MUSCLE MECHANICS - Biomechanics and Motor Control of Human Movement - page 238

A few years later Hill (1938) proposed a different mathematical relation-
ship that bore some meaning with regard to the internal thermodynamics.
Hill's curve was in the form of a hyperbola,

(P + a)(V + b) = (P 0 + a)b (9.3)

where: P 0 = maximum isometric tension
a = coefficient of shortening heat

= a · V 0 /P 0

b

V 0 = maximum velocity (when P = 0)

More recently, this hyperbolic form has been found to fit the empirical
constant only during isotonic contractions near resting length.
The maximum velocity of shortening is often expressed as a function of
l 0 , the resting fiber length of the contractile elements of the muscle. Animal
experiments have shown the maximum shortening velocity to be about 6 l 0 / s
(Faulkner et al., 1980; Close, 1965). However, it appears that this must be
low for some human activity. Woittiez (1984) has calculated the shortening
velocity in soleus, for example, to be above 10 l 0 / s (based on plantarflexor
velocity in excess of 8 rad / sand a moment arm length of 5 cm).

9.2.2 Eccentric Contractions
The vast majority of research done on isolated muscle during in vivo exper-
iments has involved concentric contractions. As a result, there is relatively
limited knowledge about the details of the force-velocity curve as the mus-
cle lengthens. The curve certainly does not follow the detailed mathematical
relationships that have been developed for concentric contractions.
This lack of information about eccentric contractions is unfortunate
because normal human movement usually involves as much eccentric as
concentric activity. If we neglect air and ground friction, level walking
involves equal amounts of positive and negative work, and in downhill
gait, negative work dominates. Figure 9.12 shows the general shape of
the force-velocity curve during eccentric contractions. It can be seen
that this curve is an extension of the concentric curve. During isotonic
eccentric action, the solid line curves apply (Winters, 1990), but during
isovelocity eccentric activity, the relationship follows the dotted lines
shown in Figure 9.12 (Zahalak, 1990; Sutarno and McGill, 1995). If the
maximum isometric force is F max , the plateau reached in the eccentric
phase varies from 1.1 F max to 1.8 F max (Winters, 1990). The reason given
for the force increasing as the lengthening velocity increases was that
within the cross-bridges the force required to break the links is greater than
that required to hold it at its isometric length. The plateau is reached at
higher velocities when the cross-bridge links simply “give way” to produce