Muscle mechanics force length relationship

Muscle Mechanics

Force - length relationship

Contribution of passive elements to muscle -
tendon force

Force - velocity relationship

Combined effects
 Some thoughts on muscle power

The joint system (building a forest from trees)
 Muscle length and moment arm
 Joint torque and angular velocity

Force - Length (CE) Relationship
From McKinley, O’Loughlin and Bidle,
Anatomy and Physiology, 2013

The magnitude of
force (CE) produced
depends on its length.

Cross - bridge theory:
- the interaction of
actin and myosin
filaments generates
force and length
change.
From Amerman E.C., Human Anatomy &
Physiology, 2016

Force - Length (CE) Relationship

Force is dependent on the number
of actin - myosin binding sites.
 At rest length (2,3&4) a
maximum number of cross -
bridges can interact.
 On the descending limb (2 to 1)
of the F - L curve, filaments are
pulled apart and fewer bond can
form; tension decreases.
 On the ascending limb (3,4 to 5)
of the F - L curve, actin filaments
overlap, decreasing the number
of bond that can form; tension
decreases
 On the ascending limb (5 to E )
of the F - L curve, myosin
filaments start to fold over
causing a steeper decline in the
descending limb of the F - L
curve.

Force - Length & Passive (PE) Element

As muscle lengthens, passive
elastic structures in parallel (PE)
are stretched and contribute (Fp)
force to CE forces (Fc) resulting a
combined effect (Ft).

At rest length (lo) or less, PE is in a
slack state and does not contribute.

The combined force length curve
for CE and PE are usually shown
for maximal activation conditions.
At submax activation PE tension
contributes in the same way
(predominately) independent of
activation. CE is under active
control, PE is function of muscle
length change only.

Force - Length & Passive (SE) Element

Force from the CE is transferred
to the bone through connective
tissue in series with the CE.

Under static conditions, if
unaccounted for, SE compliance
will influence the F - L
relationship for muscle tissue
(bottom figure).

Under dynamic conditions, SE
tissue will influence the time
course of muscle tension
transferred to the bone.

Force - Length & Passive (SE) Element

Different tissues in series will
have different load - strain (force -
length) properties (top figure).
Note how these properties are
represented by different springs
in the lower figure.

Under isometric conditions, the
CE of muscle will shorten at the
expense of SE elements
lengthening. Hence, an
isometric contraction at a fixed
joint angle can result in muscle
(CE) shortening, and therefore,
the CE force as a function of
muscle length will have
changed without a change in
joint angle.

Force - Velocity (CE) Relationship

The tension the CE of muscle
can generate decreases
dramatically as the velocity of
muscle shortening (concentric)
increases under load.

The tension the CE of muscle
can generate increases
dramatically as the velocity of
muscle lengthening (eccentric)
increases under load, to a
point (180%) on curve shown.