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F S Stafford

Publications and source records attributed to F S Stafford.

4 recordsLinked to original sources
PubMed1985

Mathematical models of central pattern generators in locomotion: I. Current problems.

As a background for subsequent studies of mathematical models of central pattern generators in locomotion (Stafford & Barnwell, 1985a, b) relevant aspects of the literature on locomotion are reviewed, concepts of locomotion discussed, and extant models considered. Advantages and disadvantages of present models are discussed, and the need for mathematical models is emphasized. It is shown that realistic models of pattern generation in locomotion must take numerous factors into account, including phases of step cycle, muscle sequencing, gait and interlimb coordination, initiation and cessation of locomotion, and many aspects of neuromuscular control and function.

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PubMed1985

Mathematical models of central pattern generators in locomotion: II. Single limb models for locomotion in the cat.

Three mathematical models of central pattern generation for locomotion in the single limb of the cat are presented. In each model, the activities in populations of neurons controlling limb joint flexors and extensors are described by a system of nonlinear differential equations. Each solution of the system for a different set of parameters corresponds to a simulation of some gait of the cat. Model I is based on unit generators for each limb joint muscle group and assumes that flexors inhibit their paired extensors, but not vice-versa. Model IIa assumes that flexors and extensors are mutually inhibitory, but that only the flexors have inherent oscillatory capability. Model IIb assumes flexors and extensors are mutually inhibitory and that both flexors and extensors have oscillatory capability. The properties of each of these models are explored, compared and contrasted, and discussed in relation to the experimental literature. All three models are shown to be capable of generating patterns consistent with various stepping rates of the cat and to show appropriate muscle sequencing and flexor-extensor interactions. Further, all three models exhibit smooth initiation and termination of stepping. However, Model I seems to provide a more parsimonious account of producing changes in stepping rate and is preferred, therefore, over models IIa and IIb.

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PubMed1985

Mathematical models of central pattern generators in locomotion: III. Interlimb model for the cat.

Possible neural connective patterns and functions with respect to interlimb coordination are studied theoretically with a mathematical model of the central pattern generating system for cat locomotion. Activities in populations of neurons controlling limb joint flexors and extensors in all four limbs are represented by a system of nonlinear differential equations. Solutions of the system for various parameter values simulate various gaits of the cat. The model is shown to be capable of generating all gaits of the cat and accounting for corresponding phase changes in interlimb coordination. The model also exhibits smooth changes of gait, and smooth initiation and termination of stepping. Further, within each limb, muscle sequencing, step cycle phases, and flexor-extensor interactions can be studied. The model suggests that one of the simplest mechanisms for a central command system to change the gait is via inhibition of specific interlimb propriospinal pathways. In a final section, properties of both proposed single limb and interlimb models are reviewed with specific reference to planning future experimental and theoretical studies.

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