Dimitar Stefanov

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Lecture 5

• Dimitar Stefanov

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Mechanical Work, Energy and Power

• Definitions
• Purpose of the muscles is to produce tension
• Metabolic efficiency the measure of a muscles
  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.

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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.
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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
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The work done by a muscle during a period t1 to
t2 is
J
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

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Energy flows
Maintenance heat amount of metabolic energy to
keep the muscles alive
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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.
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(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.)
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Total energy of a multi-segment system
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!
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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.

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Overall efficiency of human movement
The major problem is to calculate the internal
mechanical work.
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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
• 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.

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Muscle fiber
Sarcoplasm Sarcolemma the plasma
membrane Sarcomere repeating functional unit of
microfilaments (length 2.6 mm)
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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.
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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
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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.
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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
• The motoneuron (that innervates it) is larger
• 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 isnt
possible. Why?
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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.
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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.
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Series elastic tissue
Series elastic element all connective tissue in
series with the contractile component, including
the tendon.
Isometric contractions