Page 178 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIOMECHANICS OF THE MUSCULOSKELETAL SYSTEM 155

Section 7.2 begins with an overview of the mechanical properties of muscle, tendon, ligament, and
cartilage. In Secs. 7.3 and 7.4, we focus on the structure of the body-segmental (skeletal) system, empha-
sizing how musculoskeletal geometry (i.e., muscle moment arms) converts linear actuation (muscu-
lotendon forces) into rotary (joint) motion. How motor output from the CNS is converted to muscle
activation and ultimately muscle force is described in Sec. 7.5. Section 7.6 presents two methods
commonly used to determine musculoskeletal loading during human movement. Representative
results of muscle, ligament, and joint-contact loading incurred during exercise and daily activity are
given in Sec. 7.7.

7.2 MECHANICAL PROPERTIES OF SOFT TISSUE

We focus our description of the mechanical properties of soft tissue on muscle, tendon, ligament, and
cartilage. The structure and properties of bone are treated elsewhere in this volume.

7.2.1 Muscle

Gross Structure. Muscles are molecular machines that convert chemical energy into force.
Individual muscle fibers are connected together by three levels of collagenous tissue: endomysium,
which surrounds individual muscle fibers; perimysium, which collects bundles of fibers into fasci-
cles; and epimysium, which encloses the entire muscle belly (Fig. 7.2a). This connective tissue
matrix connects muscle fibers to tendon and ultimately to bone.
Whole muscles are composed of groups of muscle fibers, which vary from 1 to 400 mm in
length and from 10 to 60 μm in diameter. Muscle fibers, in turn, are composed of groups of
myofibrils (Fig. 7.2b), and each myofibril is a series of sarcomeres added end to end (Fig. 7.2c).
The sarcomere is both the structural and functional unit of skeletal muscle. During contraction,
the sarcomeres are shortened to about 70 percent of their uncontracted, resting length. Electron
microscopy and biochemical analysis have shown that each sarcomere contains two types of fil-
aments: thick filaments, composed of myosin, and thin filaments, containing actin (Fig. 7.2d).
Near the center of the sarcomere, thin filaments overlap with thick filaments to form the AI zone
(Fig. 7.2e).
In Secs. “Force-Length Property” and “Force-Velocity Property” the force-length and force-
velocity properties of muscle are assumed to be scaled-up versions of the properties of muscle fibers,
which in turn are assumed to be scaled-up versions of properties of sarcomeres.
Force-Length Property. The steady-state property of muscle is defined by its isometric force-
length curve, which is obtained when activation and fiber length are both held constant. When
a muscle is held isometric and is fully activated, it develops a steady force. The difference
in force developed when the muscle is activated and when the muscle is passive is called the
active muscle force (Fig. 7.3a). The region where active muscle force is generated is (nominally)
M
05l o M < l M < 15l o M , where l o M is the length at which active muscle force peaks; that is, F M = F ,
.
.
o
M
when l M = l ; l o M is called muscle fiber resting length or optimal muscle fiber length and
o
F o M is the maximum isometric force developed by the muscle (Zajac and Gordon, 1989). In Fig. 7.3a,
passive muscle tissue bears no force at length l o M . The force-length property of muscle tissue that
is less than fully activated can be considered to be a scaled down version of the one that is fully
activated (Fig. 7.3b). Muscle tissue can be less than fully activated when some or all of its fibers
are less than fully activated.
The shape of the active force-length curve (Fig. 7.3) is explained by the experimental observa-
tion that active muscle force varies with the amount of overlap between the thick and thin filaments
within a sarcomere (see also the subsection “Mechanism of Muscle Contraction” under Sec. 5.2).
The muscle force-striation spacing curve given in Fig. 7.3c shows that there is minimal overlap of