2005_Wu_et_al_JB.pdf

ARTICLE IN PRESS

Journal of Biomechanics 38 (2005) 981–992

www.elsevier.com/locate/jbiomech

www.JBiomech

ISB recommendation on deﬁnitions of joint coordinate systems of

various joints for the reporting of human joint motion—Part II:

shoulder, elbow, wrist and hand

Ge Wu a, ,1 , Frans C.T. van der Helm b,2 ,H.E.J.(DirkJan)Veeger c,d,2 , Mohsen Makhsous e,2 ,

Peter Van Roy f,2 , Carolyn Anglin g,2 , Jochem Nagels h,2 , Andrew R. Karduna i,2 ,

Kevin McQuade j,2 , Xuguang Wang k,2 , Frederick W. Werner l,3,4 , Bryan Buchholz m,3

a Department of Physical Therapy, University of Vermont, 305 Rathwell Building, Burlington, VT, USA

b Department of Mechanical Engineering, Delft University of Technology, Delft, The Netherlands

c Department of Human Movement Sciences, Institute for Fundamental and Clinical Movement Sciences, Amsterdam, The Netherlands

d Department of Mechanical Engineering, Delft University of Technology, Delft, The Netherlands

e Department of Physical Therapy and Human Movement Sciences, Northwestern University, Chicago, IL, USA

f Experimental Anatomy, Vrije Universiteit Brussel, Belgium

g Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada

h Department of Orthopaedics, Leiden University Medical Center, The Netherlands

i Exercise and Movement Science, University of Oregon, Eugene, OR, USA

j Department of Physical Therapy and Rehabilitation Science, University of Maryland, Baltimore, MD, USA

k Biomechanics and Human Modeling Laboratory, National Institute for Transport and Safety Research, Bron, France

l Department of Orthopedic Surgery, SUNY Upstate Medical University, Syracuse, NY, USA

m Department of Work Environment, University of Massachusetts, Lowell, MA, USA

Accepted 27 May2004

Abstract

In this communication, the Standardization and TerminologyCommittee (STC) of the International Societyof Biomechanics

proposes a deﬁnition of a joint coordinate system (JCS) for the shoulder, elbow, wrist, and hand. For each joint, a standard for the

local axis system in each articulating segment or bone is generated. These axes then standardize the JCS. The STC is publishing these

recommendations so as to encourage their use, to stimulate feedback and discussion, and to facilitate further revisions. Adopting

these standards will lead to better communication among researchers and clinicians.

Keywords: Joint coordinate system; Shoulder; Elbow; Wrist; Hand

1. Introduction

Corresponding author. Tel.: +1-802-656-2556; fax: +1-802-656-

2191.

E-mail address: ge.wu@uvm.edu (G. Wu).

1 Chairperson of the Standardization and TerminologyCommittee.

The International Societyof Biomechanics.

2 Authored shoulder and elbow.

3 Authored wrist and hand.

In the past several years, the Standardization and

TerminologyCommittee (STC) of the International

Societyof Biomechanics has been working to propose a

set of standards for deﬁning joint coordinate systems

(JCS) of various joints based on Grood and Suntay’s

JCS of the knee joint ( Grood and Suntay, 1983 ). The

primarypurpose of this work is to facilitate and

doi:10.1016/j.jbiomech.2004.05.042

Subcommittee Chair.

982

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G. Wu et al. / Journal of Biomechanics 38 (2005) 981–992

encourage communication among researchers, clini-

cians, and all other interested parties.

The STC has established a total of nine sub-

committees, involving nearly30 people who have

extensive experience (either research or clinical) in joint

biomechanics, and had developed proposals for nine

major joints in the body. These joints include: foot,

ankle, hip, spine, shoulder, elbow, hand and wrist, TMJ,

and whole body. The proposals are based on the ISB

standard for reporting kinematic data published by Wu

and Cavanagh (1995) . The ﬁrst set of these standards for

the ankle joint, hip joint, and spine was published in

Journal of Biomechanics in April 2002 ( Wu et al., 2002 ).

A response to comments to this set of standards was

later published in 2003 ( Allard et al., 2003 ).

In this publication, the proposed standards for the

shoulder joint, elbow joint, and wrist and hand are

included. For each joint, the standard is divided into the

following sections: (1) Introduction, (2) Terminology,

(3) Bodysegment coordinate systems, and (4) JCS and

motion for the constituent joints. It is then up to the

individual researcher to relate the marker or other (e.g.

electromagnetic) coordinate systems to the deﬁned

anatomic system through digitization, calibration move-

ments, or population-based anatomical relationships.

