Biomedical Engineering Reference
In-Depth Information
purely elastic spring. Potential energy is stored when the spring is stretched, and shortening
occurs when it is released. The idea of muscle elastance can be traced back to Ernst Weber
[29], who considered muscle as an elastic material that changes state during activation via
conversion of chemical energy. Subsequently, investigators retained the elastic description
but ignored metabolic alteration of muscle stiffness. A purely elastic model of muscle can be
refuted on thermodynamic grounds, since the potential energy stored during stretching is less
than the sum of the energy released during shortening as work and heat. Still, efforts to
describe muscle by a combination of traditional springs and dashpots continued. In 1922, Hill
coupled the spring with a viscous medium, thereby reintroducing viscoelastic muscle descrip-
tions that can be traced back to the 1840s.
Quick stretch and release experiments show that muscle's viscoelastic properties are
strongly time dependent. In general, the faster a change in muscle length occurs, the more
severely the contractile force is disturbed. Muscle contraction clearly arises from a more
sophisticated mechanism than a damped elastic spring. In 1935, Fenn and Marsh added
a series elastic element to Hill's damped elastic model and concluded that “muscle cannot
properly be treated as a simple mechanical system.” Subsequently, Hill embodied the
empirical hyperbolic relation between load and initial velocity of shortening for skeletal
muscle as a model building block, denoted the contractile element. Hill's previous visco-
elastic model considered muscle to possess a fixed amount of potential energy whose rate
of release is controlled by viscosity. Energy is now thought to be controlled by some
undefined internal mechanism rather than by friction. This new feature of muscle dynamics
varying with load was a step in the right direction; however, subsequent models, including
heart studies, built models based essentially on the hyperbolic curve that was measured for
tetanized skeletal muscle. This approach can be criticized on two grounds: (1) embodiment
of the contractile element by a single force-velocity relation sets a single, fixed relation
between muscle energetics and force; and (2) it yields no information on the contractile
mechanism behind this relation. Failure of the contractile element to describe a particular
loading condition led investigators to add passive springs and dashpots liberally, with
the number of elements reaching at least nine by the late 1960s. Distributed models of mus-
cle contraction, generally, have been conservative in design and have depended fundamen-
tally on the Hill contractile element. Recent models are limited to tetanized, isometric
contractions or to isometric twitch contractions.
A second, independent focus of muscle contraction research works at the ultrastructural
level, with the sliding filament theory serving as the most widely accepted contraction
mechanism. Muscle force generation is viewed as the result of crossbridge bonds formed
between thick and thin filaments at the expense of biochemical energy. The details of bond
formation and detachment are under considerable debate, with the mechanism for relaxa-
tion particularly uncertain. Prior to actual observation of crossbridges, A. F. Huxley [13]
devised the crossbridge model based on structural and energetic assumptions. Bonds
between myofilaments are controlled via rate constants
that dictate attachment
and detachment, respectively. One major shortcoming of this idea was the inability to
describe transients resulting from rapid changes in muscle length or load, similar to the
creep and stress relaxation tests previously discussed.
Subsequent models adopt increasingly complex bond attachment and detachment rate func-
tions and are often limited in scope to description of a single pair of myofilaments. Each tends
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