Friedemann Awiszus

The relationship between estimates of Ia-EPSP amplitude and conduction velocity in human soleus motoneurons

There are several parameters associated with motoneuron size, among which are the conduction velocity of the axon as well as the size of the excitatory postsynaptic potential (EPSP) induced by stimulation of Ia afferents in the corresponding muscle nerve. In particular, it has been established in animal experiments that small motoneurons with a low conduction velocity exhibit large Ia EPSPs, whereas large motoneurons with a high conduction velocity show small Ia EPSPs. Thus small motoneurons are recruited earlier than large ones. In this study, we investigated whether such a relationship between motoaxon conduction velocity and size of the Ia EPSPs could also be found for human soleus motoneurons. In total, 36 motor units from six healthy volunteers were activated by a slight voluntary contraction and exposed to 200 stimuli of the tibial nerve in the popliteal fossa. Stimuli were delivered using a special stimulus protocol ensuring a constant pre-stimulus spike density along with a constant rate of discharge of the investigated unit. From the stimulus-correlated spike train data a measure of Ia-EPSP amplitude was obtained, along with the single-unit H-reflex latency. Additionally, for each unit, the so-called surface macro EMG was recorded, which measures the complete electrical activity attributable to the unit investigated. From the macro EMG, the intramuscular delay from arrival of each action potential at the soleus muscle and the detection of the muscle-fiber action potential picked up by the recording needle electrode were measured. All single-unit H-reflex latencies were corrected for the corresponding intramuscular delays. From the corrected latencies, single-unit conduction velocities were obtained. It was found that there was a highly significant negative correlation between the estimate of the single-unit conduction velocity and the inferred size of the Ia EPSP. Thus, it was found that Ia-EPSP amplitudes in human soleus motoneurons follow the size principle.

On a method to detect long-latency excitations and inhibitions of single hand muscle motoneurons in man

SummaryThe peri-stimulus-time histogram (PSTH) analysis of stimulus-related neuronal spike train data is usually regarded as a method to detect stimulus-induced excitations or inhibitions. However, for a fairly regularly discharging neuron such as the human α-motoneuron, long-latency modulations of a PSTH are difficult to interpret as PSTH modulations can also occur as a consequence of a modulated neuronal autocorrelation. The experiments reported here were made (i) to investigate the extent to which a PSTH of a human hand-muscle motoneuron may be contaminated by features of the autocorrelation and (ii) to develop methods that display the motoneuronal excitations and inhibitions without such contamination. Responses of 29 single motor units to electrical ulnar nerve stimulation below motor threshold were investigated in the first dorsal interosseus muscle of three healthy volunteers using an experimental protocol capable of demonstrating the presence of autocorrelative modulations in the neuronal response. It was found for all units that the PSTH as well as the cumulative sum (CUSUM) derived from these responses were severely affected by the presence of autocorrelative features. On the other hand, calculating the CUSUM in a slightly modified form yielded — for all units investigated — a neuronal output feature sensitive only to motoneuronal excitations and inhibitions induced by the afferent volley. The price that has to be paid to arrive at such a modified CUSUM (mCUSUM) was a high computational effort prohibiting the on-line availability of this output feature during the experiment. It was found, however, that an interspike interval superposition plot (IISP) — easily obtainable during the experiment — is also free of autocorrelative features. Both mCUSUM and IISP of all 29 units showed a common reflex pattern in response to the electrical stimulation of low-threshold afferents. The first sizeable effect was a motoneuronal inhibition starting 50–70 ms after the stimulus followed by an excitatory period with an onset latency of 90–110 ms. Thereafter, a second inhibitory period with a duration of approximately 100 ms appeared beginning 140–160 ms after the stimulus. These long-lasting effects with long-latency could not be deduced from the “raw” PSTH or the unmodified CUSUM making it necessary to evaluate long-latency reflexes of single motoneurons by calculation of an mCUSUM and — in case of on-line requirements — by construction of an IISP.

