postgraduate orthopaedics march 2015 biomechanics
TRANSCRIPT
Postgraduate
Orthopaedics
Biomechanics
Dr Nick Caplan Reader in Clinical Biomechanics
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
What is biomechanics?
• Biomechanics – study of the mechanics of
living things
• Orthopaedic biomechanics is interested in:
– Joint function
• prothesis design
• surgical technique
– Mechanics of bones
– Soft tissue mechanics/function
– Whole body function
Postgraduate
Orthopaedics
What is assessed in biomechanics?
• Kinetics
– Force within the body
– Forces outside the body
• Kinematics
– Linear Motion – position, velocity, acceleration
– Angular Motion – position, velocity,
acceleration
• Muscle activity
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Units of measure
• Important to use correct ones
– Calculations will be incorrect if you do not
• Systeme International d’Unites (SI units)
Base units Derived units Derived units with
special names
Metre (m) – length Area (m2) Force (kg.m/s2) – newton
(N)
Kilogram (kg) – mass Volume (m3) Moment (Nm)
Seconds (s) - time Speed (m/s or m.s-1) Etc.
Acceleration (m/s2 or m.s-2)
Etc.
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Newton's laws
• Law 1: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it
• Law 2: The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma
• Law 3: For every action there is an equal and opposite reaction
Postgraduate
Orthopaedics
What is force?
• Force is a push or a pull
• Force is measured in Newtons
– 1N = 9.81kg
– 9.81 m/s/s is acceleration due to gravity if on
earth’s surface
• Force is a vector
– Magnitude and direction
Postgraduate
Orthopaedics
Different forces• Internal (to an object/material)
– Tension
– Compression
• External (to an object/material)
– Weight
– Reaction forces
– Impact forces
– Friction
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Free body diagrams
• Follow these steps:
1.Draw simplified drawing of object
2.Show location of centre of mass
3.Draw external forces
Postgraduate
Orthopaedics
Free body diagrams
bW
Postgraduate
Orthopaedics
Assumptions made in free body diagrams
• Bones are rigid bodies
• Joints are frictionless hinges
• No antagonistic muscle action
• Weight of body is concentrated at the exact centre of body mass
• Internal forces cancel each other out
• Muscles only act in tension
• The line of action of a muscle is along the centre of cross-sectional area of muscle mass
• Joint reaction forces are assumed to be only compressive.
Postgraduate
Orthopaedics
Pythagoras theorem
• Pythagoras theorem
F2 = G2 + H2
So:
H2 = F2 – G2
TASK:
If F = 5, G = 4
H = ???
H = 3
FG
H
Postgraduate
Orthopaedics
Trigonometry
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent
F = hypotenuse (longest side)
G = opposite (opposite θ)
H = adjacent (next to θ)
θ
FG
H
Postgraduate
Orthopaedics
Worked example 1
• If F = 850 N, and θ = 60°,
H = ??
cosθ = H / F
H = F x cosθ
H = 850 x cos60
H = 850 x 0.5
H = 425 N
θ
FG
H
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Moments
• Force applied at distance from pivot will
cause segment to rotate
– Distance is called the moment arm
– Rotational effect is called turning moment
– Turning moment = force x moment arm
– Also known as torque
Postgraduate
Orthopaedics
Example 1• Lower leg held at 30° below horizontal
• What muscular force is required
to hold leg stationary?WL
WB
FJ
FM
cb
a
Postgraduate
Orthopaedics
Example 2
Postgraduate
Orthopaedics
Inverse dynamic analysis
• Known values
– Forces (3D) between foot and ground
– Moments of force about 3 axes of force
platform
• Calculated
– COP on force platform (and on foot from
kinematics)
– Forces/moments (3D) at ankle, knee, hip
joints, etc.
