The ISB model for the Upper Extremity

DirkJan Veeger

Carolien van Andel

Jaap Harlaar

ESMAC Seminar “Movement Analysis of the Upper Extremity”

www.internationalshouldergroup.org

Contents

• Introduction– 3D motion description basics– Segment motion - joint motion

• The ISB model– Choices– Procedure– intricacies

• Issues – Euler angles and joint rotation– Reference values– compatibility

Introduction: 3D kinematics basics

• The full description of an object in 3D space requires the coordinates of three points on that object

• Follow the plane. The path of the nose, or the wing tips do not fully describe the plane’s motion..

• One needs at least three pointson the plane to quantitativelydescribe what it does.

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are needed to see this picture.

Introduction: 3D kinematics basics

• Orientation definition of a segment requires three markers

• These three markers describe a plane

• In motion analysis these points can be landmarks or technical markers

TS

AI

AA

Introduction: 3D kinematics basics

• From x-y-z global coordinates markers markers we can construct a local coordinate system (or: frame)

• Frame describes its orientation and position (= pose) in global space

TS

AI

AA

Yg

Xg

Zg

• Five steps to define a local frame

– step 1: define the first axis– Step 2: define a support axis

to define the plane orientation

– Step 3: define a second axis perpendicular to the plane

– Step 4: orthogonize your system: calculate the axis in the plane perpendicular to the first two

– Step 5: construct the orientation matrix

TS

AI

AA z

€

z u =AA − TS

AA − TS

• Five steps to define a local frame

– step 1: define the first axis– Step 2: define a support axis

to define the plane orientation

– Step 3: define a second axis perpendicular to the plane

– Step 4: orthogonize your system: calculate the axis in the plane perpendicular to the first two

– Step 5: construct the orientation matrix

TS

AI

AA Z

Ytemp

€

z u =AA − TS

AA − TS

y temp =AA − AI

AA − AI

• Five steps to define a local frame

– step 1: define the first axis– Step 2: define a support axis

to define the plane orientation

– Step 3: define a second axis perpendicular to the plane

– Step 4: orthogonize your system: calculate the axis in the plane perpendicular to the first two

– Step 5: construct the orientation matrix

TS

AI

AA

Xs

Zs

Ytemp

€

z u =AA − TS

AA − TS

y temp =AA − AI

AA − AI

x = y temp × z u, x u =x

x

• Five steps to define a local frame

– step 1: define the first axis– Step 2: define a support axis

to define the plane orientation

– Step 3: define a second axis perpendicular to the plane

– Step 4: orthogonize your system: calculate the axis in the plane perpendicular to the first two

– Step 5: construct the orientation matrix

TS

AI

AA

Ys

Xs

Zs

€

z u =AA − TS

AA − TS

y temp =AA − AI

AA − AI

x = y temp × z u, x u =x

x

y = z × x , y u =y

y

• Five steps to define a local frame

– step 1: define the first axis– Step 2: define a support axis

to define the plane orientation

– Step 3: define a second axis perpendicular to the plane

– Step 4: orthogonize your system: calculate the axis in the plane perpendicular to the first two

– Step 5: construct the orientation matrix = all three axes / direction vectors

TS

AI

AA

Ys

Xs

Zs

€

z u =AA − TS

AA − TS

y temp =AA − AI

AA − AI

x = y temp × z u, x u =x

x

y = z × x , y u =y

y

R = x u y u z u[ ]

• The resulting 3x3 matrix describes the orientation of a segment in the global system

• The matrix contains the three direction vectors,

• Each direction vector defines the angle of that axis with the three axes of the global coordinate system

TS

AI

AA

€

Rscapula =

cos(x, X) cos(y, X) cos(z,X)

cos(x,Y ) cos(y,Y ) cos(z,Y )

cos(x,Z) cos(y,Z) cos(z,Z)

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

P scapula = AAglobal + Rscapula ⋅ x local =

with

det(Rscapula ) =1

AAglobal = Origin scapula frame

• The segment orientations can also be expressed relative to each other :– Joint orientation matrix

€

Relbow = RhumerusT ∗R forearm

c 0 s0 1 0-s 0 c

c -s 0s c 00 0 1

1 0 00 c -s0 s c

Decomposition of a matrix:vector rotation basics

• Rotation matrices can be used to rotate a point to any given position in a plane over a specified angle: (Rz), (Ry) or (Rx)

• The transpose of these matrices rotate the axes of a coordinate system towards a given vector (which is a rotation - for Rz etc.)

• The segment-, or joint orientation matrix can be seen as built up from three rotations– This can be any order of rotations: x-y-z, y-z-y etc.

• Decomposition is the extraction of these three rotations from the orientation matrix– What order is a matter of choice, but:– Each different order yields different results

Decomposition of a matrix:vector rotation basics

Decomposition of a joint orientation matrix

• Choose meaningful axes to rotate around...– Flexion-extension - ab/adduction - axial rotation– Plane of elevation - elevation - axial rotation– ??

