Lines of action and stabilizing potential of the shoulder musculature

Abstract

The objective of the present study was to measure the lines of action of 18 major muscles and muscle sub-regions crossing the glenohumeral joint of the human shoulder, and to compute the potential contribution of these muscles to joint shear and compression during scapular-plane abduction and sagittal-plane flexion. The stabilizing potential of a muscle was found by assessing its contribution to superior/inferior and anterior/posterior joint shear in the scapular and transverse planes, respectively. A muscle with stabilizing potential was oriented to apply more compression than shear at the glenohumeral joint, whereas a muscle with destabilizing potential was oriented to apply more shear. Significant differences in lines of action and stabilizing capacities were measured across sub-regions of the deltoid and rotator cuff in both planes of elevation (P < 0.05), and substantial differences were observed in the pectoralis major and latissimus dorsi. The results showed that, during abduction and flexion, the rotator cuff muscle sub-regions were more favourably aligned to stabilize the glenohumeral joint in the transverse plane than in the scapular plane and that, overall, the anterior supraspinatus was most favourably oriented to apply glenohumeral joint compression. The superior pectoralis major and inferior latissimus dorsi were the chief potential scapular-plane destabilizers, demonstrating the most significant capacity to impart superior and inferior shear to the glenohumeral joint, respectively. The middle and anterior deltoid were also significant potential contributors to superior shear, opposing the combined destabilizing inferior shear potential of the latissimus dorsi and inferior subscapularis. As potential stabilizers, the posterior deltoid and subscapularis had posteriorly-directed muscle lines of action, whereas the teres minor and infraspinatus had anteriorly-directed lines of action. Knowledge of the lines of action and stabilizing potential of individual sub-regions of the shoulder musculature may assist clinicians in identifying muscle-related joint instabilities, assist surgeons in planning tendon reconstructive surgery, aid in the development of rehabilitation procedures designed to improve joint stability, and facilitate development and validation of biomechanical computer models of the shoulder complex.

Introduction

During the course of normal shoulder movement, muscles and tendons translate and rotate with their bone-embedded origins and insertions. Because the spatial relationship between the origins and insertions of these structures varies according to joint motion, the muscle lines of action and moment arms must also change through the range of movement (Otis et al. 1994; Krevolin et al. 2004). As a result, articulating forces, bone-stress distributions and joint stability may vary significantly during arm movement.

It has been widely reported that shoulder muscle activity stabilizes the glenohumeral joint by compressing the humeral head against the glenoid surface (Howell et al. 1988; Bigliani et al. 1996; Lee & An, 2002; Labriola et al. 2005). Imbalance in muscle activity may decrease these compressive forces and therefore destabilize the glenohumeral joint and increase humeral head translations. Several studies have attempted to assess the contribution of the shoulder muscles to glenohumeral joint stability by simulating shoulder muscle loading in vitro and measuring glenohumeral joint shear and compressive forces (Lee et al. 2000; Lee & An, 2002; Labriola et al. 2005), joint translations (Halder et al. 2001a; Kido et al. 2003; Konrad et al. 2006) or by simulating joint dislocation (McMahon et al. 2003). However, individual muscle force directions were not measured or validated in these studies and broad-origin multi-pennate muscles were approximated as single force vectors.

A muscle's contribution to joint shear and compression is dependent on the magnitude of its applied muscle force and its line of action. A muscle's potential contribution is the measure of the capacity of a muscle to impart shear and compression at a joint, and depends only on the muscle's line of action relative to the joint centre (Yanagawa et al. 2008). Thus, without knowing a muscle's force magnitude, a muscle's inclination about an instantaneous joint centre indicates the relative amounts of shear or compression that the muscle may impart and therefore whether the muscle has a potential stabilizing or destabilizing role.

During active shoulder joint motion, a potentially stabilizing muscle tends to compress the humerus into the glenoid, as, for example, in the case of a muscle with a line of action inclined more toward the joint centre, where the ratio of the shear component to the compressive component of the muscle's line of action is < 1. In contrast, a potentially destabilizing muscle has a greater capacity to generate joint shear and dislocate the joint, as its line of action is more inclined away from the joint centre; in this case, the ratio of the shear component to the compressive component of the muscle's line of action is > 1.

