Kinematic and Kinetic Data Reduction

The 3-D coordinates of the reflective markers were reconstructed with Nexus software. The virtual 3-D coordinates of the joint centers were estimated with the same software based on the positions of markers and the measured anthropometric parameters using a human body model (PlugInGait, Vicon, Centennial, CO). The 3-D coordinates of markers and virtual joint centers were exported by the software. A custom program written in Matlab (Mathworks, Natick, MA) was used for the following post-processing procedures.

3.5.1.1 Humeral and scapular kinematics

All the 3-D coordinates were filtered. The virtual 3-D coordinates of the removed scapular reference markers over the scapular anatomical landmarks (i.e. the acromion angle, the root of the spine of scapula, and the inferior angle) were calculated. With the captured static motion, a local coordinate system (LCS) was established with the three-marker triad. Then, the positions of the scapular reference markers in the static trial were converted from the global coordinate system (GCS) into the scapula LCS. The spatial relationships between the triad and the scapular anatomical landmarks were assumed to be constant during testing. The virtual 3-D coordinates of the scapular reference markers were therefore reconstructed back from the scapular LCS established with the 3-D coordinates of the scapular triad during the dynamic trials of pace- controlled scaption and maximum effort baseball throwing.

Kinematics of the humerus and scapula were calculated following the International Society of Biomechanics (ISB) recommendations.109 First, LCSs were created for the thorax, humerus, and scapula for each time frame during the dynamic trials (Figure 9). The following four markers were utilized to define the thorax LCS: the spinous processes of the 7th cervical vertebra (C7) and the 8th thoracic vertebra (T8), the jugular notch (IJ), and the xiphoid process (PX). The Y axis was defined as the line connecting the midpoint between T8 and PX with the midpoint between IJ and C7, pointing upward. The Z axis was defined as the line perpendicular to the plane formed by IJ, C7, and the midpoint between PX and T8, pointing to the right. The X axis was defined as the common line perpendicular to the Z and Y axes, pointing forward.

The virtual position of the glenohumeral joint center (GH), the lateral epicondyle of the humerus (EL), and the medial epicondyle of the humerus (EM) were utilized to define the humerus LCS. The Y axis was defined as the line connecting GH and the midpoint of EL and

EM, pointing to GH. The X axis was defined as the line perpendicular to the plane formed by EL, EM, and GH, pointing forward. The Z axis was defined as the common line perpendicular to the Y and X axes, pointing to the right.

The virtual positions of the acromial angle (AA), the root of the spine of the scapula (TS), and the inferior angle (AI) were utilized to define the scapula LCS. The Z axis was defined as the line connecting TS and AA, pointing to AA. The X axis was defined as the line perpendicular to the plane formed by AI, AA, and TS, pointing forward. The Y axis was defined as the common line perpendicular to the X and Z axes, pointing upward.

Figure 9. The local coordinate systems of the thorax, humerus, and scapula

The humeral angular kinematics was defined as the humerus LCS with respect to the thorax LCS. The decomposition sequence was Y-X’-Y’’ and the three decomposed orientation

elements were plane of humeral elevation, humeral elevation, and humeral external/internal rotation. The scapular angular kinematics was defined as the scapula LCS with respect to the thorax LCS. The decomposition sequence was Y-X’-Z’’ and the three decomposed orientation elements were scapular protraction/retraction, medial/lateral rotation, and anterior/posterior tilt. The signs of scapular kinematics values were defined as such: protraction (+), retraction (-); medial rotation (+), lateral rotation (-); anterior tilt (-), posterior tilt (+). In several previous studies, terms used for scapular kinematics were different to the ISB recommendations: protraction/retraction was called internal/external rotation, and medial/lateral rotation was called downward/upward rotation.35,49,162

3.5.1.2 Shoulder kinetics during baseball throwing

The shoulder kinetic data of the throwing shoulder were calculated using inverse dynamics, following the algorithm presented by Feltner and Dapena.99 The calculations required the joint center trajectories of the wrist, elbow, and shoulder of the throwing arm. Kinetic calculations began with determination of the linear acceleration of the joint centers utilizing a 5-point central differentiation equation. Next, for the arm and forearm of each subject, the segment mass and the center of mass coordinates were calculated based on the subject’s body height and weight using the regression equations presented by Zatsiorsky.237 These regression equations for inertial properties were chosen for two reasons: they were created with accurate Gamma-scanning method in vivo and the data were based on young and physically active subjects. With the information of segment mass, acceleration, and center of mass, forces applied at the shoulder during throwing were estimated inversely with force equilibrium equations, following the calculation of wrist and elbow forces. The calculated shoulder forces were initially represented in the X, Y, and Z axes of the GCS and then transformed into the humeral LCS for anatomical

relevance. The shoulder forces mapped onto the humeral LCS have three components: anterior/posterior, superior/inferior, and longitudinal (compression/distraction).99

3.5.1.3 Identification of events during baseball throwing

In the current study, multiple variables were correlated to scapular kinematics at SFC, and the occurrence of maximum shoulder anterior, posterior, superior, inferior, and compression forces. The event of SFC was defined as the point in time when both the linear velocity of the subtalar joint marker and the 3rd metatarsophalangeal marker decreased to below 0.7 m/s, determined with a pilot study involving ground reaction force measurements. Maximum forces were located before or after certain critical events. Maximum shoulder anterior and superior forces were located near MER; maximum shoulder compression force was located near REL, and maximum posterior and inferior forces were located near MIR. The event of MER and MIR were defined as the humerus reaching the maximum external and internal rotation angle, respectively. The event of REL was defined as one frame after the wrist joint center reaching a more anterior position than the elbow joint center.