The ISB model for the Upper Extremity DirkJan Veeger Carolien van Andel Jaap Harlaar ESMAC Seminar “Movement Analysis of the Upper Extremity”

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 points on the plane to quantitatively describe what it does.

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 YgYg XgXg ZgZg

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

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

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

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

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

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      

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

c  0s  010 -s  0c   c  -s  0 s  c    100 0c  -s  0s  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. )   

Decomposition of the joint orientation matrix (following Capozzo, 2005) Given: 1.Initially, both proximal an distal systems are thought to be coincident: R=I 2.If a rotation occurs about an axis of the proximal frame, pre- multiply the previous orientation matrix: for z p rotation: R  *I; 3.If a rotation occurs around an axis of the distal frame, the previous orientation matrix should be post-multiplied: for an x d rotation: (R  *I)*R  4.If the third rotation is again around an axis of the distal frame, after post-multiplication the matrix becomes: [(R  *I)*R  ]*R  1.Under assumption1. this is equal to R  *R  *R  2.This results in:

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! [30,120,45] 180  00 90  180  90  30  60  30  60  120  150  120  150  North Pole South Pole 45 

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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

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: issues y-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