Knowledge of the orientations of the force-producing structures of the shoulder has clinical significance in improving understanding of the mobility and stability of the normal and pathological glenohumeral joint. At present, the contributions of the shoulder musculature to joint stability during sagittal-plane movements are not well understood and the roles of the pectoralis major and latissimus dorsi in glenohumeral joint stability have received little attention in the literature. To date, no study has measured the three-dimensional lines of action of the rotator cuff, teres major, pectoralis major or latissimus dorsi during abduction and flexion of the shoulder nor assessed their potential contributions to shear and compression of the glenohumeral joint. The purpose of this investigation therefore was twofold: firstly, to measure the lines of action of 18 major muscles and muscle sub-regions crossing the glenohumeral joint during scapular-plane abduction and sagittal-plane flexion and secondly, to use these data to assess the potential contributions of individual muscles to joint stability.

Materials and methods

Specimen preparation

Eight fresh-frozen, entire upper extremities were obtained from human cadavera (four male, four female) of subjects ranging in age from 81 to 98 years, with a mean of 87 years. Ethics approval was obtained from the Health Sciences Human Ethics Sub-Committee, the University of Melbourne. All specimens had been previously screened by arthroscopy to ensure that they were free of degenerative changes such as osteoarthritis, rotator cuff tears and significant joint contracture. Specimens were thawed at room temperature for 24 h prior to dissecting and testing. The skin and subcutaneous soft tissue proximal to the glenohumeral joint were removed, and the shoulder musculature exposed. Functionally distinct sub-regions of the deltoid, pectoralis major and latissimus dorsi were defined based on electromyographic (EMG) studies reported in the literature (Inman et al. 1944; Vitti & Bankoff, 1984; Kronberg et al. 1990; Jarvholm et al. 1991; Laursen et al. 1998). The rotator cuff muscles were divided into equal-sized sub-regions to facilitate interpretation of their moment capacity at their attachments and their behaviour in the presence of full-thickness tears to specific sub-regions. Muscle sub-regions were identified and divided as described previously (Ackland et al. 2008): the deltoid (anterior, clavicular fibres; middle, acromial fibres; posterior, posterior scapula spine fibres), pectoralis major (superior, clavicular fibres; middle, sternal fibres; inferior, lower costal fibres), latissimus dorsi (superior, thoracic fibres; middle, lumbar fibres; inferior, iliac crest fibres), subscapularis (inferior, middle, superior, three approximately equal portions from the inferior, middle and superior subscapular fossa, respectively), supraspinatus (anterior, posterior, two approximately equal halves from the supraspinous fossa) and infraspinatus (superior, inferior, two approximately equal halves from the infraspinous fossa). The teres minor and teres major were identified and left intact.

With the aid of an anatomical atlas (Spalteholz-Spanner, 1967), the centroid of origin of each muscle-tendon sub-region was identified by visual inspection and marked on the scapula with pins. Muscles were dissected from their respective fossa and the scapula cleaned of soft tissue. The deltoid attachments on the scapula and clavicle, however, were left intact. Number 5-Ethibond suture was secured to all tendons of insertion. The elbow joint was fused arbitrarily in 50° of flexion with a Steinmann pin and the protruding pin end was then used to manipulate the humerus. The clavicle was pinned in the anatomical position. Specimens were kept moist by irrigation with saline solution during preparation and testing.

Experimental apparatus

The scapula was cleaned of the remaining soft tissue and mounted onto a custom-built dynamic shoulder cadaver-testing apparatus (DSCTA) (Fig. 1) by embedding it in a potting block using plaster of Paris. The potting block was fixed to a rotary frame that could be pivoted to simulate scapular rotation during humeral abduction and flexion. The scapula was mounted with the plane of the scapula oriented vertically and the glenoid initially aligned with the vertical. In order for the glenohumeral joint to remain congruent, and to remove slack in each muscle sub-region during testing, a nylon line was tied to the suture of each muscle sub-region and passed through a series of pulleys to a free weight of 10 N. The pulleys were fixed to the rotary frame but positioned such that each muscle-tendon was pulled toward the centroid of its scapular origin, as marked previously with pins. Nylon lines tied to the three deltoid sutures were pulled through screw eyelets positioned at the tendon origins.

Fig. 1.

