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Muscle Force
Muscle force
Muscle force depends upon several
factors.
The maximum force capabilities of
individual muscles (peripheral
factor).
The coordination of muscle activity
by the central nervous system
(central factor).
Peripheral factors
Peripheral factors depend upon:
The capacity of muscle to produce
force depends upon the muscle’s
physiological cross-sectional area.
The physiological cross-sectional
area is based on the number of fibres
and their individual cross-sectional
area and their angle of pennation.
Cross Sectional Area
Cross Sectional
Area is related to
the # of muscle
fibres in parallel.
Hence, it should
take into account
the pennation
angle.
Peripheral factors
The cross-sectional area increases
owing to strength training and is the
consequence of two factors:
Hyperplasia: increased numbers of
muscle fibres. This is minimal in
humans.
Hypertrophy: This is the enlargement
of the muscle fibres (the main
increase in cross-sectional area).
Sliding filament theory (Huxley,
A.F. and Huxley, H. E., 1964)
Skeletal muscle is composed of fibres, and each
fibre is made up of many parallel myofibrils,
which consist of longitudinally repeated units
called sarcomeres.
Sarcomeres consist of thin (actin) and thick
filaments (myosin). These filaments partially
overlap.
The myosin filaments have cross bridges
(helical projections) and shortening of the
sacromere (and hence the muscle) occurs as a
result of active relative sliding of the actin
filaments between the myosin filaments.
Muscle Structure
Muscle Fascicles Myofibers Sarcomeres
Structure of the Sarcomere
Myofibril
Schematic of Sarcomere Schematic of Sarcomere
Electron Microscope View
Sliding filament theory (Huxley,
A.F. and Huxley, H. E., 1964)
The force produced by the muscle is the
outcome essentially of the total number of
myosin heads available for cross bridging.
The total number of cross-bridge links in a
given sarcomere is:
The number of actin and myosin filaments
(i.e., the cross-sectional area of all the
filaments) that attach and re-attach (up to
5-6 times).
The number of myosin heads that can
interact with actin filaments (i.e., the
sarcomere length).
Force is developed at the actin-
myosin cross bridge
Thick filament is
made of myosin
(head and tail)
Actin is the
primary
component of
thin filaments
(10nm
diameter)
Sarcomere structure
A-band
I-band
Z-line
H-zone
M-line
or M-region
Shortening in the
sarcomere occurs by
a decrease in the I-
band and H-zone as
the Z-lines move
closer together; the
width of the A-band
remains constant.
Sarcomere Structrure
A-band
I-band
Z-line
H-zone
M-line
or M-region
Internal Muscle Forces
Attachments – proximal and distal
Muscle attachments can pull from
either insertion or origin points.
The arrangement of muscle fibres
and the method of attachment vary
considerably between different
muscles.
Fiber arrangement of muscles
The muscle fibres
are a series of
short, parallel,
featherlike fibres
that extend
diagonally from the
side of the long
tendon. Examples
are extensor
digitorum longus
and tibialis
posterior.
Fiber arrangement of muscles
This is a double
penniform muscle.
It has a long central
tendon with muscle
fibres extending
diagonally in pairs
from either side of
the tendon.
Examples are flexor
hallucis longus and
rectus femoris.
Fiber arrangement of muscles
These are long
strap – like muscle
fibres that lie
parallel to its long
axis. Examples are
rectus abdominis
and sartorius.
Fiber arrangement of muscles
In this type of
muscle there are
several tendons
present, with the
muscle fibres
running diagonally
between them. The
mid portion of the
deltoid muscle and
upper arm are a
good example.
Fibre arrangement of muscles
Other fibre arrangements are:
Triangular or fan shaped. This is a
relatively flat muscle whose fibres radiate
from a narrow attachment at one end to a
broad attachment at the other in the case
of the pectoralis muscle.
Fusiform: This is usually a rounded muscle
that tapers at either end, such as the
brachialis.
Muscle force and range of motion
The force a muscle can exert is
proportional to its physiological cross-
section or diameter.
A penniform muscle with the same
thickness as a longitudinal muscle is
capable of exerting greater force.
Pennate muscles are the most common
type of skeletal muscle and predominate
when forceful movements are needed.
Muscle force and range of motion
The range through which a muscle
shortens depends upon the length of its
fibres, with the average muscle fibre
capable of shortening to half its resting
length.
Therefore, longitudinal muscles, such as
sartorius, can exert force over a longer
distance than muscles with short fibres.
Pennate muscles can exert superior force,
but only through a short range of motion.
Pinnate Angle
When the line of action of the muscle does not
match the line of action of the fibres then the
muscle is known as pennate.
Since the axis of contraction of pennate muscle
fibres are not parallel to the line of muscle pull
(line of action) some muscle force is dissipated
perpendicular to the line of action.