The two major values in using Grood and Suntay’s

JCS are: (1) conceptual, since it appears easier to

communicate the rotations to clinicians when using

individual axes embedded in the proximal and distal

segments and (2) the inclusion of calculations for

clinicallyrelevant joint translations. Some confusion,

however, has arisen over their statement that the JCS is

sequence independent, whereas Euler or Cardan angle

representations are not. It should be noted that the

Grood and Suntay’s convention, without the transla-

tions, is simplya linkage representation of a particular

Cardan angle sequence; the ﬂoating axis is the second,

i.e. rotated, axis in the Cardan sequence ( Small et al.,

1992; Li et al., 1993 , Baker, 2003 ). The angles are

independent because the sequence is deﬁned bythe

mechanism; a Cardan or Euler sequence is equally

‘‘independent’’ once the sequence is deﬁned.

The starting point for the shoulder standardization

proposal was a paper by Van der Helm (1996) . More

information can be obtained at: http://www.internatio-

nalshouldergroup.org .

The standardization of motions is onlydescribed for

right shoulder joints. Whenever left shoulders are

measured, it is recommended to mirror the raw position

data with respect to the sagittal plane ðz ¼zÞ. Then, all

deﬁnitions for right shoulders are applicable.

Rotations are described using Euler angles. For a

clearer interpretation of these angles it is suggested that

the coordinate systems of the proximal and distal body

segments are initiallyaligned to each other bythe

introduction of ‘anatomical’ orientations of these

coordinate systems. The rotations of the distal coordi-

nate system should then be described with respect to the

proximal coordinate system. If both coordinate systems

are aligned, the ﬁrst rotation will be around one of the

common axes, the second rotation around the (rotated)

axis of the moving coordinate systems, and the third

rotation again around one of the rotated axes of the

moving coordinate system. This last axis is preferably

aligned with the longitudinal axis of the moving

segment. This method is equivalent to the method of

Grood and Suntay(1983) using ﬂoating axes. Theyalso

describe the ﬁrst rotation around an axis of the proximal

coordinate system and the last rotation around the

longitudinal axis of the moving segment. The second

axis is bydeﬁnition perpendicular to both the ﬁrst and

third rotation axis.

For joint displacements, a common point in both the

proximal and distal coordinate systems should be taken,

preferablythe initial rotation center (or a point on the

ﬁxed rotation axis in the case of a hinge joint). For most

shoulder motions the rotation center would be onlya

rough estimate, since onlythe glenohumeral joint

resembles a ball-and-socket joint. The deﬁnition of the

common rotation centers of the sternoclavicular joint

and acromioclavicular joint are left to the discretion of

the researcher. Displacements should be described with

respect to the axes of the coordinate system of the

segment directlyproximal to the moving segment to

represent true joint displacements.

2. JCS for the shoulder

2.2. Terminology

2.1. Introduction

2.2.1. Anatomical landmarks used in this proposal

( Fig. 1 )

Standardization of joint motions is veryimportant for

the enhancement of the studyof motion biomechanics.

The International Shoulder Group (ISG) supports the

efforts of the ISB on this initiative, and recommends

that authors use the same set of bonylandmarks; use

identical local coordinate systems (LCS); and report

motions according to this recommended standard.

Thorax: C7: Processus Spinosus (spinous process)

of the 7th cervical vertebra

T8: Processus Spinosus (spinal process)

of the 8th thoracic vertebra

IJ: Deepest point of Incisura Jugularis

(suprasternal notch)

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Fig. 1. Bonylandmarks and local coordinate systems of the thorax,

clavicle, scapula, and humerus.

reduce the occurrence of complications due to gimbal

lock ( Groot, 1998 ). The GH is strictlyspeaking not a

bonylandmark, but is needed to deﬁne the longitudinal

axis of the humerus. The GH can be estimated by

regression analysis ( Meskers et al., 1998 ) or bycalculat-

ing the pivot point of instantaneous helical axes (IHA)

of GH motions ( Stokdijk et al., 2000; Veeger et al.,

1996 ). The IHA method is preferred since it is more

accurate, and is also valid for patients in whom the GH

has changed due to degeneration of the articular

surfaces, or due to an implant. In some pathological

cases it is likelythat the GH cannot be accurately

estimated with the IHA method due to translations in

the joint. It is then, however, a question whether the

regression method will be an acceptable alternative or

whether different methods (such as CT or MRI) should

be used.