Specimen mounted on the dynamic shoulder cadaver-testing apparatus (DSCTA). Triads of retro-reflective markers were rigidly attached to the humerus and scapula to enable three-dimensional motion capture measurement of shoulder joint kinematics during abduction and flexion. RF, rotary frame of the DSCTA; P, pulleys; M, 10 N free weight; PB, scapular potting block; SMT, scapular marker triad; HMT, humeral marker triad. The scapula potting block and pulleys were rigidly fixed to the rotary frame.

In order for glenohumeral joint motion to be visible to a six-camera Vicon motion capture system, two bone-pins with triads of retro-reflective markers attached were inserted into the spine of the scapula and the distal humeral shaft. The S.D. associated with digitizing marker trajectories using the motion capture system was 1.2 mm (Chiari et al. 2005). Clinically relevant scapular and humeral reference frames were defined by digitizing bony prominences (see Appendix). Zero degrees of abduction and flexion were defined when the medial and lateral epicondyles of the humerus were aligned with the plane of the scapula, and the long axis of the humerus passed through the acromioclavicular joint.

Experimental protocol

The humerus was held passively at 0°, 30°, 60°, 90° and 120° of elevation in both abduction and flexion using a series of cables attached to the embedded Steinmann pin that was used to fuse the elbow joint. As external rotation of the humeral head is known to occur at joint angles above 120° of humeral elevation (Sharkey et al. 1994), no internal/external rotation was applied to the humerus during testing. To approximate the combined motion of the humerus and scapula relative to the thorax, commonly referred to as ‘scapulohumeral rhythm’, at 60°, 90° and 120° of abduction and flexion the scapula was rotated 10°, 20° and 30° to the vertical, achieved by pivoting the rotary frame of the DSCTA. This resulted in a 2 : 1 ratio of scapular to humeral motion beyond 30° of humeral elevation, or 2° of humeral elevation (relative to the glenoid) for every 1° of scapular rotation (relative to the thorax), which has been documented by others (Inman et al. 1944; Poppen & Walker, 1976). Joint angles were computed using bone-pin data reconstructed in Vicon Nexus 1.1. Joint angles were calculated using a Y-X-Z Euler angle sequence. All data were filtered in Matlab 7.0 using a fourth order, low-pass, Butterworth filter with a cut-off frequency of 5 Hz. Muscle lines of action were then determined at each joint angle by digitizing bony and soft tissue landmarks using a marker wand. Lines of action for each scapulohumeral muscle bundle were defined by the force-vector projection from the last tendon wrapping via point (the point where the muscle-tendon loses contact with the humerus) to the centroid of origin of the muscle sub-region. The resultant three-dimensional force vectors defining the muscle lines of action were expressed in the scapular reference frame (Fig. 2A). Each vector was then resolved in the scapular and transverse planes, and its direction in each plane was described by an angle, θ, measured from the mediolateral axis as shown in Fig. 2B,C.

Fig. 2.

(A) Bone-embedded scapular reference frame used in this study. The negative x axis corresponds to the medial (compressive) direction, the y axis to the anterior direction and the z axis to the superior direction (see Appendix). The projected angles of the muscle force vectors were calculated with respect to the scapular reference frame defined in (A) in both the scapular plane (B) and the transverse plane (C). Directions of all muscle force vectors were measured anti-clockwise from the mediolateral (x) axis.

For each sub-region of the pectoralis major and latissimus dorsi, lines of action were determined at 0°, 30°, 60°, 90° and 120° of abduction and flexion using a computational model described elsewhere (Garner & Pandy, 2001). This approach was taken due to the difficulty in accurately measuring the three-dimensional lines of action of these muscles in vitro. The model musculoskeletal geometry was based on the Visible Human Male dataset (Spitzer et al. 1996). The model muscle paths followed muscle cross-sectional centroids, wrapping around other muscles and bony prominences according to the obstacle-set method (Garner & Pandy, 2000). The abduction and flexion bone kinematics of the entire shoulder girdle were based on subject bone-pin data (Yanagawa et al. 2008) and the muscle geometries previously validated against muscle moment arm and muscle architecture data reported in the literature (Garner & Pandy, 2001; Garner & Pandy, 2003). The lines of action of the pectoralis major and latissimus dorsi therefore reflect the combined three-dimensional scapulohumeral and thoracoscapular motion that occurs during shoulder elevation.

