Optimal filtering of nerve singnals

Recording from multiple electrodes at different sites along a peripheral nerve permits the application of powerful filtering methods to extract the activity of populations of fibres within the nerve which differ in temporal or spectral characteristics. The design of optimal linear filters is initially treated as a general problem in the calculus of variations in which the signals from one population of nerve fibres are extracted so as to minimize those from a second population of nerve fibres or from other sources (noise). A particularly important application arises when the signals at two electrodes are related by weighting functions. In the simplest example the weighting function represents the time delay for nerve impulses to conduct from one electrode to the other, but explicit results are also derivable when there are a range of conduction delays with probabilities distributed according to well-known functions such as the sinc² function.This work was partially supported by the National Research Council of Canada and Medical Research Council of Canada by Grant NRC A-4345 to MNO and Grant MRC MA-3307 to RBS through the University of Alberta     

Mathematical analysis of optimal multichannel filtering for nerve signals

This paper extends recent analyses (Roberts and Hartline, 1975; Ouztöreli and Stein, 1977) of optimal linear filters for separating neural signals from more than one electrode site. Roberts and Hartline's result, using a matched filter criterion, represents one of a class of optimal filters with different, but symmetrical, output waveforms derived by Ouztöreli and Stein (1977). Another narrow bandwidth filter of this class will give the optimal results according to an energy criterion, but may be less useful in practical situations.This work was partially supported by the Medical Research Council of Canada (Grant MRC-MT3307), the Technical Research Council of Denmark (Grant 516-6703 E406) and the National Research Council of Canada (Grant NRC A-4345)     

神经传导测定技术对腕管综合征病情评估的价值

目的:近年来腕管综合征发病率逐年升高,然而其慢性、隐匿性不易引起人们的重视,发现时往往已造成较大的危害。本文探讨腕管综合征的神经传导测定对病情评估的临床价值,旨在为患者腕管综合征早期发现和后续治疗提供进一步的临床参考依据。方法:选取我院124例确诊的腕管综合征患者。其中无大鱼际肌萎缩者有64例,并选取平均年龄相近的64例正常人作为对照(组A);有大鱼际肌畏缩者60例,并选取平均年龄相近的60例正常人作为对照(组B)。A、B组均经行神经电图检查,握力测定和两点辨别觉测定,分析神经传导速度改变与感觉、运动功能减退程度的关系。结果:A、B两组患者均有不同程度的神经传导改变:在A组患者神经传导改变中,运动和感觉传导速度(MCV和SCV)轻度下降,运动和感觉电位波幅(CMAP和SNAP)轻度下降,潜伏期(ML)轻度延长;在B组患者神经传导中,运动和感觉传导速度(MCV和SCV)明显下降,运动和感觉电位波幅(CMAP和SNAP)明显下降,潜伏期明显延长。结论:腕管综合征患者不同的临床表现有不同程度的神经电图表现,因此神经电图对神经传导的测定结果对腕管综合征患者的病情有良好的评估价值,值得临床推广。     

Global dynamics of a selection model for the growth of a population with genotypic fertility differences

A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-8130Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-4823Research supported by NSF Grant MCS 7901069. A portion of the work was carried out while the author was a Visiting Professor at the University of Utah, Salt Lake City, Utah     

Evolutionary games for spatially dispersed populations

An evolutionary game model is developed that incorporates both spatial dispersion and density effects in the evolutionary dynamic. It is shown that a stable equilibrium (e.g. an evolutionarily stable strategy) of the non-dispersed frequency dynamic becomes a stable equilibrium of the larger system if population density stabilizes at these fixed frequencies. It is also shown, by example, that other equilibria, whose frequencies change from one location to another, may appear when dispersal rates are relatively small.Research supported by Natural Sciences and Engineering Research Council of Canada Operating Grant A6187Research supported by Natural Sciences and Engineering Research Council of Canada Operating Grant A7822     

The effects of multiple reflex pathways on the oscillations in neuro-muscular systems

Summary A model of mammalian neuro-muscular systems described previously (Ouztöreli and Stein, 1975) has been extended to include multiple reflex pathways, as have been shown to exist in primates, including man (Milner-Brown et al., 1975). A number of general mathematical properties of the extended system are described. In the final section, using computer solutions, it is shown that the presence of multiple reflex pathways can effectively reduce the tendency for oscillation which will exist if high reflex gain were concentrated in a single pathway. High loop gain is desirable for good control in any negative feedback system, so the presence of multiple reflex pathways could improve reflex control, while limiting the magnitude of tremor or other unwanted oscillations in neuromuscular systems.This work was partly supported by the National Research Council of Canada (Grant NRC-A4345) and by the Medical Research Council of Canada (Grant MRC-MA 3307) through the University of Alberta.     

Some applications of the concept of body forces for the myocardium

A mathematical theory of the dynamics of the myocardium based on the concept of body forces is applied to account for two different experimental results. The first result consists of a relation between oxygen consumption and the kinetic energy of the myocardium. The second set of results provides a consistent interpretation of the relationship between different indices used to assess the ventricular performance. This work has been supported by the Medical Research Council of Canada, Grant MA-5766.     