PX: Processus Xiphoideus (xiphoid

process), most caudal point on the

sternum

Clavicle: SC: Most ventral point on the

sternoclavicular joint

AC: Most dorsal point on the

acromioclavicular joint (shared with

the scapula)

Scapula: TS: Trigonum Spinae Scapulae (root of

the spine), the midpoint of the

triangular surface on the medial

border of the scapula in line with the

scapular spine

AI: Angulus Inferior (inferior angle),

most caudal point of the scapula

AA: Angulus Acromialis (acromial angle),

most laterodorsal point of the

scapula

PC: Most ventral point of processus

coracoideus

Humerus: GH: Glenohumeral rotation center,

estimated byregression or motion

recordings

EL: Most caudal point on lateral

epicondyle

EM: Most caudal point on medial

epicondyle

Forearm: RS: Most caudal–lateral point on the

radial styloid

US: Most caudal–medial point on the

ulnar styloid

2.3. Body segment coordinate systems

2.3.1. Thorax coordinate system—X t Y t Z t (see Figs. 1

and 2 )

O t : The origin coincident with IJ.

Y t : The line connecting the midpoint between PX

and T8 and the midpoint between IJ and C7,

pointing upward.

Z t : The line perpendicular to the plane formed by

IJ, C7, and the midpoint between PX and T8,

pointing to the right.

X t : The common line perpendicular to the Z t -and

Y t -axis, pointing forwards.

2.3.2. Clavicle coordinate system—X c Y c Z c (see Figs. 1

and 3 )

O c : The origin coincident with SC.

Z c : The line connecting SC and AC, pointing to

AC.

X c : The line perpendicular to Z c and Y t , pointing

forward. Note that the X c -axis is deﬁned with

respect to the vertical axis of the thorax (Y t -

axis) because onlytwo bonylandmarks can be

discerned at the clavicle.

For the clavicle onlytwo bonylandmarks can be

discerned: SC and AC. Hence, the axial rotation of the

clavicle cannot be determined through non-invasive

palpation measurements, but can be estimated on the

basis of optimization techniques ( Van der Helm and

Pronk, 1995 ). In contrast to Van der Helm (1996) , the

use of the landmark AA is now proposed instead of the

acromioclavicular joint (AC joint). This choice will

Fig. 2. Thorax coordinate system and deﬁnition of motions.

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G. Wu et al. / Journal of Biomechanics 38 (2005) 981–992

Fig. 3. Clavicule coordinate system and deﬁnition of SC motions. Y t is

the local axis for the thorax coordinate system, which is initially

aligned with Y c of the clavicle.

Fig. 5. Humerus coordinate system and deﬁnition of GH motions. Y s

is the local axis for the scapula coordinate system.

2.3.5. Humerus (2nd option) coordinate system—

X h2 Y h2 Z h2

Fig. 4. Scapula coordinate system and deﬁnition of AC motions. Y c is

the local axis for the clavicle coordinate system (Please note, the origin,

shown here at AC, should be placed at AA).

O h2 : The origin coincident with GH.

Y h2 : The line connecting GH and the midpoint of

EL and EM, pointing to GH.

Z h2 : The line perpendicular to the plane formed by

Y h2 and Y f (see Section 2.3.6), pointing to the

right.

X h2 : The common line perpendicular to the Z h2 -and

Y h2 -axis, pointing forward.

Y c : The common line perpendicular to the X c - and

Z c -axis, pointing upward.

Note 1: The second deﬁnition of humerus coordinate

system is motivated by the high error sensitivity of the

direction connecting EL and EM due to the short

distance between them. Since it cannot be assured that

the Z h2 -axis is equal to the joint rotation axis, its

orientation depends on the position of the upper arm

and forearm as well as the forearm orientation ( Wang,

1996 ). Therefore, bydeﬁnition, the Z h2 -axis is taken

with the elbow ﬂexed 90 in the sagittal plane and the

forearm fullypronated.

Note 2: We are faced with two difﬁculties in deﬁning

Z h : (1) the anatomical deﬁnition of neutral humeral

internal/external rotation is unclear; and (2) the

numerical and practical inaccuracies in deﬁning EL

and EM mayswamp the accuracyof our deﬁnition. The

1st and 2nd deﬁnitions will not agree if the true EM–EL

line is rotated with respect to the forearm axis (in

pronation). For the humerus, the difference will only

affect the value for internal/external rotation; for the

forearm it will affect all three angles to some degree,

most signiﬁcantlypro/supination. Our recommendation

is to use option 2 when the forearm is available for

recording and otherwise to use option 1.

2.3.3. Scapula coordinate system—X s Y s Z s (see Figs. 1

and 4 )

O s : The origin coincident with AA.

Z s : The line connecting TS and AA, pointing to

AA.

X s : The line perpendicular to the plane formed by

AI, AA, and TS, pointing forward. Note that

because of the use of AA instead of AC, this

plane is not the same as the visual plane of the

scapula bone.

Y s : The common line perpendicular to the X s - and

Z s -axis, pointing upward.

