Are there general principles for pattern generation? We examined this question by analyzing the operation of large populations of evolved model central pattern generators (CPGs) for walking. Three populations of model CPGs were evolved, containing three, four, or five neurons. We identified six general principles. First, locomotion performance increased with the number of interneurons. Second, the top 10 three-, four-, and five-neuron CPGs could be decomposed into dynamical modules, an abstract description developed in a companion article. Third, these dynamical modules were multistable: they could be switched between multiple stable output configurations. Fourth, the rhythmic pattern generated by a CPG could be understood as a closed chain of successive destabilizations of one dynamical module by another. A combinatorial analysis enumerated the possible dynamical modular structures. Fifth, one-dimensional modules were frequently observed and, in some cases, could be assigned specific functional roles. Finally, dynamic dynamical modules, in which the modular structure itself changed over one cycle, were frequently observed. The existence of these general principles despite significant variability in both patterns of connectivity and neural parameters was explained by degeneracy in the maps from neural parameters to neural dynamics to behavior to fitness. An analysis of the biomechanical properties of the model body was essential for relating neural activity to behavior. Our studies of evolved model circuits suggest that, in the absence of other constraints, there is no compelling reason to expect neural circuits to be functionally decomposable as the number of interneurons increase. Analyzing idealized model pattern generators may be an effective methodology for gaining insights into the operation of biological pattern generators.

Algorithms↗

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Evolution and analysis of model CPGs for walking: I. Dynamical modules.

Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on the concept of a dynamical module, a set of neurons that simultaneously make their transitions from one quasistable state to another while the synaptic inputs that they receive from other neurons remain essentially constant, thus temporarily reducing the dimensionality of the circuit dynamics. Using the mathematical tools of dynamical systems theory, we describe a method for identifying dynamical modules and demonstrate that this concept can be used to quantitatively characterize constraints on neural architecture, account for phase durations, and predict the effects of parameter changes. Moreover, this abstract description reveals coordinated parameter changes that leave the overall circuit dynamics essentially unchanged. In a companion article we employ this abstract description to examine the relationship between general principles and individual variability in large populations of evolved model pattern generators.

Gait↗

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Meeting the bean half way.

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Clinical Trials as Topic↗

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Tracheobronchiomegaly.

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Adult↗

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Solitary asymptomatic plaque of demyelination in the medulla oblongata.

Clinically benign and clinically silent multiple sclerosis is now recognized. The corresponding plaques of demyelination in such cases are usually located in silent areas of the brain. We report a case where a solitary 3 x 3 mm plaque of demyelination was incidentally found in the medulla oblongata at autopsy. Although the plaque should have produced sensory symptoms by virtue of its location, no such history was obtainable even after direct questioning of the spouse of the deceased. The case illustrates that a single episode of demyelination may take place within the CNS without recurrence, and that a demyelinating plaque may be asymptomatic due to a functionally benign local effect, and not only by location in a silent area of the brain.

Humans↗

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Examination of prevalence rates of possible risk factors in a population with a fracture of the proximal femur.

No statistical increase in the prevalence of either diabetes, rheumatoid arthritis or primary hyperparathyrodism was found among the hip fracture patient population. Since the relative risks for these diseases is small, the statistics suggest that these conditions are either noncontributory or represent only a minor risk factor in the overall pathogenesis of hip fractures. About 20% of the hip fracture patients had a history of other identifiable risk factors such as thyrotoxicosis, hemiplegia, malabsorption syndromes and corticosteroid therapy. Of these conditions only thyrotoxicosis could be evaluated by comparison of prevalence rates, and a significant increase was found among the fracture patients. A highly significant correlation was found between the side of a previous hemiplegia and side of he subsequent hip fracture; this may be due to the development of disuse osteoporosis in the hemiplegic limb. Recent reports have shown that a reduction in the number of hip fractures is associated with a high calcium intake or prophylactic estrogen therapy. Preventive therapy in patients with hemiplegia, thyrotoxicosis, or other predisposing conditions leading to osteopenia might result in a further reduction of the hip fracture rate.

Aged↗

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Epidemiology of fractures of the proximal femur in Rochester, Minnesota.

An incidence study of fractures of the proximal femur has been conducted over a 10-year period. The results show a doubling of the fracture rate in each decade of life after age 50 years. A comparison of age-adjusted fracture rates with populations in different countries shows that in both men and women, the hip fracture is highest in the United States population examined in this study. The fracture rate is much greater in women than in men, and by age 90 years, about 32% of women and 17% of men had suffered a fracture. An estimate of the number of proximal hip fractures occurring in the United States suggests that approximately 113,000 women and 34,000 men older than 50 years of age will suffer a hip fracture each year. This represents a considerable cost, approaching one billion dollars annually, to health care in the United States.

Adult↗

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The national cost of acute care of hip fractures associated with osteoporosis.

During 1976, the median cost of the direct medical care for a fracture of the proximal femur related to osteoporosis in Rochester, Minnesota, was $5,644. Age- and sex-specific incidences for this fracture were determined for a 10-year period in the same population. When these data are applied to the United States population, it can be estimated that osteoporosis leads to over 150,000 hip fractures annually, with a short-term direct cost in excess of one billion dollars.

Aged↗