Postgraduate
Orthopaedics
How inverse dynamics works:
2D example
Postgraduate
Orthopaedics
Ax, Ay, Ma now used
Postgraduate
Orthopaedics
Kx, Ky, Mk now used
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Kinematics• Study of motion
• Interested in linear or angular displacement, velocity and acceleration
• Most joints have 6 degrees of freedom– Linear (inline with joint axes)
1. Medial-lateral
2. Anterior-posterior
3. Proximal-distal (longitudinal)
– Angular (about joint axes)1. Flexion-extension (about ML axis)
2. Internal-external rotation (about longitudinal axis)
3. Adduction-abduction (about AP axis)
Postgraduate
Orthopaedics
Planes of motion
Postgraduate
Orthopaedics
Example: sagittal knee ranges
Activity Knee flexion
(degrees)
Walking 67
Climbing stairs 83
Descending stairs 90
Sitting down 83-110
Squatting 130
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Determining knee joint
kinematics and kinetics
• 3D Gait analysis
– Retroreflective markers
– Marker trajectories recorded by infrared
cameras
– GRF measured by force platform
Postgraduate
Orthopaedics
Force platforms
High speed camera
IR camera
Postgraduate
Orthopaedics
Postgraduate
Orthopaedics
Typical lower limb marker set
Postgraduate
Orthopaedics
Example gait analysis
Postgraduate
Orthopaedics
Example gait analysis
Postgraduate
Orthopaedics
Kinematic and kinetic analyses
• Joint angles calculated between adjacent
segments
– Flexion-extension
– Internal-external rotation
– Adduction-abduction
• Inverse dynamics estimates joint loading
Postgraduate
Orthopaedics
Example data:
Walking GRF
data
Postgraduate
Orthopaedics
20 40 60 80 100
-20
0
20
40 Flexion
Extension
Percentage time (%)
angle
(degre
es)
20 40 60 80 100
-1
0
1
Extension
Flexion
Percentage time (%)
mom
ent (N
mm
/kg)
20 40 60 80 100
-10
-5
0
5
10 Adduction
Abduction
Percentage time (%)
angle
(degre
es)
20 40 60 80 100
-0.5
0.0
0.5
1.0
1.5 Abduction
AdductionPercentage time (%)
mom
ent (N
mm
/kg)
20 40 60 80 100
-20
-10
0
10
20 Int. rotation
Ext. rotation
Percentage time (%)
angle
(degre
es)
20 40 60 80 100
-0.2
-0.1
0.0
0.1
0.2 Int. rotation
Ext. rotation
Percentage time (%)
mom
ent (N
mm
/kg)
Example data:
Walking gait
data for healthy
controls
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Influence of hip OA
20 40 60 80 100
-20
0
20
40
60 Flexion
ExtensionPercentage time (%)
angle
(degre
es)
Postgraduate
Orthopaedics
Example data:
Walking gait
data for healthy
controls
Vs
THA patients
20 40 60 80 100
-20
0
20
40
60 Flexion
ExtensionPercentage time (%)
angle
(degre
es)
20 40 60 80 100
-1
0
1
Extension
Flexion
Percentage time (%)
mom
ent (N
mm
/kg)
20 40 60 80 100
-10
-5
0
5
10
15 Adduction
Abduction
Percentage time (%)angle
(degre
es)
20 40 60 80 100
-0.5
0.0
0.5
1.0
1.5 Abduction
AdductionPercentage time (%)
mom
ent (N
mm
/kg)
20 40 60 80 100
-20
-10
0
10
20
30 Int. rotation
Ext. rotation
Percentage time (%)angle
(degre
es)
20 40 60 80 100
-0.2
-0.1
0.0
0.1
0.2 Int. rotation
Ext. rotation
Percentage time (%)
mom
ent (N
mm
/kg)
Postgraduate
Orthopaedics
Outline
• What is biomechanics?
• Units of measure
• Newton’s laws of motion
• Free body diagrams
• Kinetics
• Kinematics
• Gait analysis
• Example: Hip OA and arthroplasty
• Example: Knee instability
Postgraduate
Orthopaedics
Patellofemoral loading
• Joint reaction force
– Walking = 385 N
– Stair ascent/decent = 2400 – 2500 N
– Landing from jump = 5792 N
• Pressure more important for injury/PFJP
– Walking = 2 Mpa
– Landing = 55 MPa
area
forcepressure
Postgraduate
Orthopaedics
Q angle
• Normal Q angle
– Women = 16° (approx.)
– Men = 11° (approx.)
• Increased Q angle
– linked to instability
– Increased PF pressure
Postgraduate
Orthopaedics
Q angle - biomechanics
FQ
FPT
FP
θ
FQ
FPT
FP
θ
Postgraduate
Orthopaedics
Q angle – patellar kinematics
(Mizuno et al, 2001)
Postgraduate
Orthopaedics
Thank you
for listening
Postgraduate
Orthopaedics
Bonus
material
Postgraduate
Orthopaedics
Example exam questions
• What do you understand by the term “free body diagram”?
• Can you draw a free body diagram of the hip joint?
• Describe the kinematic behaviour of the knee during flexion.
