Fig 1.
The degrees of freedom (DoF), and the anatomical segments of the Rugby Model.
Body segments were divided into lower limbs (femur, tibia, talus, calcaneus and toe), pelvis, trunk, seven cervical spine vertebrae (C1-C7), scapula, clavicle, upper limbs (humerus, radius, ulna, hand) and head (skull and jaw). The 23 actuators of the model were associated to shoulder, elbow, spine, hip, knee, and ankle degrees of freedom.
Fig 2.
The SCJ’s reference systems on scapula (acromionclavicular) and clavicle (sternoclavicular) joints and their coupling functions driven by humeral elevation.
The sternoclavicular joint origin on the sternal extremity of the clavicle and its reference system were designed to allow depression/elevation rotation about the x-axis, protraction/retraction rotations about the y-axis, and axial rotation about the z-axis. The motion of this joint is driven by the humeral elevation via 3 coordinate-coupler constraints based on spline functions. The acromionclavicular joint was designed with a glenoid-based reference system which allows lateral/medial rotation on x-axis, protraction/retraction rotations on y-axis, and anterior-posterior tilt on z-axis. The glenoid based system had the z-axis perpendicular to the glenoid plane, the y-axis directed superiorly toward the superior glenoid tubercle, and the x-axis directed anteriorly perpendicular to the other 2 axes. The motion of the acromionclavicular joint is driven by the sternoclavicular joint motion via 3 coordinate-coupler constraints based on linear functions.
Table 1.
Mass distribution of the MASI derived from previous models and values from in vitro study [43].
Mass distribution of the Rugby Model calculated from DEXA values of a rugby forward player (1.84 m; 120.4 Kg). Masses are reported as percentage of total body mass. The principal moment of inertia (IXX, IYY, IZZ) for the Rugby Model are shown in the las three columns of the table, and are expressed in kgm2.
Table 2.
Neck strength values are reported from in vivo and in silico studies.
Extension (Ext), flexion (Flex), axial rotation (Axial Rot), and lateral bending (Lat Bend) scaling factors are shown for adult rugby players (Rugby Front Row) and adult healthy males (Healthy Male). The scaling factors used to scale the MASI and Rugby Model neck muscles are calculated independently for flexors and extensors in order to match maximum extension and lateral bending neck strength values for a healthy male (Healthy Male) and a front row rugby player (Rugby Front Row), respectively. Head-Neck Model [30] was used as scaling reference, thus its scaling factor is 1.
Fig 3.
Sternoclavicular (SC) (left column) and acromioclavicular (AC) (middle and right columns) motions during humeral elevation.
The black diamonds in the left and middle columns graphs represent SC and AC kinematics during in vivo measurements [40], whereas black solid lines are the respective SC and AC kinematics generated by the SCJ. The SC and AC joints angles (black solid line) are within 2SD from in vivo values [40] (black dotted lines). In the right column graphs, the AC kinematics generated by SCJ is compared with another in vivo study and an in silico study. The AC motions generated by the SCJ (black solid line) is within 2SD (black dotted lines) from in vivo studies in the literature [41] (black squares) and comparable to the output of the Holzbaur’s model [26] (black dash-dot line). The glenoid reference system of the scapula was roto-traslated in order to express scapula motion with respect to the acromioclavicular joint reference system, and compare it with Ludewig, Hassett (42) and Holzbaur, Murray (26) studies.
Fig 4.
Moment arms of elevator scapulae (A) and sternocleidomastoid (B) muscles throughout humeral elevation when the neck was fully extended (Ext—black dashed and dotted line), flexed (Flex—black dotted line) and in neutral position (Neutral—black solid line). Vasavada’s (grey circles) and Holzbaur’s moment arms (red solid line) across humeral elevation are compared with MASI’s moment arms when the neck is at neutral position. (C) Muscles’ moment arms maximum changes of flexion (FLEX), extension (EXT), lateral bending (LAT BEND) and axial rotation (AXIAL ROT) moments during humeral elevation when the neck is fully flexed, extended, laterally bent, axially rotated and in neutral position (NEUTRAL). Positive values represent an increase whilst negative values a decrease of the moment arm across humeral elevation.
Fig 5.
Neck joints motion under a 2 Nm (flexion-extension and lateral bending) and 4Nm (axial rotation) load applied at C2 vertebra.
MASI’s neck motion (black bars) and Rugby Model’s neck motion (black downward diagonal bars) are compared with an average value from different in vivo studies (grey bars) and two protocols of an in vitro study: ‘2-4-2’ protocol (white dotted bars) and ‘1:1:1’ protocol (white bars). Average in vivo values were not available for lateral bending individual joint motion (middle graph).
Fig 6.
Rugby Model simulated neck muscle activation.
Simulated muscle activation from computed muscle control (solid black line) and experimental EMG (dashed black line) of sternocleidomastoid (left column) and upper trapezius (right column) muscles during flexion, extension, lateral bending (right and left bending) and axial rotation (right and left rotation). Experimental EMG signal were normalized using maximum voluntary contraction data and defined between 0% and 100%. Simulated activations are defined between 0% (no activation) and 100% (full activation).
Fig 7.
MASI simulated muscle activation.
Simulated muscle activation from computed muscle control (solid black line) and experimental average rectified EMG (dashed black line) of sternocleidomastoid (left column) and upper trapezius (right column) muscles during flexion, extension, lateral bending (right bending) and axial rotation (right rotation). Experimental EMG signal were normalized using maximum voluntary contraction data and defined between 0% and 100%. Simulated activations are defined between 0% (no activation) and 100% (full activation).
Fig 8.
(A) The three main phases of a rugby scrummaging activity: pre-engagement phase, engagement phase, and sustained-push. (B) Average flexion-extension joint angle across cervical spine joints during ‘Pre-Eng’ and ‘Engagement’ phases. Extension motion is positive in the graph. (C) Flexion-extension joint moment values during pre-engagement and engagement phases across the cervical spine vertebral joints. Extensor moment is positive in the graph. The graph shows the decreasing pattern of extensor moment from C7-C6 joint to C1-Head, which is mainly due to resist the flexion moment generate by the gravity force.
Fig 9.
Typical joint reaction force traces of scapula, clavicle, thorax (thoracic and lumbar spine plus ribcage) and cervical spine bodies during a machine trial.
The graph at the top shows the joint reaction force in anterior-posterior direction (X axis), whilst the central and bottom graphs show respectively the joint reaction forces in the longitudinal (Y axis) and mediolateral (Z axis) directions. The time of real engagement (tENG) is highlighted by the dashed vertical line. The red arrow highlights the increasing pattern of tensile load at cervical spine level.