1. A Tutorial on the Measurement of Joint Motion
with Application to the Shoulder

2. 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
Meeting one part of this challenge is relatively easy. Meeting both parts is considerably more difficult. In this presentation, I will discuss several approaches to upper extremity measurements. In order to facilitate discussion of these approaches, I’ve organized the presentation in the following manner:

3. Motion of the Shoulder Scapula/clavicle relative to the trunk
Humerus relative to the scapula
Humerus relative to the trunk
I will focus primarily on the motion of the shoulder and, specifically, on the motion of the humerus or arm with respect to the trunk, as this represents the most challenging scenario.

4. 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
In order to measure segment motion, we must first define a marker set that allows us to identify each segment’s anatomical axes, and to know the orientation of these axes relative to the room and to other parts of the body. Over the years as technology has enabled us to track smaller and smaller markers, our options for placing markers on the upper extremities have improved. In 1988, we were using sparse marker sets to measure arm motion during throwing. The sparse sets were used because 1) the markers that could be tracked at high sample rates were quite large, and placement of too many markers restricted motion, 2) because of the large marker size, the spacing between markers had to be substantial, which made it difficult to place multiple markers on the wrist or hand. The current state of camera and reflective material technology enables us to use much smaller markers (~ 5mm), which means that additional markers can be added to facilitate the identification of joint centers and anatomical axes. Consequently, this is reflected in the marker sets proposed by the International Shoulder Group.

5. Considerations for Marker Placement
When applying markers to the upper extremities, we have to pay additional attention to the motion of soft tissue, especially as the speed of movement increases. As you can see, the placement of markers on the upper arm anywhere between the shoulder and the elbow will provide results that contain substantial movement artifact. If the goal of placing markers is to estimate the position of the underlying skeletal structures, then we have to be very careful where markers on the upper arm are placed. Consequently, using marker sets similar to those used on the lower extremities will not yield very appealing results.

6. 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
The marker set recommended by the ISG is substantially populated and attempts to enable the estimation of trunk, scapula, clavicle, and humerus motion. On the dorsal side of the body, the marker set consists of:

7. 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

8. ISG Recommended Marker Locations
Humerus Markers
Glenohumeral center of rotation
Medial and lateral epicondyles
Wrist & Hand
Radial Styloid
Ulnar Styloid
2nd Metacarpal Head

9. 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
Marker translation technique from Meskers et al and Rab et al

10. 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
The marker sets recommended by the ISG allow for the creation of trunk, scapula, clavical, and humeral coordinate systems. In the trunk, the vertical Y vector is the primary vector. It originates at the midpoint of the markers located at the Xiphoid process on the ventral side and at T8 on the dorsal side, and is directed toward the midpoint of the markers located at C7 and the suprasternal notch. The X vector is formed by crossing Y onto the vector formed by the Xiphoid process (origin) and T8. The Z axis is formed by crossing X onto Y.

11. 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

12. 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

13. 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)
Z-vector from Ulnar to Radial Styloid vector crossed onto Y-vector

14. 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

15. Modifications to ISG Marker Locations
Remove the following markers from the Dorsal side:
Angulus Acromialis
Trigonum Spinae Scapulae
Inferior Angle of Scapula
Some of you may be wondering about the logic of putting 5 markers on the scapula since the scapula is known to move relatively independent of the skin surface. The ISG recommendation for 5 scapular markers is fairly ambitious, and should work well when static measures are of interest since most landmarks can be identified through palpation. However, the placement of 5 markers will likely be ineffective especially for motions that involve substantial scapular displacements. Consequently, we eliminate 4 of the 5 scapular markers in our upper extremity analyses of movements such as walking or throwing.

16. Modifications to ISG Marker Locations
Remove the following markers from the ventral side:
Sternoclavicular joint
Ventral point of Coracoid Process

17. 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
Elimination of 4 of the scapular markers requires a different strategy for creation of the ‘scapular’ or in this case, the shoulder coordinate system. Using the remaining scapular marker, the primary shoulder vector is the X vector, which originates at the midpoint between C7 and the suprasternal notch and extends to the marker on the Acromion Process. The X vector is then crossed onto the trunk’s Y vector to create the shoulder’s Z vector. Y is then created by crossing Z onto X.

18. 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
Once the segment coordinate systems have been established, the next step is to calculate the orientation of the distal segments relative to the proximal segments. In our case, we’re calculating the orientation of the upper arm relative to the trunk.
We are going to take a closer look at the first 3 of these approaches as they relate to shoulder motion. First, for those of you who don’t get to work with methods of measuring orientations on a daily basis, I’ll review the basic concepts behind each approach. Then, we’ll examine how each approach reports arm orientation during a series of fundamental shoulder motions. Finally, we’ll make recommendations based on the results.

