Lecture 5
Dimitar Stefanov
Mechanical Work, Energy and Power
Definitions:
•Purpose of the muscles is to produce tension
•Metabolic efficiency – the measure of a muscle’s ability to convert metabolic
energy to muscle tension (Example, cerebral palsy patient)
•Mechanical efficiency – the ability of the central nervous system to control the
tension patterns (the ability of the muscle to perform mechanical work)
•Overall muscle efficiency – mechanical efficiency + metabolic efficiency
•There are two types of work done by muscles:
Internal work – the work done by the muscles to move the limb segments
through some desired patterns (Example: walking and running)
External work – the work done by the muscles against forces and
moments, which are external for the body (Examples: weight lifting,
pushing a car)
•Net mechanical work – internal work + external work.
Positive and negative work of muscles
Net work done by the muscles = integral of the power of the muscle over the time of the
muscle contraction.
Positive work is done when the muscle moment acts in the same direction as
the angular velocity of the joint.
EXTENSOR
FLEXOR
Negative work is done when the muscle moment acts in the opposite direction to the
movement of the joint.
The external force Fext acts on the segment and produces a joint moment
greater than the muscle moment.
Muscle mechanical power
At a given joint, muscle power is a product of the net muscle moment and
angular velocity of the of the joint.
The sign of the muscle power
changes during the movement
performance.
Example:
The work done by a muscle during a period t1 to t2 is:
t2
Wm   Pm dt
[J]
t1
Pm – muscle power
Example.
Causes of insufficient movement
•Co-contractions
•Isometric contractions against
gravity
•Jerky movements
•Generation of energy at one joint
and absorption at another
Energy flows
Maintenance heat – amount of metabolic energy to keep the
muscles alive
Forms of energy storage
(1) Potential energy, P.E.
Energy due to gravity. It increases with the height of the body above ground.
(2) Kinetic energy, K.E.
Translational K.E due to the translational velocity and rotational K.E due
to the rotational velocity.
(3) Total energy and exchange within a segment, Es
Energy exchange between segments
Example:
Mid-stance phase
Double support phase
Plot of vertical displacement and horizontal velocity of head-arms-trunk (H.A.T.)
Total energy of a multi-segment system
n
E b   Ei
i 1
where:
Ei – the total energy of the i-th segment
n is the number of the segments
Eb is the total body energy.
Positive and negative work of the total body
Example of a pendulum
100% conservative
system!
Pendulum system with muscles
Muscle is not contracted
Muscle is contracted
•The total body energy increases when muscles do positive work.
•The total body energy decreases when muscles do negative work.
Overall efficiency of human movement
The major problem is to calculate the internal mechanical work.
MUSCLE MECHANICS
Motor unit
The smallest subunit that can be controlled is
called motor subunit because it is separately
innervated by a motor axon.
The motor unit consists of:
1.
2.
3.
Synaptic junction in the ventral root of the spinal cord
Motor axon
Motor end plate in the muscle fibers.
• The number of the muscle fibers that are under control of 1 motor unit varies
from 3 to 20,000 depending on the fineness of the control required.
•A muscle fiber is about 100 mm in diameter consisting of fibrils about 1 m in
diameter.
•Fibrils consist of interacting action and myosin filaments.
Muscle fiber
Sarcoplasm
Sarcolemma – the plasma membrane
Sarcomere – repeating functional unit of microfilaments (length 2.6 mm)
Basic structure of of the
muscle contractive
element
Myofibril
Sarcomere
Many filaments are in parallel and many sarcomere elements are in series to make up a single
contractive element.
Recruitment of motor units
Excitation of the motor unit
all-or-nothing event
•All muscle fibers in a single motor unit contact at the same time;
•Muscle fibers in the same muscle but belonging to different motor units may
contract at different times.
Two indications of the activation of the motor unit:
• Motor unit action potential (electrical indication)
• Twitch of tension (mechanical indication).
EMG signal from indwelling electrode in a muscle
Size principle of recruitment of motor units
• How the motor units are recruited?
• Which motor units are recruited first?
• Are the motor units always recruited in the same order?
Hinneman – The size of the newly recruited motor unit
increases with the tension level at which it is recruited.
•The smallest unit is recruited first and the
largest unit last. Because of the smallest
units the tension can be changed in
finely graded steps.
•Movements requiring high forces but
not needing fine control are
accomplished by recruiting the larger
motor units.
M.U. = motor unit;
M.U.1 – smallest M.U.
M.U.3 – largest M.U.
The muscle action potential (m.a.p.) increases with the
size of the motor unit with which it is associated.
WHY?
If the motor unit is larger then:
1. The motoneuron (that innervates it) is larger
2. The depolarization potentials associated with the motor
end plate is greater.
Can we predict the size of a motor unit from the amplitude of
the recorded signal? – No, it isn’t possible. Why?
Two types of motor units (M.U.):
Type I – It considers the smaller units which produce
low tension and have low time to peak (60 to 120
msec). (tonic M.U.)
Type II – It includes the larger, fast twitch motor
units (phasyc M.U.)
M.U. controlled by any
motoneuron pool form
a spectrum of sizes and
excitations.
Force-length curve of a contractile element
4 mm
Influence of parallel connective tissue
The connective tissue surround the contractive elements. The connective
tissue is called the parallel elastic component.
Ft = Fc + Fp
Ft – tendon force;
Fc – force of the contractive element
Fp – force of the parallel elastic
component.
Series elastic tissue
Series elastic element – all connective tissue in series with the contractile
component, including the tendon.
Isometric contractions