Joint and segment definition and joint rotation order

The ISB proposed standards for defining joint coordinate systems of the upper limb are presented in Wu et al. (2005). These are the primary reference for the 3D upper limb model used in this research. Wu et al. (2005) established the bony landmarks used to define each segment and joint of the upper limb, their local coordinate systems (LCS) and a

standard method of reporting joint and segment motion. Anatomical frames for both the proximal and distal segment forming the joint were used to define each joint coordinate system in addition to the joint

rotation/decomposition order as recommended by the ISB (Kontaxis et al., 2009).

2.4.1.1 Humeral coordinate system definition

The humerus was defined by three points: the medial humeral epicondyle (EM), lateral humeral epicondyle (LM) and the GH joint rotation centre. Technically the GH joint rotation centre is not a bony landmark but it is required to define the longitudinal axis of the humerus. The ISB

recommended its estimation via linear regression (Meskers et al., 1998a) or by calculating the pivot point of instantaneous helical axes of GH

motions (Stokdijk et al., 2000). For this research, Meskers’ approach was chosen. This method estimated the GH joint rotation centre from the relationship between scapula geometry parameters, calculated by a linear regression method. It was demonstrated by Meskers et al., (1998a) that a close relationship exists between the shape of the scapula and the factors that determine the position of the GH joint rotation centre i.e. the

orientation of the glenoid and size of the humeral head. The 3D positions of five scapular bony landmarks were defined by LED markers. These landmarks were: the most dorsal point of the acromioclavicular joint; trigoneum spinae; angulus inferior; angulus acromialis and processus coracoideus. In its original paper this method resulted in a root mean square error (RMSE) of 2.32mm for the x-coordinate, 2.69mm for the y- coordinate and 3.04 for the z-coordinate (Meskers et al., 1998a). These errors were about 15% and 20% of intra and inter-subject variability.

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While acknowledging its limitations, it was the most appropriate method due to the potential for reduced active ROM available in the OBPP group which would lead to inaccurate estimation using the instantaneous helical axes method.

Due to the relatively short distance between the EM and EL the effect of measurement errors, in particular on humeral AR (Zh axis), can be problematic (Veeger et al., 2003). Two options for defining the humeral coordinate system are recommended by the ISB (Wu et al., 2005). Option one uses the plane formed by EL, EM, and GH joint rotation centre

pointing forward to estimate the Zh local coordinate axis. Option two uses the plane formed by the upper arm and the forearm (elbow flexed to 90⁰, forearm pronated) to estimate the same axis. The ISB recommended option two when the forearm was available for recording. As the forearm was recorded option two was used in this research. The position of the elbow as described above is critical to the accurate definition of the humeral coordinate system. When the elbow is flexed to 90⁰ with full pronation, a more accurate calculation of the humeral coordinate system is possible. However, when the elbow is close to full extension its

calculation becomes unreliable due to kinematic singularity i.e. the longitudinal axes of the humerus and the forearm are in near alignment (Schmidt et al., 1999). To account for this the static calibration was taken with the elbow in the required position, start and end positions for all tasks were with the hand resting palm down on ipsilateral knee with hips and knees at 90 to ensure a resting posture of elbow 90⁰ flexion and full pronation. With the exception of the Abduction Task, all tasks demanded increased degrees of elbow flexion rather than extension thereby avoiding this position as much as possible. For the Abduction Task this limitation of the model was considered when interpreting data.

2.4.1.2 Rotation order for joint angle definition

Rotation orders for each joint and segment were chosen to ensure angles produced were as close as possible to clinical definitions of joint and segment motions. While acknowledging the importance of clinical

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interpretation in defining motion, differences as a consequence of mathematical calculations were unavoidable. Use of the ISB

recommended sequence for GH joint motion has been shown to result in a gimbal lock effect especially at 0⁰ and 180⁰ humeral elevation in flexion and abduction (Šenk and Chèze, 2006). Gimbal lock is a mathematical in- determination of angle values dependent on sin B close to zero. As the joints approach 0⁰ or 180⁰ (Euler) or 90⁰ or -90⁰ (Cardan) there is an interruption of the resultant curve that does not correspond with clinical expectation e.g. curve jumps from positive 170⁰ to -170⁰.

Several articles have explored alternative rotation sequences to reduce the incidence of gimbal lock while retaining clinical relevance of the resultant angles. Šenk and Chèze (2006) examined the clinical

interpretation of the proposed ISB rotation sequence for GH joint (YXY). They found that the YXY sequence was convenient as long as movements did not go through a singular position (arm beside thorax) nor reach

maximal ROM. This sequence is of particular interest when the movement is performed outside the anatomical plane, seen in all functional

movements of daily living. Two rotation sequences, Euler (YXY)/Cardan (XZY), used to describe GH joint motion during abduction in scapular plane were compared by Phadke et al. (2011). They compared plane of elevation (POE) as described by first rotation axis in YXY and second in XZY; angle of elevation as in second rotation axis in YXY and first in XZY; AR as described by the third axis in both sequences. They found

significant differences between the two sequences when describing positions of humeral POE, the magnitude of which was reduced at higher levels of humeral elevation. In the YXY sequence the humerus was significantly more anterior to plane of scapula, elevation angle was higher and the humerus was consistently more externally rotated. Two of their findings were that the YXY sequence was challenging to clinicians as the terminology was not common to clinical practice. The XZY sequence was better able to capture AR with arm by side of thorax in a more clinically meaningful manner. They concluded that there was no ideal way to capture GH motions through all ROM and planes. Alternative Euler

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decompositions of XZY when elevating the arm in the sagittal plane or ZXY when elevating in the scapular plane were recommended by Kontaxis et al. (2009). However, as the tasks analysed in this study were

functional, not planar specific and no single rotation sequence has been identified to fulfil all requirements, the ISB recommendations were used to enable comparison of results with previous research.