A best-fitting third-order polynomial regression analysis was used to determine the line of action of each muscle as a function of abduction and flexion angle. R² values were used to assess the disparity between third-order polynomials obtained from the regression analysis and the measured muscle lines of action (see Appendix). Muscles with a capacity to compress, and therefore stabilize, the glenohumeral joint had lines of action inclined toward the negative x-direction (mediolateral axis) as defined in Fig. 2. In the scapular plane, a line of action greater than 180° would generate superior shear at the glenohumeral joint and that less than 180° would generate inferior shear (Fig. 2B). In the transverse plane, a line of action greater than 180° would generate posterior shear at the glenohumeral joint and that less than 180° would generate anterior shear (Fig. 2C).

For each muscle, average stability ratios were computed to assess the muscle's potential contributions to anterior/posterior and superior/inferior glenohumeral joint stability. Average anterior and superior stability ratios were computed by dividing the average anterior/posterior and superior/inferior shear components of a muscle's line of action, respectively, by the average magnitude of its compressive component. Thus,

where R_A and R_S are the anterior and superior stability ratios, respectively, f_x, f_y and f_zare the direction cosines, and i, j and k are unit vector directions of the x, y and z axes of the scapular reference frame shown in Fig. 2A(see Appendix). A muscle with a stability ratio of > 1 was considered a destabilizer, as the shear component of its line of action was larger than the compressive component. Conversely, a muscle with a stability ratio of < 1 was considered a stabilizer, as the shear component of its line of action was smaller than the compressive component. A positive anterior (superior) stability ratio represented a muscle with an anterior (superior) shear component, whereas a negative anterior (superior) stability ratio represented a muscle with a posterior (inferior) shear component.

Data analysis

A two-way anova was conducted to compare mean lines of action of each muscle sub-region through the range of abduction and flexion. The dependent variable was line of action and the independent variables were joint angle and muscle sub-region; anovawas also used to assess interactions between the independent variables. A one-way anovawas conducted to compare the mean stability ratios of each muscle sub-region during abduction and flexion, with the dependent variable being stability ratio and the independent variable being muscle sub-region. The level of significance was defined as P < 0.05. The S.D. of each line of action and stability ratio across the eight specimens was computed and used as the measure of the dispersion of results. In the case of the pectoralis major and latissimus dorsi, as their lines of action and stability ratios were derived from a computational model, anovawas not performed and S.D.s were not computed.

Results

Lines of action

During abduction and flexion, both joint angle and muscle sub-region significantly influenced the lines of action of the deltoid (P < 0.05) and had notable effects on the lines of action of the pectoralis major and latissimus dorsi (Figs 3, 4). Throughout abduction and in early flexion, the line of action of the superior pectoralis major had the largest superior inclination from the mediolateral axis. The anterior deltoid also had a prominent superior line of action in abduction and flexion. The line of action of the inferior latissimus dorsi was more inferiorly inclined than any other muscle line of action during early abduction and flexion. Direction cosines of the three-dimensional unit force vectors describing the muscle lines of action are given in the Appendix.

Fig. 3.

Muscle lines of action in the scapular and transverse planes as a function of humeral elevation angle during abduction. In the scapular plane, a muscle with a line of action greater than 180° had the potential to apply a superior shear force to the glenoid; conversely, a line of action less than 180° indicates that the muscle had the potential to apply an inferior shear force. In the transverse plane, a muscle with a line of action greater than 180° had the potential to apply a posterior shear force to the glenoid; a line of action less than 180° indicates that the muscle had the potential to apply an anterior shear force. The two diagrams between the graphs illustrate how the line of action of a muscle, described by the angle θ, is defined in the scapular and transverse planes. θ is measured anti-clockwise from the mediolateral (x) axis.

Fig. 4.

Muscle lines of action in the scapular and transverse planes as a function of humeral elevation angle during flexion. In the scapular plane, a muscle with a line of action greater than 180° had the potential to apply a superior shear force to the glenoid. In the transverse plane, a muscle with a line of action greater than 180° had the potential to apply a posterior shear force to the glenoid. The two diagrams between the graphs illustrate how the line of action of a muscle, described by the angle θ, is defined in the scapular and transverse planes. θ is measured anti-clockwise from the mediolateral (x) axis.