19. Representative Coordinate Systems
Before reviewing the methods, I’d like to establish the nomenclature that I’ll be using to describe the segment coordinate systems. The trunk’s coordinate system is described by the vectors with the hats at the end, and the arm’s coordinate system is described by the vectors with the cubes on the end. The orientation of the coordinate systems are in accordance to the ISG recommendations, and the X,Y, and Z axes correspond to the colors R, G, and B respectively.
R = X
G = Y
B = Z

20. Review of Cross-Products
Review of Analysis Methods
Review of Cross-Products
Second, I’d like to make sure that everyone understands the concept of a crossproduct, since they are require in order to implement some of the approaches. When one vector is ‘crossed’ onto another, it creates a third vector that is at right angles (orthogonal) to each of the vectors from which it was created. Its direction is dictated by the direction of the cross and it follows the right hand rule. Specifically, if you use the palm of your right hand to push one of the vectors toward the other (with the vector pointing toward your fingertips), the orientation of the resultant crossproduct will match that of your extended thumb.

21. Grood and Suntay Approach
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

22. 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

23. Yarm crossed onto Ytrunk results in an orthogonal Intermediate Vector
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

24. Intermediate Vector with Respect to the Trunk’s Coordinate System
Review of Analysis Methods : Grood & Suntay
Intermediate Vector with Respect to the Trunk’s Coordinate System
The intermediate vector indicates the amount of horizontal flexion/extension when viewed in the trunk’s coordinate system.

25. Intermediate Vector with Respect to the Arm’s Coordinate System
Review of Analysis Methods : Grood & Suntay
Intermediate Vector with Respect to the Arm’s Coordinate System
The intermediate vector indicates the amount of internal and external rotation when viewed in the arm’s coordinate system.

26. Other Combinations of Vectors
Review of Analysis Methods : Grood & Suntay
Other Combinations of Vectors
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.

27. Review of Analysis Methods
Euler Angles
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

28. 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
The six ordered sequences on the left produce angles that are sometimes referred to as Cardan angles, and the six on the right produce angles that are referred to as Euler angles. In the case of the legs, the Euler angles are actually Cardan angles, although many engineers and mathematicians refer to all twelve sequences as Euler rotations. The YZY approach (in red) is the order recommended by the ISG. The orders highlighted in green represent the other possible orders that could be used to describe shoulder motion.

29. Calculation of 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)

30. Y-Z-Y Euler Rotation Sequence
Review of Analysis Methods: Euler Rotations
Y-Z-Y Euler Rotation Sequence
1) Rotate the intermediate coordinate system about the arm’s Y-axis (angle = int/ext rotation
2) Rotate the intermediate coordinate system about the intermediate Z-axis (angle = ab/adduction)
3) Rotate the intermediate coordinate system about the trunk’s Y axis (angle = horiz flex/ext

31. YZY Euler Sequence (ISG Recommendation)

32. ZXY Euler Sequence (Adduction/Abduction Priority)

33. XZY Euler Sequence (Flexion/Extension Priority)

34. Angles from Helical Axis Decomposition
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

35. Angles from Helical Axis Decomposition
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

36. Alternative Approaches to Measuring Shoulder Orientation
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

37. 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

38. 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)

39. 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

40. 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

41. Shoulder Orientation Measured during Walking
Review screen layout before analyzing motion.

42. Shoulder Orientation Measured during Abduction/Adduction

43. Shoulder Orientation Measured during Flexion/Extension

44. Shoulder Orientation Measured during Int/Ext Rotation(Adducted)

45. Shoulder Orientation Measured during Int/Ext Rotation(Abducted)

46. Shoulder Orientation Measured during Horizontal Flex/Ext

47. Shoulder Orientation Measured during Codman’s Motion

48. Shoulder Orientation Measured during Circumduction

49. Shoulder Orientation Measured during Overhand Throw

50. Summary of Analysis MethodsX
Walk
Throw X-
Codman
Circumduction
IE Adducted
IE Abducted
H. Flexion
Flexion
Abduction
Helical
XZY (F/E)
ZXY (Ab/Ad)
YZY (ISG)

51. Using Instantaneous Approaches
Instantaneous Helical or Euler angles
Both provide excellent sense of motion
Both require an initialization point
Neither provide accurate orientation angles

52. Other Approaches to Getting Better Results
Change the arm’s reference position to what would normally be considered 90 degrees of abduction
Cut out sections of the curve where discontinuities in motion occur, and then interpolate for the missing data
Splice results from different rotation sequences together depending on the arm’s location relative to the trunk

53. Final Recommendations for Measurement of the Shoulder
View the results using each of the measurement approaches, giving greater weight to the approach that best measures the dominant arm motion
Select the approach that makes the most sense clinically
Report the method used

54. Acknowledgements
Scott Coleman, for his help with the graphics and animations
John Henley, for his willingness to serve as a sounding board for numerous unusual measurement strategies
Dave Hudson, for letting me use pictures of him shot in profile

55. The End