Postgraduate orthopaedics march 2015 biomechanics

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