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A Tutorial on the Measurement of Joint Motion with Application to the Shoulder. The Challenge. The challenge associated with measuring upper extremity motion is to provide clinicians with: anatomically meaningful descriptions of position, and a clinically relevant sense of motion.
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A Tutorial on the Measurement of Joint Motion with Application to the Shoulder
The Challenge The challenge associated with measuring upper extremity motion is to provide clinicians with: • anatomically meaningful descriptions of position, and • a clinically relevant sense of motion
Scapula/clavicle relative to the trunk • Humerus relative to the scapula • Humerus relative to the trunk Motion of the Shoulder
Marker Set Options • Marker set similar to those used on lower extremities • Sparse marker sets (1 shoulder, 1 elbow, 1 or 2 wrist markers, 1 hand marker) • More robust marker sets such as the one recommended by the International Shoulder Group
ISG Recommended Marker Locations Trunk Markers (Dorsal Side) • C7 • T8 Scapula Markers (Dorsal Side) • Acromioclavicular joint • Angulus Acromialis • Trigonum Spinae Scapulae • Inferior Angle of Scapula Humerus Markers • Glenohumeral center of rotation • Medial and lateral epicondyles
ISG Recommended Marker Locations Trunk (Ventral Side) • Suprasternal Notch • Xiphoid Process Scapula Markers (Ventral Side) • Ventral point of Coracoid • Process Clavicle Markers • Acromioclavicular joint • Sternoclavicular joint
ISG Recommended Marker Locations Humerus Markers • Glenohumeral center of rotation • Medial and lateral epicondyles Wrist & Hand • Radial Styloid • Ulnar Styloid • 2nd Metacarpal Head
Determination of Glenohumeral Center of Rotation Translation from Acromioclavicular marker • Determine shoulder coordinate system • Translate AC marker a fixed distance along the shoulder’s Y-axis Spherical (or Helical) fitting • Measure motion of the elbow joint center (or epicondyle marker) relative to the shoulder coordinate system using the AC marker as the point of origin • Sphere centroid relative to AC marker in the shoulder coordinate system approximates glenohumeral center of rotation
ISG Recommended Coordinate Systems Trunk • Y-vector from midpoint of T8-Xiphoid to midpoint of C7-Suprasternal Notch • X-vector from Y crossed onto vector from Xiphoid to T8 • Z-vector from X crossed onto Y
ISG Recommended Coordinate Systems Scapula • X-vector follows Scapular Spine • Vector from Scapular Spine marker to Inferior Angle marker crossed onto the X-vector creates the Z-vector • Y-vector from Z crossed onto X-vector
ISG Recommended Coordinate Systems Upper Arm • Y-vector from midpoint of medial and lateral epicondyles to the center of rotation of the Glenohumeral head • Z-vector from medial to lateral epicondyle vector crossed onto Y-vector • X-vector from Y-vector crossed onto Z-vector
Distal Arm Segment Coordinate Systems Forearm (Proximal) • Y-vector from wrist center to elbow center • Z-vector from upper arm X-vector crossed onto forearm Y-vector • X-vector from Y-vector crossed onto Z-vector Forearm (Distal) • Y-vector from wrist center to elbow center • Z-vector from Ulnar to Radial Styloid vector crossed onto Y-vector • X-vector from Y-vector crossed onto Z-vector
Distal Arm Segment Coordinate Systems Hand • Y-vector from hand marker (2nd met head) to wrist center • Z-vector from Ulnar to Radial Styloid vector crossed onto Y-vector • X-vector from Y-vector crossed onto Z-vector
Modifications to ISG Marker Locations Remove the following markers from the Dorsal side: • Angulus Acromialis • Trigonum Spinae Scapulae • Inferior Angle of Scapula
Modifications to ISG Marker Locations Remove the following markers from the ventral side: • Sternoclavicular joint • Ventral point of Coracoid Process
Modification to ISG Coordinate Systems Scapula (Shoulder) • X-vector from midpoint of C7 and Suprasternal Notch to the Acromion Process marker • Z-vector from shoulder X-vector crossed onto trunk Y-vector • Y-vector from shoulder Z-vector crossed onto shoulder X-vector
Methods of Measuring Arm Orientation Relative to the Trunk or Shoulder • Joint Coordinate Angles (Grood & Suntay) • Euler or Cardan Angles • Helical Axis Decomposition (described by Woltring) • Instantaneous Helical and Euler Angles • Rotation Matrices • Quaternions, Angle-axis, Rodriguez vectors
Representative Coordinate Systems R=X G=Y B=Z
Review of Analysis Methods Review of Cross-Products
Review of Analysis Methods Grood and Suntay Approach • Select 1 vector from the trunk • Select 1 vector from the upper arm • The angle formed by the two vectors represents one of the anatomical angles • Cross the vector from the trunk onto the vector from the upper arm • The resulting intermediate vector provides remaining orientation information depending on the segment to which it is referenced
Review of Analysis Methods: Grood & Suntay The angle between Yarm and Ytrunk represents the amount of shoulder abduction • Select 1 vector from the trunk • Select 1 vector from the upper arm • The angle formed by the two vectors represents one of the anatomical angles
