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  • 1
    Electronic Resource
    Electronic Resource
    A neuronal model for the discharge patterns produced by cyclic inputs (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 337-353 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract To understand the patterns of nerve impulses produced by sinusoidal stimuli, a simple model is considered which integrates input currents with a finite time constant until a threshold voltage is reached, whereupon an output pulse is produced and the process is restarted. We show here that (a) a general analytic solution exists for this model driven by sinusoidal stimuli, determining the interval between every member of the pulse train, (b) for all values of the parameters of the model a pattern exists which repeats periodically after a finite number of pulses in the absence of noise, (c) the system will approach a stable pattern which, if perturbed, will be recovered once the perturbation is removed, (d) the linear integrator or relaxation oscillator and the curren multiplier are limiting cases of this model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476873
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  • 2
    Electronic Resource
    Electronic Resource
    Differences in Variability of Discharge Frequency between Primary and Secondary Muscle Spindle Afferent Endings of the Cat (1965)
    [s.l.] : Nature Publishing Group
    Nature 208 (1965), S. 1217-1218 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] In order to check this observation and to compare the predictions of two different mathematical models for the cause of the variability5'6, approximately 200,000 inter-spike intervals from thirteen muscle spindle afferents (seven primaries, six secondaries) from the soleus muscle of the ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/2081217a0
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  • 3
    Electronic Resource
    Electronic Resource
    Mathematical analysis of optimal multichannel filtering for nerve signals (1979)
    Springer
    Biological cybernetics 32 (1979), S. 19-24 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract This paper extends recent analyses (Roberts and Hartline, 1975; Oğuztöreli 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 Oğuztöreli 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337447
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  • 4
    Electronic Resource
    Electronic Resource
    Application of optimal multichannel filtering to simulated nerve signals (1979)
    Springer
    Biological cybernetics 32 (1979), S. 25-33 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract The optimal linear filters derived in the preceding paper can be thoroughly evaluated using computer simulations, based on the properties of mammalian sensory and motor nerve fibres. Using reasonable values for action potential waveforms, conduction velocity and electrode noise, good separation of motor and sensory signals can be obtained. The performance of the filters is degraded by 1) increasing the electrode noise, 2) introducing dispersion in the conduction velocities, or 3) variation in the waveform of the action potentials from that used in designing the filters. However, the variations needed to seriously degrade performance are quite large compared to those which are likely to be present in mammalian nerves. Use of these filters to distinguish different classes of sensory (or motor) signals based on conduction velocity is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337448
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  • 5
    Electronic Resource
    Electronic Resource
    Improved neuronal models for studying neural networks (1974)
    Springer
    Biological cybernetics 15 (1974), S. 1-9 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00270755
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  • 6
    Electronic Resource
    Electronic Resource
    The estimation of the frequency response function of a mechanoreceptor (1972)
    Springer
    Biological cybernetics 11 (1972), S. 15-23 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00267761
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  • 7
    Electronic Resource
    Electronic Resource
    Optimal filtering of nerve singnals (1977)
    Springer
    Biological cybernetics 27 (1977), S. 41-48 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00357709
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  • 8
    Electronic Resource
    Electronic Resource
    The role of γ-motoneurons in mammalian reflex systems (1981)
    Springer
    Biological cybernetics 39 (1981), S. 171-179 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A γ-motoneuron pathway to intrafusal muscle has been added to a previously studied model of the neuromuscular system and its reflex pathways. A general differential-difference equation is derived for the system which can be solved analytically and numerically. The homogeneous part of the solution determinas the stability of the feedback pathway which to a first approximation is unchanged from the previous model. However, the additional filtering in the γ-pathway reduces the tendency for oscillations to central inputs, which is illustrated for the particular solutions to sinusoidal and impulse inputs. Thus, the gamma pathway offers the advantage of stability at the expense of increased sluggishness of response.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00342770
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  • 9
    Electronic Resource
    Electronic Resource
    Analysis of a model for antagonistic muscles (1982)
    Springer
    Biological cybernetics 45 (1982), S. 177-186 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In the present work a linear model for a pair of antogonistic muscles is analysed. Each constituent muscle in this model is identical to ones considered previously (Stein and Oğuztöreli, 1976). Analytical properties of the antagonistic muscles and dynamics of the system are described and some numerical results are discussed. The natural modes of the system are determined by a fourth order polynomial, which most commonly has one pair of conjugate complex roots and two negative real roots. The filtering of neural inputs through the active state properties of the muscle increases the order of the system to fifth order for these inputs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00336190
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  • 10
    Electronic Resource
    Electronic Resource
    The radial decline of nerve impulses in a restricted cylindrical extracellular space (1978)
    Springer
    Biological cybernetics 28 (1978), S. 159-165 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In order to increase the potentials recorded extracellularly from nerve fibres, peripheral nerves are often placed in restricted space with cylindrical geometry. Equations are derived for computing the potentials expected at the surface of the cylinder, based on the potentials at the external surface of a small nerve fibre located on the long axis of the cylinder. These equations are evaluated numerically, using two formulae for a nerve impulse given in the literature. In both cases there is little attenuation for cylinders with radii less than 0.5 mm, but the potential declines approximately as a power of radius b for 1〈b〈10 mm. Various factors which might affect these results under different experimental conditions are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337137
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