Therefore, force output = # of fibres x cosine
of angle of insertion
The advantage of pennation is to increase the
force output of a muscle by having more fibres
in a given volume of space.
Pinnate Angle
This is the angle between the muscle
fibres and the line of action
Pinnate Angle
• The maximum amount a sarcomere can shorten is
50-60% of its resting length.
• Therefore, the maximum excursion (change in
length) of muscle = 50-60% of its fibre length.
• Parallel (longitudinal) fibres can shorten to their
maximum.
• Pennate fibres cannot shorten to their maximum
with out dislodging themselves from their tendons
• Thus pennate muscles have a shorter excursion.
Static Properties
The fibre length and pinnation
angle of muscles can vary
considerably.
Gastrocnemious has short,
pennate fibers and a long
tendon
Sartorius has long, parallel
fibers and very little tendon
Excursion and Force
Parallel fibres: Pennate fibres:
Long excursion, Short excursion,
Lower forces Higher forces
Examples of Pennation and PCA
Force and Pinnate angle
We can express these relationships
as a series of equations:
Fmax = PCA x K
Where Fmax is the maximum force
the muscle can generate, PCA is the
physiological cross sectional area and
K is a constant (20 to 100 N.cm-2).
Force and Pinnate angle
For non-pennate muscles
PCA = m / (p L)
Where m is the mass of the muscle,
p is its density (1.056 g.cm-2) and L
is the length of the muscle fibres.
Force and Pinnate angle
For pennate muscles
PCA = m cos θ / (p L)
Where θ is the pinnate angle.
Length – tension relationship
There is an optimal length at which a
muscle, when stimulated, can exert
maximal tension.
This length is generally slightly greater
than the muscle’s resting length.
This relationship applies to isometric,
concentric and eccentric contractions.
Optimal joint angles and maximal
strength varies over their full ROM and
are known as human strength curves.
Force-velocity relationship for
muscle
The force-velocity relationship is a parametric
relationship.
Motion velocity decreases as external
resistance increases.
Maximum force is attained when velocity is
small.
Maximum velocity is attained when resistance
is small.
This leads to a hyperbolic force-velocity curve
for muscle force/torque with a ratio of around
0.3 for power athletes. That is maximum
power is achieved at 30% maximum velocity
and this is around 50% maximum force.
Force-velocity curve
Force
Isometric
Force
0
Eccentric Velocity Concentric
Force Force
Force-velocity relationship in muscles
It takes time to develop maximal force for a
given motion and varies between individuals.
On average for isometric force it is around 0.3-
0.4 s
Force is task dependent and maximum force is
essentially force that is maximally possible for
a muscle.
A shot putter may be able to maximally extend
the arm during weight training for 110-120 kg
but the maximal force they apply to the shot in
competition is around 50-60 kg.
The difference between the maximal force
possible and the force applied for any given
task is known as the explosive strength deficit.
Hill’s Equation
The Hill equation is
(v + b) (P + a) = b (Po + a)
P is the load or tension in the muscle
v is the velocity of contraction
P0 is the maximum load or tension generated in the
muscle
a and b are constants
Hill's equation demonstrates that the relationship
between P and v is hyperbolic. Therefore, the higher
the load applied to the muscle, the lower the
contraction velocity. Similarly, the higher the
contraction velocity, the lower the tension in the
muscle.
A. V. Hill The Heat of Shortening and the Dynamic Constants
of Muscle Proceedings of the Royal Society of London. Series B,
Biological Sciences, Vol. 126, No. 843 (Oct. 10, 1938), pp. 136-
195
Muscle Elasticity
Hill (1970) showed muscle tendons represented
spring-like elastic component located in series with
the contractile component (contractile proteins:
myosin and actin).
He found a second elastic component located in
parallel with the contractile component (epimysium,
perimysium, endomysium and sarcolemma).
When the parallel and series elastic components
stretch during active contraction and passive
extension of a muscle, tension is produced and
energy is stored; when they recoil with muscle
relaxation, this energy is released.
The series elastic fibres are more important in the
production of tension than the parallel elastic fibres.
Muscle Elasticity
The distensibility and elasticity of the elastic
components are valuable to the muscle in several
ways:
They tend to keep the muscle in readiness for
contraction and ensure muscle tension is produced
and transmitted smoothly during contraction.
They assure the contractile elements return to their
original (resting) positions when contraction is
terminated.
They may prevent passive over-stretch of the
contractile elements possibly lessening injury.
The viscous property of the series and parallel elastic
components allows them to absorb energy
proportional to the rate of force application and to
dissipate energy in a time dependent manner.
Viscoelastic behaviour
Viscoelastic behaviour is found under
increased loading of the elastic tissues.