Review of Analysis Methods : Grood & Suntay Yarm crossed onto Ytrunk results in an orthogonal Intermediate Vector Cross the vertical vector from the trunk onto the vector representing the long axis of the upper arm to create the intermediate vector
Review of Analysis Methods : Grood & Suntay The intermediate vector indicates the amount of horizontal flexion/extension when viewed in the trunk’s coordinate system. Intermediate Vector with Respect to the Trunk’s Coordinate System
Review of Analysis Methods : Grood & Suntay The intermediate vector indicates the amount of internal and external rotation when viewed in the arm’s coordinate system. Intermediate Vector with Respect to the Arm’s Coordinate System
Review of Analysis Methods : Grood & Suntay Other combinations of vectors can be used to determine angles using Grood and Suntay’s method. For example, we could use the trunk’s Z vector and the arm’s Y vector to calculate shoulder angles as well. Each combination of vectors will give you different results for one or more of the joint angles. Other Combinations of Vectors
A second approach to describing joint orientation involves the use of Euler angles. Euler angles are easily interpreted but are prone to discontinuities at 90 degree and 180 degree crossings, depending on the rotation order that is being used. For the legs, the order of rotation is: 1) Flexion/Extension, 2) Ab/Adduction, and 3) Int/Ext Rotation Review of Analysis Methods Euler Angles
There are 12 different rotation sequences that can be used in this approach. They are: XYZ XZY XYX XZX YXZ YZX YXY YZY ZXY ZYX ZXZ ZYZ Review of Analysis Methods Euler Angles
Review of Analysis Methods Calculation of Euler Angles • Use YZY order of rotation as recommended by the International Shoulder Group • Start with an intermediate coordinate system aligned with the trunk coordinate system • Rotate the intermediate coordinate system about the trunk’s Y axis (angle = horiz flex/ext) • Rotate the intermediate coordinate system about its own Z axis (angle = ab/adduction) • Rotate the intermediate coordinate system about the arm’s Y-axis (angle = int/ext rotation)
Review of Analysis Methods: Euler Rotations 2) Rotate the intermediate coordinate system about the intermediate Z-axis (angle = ab/adduction) 1) Rotate the intermediate coordinate system about the arm’s Y-axis (angle = int/ext rotation Y-Z-Y Euler Rotation Sequence 3) Rotate the intermediate coordinate system about the trunk’s Y axis (angle = horiz flex/ext
Review of Analysis Methods Angles from Helical Axis Decomposition • Find the axis about which the trunk coordinate system can be rotated to match the orientation of the arm coordinate system • Unitize the axis, and multiply it by the magnitude of rotation • Resolve the resulting vector into the appropriate coordinate system
Review of Analysis Methods: Helical Axis Decomposition Angles from Helical Axis Decomposition Find the axis about which the trunk coordinate system can be rotated to match the orientation of the arm coordinate system
Review of Analysis Methods Alternative Approaches to Measuring Shoulder Orientation Quaternions, Angle-Axis representation, and Rodriguez vectors • All in the family of helical axis • Do not relate directly to anatomical conventions • Can be converted into Euler angles Rotation Matrices • Used in all other methods of calculating joint angles • By themselves, cannot be interpreted into meaningful anatomical angles
Alternative Approaches to Measuring Shoulder Orientation Instantaneous Helical and Euler Angles • Determine starting orientation of limb segment • Calculate joint angle change between frames • Integrate results Advantages • Provides excellent sense of motion Drawbacks • Resultant orientations aren’t exact • Need accurate reference orientation
Angle Measures at the Elbow • Segments on either side of the elbow share a common flexion/extension axis • No measure of internal/external rotation • Euler approach using same rotation order as the legs will work fine (F/E, Ab/Add)
Angle Measures at the Wrist • Segments on either side of the wrist share a common flexion/extension axis • No measure of internal/external rotation • Euler approach using same rotation order as the legs will work fine (F/E, Ab/Add) • Calculating the angle between the proximal and distal forearm coordinate systems provides the pronation/supination angle
Application of Methods at the Shoulder Given: • Clearly defined marker sets • Well defined segment coordinate systems • Several methods of measuring orientations We could easily believe that: Describing orientation of the upper arm relative to the scapula or trunk should pose a simple problem
Shoulder Orientation Measured during Int/Ext Rotation(Adducted)
Shoulder Orientation Measured during Int/Ext Rotation(Abducted)
YZY (ISG) ZXY (Ab/Ad) XZY (F/E) Helical Abduction X- X Flexion X X H. Flexion X IE Abducted X X IE Adducted X X X Circumduction X Codman X- Throw X Walk X X X Summary of Analysis Methods