• Standard protocol necessary!

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[30,120,45]

180

0

90

180

90

30

60

30 60 120 150

120

150

North Pole

South Pole

45

€

let : Rx =

1 0 0

0 cosα −sinα

0 sinα cosα

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥,Ry =

cosβ 0 sinβ

0 1 0

−sinβ 0 cosβ

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥,Rz =

cosγ −sinγ 0

sinγ cosγ 0

0 0 1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

Rzxy =

r11 r12 r13

r21 r22 r23

r31 r32 r33

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥= Rz ⋅ I( ) ⋅Rx( ) ⋅Ry( ) = Rzg ⋅Rxl ⋅Ryl

=

cosγ cosβ − sinγ sinα sinβ −sinγ cosα cosγ sinβ + sinγ sinα cosβ

sinγ cosβ + cosγ sinα sinβ cosγ cosα sinγ sinβ − cosγ sinα cosβ

−cosα sinβ sinα cosα cosβ

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

Decomposition example (see Capozzo, 2005)

This value in the orientation matrix can be used to calculate , the

rotation around the x-axis.

These values can be used to calculate

, the rotation around the z-axis

• Definition of local coordinate systems– Landmarks – Axis directions

• Definition of decomposition orders– Full text: see Wu et al, 2005

• Now: example humerus– Landmarks– Decomposition order

ISB Upper extremity model: choices

• ISB choice: local frames based on anatomical landmarks

ISB Upper extremity model: procedure

Procedure sensitive to landmark estimation errors

– Local humerus frame defined on three landmarks:

• EM, EL and GH

– GH has to be estimated• From kinematics (Helical axes or sphere

fit)• based on regression (Meskers et al. 1998)

• Alternative proximal marker in fixed position

– Long axis defined first, followed by axis perpendicular to plane

• Alternative procedure:– Use GH, EL, EM and forarm

markers

• Forearm used for definition of plane– Dependent on elbow angle: ISB

suggests 90° flexion and 90° pronation as reference position

• Long axis defined first, followed by axis perpendicular to plane

ISB Upper extremity model: procedure

[30,120,45]

180

0

90

180

90

30

60

30 60 120 150

120

150

North Pole

South Pole

45

• Proposed decomposition order:– Plane of elevation– Elevation– Axial rotation

• Gimbal lock when Plane of elevation is 0°, or 180°

• Applicable for thoracohumeral and glenohumeral motion

• “Comply or Explain”

ISB Upper extremity model: procedure

• Landmarks on the scapula can not directly be measured!

ISB Upper extremity model: intricacies

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• Landmarks on the scapula can not directly be measured!– Use scapula locator

• (quasi static)

– Use markers on acromion• Reliability above 100° elevation?

– Estimate from thorax and arm orientation

• Tricky in patients..

ISB Upper extremity model: intricacies

Scapula locator

• Not unique to the ISB UX approach, but:– Model assumes that local coordinate systems are

aligned: no reference position• In full extension, the long axes of the arm might not be

exactly aligned: leads to variations in the second rotation.• These variations are NOT elbow abduction.... Or change in

carrying angle

ISB Upper extremity model: intricacies

• Not unique to the ISB UX approach, but:

– Upper extremities have large axial rotations and:• Landmarks / sensors sensitive to soft tissue deformation in axial

rotation• Local coordinate definition very sensitive to relative positions of

landmarks during calibration (= definition of local coordinate systems)

– Advice: always measure a separate reference position, preferably 0° arm elevation, 90° arm axial rotation, 90° flexion and 90° pronation

ISB Upper extremity model: intricacies

– ISB model is based on anatomical frames and not functional axes

– Euler angles and joint rotations are not the same:

• Elbow motion = forearm segment relative to arm segment

• Decomposition yields three Euler angles, but NOT actual elbow joint motion!

• The second rotation: ab-adduction is due to ‘mis’alignment, but:

– The Euler angles DO describe relative segment motion

• For ‘real’ joint motion (flexion, pro-supination), use other axes, or fit a kinematic model

ISB Upper extremity model: issuesy-axis arm

y-axis forearm

z-axis arm

– Compatibility: dependent on all steps of the procedure

• Landmark choice and definition• Definition order of local segment axes• Decomposition order of orientation matrix

– Comply or Explain!

ISB Upper extremity model: issues

Summary

• The ISB protocol is based on anatomical frames– Other options possible, but not interchangeable

• The ISB protocol gives a prescribed definition order for local frame axes

– Other options possible, but not interchangeable

• The ISB protocol defines the decomposition order for segment- and joint orientation matrices / frames

– Other options possible, but not interchangeable

• ISB protocol is not perfect, but still seems to be the basis for UE motion analyses