Continuous functions determined by spike trains of a neuron subject to stimulation

Abstractseveral ways of estimating a continuous function from the spike train output of a neuron subjected to repeated stimuli are compared: (i) the probability of firing function estimated by a PST-histogram (ii) the rate of discharge function estimated by a “frequencygram” (Bessou et al. 1968) and (iii) the interspike-interval function which is introduced in this paper. For a special class of neuronal responses, called deterministic, these functions may be expressed in terms of each other. It is shown that the current clamped Hodgkin-Huxley model of an action potential encoding membrane (Hodgkin and Huxley 1952) is able to generate such deterministic responses. As an experimental example, a deterministic response of a primary muscle spindle afferent is used to demonstrate the estimation of the functions. Interpretability and numerical estimatability of these spike train describing functions are discussed for deterministic neuronal responses.

Quantification and statistical verification of neuronal stimulus responses from noisy spike train data

Usually neuronal responses to short-lasting stimuli are displayed as peri-stimulus time histogram. The function estimated by such a histogram allows to obtain informations about stimulus-induced postsynaptic events as long as the interpretation is restricted to the first response component after the stimulus. The interpretation of secondary response components is much more difficult, as they may be either due to stimulus effects or represent an “echo” of the primary response. In the present paper two output functions are developed that do not show such an echoing of responses. The first one, the interspike interval change function, represents an ideal way to quantify a neuronal stimulus response as its amplitude was found to be almost independent of the stimulation strategy used during acquisition of the spike train data. The other function, the displaced impulses function, allows to verify the statistical significance of an observed response component. Both functions may be estimated from stimulus-correlated spike train data, even if the neuron under investigation shows considerable interspike-interval variability in the absence of stimulation. The concepts underlying these neuronal output functions are developed on simulated responses of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature that is exposed to a transient excitatory conductance increase. Additionally, estimation of these output functions is also demonstrated on responses of human soleus motoneurons that were exposed to electrical stimuli of the tibial nerve in the popliteal fossa.

Effects of paranodal potassium permeability on repetitive activity of mammalian myelinated nerve fiber models

Almost all potassium channels within mammalian myelinated nerve fibers are covered by the myelin sheath and their majority is concentrated in a small paranodal region. In order to investigate effects of this paranodal potassium permeability on nerve fiber behavior via a simulation approach, a myelinated fiber model is required that treats myelin sheath and internodal axolemma as separate entities. Such a fiber description was developed by Blight (1985) and his model was used to investigate the effects paranodal potassium channels have on the ability of maintaining repetitive firing in response to a constant current injected into the fiber. It was found that increasing the potassium channel density at the paranode from low to moderate values widened the range of injected currents with a repetitive response. This promotion of repetitive activity by the introduction of additional potassium channels occurred up to an “optimal” value beyond which a further increase in paranodal potassium permeability narrowed the range of currents with a repetitive response. Finally, if a certain limit in paranodal potassium channel density was exceeded, repetitive activity was abolished completely. These results were obtained regardless of the assumptions about the electrical resistance of the myelin sheath. On the other hand, in the absence of potassium channels repetitive firing could be observed only when a high resistance myelin sheath was assumed, whereas a nerve fiber model with electrical properties inferred from intracellular recordings needed at least some potassium channels within the paranodal region for repetitive firing in response to an injected current.

Correlations between size parameters and the amplitude of the excitatory postsynaptic potential evoked by magnetic brain stimulation in human hand muscle motoneurons

