Biomechanics - Introduction to Biomedical Engineering - page 174

to focus on description of a single type of experiment. No model has been shown to broadly
describe all types of contractile loading conditions. Crossbridge models have tended to rely
on increasingly complex bond attachment and detachment rate functions. This trend has
reversed the issue of describing complex muscle dynamics from the underlying, simpler cross-
bridges to adopting complex crossbridge dynamics to describe a particular experiment.
Alternatively, Palladino and Noordergraaf [22] proposed a large-scale, distributed muscle
model that manifests both contraction and relaxation as the result of fundamental mechan-
ical properties of crossbridge bonds. As such, muscle's complex contractile properties emerge
from its underlying ultrastructure dynamics—that is, function follows from structure. Bonds
between myofilaments, which are biomaterials, are described as viscoelastic material. The ini-
tial stimulus for contraction is electrical. Electrical propagation through cardiac muscle occurs
at finite speed, implying spatial asynchrony of stimulation. Furthermore, Ca þþ release from
the sarcoplasmic reticulum depends on diffusion for availability at the myosin heads. These
effects, as well as nonuniformity of structure, strongly suggest that contraction is asynchronous
throughout the muscle. Recognition of muscle's distributed properties by abandoning the
assumption of perfect synchrony in contraction and consideration of myofilament mass allow
for small movements of thick with respect to thin filaments. Such movements lead to bond
detachment and heat production. Gross movement such as muscle shortening exacerbates this
process. Quick transients in muscle length or applied load have particularly strong effects and
have been observed experimentally. Muscle relaxation is thereby viewed as a consequence of
muscle's distributed properties.
The distributed muscle model is built from the following main features: sarcomeres consist
of overlapping thick and thin filaments connected by crossbridge bonds that form during
activation and detach during relaxation. Figure 4.28 shows a schematic of a muscle fiber com-
posed of a string of series sarcomeres. Crossbridge bonds are each described as three-element
viscoelastic solids, and myofilaments as masses. Force is generated due to viscoelastic cross-
bridge bonds that form and are stretched between the interdigitating matrix of myofilaments.

sa rcomere 1 sa rcomere 2

sar comere N

. . .

bond 1,1 bond 1,2 bond 1,3 bond 1,4 bond 1,2N-1 bond 1,2N

bond 2,1 bond 2,2 bond 2,3 bond 2,4 bond 2,2N-1 bond 2,2N

. . .

bond M,1 bond M,2 bond M,3 bond M,4 bond M,2N-1 bond M,2N
FIGURE 4.28 Schematic diagram of a muscle fiber built from a distributed network of N sarcomeres. Each
sarcomere has M parallel pairs of crossbridge bonds. Adapted from [22].