method introduced by Kudina and Alexeeva (1992).

RESULTS. Typical (Tm) plot consisted of two linear portions with slopes different for short and long ISI range. Transition between both ranges was usually curvilinear, although two-straight line approximation was often quite satisfactory for the whole relationship.

The position of (Tm) plot with respect to the mean ISI axis depended on the AHP duration (Fig. 2a). Note that the slope of the long-interval portion is the bigger, the longer is the break point interval. Similar correlation was observed in the experiment (Fig. 2b).

Fig.2. The comparison of (Tm) plot for three different AHP durations: a) simulation: (version A2): triangles - 95 ms; squares - 145 ms; circles - 200 ms; b) experiment: circles and squares - BB, triangles - SOL

Not only the simulation results, but also the recent study on animal motoneurones, which were activated by injected current with added noise (Binder, personal communication) confirm that it is the AHP duration, which is responsible for this shift of the plot.

Break point of the (Tm) relationship was correlated with AHP duration (Fig. 3a). Similar correlation was obtained experimentally for 6 MNs, for which both break point and AHP duration were estimated (Fig. 3b). Although the number of experimental observations was very small so that the correlation was not significant, the striking similarity of both plots cannot be denied.

Model Experiment

Break-point interval, ms

Fig.3. An interrelation between AHP duration and break point: a) simulation (version A2); b) experiment; dotted line - line of identity

In most of experimental plots, the short-interval portion had a considerable slope (cf. Fig. 2 and Table). There were however about 17% of the plots with plateau in this ISI range. Simulations show that the plateau is observed when interspike voltage trajectories in short-interval range are parallel to each other. Trajectories of this kind were in-

deed recorded by Schwindt and Calvin (1972) in number of experiments in the primary range of firing rates of cat motoneurones. The slope of the short-interval portion of (Tm) plot could be obtained in simulations by the gradual increase in AHP amplitude with increasing excitation level, which resulted in fan-shaped set of interspike potential trajectories (see insert to Fig. 4). Experimental results suggest therefore that the fanshaped trajectories are much more common among human MNs supplying both muscles investigated. The degree of divergence varies between individual motoneurones. Indeed, Baldissera and Gustafsson (1974) have shown that the typical set of primary range trajectories should be fan-shaped. Nevertheless our experimental results suggest that among human MNs the trajectories close to parallel are also present.

Most of researchers dealing with (Tm) relationships, paid attention to calculate

means and SDs from the stationary fragments of ISI trains. The influence of this procedure on the results was tested in simulations by addition of an increasing trend to the synaptic inflow. The resulting spike trains were then subdivided to fragments of about 100 spikes, from which mean ISI and SD were computed. The results were compared with those calculated from stationary fragments of 400 potentials. As follows from the comparison (Fig. 5), there is no difference between both ways of calculation. Therefore seeking stationary fragments for SD and mean ISI computing is not necessary.

Fig.4. The comparison of the (Tm) plots obtained for the set of parallel (squares) and fan-shaped (circles) trajectories. Trajectory sets given in insert

Fig.5. The comparison of the o(Tm) plots obtained from stationary fragments (400 intervals, circles) and from fragments with increasing trend (100 intervals, squares)

CONCLUSIONS. The features of the relationship SD(Tm) reflect the features of interspike potential trajectory of a MN. The position of this relationship with respect to the mean ISI axis, can be considered as a measure of the AHP duration of a motoneu-rone. The slope of the short-interval part is related to the degree of the convergence between the trajectories for different mean ISI. The results prove that the trajectories for most of MNs are fan-shaped although there are also MNs with parallel trajectories.

The considerable range of break points and slopes for both parts of SD(Tm) relationships for each muscle indicate that the MN properties in the sample investigated vary to great extent.

It is suggested that seeking stationary fragments for SD and mean ISI calculation is not necessary.

REFERENCES

1. Baldissera F, Gustafsson B (1974) Firing behaviour of a neuron model based on the afterhyperpolarization conductance time course and algebraic summation. Adaptation and steady state firing. Acta Physiol Scand 92:27-47

2. Kudina LP, Alexeeva NL (1992) After-potentials and control of repetitive firing in human motoneurones. Electroencephal Clin Neurophysiol 85:345-353

3. PiotrkiewiczM(1999) An influence of AHP on the pattern of motoneuron rhythmic activity. J Physiol (Paris) 93:125-133

4. Schwindt P, Calvin W (1972) Membrane-potential trajectories between spikes underlying motoneuron firing rates. J Neurophysiol 35:311-325

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РОЛЬ МИКРОЭЛЕМЕНТОЗОВ В ЭТИОПАТОГЕНЕЗЕ ЗАБОЛЕВАНИЙ

ГЛАЗ

В настоящее время наиболее информативным методом обследования больных является метод плазменно-эмиссионного анализа с индуктивно связанной аргоновой плазмой (система GB - Астралия), который дает информацию о 24-25 микроэлементах одновременно, т.е. обо всех эссенциальных и токсичных микро-, . Этот метод был применен авторами совместно с Московским научномедицинским центром по изучению микроэлементозов для определения характера микроэлементозов у больных с сосудистыми заболеваниями глаз и их связей с общими заболеваниями при обследовании группы больных с уже установленным

..

Для исследования глазного дна в свете различного спектрального состава мы пользовались офтальмохромоскопией AM. Водовозова со следующими свето-

: - 18 ( 400 600 ) -

красном свете; КС-10 (дайна волны от 560 до 700 ммк) для офтальмоскопии в . -освещения для исследований глазного дна в непрямом красном свете. ЖС - 17 в

( - ); ПС-11 в сочетании с КС - 10 (для офтальмоскопии в пурпурном свете).

Офтальмохромоскопия с контрастом. Больному с максимально расширенным зрачком давали выпить раствор флюоресциина натрия (1,5 гр. вещества на 100,0

). 30-60 ( ) -

водили офтальмохромоскопию, пользуясь, синим фильтром.

Прямую офтальмоскопию проводили с помощью ручного электрического офтальмоскопа со световодом и на щелевой лампе фирмы «Карл Цейс Йена», с применением в ряде случаев линзы Г ольдмана.

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