According to the size principle for motoneurons one would expect that an excitatory stimulus given to a motoneuronal pool should evoke small excitatory postsynaptic potentials (EPSPs) in large and large EPSPs in small motoneurons of the pool. In this study this expectation was tested for the motoneuron pool of the first dorsal interosseus muscle of man excited by a magnetic stimulus given to the contralateral motor cortex. In total, 60 first dorsal interosseus motor units from three healthy volunteers were investigated. For each unit the EPSP size induced by the magnetic brain stimulus was assessed indirectly through a cross correlation of magnetic brain stimuli with motor unit discharges during a slight voluntary contraction. In addition to the indirect measurement of EPSP size, three indicators of motoneuronal size were obtained for each unit: the area the macroelectromyogram (Macro EMG) of the unit encloses with the baseline, the peak-to-peak amplitude of the Macro EMG, and the “true” latency from the magnetic stimulus to the motor unit which in turn provides an indirect estimate for the conduction velocity of the motoneuronal axon. It was found that all three measures of motoneuron size were significantly negatively correlated with the estimates of EPSP amplitude. Such significant negative correlations were found not only in the pooled data but also in the data from each subject individually. These correlations reveal that a magnetic brain stimulus induces small EPSPs in large and large EPSPs in small motoneurons of the first dorsal interosseus muscle of man.

On the description of neuronal output properties using spike train data

Neuronal output properties for input stimuli that evoke a deterministic response can be efficiently described by the interspike-interval function (Awiszus 1988a). It is shown in this paper that there are stimuli for which both the Hodgkin-Huxley (HH-) model of an action potential encoding membrane (Hodgkin and Huxley 1952) and a muscle spindle primary afferent generate responses which violate the conditions for a deterministic one. Instead of being stochastic threse responses follow systematic rules, namvely those for a semi-deterministic response, a class of neuronal responses established in this paper that includes the deterministic one. Instead of being stochastic these output properties are best described by the intersp-ikeinterval curve. A phase plane analysis of the internal properties of the HH-model underlying such responses shows that it is reasonable to assume that responses of an HH-model and consequently, all neurons for which an HH-model is a valid description of the action potential encoding process, always fall into the class of semi-deterministic responses, regardless of the input current density time course as long as it is large enough to maintain spike activity. Consequences of this assumption for the analysis of neuronal output properties are discussed with respect to output measures and efficient input stimuli.

Sensitivity of different stimulus-timing strategies for the detection of small excitations in noisy spike train data

There are several different strategies to control the timing of a stimulus with respect to the ongoing discharge during the recording of neuronal stimulus-response characteristics. One possible strategy consists of delivering stimuli in such a way that a constant pre-stimulus spike density is reached. Another strategy enforces spike application with a constant stimulus latency after a spontaneous discharge. In this paper the sensitivity of these different strategies for statistical verification of small excitatory response components was investigated. It was found that the difference between observed poststimulus spike distribution and expected spike distribution under the null hypothesis of no stimulus effect was larger using a constant-stimulus-latency (CSL) strategy with an appropriate value for the stimulus latency. Thus, the statistical verification of neuronal response components is clearly facilitated if a CSL strategy is used. This superiority of the CSL strategy is marked, especially for small excitations at neurons discharging slowly with low discharge variability.

The RIPP density estimate: an alternative method for the estimation of peri-stimulus spike density.

Cross-correlation between stimuli and neuronal discharges determines the peri-stimulus spike density. This density function is usually estimated by the peri-stimulus time histogram (PSTH). In this paper an alternative method for spike-density estimation is considered that employs estimation of the rate of an inhomogeneous Poisson process by Jth waiting times. This procedure is called the RIPP density estimate. It involves sorting the spike times for all trials and obtaining the Poisson rates for successive groups of spikes. By application of this procedure to simulated action-potential sequences from the leaky-integrator model subject to a realistic input, it is shown that the RIPP density estimate reveals much more information from a given set of spike train data than a PSTH. An application of the RIPP density estimate to experimental spike train data from a human hand muscle motoneuron subject to a low-threshold-afferent volley is also presented.

The relationship between a neuronal cross-correlogram and the underlying postsynaptic current

Cross-correlations between stimuli and neuronal discharges yield information about synaptic events at the investigated neuron. In this paper it is shown that the time course estimated by a cross-correlogram, the cross-correlation function (ccf), represents the input current that upon injection into the perfect integrator model evokes spike sequences that are (almost) identical to those used for estimation of the ccf. Thus, the shape of a ccf may be regarded as an estimate of the underlying postsynaptic current, if the neuron investigated behaves, at least to a first approximation, like a perfect integrator model.