The relationship between signal response selectivity and the functional structure of complex retinal neural networks

In this paper we simulate the simultaneous responses of 45 neurones within a hypothetical retina to a variety of spatio-temporal signals. Our results demonstrate how specific convergent and divergent excitatory and inhibitory connections are sufficient to determine signal response selectivity of specific ganglion cells and so delimit the known types of center-surround receptive fields.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 to M.N.O. and Grant A-4395 to T.M.C. through the University of Alberta     

Predator-prey systems with group defence: The paradox of enrichment revisited

The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically). Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823. Research partially supported by a Natural Sciences and Engineering Research Council of Canada postdoctoral fellowship.     

Estimation of the muscle fibre semi-length under varying joint positions on the basis of non-invasively extracted motor unit action potentials.

Changes in muscle fibre length and surface electrode position with respect to the muscle fibres affect the amplitude and frequency characteristics of surface electromyography (SEMG) in different ways. Knowledge of changes in muscle fibre length would help towards a better interpretation of the signals. The possibility of estimating the length through SEMG during voluntary contractions was checked in this study. The fibres' semi-length was estimated from the product of the conduction velocity and conduction time during which the wave of excitation propagated from the end-plate region to the ends of the fibres. Short (10 s), moderate (30% of maximum voluntary contraction) isometric contractions were performed by 10 subjects at different elbow joint angles (80-140 degrees in steps of 20 degrees ). Monopolar signals were detected non-invasively, using a two-dimensional electrode array. High spatial resolution EMG and a decomposition technique were utilised to extract single motor unit activities for triggered averaging and to estimate conduction velocity. A significant increase with joint angle was found in conduction time and estimated fibre semi-length. Changes in conduction velocity with joint angle were found to be not significant. The methodology described allows the relative changes in fibres' semi-length to be estimated from SEMG data.     

A leukocyte culture and chromosome preparation technique for avian species

Summary A technique for avian leukocyte culture and chromosome analysis is described. The method is simple and allows karyotypic analysis by a variety of chromosome banding methods. It is applicable to a wide variety of species and may be useful in determining the genetic sex of monotypic species in captivity or for population studies of specimens in the wild. This work was supported by Medical Research Council (Canada) Grant MA-4655. B. M. B. is a recipient of a Medical Research Council Fellowship.     

The linear electrode array: a useful tool with many applications.

In this review we describe the basic principles of operation of linear electrode arrays for the detection of surface EMG signals, together with their most relevant current applications. A linear array of electrodes is a system which detects surface EMG signals in a number of points located along a line. A spatial filter is usually placed in each point for signal detection, so that the recording of EMG signals with linear arrays corresponds to the sampling in one spatial direction of a spatially filtered version of the potential distribution over the skin. Linear arrays provide indications on motor unit (MU) anatomical properties, such as the locations of the innervation zones and tendons, and the fiber length. Such systems allow the investigation of the properties of the volume conductor and its effect on surface detected signals. Moreover, linear arrays allow to estimate muscle fiber conduction velocity with a very low standard deviation of estimation (of the order of 0.1-0.2 m/s), thus providing reliable indications on muscle fiber membrane properties and their changes in time (for example with fatigue or during treatment). Conduction velocity can be estimated from a signal epoch (global estimate) or at the single MU level. In the latter case, MU action potentials are identified from the interference EMG signals and conduction velocity is estimated for each detected potential. In this way it is possible, in certain conditions, to investigate single MU control and conduction properties with a completely non-invasive approach. Linear arrays provide valuable information on the neuromuscular system properties and appear to be promising tools for applied studies and clinical research.     

Detection of feedback in the central nervous system using system identification techniques

An analysis method to detect the presence of feedback between biological signals, particularly those associated with the central nervous system, is presented. The technique is based on recent results in the system identification literature involving the concept of a feedback free process. It may be applied to volume conducted signals such as EEG and EMG, as well as to neuronal spike trains through the use of a data transformation procedure. The utility of the technique is then demonstrated in a study of the relationship between Parkinsonian tremor and certain tremor cells found in the thalamus of Parkinsonian patients, using data collected during thalamotomies. The results obtained suggest that feedback mechanisms may be an important factor contributing to Parkinsonian tremor.This research was supported by the Natural Sciences and Engineering Research Council of Canada, The Medical Research Council of Canada, and Bell-Northern Research     

Detection of certain African,insectivorous bats by sympatric,tympanate moths

Summary The tympanic organs of moths we studied in Zimbabwe responded differentially to the echolocation/hunting signals of sympatric, insectivorous bats. Bats employing very high frequencies (> 110 kHz) and/or low intensity cries tend to be first detected by tympanal preparations at distances considerably less than those with more intense, mid-frequency (20–60 kHz) cries. There appears to be some positive correlation between acoustically inconspicous bats and the amount of auditive prey they feed on although there are theoretical disadvantages in producing highly undetectable orientation cries.This project was financed through Natural Sciences and Engineering Research Council of Canada Pre- and Post-doctoral awards to DWT and JHF and a National Geographic Society Research Grant to JHF. The authors wish to thank M.B. Fenton, G.P. Bell, D.H.M. Cumming and the staff of the Sengwa Wildlife Research Area, Zimbabwe, for their assistance and support.     