2.3.4. Humerus (1st option) coordinate system—

X h1 Y h1 Z h1 (see 1 and 5; see also notes 1 and 2)

O h1 : The origin coincident with GH.

Y h1 : The line connecting GH and the midpoint of

EL and EM, pointing to GH.

X h1 : The line perpendicular to the plane formed by

EL, EM, and GH, pointing forward.

Z h1 : The common line perpendicular to the Y h1 - and

Z h1 -axis, pointing to the right.

2.3.6. Forearm coordinate system—X f Y f Z f (see Figs. 1

and 6 )

O f : The origin coincident with US.

Y f : The line connecting US and the midpoint

between EL and EM, pointing proximally.

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X f : The line perpendicular to the plane through US,

RS, and the midpoint between EL and EM,

pointing forward.

Z f : The common line perpendicular to the X f and

Y f -axis, pointing to the right.

e1: The axis coincident with the Z g -axis of the

global coordinate system.

Rotation (a GT ): ﬂexion (negative) or extension

(positive).

e3: The axis ﬁxed to the thorax and coincident with

the Y t -axis of the thorax coordinate system.

Rotation (g GT ): axial rotation to the left

(positive) or to the right (negative).

e2: The common axis perpendicular to e1ande3,

i.e., the rotated X t -axis of the thorax.

Rotation (b GT ): lateral ﬂexion rotation of the

thorax, to the right is positive, to the left is

negative.

2.4. JCS and motion for the shoulder complex

In the shoulder, it can be useful to report two types of

rotations. One is joint rotation, i.e., rotation of a

segment with respect to the proximal segment including

the clavicle relative to the thorax (SC joint), the scapula

relative to the clavicle (AC joint), and the humerus

relative to the scapula (GH joint). The other is segment

rotation, i.e., rotation of the clavicle, scapula, or humerus

relative to the thorax (the non-existent thoracohumeral

joint, often looselydeﬁned as the shoulder joint). The

deﬁnition of joint displacements is onlyuseful if it is

deﬁned with respect to the proximal segment.

Manyrotation orders are possible (such as X–Y–Z in

Cardan angles or Y–Z–Y in Euler angles). We have

chosen rotation orders so that the angles remain as close

as possible to the clinical deﬁnitions of joint and

segment motions. Differences are unavoidable since

these clinical deﬁnitions are not consistent in 3-D. For

example, although ﬂexion and abduction each is clearly

deﬁned in 2-D, ﬂexion followed byabduction gives a

different result than abduction followed byﬂexion (see

Anglin and Wyss, 2000 , Section 8.1).

In the following deﬁnitions, a is around the Z-axis, b

around the X-axis, and g around the Y-axis, irrespective

of the order of rotation.

2.4.2. JCS and motion for the SC joint (clavicle relative

to the thorax, Y–X–Z order, Fig. 3

Displacement (q): corresponds to translations of the

common rotation center of the SC joint with respect to

the thorax coordinate system.

e1: The axis ﬁxed to the thorax and coincident with

the Y t -axis of the thorax coordinate system.

Rotation (g SC ): retraction (negative) or protrac-

tion (positive).

e3: The axis ﬁxed to the clavicle and coincident

with the Z c -axis of the clavicle coordinate

system.

Rotation (a SC ): axial rotation of the clavicle;

rotation of the top backwards is positive,

forwards is negative.

e2: The common axis perpendicular to e1 and e3,

the rotated X c -axis.

Rotation (b SC ): elevation (negative) or depres-

sion (positive).

2.4.1. JCS and motions of the thorax relative to the

global coordinate system (Z–X–Y order, Fig. 2

Displacement (q): corresponds to motions of IJ with

respect to the global coordinate system ðX g –Y g –Z g

deﬁned by Wu and Cavanagh (1995) ).

2.4.3. JCS and motion for the AC joint (scapula relative

to the clavicle, Y–X–Z order, Fig. 4

Displacement (q): corresponds to translations of the

common rotation center of the AC joint with respect to

the clavicle coordinate system.

Note: The following sequence is supported by

Karduna et al. (2000) , who studied the six possible

Euler sequences for scapular motion. Theyfound that

the proposed sequence is ‘‘consistent with both research-

and clinical-based 2-D representations of scapular

motion’’. Theyalso found that changing the sequence

resulted in ‘‘signiﬁcant alterations in the description of

motion, with differences up to 50 noted for some

angles’’. Since the scapular coordinate system is initially

aligned with the clavicular coordinate system even

though this position is never assumed anatomically,

typical angle values are offset from zero (either positive

or negative).

Fig. 6. Deﬁnition of forearm coordinate system.

e1: The axis ﬁxed to the clavicle and coincident with

the Y c -axis of the clavicle coordinate system.

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