5.4 Mechanical Properties of Contractile Fibers
219
For k = 0, the cytoskeleton constrains the deformation, and the extent of fiber
shortening decreases with increasing values of k, while tension increases away from
the free end. Note also that, as k increases, λ and σ become more uniform except
near the free end, where a “boundary layer” develops. In this region, the solution
changes rapidly to satisfy the zero-stress boundary condition.
If it is attached to the nucleus (k n = 1), the stress fiber shortens considerably less,
but a boundary layer still forms (Fig. 5.6c,d). As k increases, the cytoskeleton bears
more of the load, and the stress exerted on the nucleus, i.e., σ (L), decreases.
5.4 Mechanical Properties of Contractile Fibers
Experiments on muscle tissue have provided most of what is currently known about
the mechanical properties of contractile structures. Tests on both striated and smooth
muscles suggest that the passive strain-energy density function W p should have a
transversely isotropic or orthotropic form, e.g., Eqs. (3.230) or (3.234). In the early
embryo, where cellular microstructure is generally less organized, an isotropic form
may sometimes be more appropriate.
Active mechanical properties are generally more complex and still not
completely understood, even for skeletal muscle, which has been studied for
many decades. Different physiological functions necessarily lead to differences
in mechanical behavior between various types of CFs. On the other hand, since all
CFs contract through the interaction of actin and myosin, there are also common
features. This section details differences, as well as similarities, in the active
behavior of various contractile structures. This information is then used to construct
active constitutive relations.
5.4.1 Fundamental Contractile Behavior
Twitch and Tetanus
All muscles contract when subjected to appropriate stimuli. In response to a brief
stimulus, striated muscles undergo a single twitch. If the muscle is held at a
fixed length, the active force, obtained by subtracting the passive force from the
total force, increases to a peak and then falls back to zero. In skeletal muscle, a
second stimulus elicits a second twitch even if the first twitch has not yet ended,
with the force reaching a higher peak than during the first twitch (Fig. 5.7a). As
the stimulation frequency increases, successive twitches lead to higher and higher
forces. Above a critical frequency, the twitches fuse together into a steady-state
contraction called tetanus (Fig. 5.7a).
219
For k = 0, the cytoskeleton constrains the deformation, and the extent of fiber
shortening decreases with increasing values of k, while tension increases away from
the free end. Note also that, as k increases, λ and σ become more uniform except
near the free end, where a “boundary layer” develops. In this region, the solution
changes rapidly to satisfy the zero-stress boundary condition.
If it is attached to the nucleus (k n = 1), the stress fiber shortens considerably less,
but a boundary layer still forms (Fig. 5.6c,d). As k increases, the cytoskeleton bears
more of the load, and the stress exerted on the nucleus, i.e., σ (L), decreases.
5.4 Mechanical Properties of Contractile Fibers
Experiments on muscle tissue have provided most of what is currently known about
the mechanical properties of contractile structures. Tests on both striated and smooth
muscles suggest that the passive strain-energy density function W p should have a
transversely isotropic or orthotropic form, e.g., Eqs. (3.230) or (3.234). In the early
embryo, where cellular microstructure is generally less organized, an isotropic form
may sometimes be more appropriate.
Active mechanical properties are generally more complex and still not
completely understood, even for skeletal muscle, which has been studied for
many decades. Different physiological functions necessarily lead to differences
in mechanical behavior between various types of CFs. On the other hand, since all
CFs contract through the interaction of actin and myosin, there are also common
features. This section details differences, as well as similarities, in the active
behavior of various contractile structures. This information is then used to construct
active constitutive relations.
5.4.1 Fundamental Contractile Behavior
Twitch and Tetanus
All muscles contract when subjected to appropriate stimuli. In response to a brief
stimulus, striated muscles undergo a single twitch. If the muscle is held at a
fixed length, the active force, obtained by subtracting the passive force from the
total force, increases to a peak and then falls back to zero. In skeletal muscle, a
second stimulus elicits a second twitch even if the first twitch has not yet ended,
with the force reaching a higher peak than during the first twitch (Fig. 5.7a). As
the stimulation frequency increases, successive twitches lead to higher and higher
forces. Above a critical frequency, the twitches fuse together into a steady-state
contraction called tetanus (Fig. 5.7a).