Control mechanisms of a neural network

In this paper we consider some classical control theoretic properties of a nonlinear neural network proposed by Ouztöreli (1979) to represent the activities of constiuent neurones in terms of the input signals and coupling (associative) properties. By breaking the network into linear and nonlinear components we have been able to localize the nonlinearities in the individual neural response latencies through the system.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada by Grant NSERC-A 4345 to M.N.O. and Grant NSERC-A 2568 to T.M.C. through the University of Alberta     

An inverse problem in neural processing

Any neural network aimed at the coding sensory events must contain computational properties which generally allow the organism to reconstruct the input signals with some degree of accuracy-else the association between stimulus and response would, at best, be uncertain. In this paper we investigate the problem of reconstructing external input signals to neural networks when the activity profiles of only some of its member cells are known. The evolution and activities of such cells are defined by an earlier formulation of one of us (Ouztöreli 1979) and, here, we restrict our application to local curcuits within the vertebrate retina. Solutions to this inverse coding problem are presented for specific network equations and examplified with 1, 3, and 5 neuron cases.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 to M.N.O. and grant A-4395 to T.M.C. through the University of Alberta     

Influence of timing variability between motor unit potentials on M-wave characteristics

The transient enlargement of the compound muscle action potential (M wave) after a conditioning contraction is referred to as potentiation. It has been recently shown that the potentiation of the first and second phases of a monopolar M wave differed drastically; namely, the first phase remained largely unchanged, whereas the second phase underwent a marked enlargement and shortening. This dissimilar potentiation of the first and second phases has been suggested to be attributed to a transient increase in conduction velocity after the contraction. Here, we present a series of simulations to test if changes in the timing variability between motor unit potentials (MUPs) can be responsible for the unequal potentiation (and shortening) of the first and the second M-wave phases. We found that an increase in the mean motor unit conduction velocity resulted in a marked enlargement and narrowing of both the first and second M-wave phases. The enlargement of the first phase caused by a global increase in motor unit conduction velocities was apparent even for the electrode located over the innervation zone and became more pronounced with increasing distance to the innervation zone, whereas the potentiation of the second phase was largely independent of electrode position. Our simulations indicate that it is unlikely that an increase in motor unit conduction velocities (accompanied or not by changes in their distribution) could account for the experimental observation that only the second phase of a monopolar M wave, but not the first, is enlarged after a brief contraction. However, the combination of an increase in the motor unit conduction velocities and a spreading of the motor unit activation times could potentially explain the asymmetric potentiation of the M-wave phases.     

Simulation analysis of the ability to estimate motor unit propagation velocity non-invasively by different two-channel methods and types of multi-electrodes.

Ability to estimate motor unit propagation velocity correctly using different two-channel methods for delay estimation and different non-invasive spatial filters was analysed by simulation. It was established that longitudinal double difference electrodes could be not a better choice than simple bipolar parallel electrodes. Spatial filtration with a new multi-electrode (performing difference between signals detected by two transversal double difference electrodes positioned along the muscle fibres) promises to give the best estimate. Delay estimation between reference points is more preferable than that based on the cross-correlation technique, which is considerably sensitive to the fundamental properties of the muscle fibre extracellular fields. Preliminary averaging and approximation of the appropriate parts of the signals around chosen reference points could reduce the larger noise sensitivity and the effects of local tissue inhomogeneities as well as eliminate the sampling problem. A correct estimate of the propagation velocity could be impossible, even in the case of not very deep motor units (15 or 10 mm, depending on the spatial filter used) with relatively long (about 120 mm) muscle fibres. In the case of fibres with asymmetrical location of the end-plates in respect to the fibre ends, the propagation velocity estimates could be additionally biased above the longer semilength of the motor unit fibres.     

A kinetic study of muscular contractions

Summary In the present work the kinetics of muscular contractions are studied, based on a three-state model which is introduced in Section I. The general properties of this class of models for muscular contractions are derived in Sections II–VI. The kinetic equations are solved for four particular examples in Sections VII–X. These analytical results should be useful for comparison with experimental data to determine the functional dependence of the rate constants and on muscle length.This work was partly supported by the National Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MA-3307 through the University of Alberta.     

A method for the short-term in vitro cultivation of the chick embryo on liquid media

Summary Use of sterile membrane filters (Millipore) as a surface for embryo attachment and growth was attempted with success. Embryos attached to the filters readily and showed development equal to or better than the controls which were maintained on a whole egg-agar medium. This investigation was supported by grant A 6059 from the National Research Council of Canada.