With increased strain (stretch) the
mechanical properties of the tissues
change with different loading rates.
The linear portion of the stress-strain
curve becomes steeper, indicating
increased stiffness of the tissue at higher
strain rates.
With increased strain rates the tissues
store more energy, require more force to
rupture and undergo increased elongation.
Practical applications
Explosive strength deficit.
ESD = 100 (Fmax – F)
Fmax
ESD for the shot putter is
100 (120 kg – 60 kg)
120 kg
= 50%
The ESD shows the percentage of the
athletes strength potential that was not
used in a particular activity.
Explosive strength deficit.
There are two ways to increase the force
output in explosive motions.
Increase maximal force. This works well with
beginners; that is increase their strength. This
is not an effective method for improving the
performance of elite athletes.
The second method is develop explosive
strength; exerting maximal forces in a minimal
time, which is a large part of elite athletes
training.
Why do shot putters spend 50% of training
developing strength when javelin throwers only
spend 15% of their time developing strength?
Explosive strength
The index for explosive strength is:
IES = Force (peak force for activity)
Time (to peak force)
Time to peak force can be viewed for
particular phases of a sports
movement following the theory of
the kinematic chain.
Central Factors
The central nervous system (CNS) is of
paramount importance in the
development of muscle strength.
Muscle force is not only the quantity of
muscles involved but the extent to
which each muscle is activated
(intramuscular coordination).
Maximal muscle force is a skilled act in
which many muscles must be
appropriately activated in a coordinated
manner (intermuscular coordination).
Intramuscular coordination
The nervous system uses three options for
varying muscle force production.
Recruitment: the gradation of total muscle
force by the addition and subtraction of
active motor units.
Rate coding: changing the firing rate of
motor units, and
Synchronisation: the activation of motor
units in a more or less synchronised
manner.
Recruitment
During voluntary contractions, the orderly
pattern of recruitment is controlled by the
size of motorneurons (size principle).
Small motorneurons are recruited first
because they have the lowest firing
threshold.
Motor units with the largest motorneurons,
which have the largest and fastest twitch
contractions, have the largest threshold and
are recruited last.
Therefore, slow twitch motor units are
recruited first and only trained athletes are
capable of activating fast twitch motor units.
Full activation of fast twitch motor units is
difficult to achieve.
Twitch and Tetanus
The mechanical response of a muscle to a
single stimulus of its motor nerve is
known as a twitch, which is the
fundamental unit of recordable muscle
activity.
When mechanical responses to successive
stimuli are added to an initial response,
the result is known as summation.
When maximal frequency is reached
beyond which tension no longer increases
from summation the muscle is said to
contract tetanically.
Rate coding
Rate coding refers to the discharge frequency
of motorneurons and can vary considerably
depending upon the force and power
production required.
Rate coding and recruitment’s relative
contributions differ between large and small
muscles.
In small muscles most motor units are
recruited at 50% maximal force, thereafter rate
coding plays the major role.
In large muscles such as the deltoid the
recruitment of additional motor units appears
to be the main mechanism for increasing force
up to about 80% maximal force.
Synchronisation
Normally motor units work
asynchronously to produce a smooth,
accurate movement.
However, there is evidence that elite
power athletes activate their motor
units synchronously during maximal
voluntary efforts.
Practical Applications
Intermuscular coordination
Even simply activities require skilled
coordination of numerous muscle
groups.
Here it should be noted that strength
training machines are designed to
train muscles not movement.
Taxonomy of muscular strength
Type of Strength Manifestation
Static strength Isometric and slow
concentric actions
Dynamic Strength Fast concentric
movements
Yielding strength Eccentric actions
Body weight
Muscle mass constitutes a substantial part of
the human body mass.
Elite weight lifters for example, have 50% of
their body mass as lean muscle tissue.
Therefore, greater body mass demonstrates
greater absolute strength.
Elite weight lifters have shown a very strong
correlation between performance level and
body weight, 0.93.
However, the correlation with the untrained is
very low or even zero.
Absolute and relative strength
Muscular strength when not related to
body weight is absolute strength.
Relative strength is when comparison
between persons is required and it is
strength per kilogram of body mass.
Relative strength = absolute strength
body mass
External force and muscle action
Any slow controlled movement in the
downward direction of gravity’s force uses
the same muscles in eccentric contraction
that it uses in concentric contraction to
perform the opposite upward movement
against gravity.
A forceful movement downward, however
uses the muscles that extend the limb in a
concentric action.
Gravity can move a limb with no muscle
action.
Methods of studying the action of
muscles
Conjecture and reasoning
Dissection
Inspection and palpation
Models and gadgets
Muscle stimulation
Electromyography (EMG)
Question
Do a leg extension in the supine and
sitting position with resistance (a
persons hand). Explain the different
motions.
