MUSCLE INDETERMINACY

1
MUSCLE INDETERMINACY

• Overview
• Definitions
• Estimating force in a single muscle
• In two muscles problem of indeterminacy
• Working around indeterminacy

2
Force Generated by One Muscle
a 0

• inverse dynamics

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Inverse Dynamics

• MNET I a
• MELBOW - MWEIGHT IFOREARM aFOREARM
• MELBOW - 50 N (0.32 m) IFOREARM aFOREARM
• MELBOW - 16 N m IFOREARM (0)
• MELBOW - 16 N m 0
• MELBOW 16 N m

4
Single-Muscle Example

• Muscular elbow moment moment produced by
• MBICEPS MELBOW
• Biceps moment arm
• MBICEPS
• 16 N m
• FBICEPS

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An Easy Question

• What is the pulling force necessary to support
  the weight?

100 N
6
A Harder Question

• What is

F1
F2
100 N
7
Muscle Indeterminacy

• Addition of
• easy to determine how
• impossible
• Knowing weight ltgt
• Cables forces ltgt

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Mathematics of Indeterminacy

• Example
• Number of
• Equations may be solved if
• though a unique solution

9
Force Generated by Two Muscles
FBICEPS ?
FBRACHIORADIALIS ?
50 N
10

• MELBOW
• Elbow moment moment produced by
• Assume
• dBICEPS 4 cm (as before) dBRA 6 cm
• MELBOW
• 16 N m
• One equation, two unknowns

11
Three Solutions to Muscle Indeterminacy Problem

• Reduction Reduce number of unknowns by
• Optimization Assume that the body tries to meet
• EMG to force processing Use known mechanical
  properties

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Reduction Method
FBICEPS ?
FBRACHIORADIALIS 0 (assumed)
50 N
13
Reduction Method (cont)

• Assumptions usually
• Advantage
• Disadvantages
• Co-contraction forces
• Assumption rarely

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Optimization Method

• Example 2 F 3 G 12
• Assume that the right values for F and G are ones
  that
• F G F2 G2
• 0 4
• 6 0
• 3 2
• Minimization results in F 1.84 G 2.77 F2
  G2 11.08

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Optimization Method (cont)

• Optimization criteria
• minimal total muscle force
• minimal total squared muscle force
• minimal total muscle stress
• minimal total ligament force
• minimal total joint force
• minimal energy expenditure

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Optimization Method (cont)

• Can produce force predictions that
• Disadvantages
• Best optimization criterion
• Optimization doesnt make sense in

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EMG to Force Processing

• A muscles force depends on its
• If these quantities can be measured, each
• Indeterminacy problem

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Review Muscle Indeterminacy
F1
F2
100 N
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MUSCLE PROPERTIES I

• Overview
• Muscle as a machine
• Terminology and classification
• Muscular contraction
• Series vs. parallel organization

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• This Lecture What is muscle? How does it
  generate force?
• Next Lecture Mathematical models of muscle force
  production

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Muscle Meat and Machinery
Everyone knows that meat is really muscle.
Muscle is the only known piece of machinery which
can be cooked in many ways. - T.A. McMahon
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Muscle versus Machine

• force weight speed direction
• (N) (N) (mm/s)
• push/pull

Jordan Controls LA-1100 linear actuator vastus m
edialis
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Desirable Qualities of Muscle

• Excellent
• Built-in
• Self-

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Muscle-tendon Terminology
origin - tendon (proximal) muscle belly -
actively tendon (distal) insertion -
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Muscle Classifications

• Smooth,
• Also classified by
• Pennation
• Pennation also

q
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Muscle Classifications (cont)
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Muscle Fiber Types

• Slow
• Fast

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Muscle Fiber Types (cont)

• Soleus
• Brachioradialis
• Most large muscles

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Microscopic Structure
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Force Generation at the Molecular Level
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Sliding Myofilaments

• Actin and myosin
• Force generated by

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Muscle Contraction
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Muscle Contraction (cont)
1. 2. 3. 4. 5. 6. Rigor mortis
muscles become rigid in death when
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Muscle Contraction (cont)
F
two twitches, far apart
t
two twitches, close together
tetanus
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Muscle Contraction (cont)

• isometric
• concentric
• eccentric

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Linking in Series
F

• When force bearing elements are linked in series,
• Examples

F
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Linking in Parallel

• When force bearing elements are linked in
  parallel,
• Examples

2 F
F
F
F
F
2 F
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Use It or Lose It

• When muscle is not used
• Atrophy
• Reverse occurs
• Hypertrophy
• Less common
• Hyperplasia