• What is a moment?
• What is a force?
• What are the assumptions made when drawing a free body diagram
• What are the three Newton’s physical laws of motion?
Postgraduate
Orthopaedics
Question: What do you understand
by the term “free body diagram”?
• This is a method used to illustrate the various forces
acting on a structure such as a bone, and to illustrate
how far from a joint or other pivot point these forces are
acting. From knowing these forces and distances, the
moments of force acting to maintain the structure in
static equilibrium can be calculated.
Postgraduate
Orthopaedics
Question: Can you draw a free
body diagram of the hip joint?
bW
Postgraduate
Orthopaedics
Question: Describe the kinematic
behaviour of a normal knee
• The movements of the normal knee in early to mid flexion (10 to 120
degrees) are a consequence of lateral femoral rollback, internal
rotation of the tibia and unequal radii of the centre of rotation of the
medial and lateral femoral condyles. During knee flexion the tibio-
femoral contact point moves posteriorly to a significantly greater
extent in the lateral compartment as the tibia internally rotates to the
extent that during deep flexion there is no bony contact between the
lateral femoral condyle and lateral tibial plateau as the femoral
condyle and mobile posterior horn of the lateral meniscus drop over
the posterior tibia.
• Could also describe patellar kinematics…
Postgraduate
Orthopaedics
Question: What is a moment?
• A moment is generated as a result of a force acting at a distance
away from a pivot point or joint. For example, the muscles acting
about a joint, with their origins/insertions at a distance away from the
joint, will act to generate a turning moment about that joint that can
either act to keep the joint in static equilibrium - by balancing all the
moments generated by the agonist and antagonist muscles – or to
generate rotation about the joint – as a result of moments on one
side of the joint being greater than on the other side of the joint.
Postgraduate
Orthopaedics
Question: What is a force?
• A force is a load acting on a structure or object. It can be either a
push (compressive force) or a pull (tensile force). Forces can either
be external to the body (e.g. ground reaction forces, gravity, etc.) or
internal to the body (e.g. joint contact forces, muscle contractile
forces, ligamentous constraint forces). Forces are vectors, such that
they have both magnitude and direction. Forces can therefore be
resolved into their components in the x, y and z axes using
Pythagoras’ theorem.
Postgraduate
Orthopaedics
Question: What are the
assumptions made when drawing
a free body diagram
• Bones are rigid bodies
• Joints are frictionless hinges
• No antagonistic muscle action
• Weight of body is concentrated at the exact centre of body mass
• Internal forces cancel each other out
• Muscles only act in tension
• The line of action of a muscle is along the centre of cross-sectional
area of muscle mass
• Joint reaction forces are assumed to be only compressive.
Postgraduate
Orthopaedics
Question: What are the three
Newton’s physical laws of motion?
• Law 1: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it
• Law 2: The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma
• Law 3: For every action there is an equal and opposite reaction
Postgraduate
Orthopaedics
Moments worked example• Lower leg held at 30° below horizontal
• What muscular force is required
to hold leg stationary?WL
WB
FJ
FM
cb
a
Postgraduate
Orthopaedics
Moments worked example
• Known values:
• WB (weight of boot) = 80 N
• WL (weight of leg) = 40.6N
• Unknown values:
• FM (muscular forces)
• FJ (joint reaction forces)WL
WB
FJ
FM
cb
a
Postgraduate
Orthopaedics
Moments worked example
• If in static equilibrium, sum moments about
knee joint:
• MWB + MWL + MFJ + MFM = 0
• Known distances:
• a = 0.0224 m
• b = 0.110 m
• c = 0.320 m WL
WB
FJ
FM
cb
a
Postgraduate
Orthopaedics
Moments worked example
• MFJ is zero, so
• MWB + MWL + MFM = 0
or
• MWB + MWL = -MFM
• Calculate moments:
• MBW = c x WB = 0.320 x 80 = 25.6 Nm
• MWL = b x WL = 0.110 x 40.6 = 4.47 Nm
WL
WB
FJ
FM
cb
a
Postgraduate
Orthopaedics
Moments worked example• Substitute back into equation
• MWB + MWL = 25.6 + 4.47 = 30.07 Nm
• MFM = -30.07 Nm (torque)
• MFM = a x FM, so
• FM = MFM / a
• FM = 30 / 0.0224 = 1340 N
• Quadriceps muscles must apply
• 1340 N of force to lower leg
• to stabilise limb position WL
WB
FJ
FM
cb
a