The transverse-plane lines of action of the inferior, middle and superior pectoralis major were more anteriorly inclined than any other muscle lines of action, with the line of action of the inferior pectoralis major being most steeply inclined to the mediolateral axis. In contrast, the transverse-plane line of action of the middle deltoid was significantly more posteriorly inclined than any other muscle line of action throughout abduction and flexion (P < 0.007).

The lines of action of the rotator cuff muscles were more aligned with the mediolateral axis than those of the prime movers (Figs 3, 4). Throughout abduction and flexion, the posterior rotator cuff (infraspinatus and teres minor) had lines of action that were directed anteriorly, whereas the anterior rotator cuff (subscapularis) had posteriorly-directed lines of action. The scapular-plane and transverse-plane lines of action of the anterior supraspinatus remained close to 180° throughout abduction and flexion.

Stability ratios

During abduction and flexion, the superior pectoralis major had the largest averaged superior stability ratio and was therefore the largest potential superior destabilizer (Fig. 5). The inferior latissimus dorsi was the most prominent inferior destabilizer during abduction, with the teres minor, inferior infraspinatus and inferior subscapularis also contributing significantly in this respect. In flexion, the inferior subscapularis was the largest potential inferior destabilizer, with the destabilizing contribution of the inferior latissimus dorsi also prominent.

Fig. 5.

Averaged superior and anterior stability ratios of muscles crossing the glenohumeral joint during abduction and flexion. For superior stability ratios, positive bars indicate a muscle with an average superior stability ratio (a superior shear component). For anterior stability ratios, positive bars indicate a muscle with an average anterior stability ratio (an anterior shear component). Muscles with superior and anterior stability ratios of < 1 were defined as potential joint stabilizers (stabilizing region).

The inferior and middle pectoralis major were the only potential anterior destabilizers during abduction and flexion (Fig. 5). No muscle was potentially posteriorly destabilizing throughout abduction; in flexion, however, the middle deltoid was the most significant contributor to potentially destabilizing posterior shear (P < 0.001).

The magnitudes of the averaged rotator cuff muscle anterior stability ratios during abduction and flexion were small compared with their superior stability ratios, indicating the greater capacity of these muscles to stabilize the glenohumeral joint in the transverse plane than in the scapular plane. The anterior supraspinatus was the most significant potential joint stabilizer, as it had the smallest average anterior and superior stability ratios during abduction, and the smallest average superior stability ratio during flexion (P < 0.05) (Fig. 5). The posterior deltoid had the smallest negative anterior stability ratio during flexion and therefore exhibited a significant capacity to stabilize the glenohumeral joint. In a similar manner, the middle and inferior subscapularis were also effective potential stabilizers during both abduction and flexion. The inferior latissimus dorsi, inferior infraspinatus and teres minor all had small anterior stability ratios during abduction and flexion, indicating low anterior shear potential, and prominent capacity to stabilize the joint.

Discussion

It is generally accepted that both static and dynamic factors play a role in glenohumeral joint stability and that, during the mid-range of motion, dynamic glenohumeral stability must be provided by active muscle contraction. However, despite numerous studies reporting on the anatomical basis of glenohumeral stability (Bigliani et al. 1996; Lee et al. 2000; Halder et al. 2001b; Labriola et al. 2005), no study has documented muscle lines of action of the shoulder musculature or measured individual muscle contributions to glenohumeral joint stability throughout both abduction and flexion. Furthermore, no study has quantified the contributions of sub-regions of broad, multi-pennate shoulder muscles, such as the pectoralis major and latissimus dorsi, to glenohumeral joint stability. Broad-origin, multi-pennate muscles often exhibit divergence of their fascicles (Johnson et al. 1996) and therefore may exert moments at their origin attachment sites. In addition, EMG studies have shown such muscles to have functionally independent sub-regions (Inman et al. 1944; Jarvholm et al. 1991; Kronberg et al. 1990; O’Connell et al. 2006). Therefore, studies that represent broad-origin muscles as single lines of force may be limited in their ability to predict muscle-induced moments or contributions to joint stability. The present study provides a comprehensive dataset of the lines of action of 18 major muscles and muscle sub-regions spanning the shoulder joint during abduction and flexion, and highlights their potential contributions to glenohumeral joint stability.