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Review Series Arrangement
FBD for weight
FBD for bottom link
FBD for middle link

• Each link
• Each sarcomere

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Review Parallel Arrangement

• Lifters arranged in parallel each
• Muscle fibers
• Stronger muscles have

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Review Contractile Proteins
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MUSCLE PROPERTIES II

• Overview
• Idea of a muscle model
• Force-length relationship
• Force-velocity relationship
• Electromyographic activity
• Hill muscle model

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Mathematical Models

• Model
• Examples
• Ethical considerations make
• Mathematical model uses

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Mathematical Model of a Spring

• Pulling on a spring
• What kind of model (equation) would

x
F
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Spring Model (cont.)
F (N) x (mm) 0 0.0 1 4.1 2 8.1 3 11.9

• Equation F kx (with k 4) is a
• Would model
• Model only valid

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Muscle Force-Length Passive

• Passive (not contracting) muscle acts like a
• Pulling force
• Caused by

F
length
lo
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Muscle Force-Length Active

• Active force
• Crossbridges arranged
• Number of crossbridges depends on

actin (thin) filament
myosin (thick) filament
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Crossbridge formation increases, then decreases
with filament overlap
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Active Force Length Curve for Muscle
F
plateau
length
lo
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Total Force-Length Active Passive
note peak in active curve occurs at length lo
F
Fo
passive
lo
length
Fo max isometric force
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Determination of F-L Curves

• Experiments done on
• Muscle held at constant length while
• passive
• total
• Active force-length curve determined

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Force-Velocity Effect

• Quick-release experiments show that
• than
• than
• Quick-release experiment

W1
string cut
W2
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Force-Velocity Curve
lengthening force gt isometric force
isometric force
shortening force lt isometric force
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Electromyographic (EMG) Activity

• Electrical activity of muscle
• Measured using
• Active F-L, F-V curves

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Scaling of F-V Curve by EMG
F
EMG level
100
75
Fo
50
25
shortening
lengthening
velocity
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Hill-Type Muscle Model
CE
SE

• Proposed by A.V. Hill (1938)
• Accurate for
• Three components

PE
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The Hill Equation

• Describes behavior of
• v b (Fo - F) / (a F)
• where v Fo isometric force a, b
  parameters unique to each muscle
• Note that for
• Plotting the Hill equation (F vs v) gives

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Muscle Viscoelasticity

• Viscoelastic effect
• Ex.
• Stretching exercises may reduce

F
no stretching
with stretching
length
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Review Muscle Force-Length Curves
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Review Active Force Length Curve
F
length
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Review Force-Velocity Curve
lengthening force gt isometric force
isometric force
shortening force lt isometric force
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Review Predicting Muscle Force
EMG to Force
EMG
Force-Length
muscle length
force
Force-Velocity
shortening velocity
muscle model equations that predict force from
EMG, length, and/or velocity
63
ENERGY AND POWER IN BIOMECHANICS

• Overview
• Energy
• Energy storage/transfer in walking and running
• Power
• Analysis of ankle power in terminal stance

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Energy

• Energy
• Forms of energy
• Energy may be
• Unit
• 1 J of energy necessary to

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Kinetic Energy (KE)

• Any body that
• translational
• rotational
• As body loses KE (comes to a stop),
• or

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Potential Energy (PE)

• Stored energy that
• Gravitational PE
• PE
• Elastic PE -
• for a spring, PE

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Example Ball Thrown Upward

• As ball reaches peak,
• Top
• Bottom
• Total energy

KE
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Energy Transfer in Walking
energy
total
KE
PE
time
Energy switches between
Total energy
lower v
higher v
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Example Bouncing Ball

• Ball has
• Ball has
• Ball has

KE transformed to elastic PE stored in ball when
it is deformed
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Energy Transfer in Running
energy
KE PE metabolic
KE
PE
time

• KE, PE are
• Energy fluctuations apparent even when
• Where does
• Where does

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Energy Transfer in Running (cont)

• At lowest point energy
• Bone, crossbridges
• Tendon stretch allows

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Power

• Power
• Forms of power
• Unit
• 1 W represents
• 100 W lightbulb
• Joint power

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Push-Off vs. Rollover

• Push-off
• ankle power
• Rollover
• ankle power

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Ankle Power Measurement
power
gait cycle
TO
100

• Winter (1983)
• Large late stance power peak
• Later study by Winter et al. (1990) showed