Biomedical Engineering Reference
In-Depth Information
equations of motion are derived, theymust be solved to yield themotion of the skeletal
system (movement is influenced by the constraints imposed by its articulations, by
the external muscle forces, by gravity and by the environment). Thus, external forces
are required for the solution of the skeletal equations of motion. These forces are
quantified by their magnitude, direction, and their point of application on the skeletal
system. The calculation of a given muscle force is needed (also referred to as muscle
tendon actuator) but its correct application to the skeletal system requires accurate
knowledge of the musculotendon path running from the origin to the insertion of the
muscle (also known as musculotendon geometry). In the past, the musculotendon
path has been modeled as a straight-line path [
23
,
24
], as a centroid line method [
25
]
or by finite element modeling of the path of individual muscle fibers [
26
]. Moreover,
to accurately represent the musculotendon geometry, it is often required to simulate
how muscles wrap around adjacent structures and different techniques employing
cylinders, spheres, and ellipsoids have been used as wrapping surfaces [
27
-
29
].
Finally, muscle force has a crucial role in musculoskeletal modeling. The func-
tion of individual muscles is influenced by the architecture of each muscle, which
must thus be considered. Muscle architecture refers to the arrangement of fascicles
within the muscle and has been defined as “the arrangement of muscle fibers within
a muscle relative to the axis of force generation” [
30
]. Scientists typically categorize
muscle fiber arrangements in three general conceptual classes: muscle fibers that run
(1) parallel, (2) at a fixed angle (unipennate architecture) and (3) at several angles
(multipennate architecture) relative to the muscle force generating axis. These archi-
tectural differences between muscles are important predictors of force generation.
The force-length relationship of the muscle is well established and thus, it is known
that once the muscle begins to develop force the tendon begins to carry load and
transfers force from the muscle to the bone. Therefore, much of the muscle-tendon
length change does not occur in the fibers themselves but in the associated tendon
and muscle (muscle-tendon mechanics) aponeurosis [
30
].
Inmusculoskeletal modeling, the muscle force generation is generally represented
by a Hill-type muscle model in which the muscle-tendon unit acts as the spring in
a spring-mass system [
31
,
32
]. This model typically requires four parameters to
scale generic curves for active and passive force generation of the muscle-tendon
unit: optimal fiber length, maximum isometric force, pennation angle (angle from
the muscle fibers with respect to the tendon), and tendon slack length [
13
].
These parameters are obtained from cadaveric measurements. As pointed out by
Blemker et al. [
33
], one main disadvantage is that fascicle length measurements from
each muscle are averaged in most cadaveric studies, giving a single length estimate;
therefore, models of muscle generally assume that all fascicles within each muscle
have the same length. Furthermore, Hill-type muscle models also assume that the
pennation angle is constant across all fibers.
In summary, development of an adequate musculoskeletal model is not an easy
task and has been achieved through several years of research. Some of the limita-
tions or difficulties are that (1) musculoskeletal models are constructed on the basis
of assumptions on the geometrical relationships within the musculoskeletal system
[
34
], (2) muscle models tend to be parameterized by the limited data available from
