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  • 1
    Electronic Resource
    Electronic Resource
    The effects of multiple reflex pathways on the oscillations in neuro-muscular systems (1976)
    Springer
    Journal of mathematical biology 3 (1976), S. 87-101 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary A model of mammalian neuro-muscular systems described previously (Oğuztöreli 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00307860
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  • 2
    Electronic Resource
    Electronic Resource
    A kinetic study of muscular contractions (1977)
    Springer
    Journal of mathematical biology 5 (1977), S. 1-31 
    Details
    ISSN: 1432-1416
    Keywords: Kinetics of muscular contractions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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 α and β on muscle length.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275803
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  • 3
    Electronic Resource
    Electronic Resource
    An analysis of oscillations in neuro-muscular systems (1975)
    Springer
    Journal of mathematical biology 2 (1975), S. 87-105 
    Details
    ISSN: 1432-1416
    Keywords: Oscillations in neuro-muscular systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary In a recent work the mammalian neuro-muscular system has been investigated by the authors from the physiological point of view. This system is described by a nonlinear differential-difference equation. In the present work we analyse the differential-difference equation and investigate the oscillations pertaining to the neuro-muscular system. The dependence of these oscillations on the muscular and neural feedback parameters has been studied systematically. Several simple relationships are described which can be compared with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275922
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  • 4
    Electronic Resource
    Electronic Resource
    Interactions between centrally and peripherally generated neuromuscular oscillations (1979)
    Springer
    Journal of mathematical biology 7 (1979), S. 1-29 
    Details
    ISSN: 1432-1416
    Keywords: Neuromuscular oscillations ; Non-linear integro-differential difference equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary An experimentally based model of the mammalian neuromuscular system has been extended to include the interaction of sinusoidal inputs generated within the central nervous system and those produced peripherally by reflex pathways, together with muscle properties and external loads. Multiple reflex pathways and pathways having acceleration as well as velocity and length sensitivity are considered. The responses are analyzed for brief inputs (Dirac δ-functions), sinusoidal driving functions and mixtures of the two over ranges in which the model behaves either linearly or non-linearly. Approximate solutions are derived for the non-linear range, and exact numerical solutions are computed for a few examples within the linear range. The extent to which brief inputs can reset ongoing oscillations and the extent to which sinusoidal inputs can entrain these oscillations are of particular interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276411
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  • 5
    Electronic Resource
    Electronic Resource
    Effects of elastic loads on the contractions of cat muscles (1976)
    Springer
    Biological cybernetics 22 (1976), S. 129-137 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract The nerves to plantaris and soleus muscles in the cat were stimulated with maximal single shocks and with random stimulus trains which produced partially fused contractions. In order to obtain information on the mechanism of muscular contraction, the effects of allowing the muscles to shorten against various elastic loads were studied in the time domain and in the frequency domain. When springs of increasing stiffness were placed in series with the muscle, the twitch tension increased greatly. The gain of the frequency response curve was also much greater with stiffer springs. The shape of the frequency response curve for plantaris muscle could usually be described by that expected for a second-order system with two real time constants or rate constants. The rate constants changed in qualitatively similar ways in response to increased stiffness of an elastic load, increased muscle length and increased mean rate of nerve stimulation. These results are in agreement with the hypothesis that the linear responses of muscles working against elastic loads are determined by the values of two rate constants. Thus, of the many processes associated with contraction, only two are rate-limiting: one associated with the viscoelastic properties of muscle and the second associated with the reuptake of Ca into the sarcoplasmic reticulum. Non-linear aspects of muscular contraction are also discussed. These are more prominent in soleus muscle than in plantaris muscle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00365523
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  • 6
    Electronic Resource
    Electronic Resource
    Dynamics of a long-latency reflex pathway in the monkey (1979)
    Springer
    Biological cybernetics 34 (1979), S. 107-110 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Angular wrist displacements in the monkey result in a short-latency (20–25 ms) “reflex” response of motor cortical cells in area 4 and separate peaks of activity in the gross EMG of the stretched muscles. Frequency domain analysis was carried out between (1) wrist position as input and motor cortical neuron response as output, (2) position as input and EMG response as output, and (3) motor cortical neuron response as input and EMG response as output. The results show that the dynamics of primary spindle afferents characterize the dynamics of the pathway to the motor cortex and that of the reflex loop. Results are discussed in terms of “long-loop” reflexes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00365474
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Tremor and other oscillations in neuromuscular systems (1976)
    Springer
    Biological cybernetics 22 (1976), S. 147-157 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A model has been analyzed which is based on recent experimental evidence concerning the properties of muscles and the sensory feedback pathways from muscles. Damped oscillations can arise in the absence of sensory feedback due to the interaction of a muscle with inertial loads. These mechanical oscillations can have a wide range of frequencies depending on the inertial and elastic loads that are attached to the muscle. Small amounts of sensory feedback will tend to reduce deviations from a steady muscle length, but larger amounts of feedback can produce oscillations. The frequency of these reflex oscillations is determined by the properties of the muscle and feedback pathway, and is rather independent of load. If the strength of the sensory feedback is sufficient, either the mechanical oscillations or the reflex oscillations or both can grow, rather than decay, with time. The growth of these oscillations is limited by saturation non-linearities in the muscle receptors and the muscle itself, so that the oscillations approach a steady amplitude and frequency. Using typical properties of muscles and spinal reflex pathways, the frequency of reflex oscillations will be within the range 8–12 Hz found for physiological tremor. With the longer latency found for supraspinal reflexes, oscillations will occur in the range 4–6 Hz which is characteristic of Parkinson's and cerebellar diseases. The role of longer latency reflexes in the generation of these tremors is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00365525
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  • 9
    Electronic Resource
    Electronic Resource
    Does the velocity sensitivity of muscle spindles stabilize the stretch reflex? (1976)
    Springer
    Biological cybernetics 23 (1976), S. 219-228 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A model of the stretch reflex based on detailed experimental studies of muscles, muscle receptors and reflex pathways has been analysed. Muscle receptors respond to the velocity and the acceleration of movement, as well as to muscle length. The effect of the velocity sensitivity on the stability of the stretch reflex is considered. It is concluded that the velocity sensitivity can compensate to some extent for the sluggishness of muscles and the delays introduced by reflex pathways. However, the value of velocity sensitivity found experimentally is greater than that required to stabilize the stretch reflex optimally. The velocity sensitivity will have some tendency to produce oscillation, and it is suggested that a small degree of oscillation may be beneficial to linearize muscle properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00340338
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  • 10
    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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