Biomedical Engineering Reference
In-Depth Information
would be interrupted or they would even stumble
forward… For this reason, then, animals do not
move separately with their front and back legs.”
Following the legend, modern gait analysis also
originated with a horse, namely, a bet concern-
ing the animal's gait (Taft, 1955). In the 1870s,
Leland Stanford, the former governor of the state
of California, became involved in an argument
with Frederick MacCrellish over the placement
of the feet of a trotting horse. Stanford put 25,000
dollars behind his belief that at times during the
trot, a horse had all of its feet off the ground. To
settle the wager, a local photographer, Eadweard
Muybridge, was asked to photograph the different
phases of the gaits of a horse. As a matter of fact,
Stanford was correct in his bold assertion.
Aristotle and Stanford's insights into horse
gaits can be viewed as the classical representa-
tions of embryonic ideas which lead to
the modern
studies of rhythmic pattern formation. After the
case of Stanford there followed about
eighty years
of silent time till the 1950s, when A. M. Turing
(1952) analysed rings of cells as models of mor-
phogenesis and proposed that isolated rings could
account for the tentacles of hydra and whorls of
leaves of certain plants. Meanwhile, A. L. Hodgkin
and A. F. Huxley published their influential paper
(1952) on circuit and mathematical models of the
surface membrane potential and current of a gi-
ant nerve fibre. The history has never seen such
a prosperous era in the development of science
and technology during the recent fifty years. With
the rapid development of computational methods
and computer techniques, many great scientific
interdisciplines such as neural networks have
been born and grew astonishingly. Obviously
,
it
is not exaggerative at all to say that Turing et al.'s
pioneer works on pattern formation are the cradle
of modern connectionism. It is also interesting to
notice that the macro- and microscopic approaches
have coexisted since the initial stage of the modern
biological rhythmic pattern research, just as the
two examples stated above.
Rhythmic Patterns in Artificial
Neural Networks
It is widely believed that animal locomotion is
generated and controlled, in part by central pattern
generators (CPG), which are networks of neurons
in the central nervous system (CNS) capable of
producing the rhythmic outputs. Current neuro-
physiological techniques are unable to isolate such
circuits from the intricate neural connections of
complex animals, but the indirect experimental
evidence for their existence is strong (Grillner,
1975, 1985; Stein, 1978; Pearson, 1993).
The locomotion patterns are the outputs of
musculoskeletal systems driven by CPGs. The
study of CPGs is an interdisciplinary branch of
neural computing which involves mathematics,
biology, neurophysiology and computer sci-
ence. Although the CNS mechanism underlying
CPGs is not quite clear to date, artificial neural
networks (ANN) have been widely applied to
map the possible functional organisation of the
CPGs network into the muscular motor system
for driving locomotion.
The
constituents of the locomotory motor
system are traditionally modelled by nonlinear
coupled oscillators, representing the activation
of flexor muscles and the activation of extensor
muscles by, respectively, two neurophysiologi-
cally simplified motor neurons. Different types
of neuro-oscillators can be chosen and organised
in a designed coupled mode, and usually with
appropriate topological shape to allow simulat-
ing the locomotion of relative animals (Bay &
Hemami
, 1987; Linkens et al., 1976; Tsutsumi
& Matsumoto, 1984). All internal parameters
and weights of coupled synaptic connections of
the oscillator network are controlled by the en-
vironmental stimulations, CNS instructions and
the network itself. The nature of the parallel and
distributed processing (PDP) is the most prominent
characteristic of this oscillatory circuit that can
be canonically described by a group of ordinary
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