Page 181 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

158 BIOMECHANICS OF THE HUMAN BODY

F M
A a(t) = 1
<1.8 F M
O

F M
O

–V M
0 V max

Lengthening Shortening

B a(t) = 0.5 F M

0.5 F M
O
–V M
0 0.5V max V max
FIGURE 7.4 Force-velocity curve for muscle when (a) muscle tissue is
fully activated, and (b) when activation is halved. Symbols defined in text.
Modified from Zajac and Gordon (1989).

Force-Velocity Property. When a constant load is applied to a fully activated muscle, the muscle
will shorten (concentric contraction) if the applied load is less than the maximum isometric force
developed by the muscle for the length at which the muscle is initially contracting. If the applied load
is greater than the muscle’s maximum isometric force at that length, then the muscle will lengthen
(eccentric contraction). From a set of length trajectories obtained by applying different loads to short-
ening and lengthening muscle, an empirical force-velocity relation can be derived for any muscle
length l M (Fig. 7.4a). At the optimal fiber length l o M , a maximum shortening velocity v max , can be
defined such that the muscle tissue cannot resist any load even when it is fully activated (Fig. 7.4a).
As with the force-length curve, it is commonly assumed that the force-velocity relation scales pro-
portionally with activation, although some studies have found that the maximum shortening velocity,
v , is also a function of muscle length (Fig. 7.4b).
max

7.2.2 Tendon and Ligament
Gross Structure. Tendon connects muscle to bone, whereas ligament connects bone to bone. The
main difference between the structure of tendon and ligament is the organization of the collagen
fibril. In tendon, the fibrils are arranged longitudinally in parallel to maximize the resistance to tensile