The results showed that, during abduction and flexion, the rotator cuff muscle sub-regions are more favourably aligned to stabilize the glenohumeral joint in the transverse plane than in the scapular plane and that, overall, the anterior supraspinatus was most favourably oriented to apply joint compression. The superior pectoralis major and inferior latissimus dorsi were the chief scapular-plane destabilizers, demonstrating the most significant capacity to impart superior and inferior shear to the glenohumeral joint, respectively. The middle and anterior deltoid were also prominent potential contributors to superior shear, opposing the combined destabilizing inferior shear potential of the latissimus dorsi and inferior subscapularis. No muscle sub-regions, apart from those of the pectoralis major, showed an anterior destabilizing capacity during abduction and flexion and only the middle deltoid during flexion demonstrated a posterior destabilizing capacity.

Before interpreting these results, it is important to consider the limitations of this study. First, the resolution of the data obtained was limited to 30° intervals. Although the data obtained may not reflect a continuum of muscle lines of action throughout abduction and flexion, the sample points were chosen to illustrate the general progression of muscle-force-vector orientations during which dynamic stability is maintained by active muscle contraction. Second, the cadaver specimens used were taken from an elderly sample; however, although lower averaged muscle cross-sectional areas may have had some influence on positions of tendon wrapping via points, we believe that the measured muscle lines of action are a reasonable approximation of those of an average adult person. Third, the lines of action of the anterior deltoid may be subject to some error, as the clavicle was pinned in the anatomical position during each trial. Fourth, muscle lines of action of the pectoralis major and latissimus dorsi were computed from a model based on anatomical data obtained from a single specimen, the Visible Human Male cadaver. This model was developed from high-resolution images of cross-sections of a human male cadaver taken at 1 mm intervals. Measurements of muscle moment arms and muscle architecture reported in the literature were used to validate the musculoskeletal geometry assumed in the model (Garner & Pandy, 2001; Garner & Pandy, 2003). We are therefore confident that the anatomical geometry of the model is a realistic representation of the musculoskeletal geometry present in the anatomical shoulder. Finally, scapulohumeral rhythm involves three-dimensional movement of the scapula relative to the thorax (Kondo, 1986) and, in the present study, only superior/inferior scapular rotation was simulated using the DSCTA. Although protraction/retraction and elevation/depression movements of the scapula on the rib cage may lead to more complicated glenohumeral joint motions during humeral abduction and flexion, the majority of scapulothoracic motion during arm elevation results in superior/inferior scapular rotation. We used a ratio of scapular to humeral motion that has been measured previously (Inman et al. 1944; Poppen & Walker, 1976) and that closely approximates in-vivo shoulder kinematics obtained from bone-pin data (Yanagawa et al. 2008).

In addition to a muscle's stabilizing capacity by virtue of its orientation about a joint, its stabilizing function may also extend to its capacity to counteract forces caused by opposing muscles or external joint moments. For example, co-activation of two potentially destabilizing muscles of opposing lines of action may combine to produce a resultant compressive joint force, thereby stabilizing the joint. The present study showed that, throughout abduction and flexion, the superior pectoralis major was a potential superior destabilizer, whereas the inferior latissimus dorsi was a potential inferior destabilizer. The scapular-plane lines of action of these muscles varied significantly with joint angle due to the effects of scapulothoracic motion, resulting in greater shear potential during early abduction and flexion. Despite the apparent destabilizing potentials of these prime-mover muscle sub-regions, the combined action of the pectoralis major and latissimus dorsi may function to stabilize the glenohumeral joint. EMG analysis has shown that the pectoralis major and latissimus dorsi are activated simultaneously during abduction and flexion (Kronberg et al. 1990). Therefore, because the latissimus dorsi shear forces point inferiorly, in the opposite direction to the superior shear force applied by the superior pectoralis major, the resultant of the two muscle force vectors in the plane of the scapula may tend to produce a compressive force.

Only the pectoralis major showed an anterior destabilizing capacity during abduction and flexion, indicating its potential role in anterior instability. For example, in the presence of an infraspinatus/teres minor deficiency, there may be insufficient compressive joint force to stabilize the glenohumeral joint from anterior subluxation under the action of the pectoralis major. A number of cadaveric models have suggested that the pectoralis major may increase anterior shear and anterior joint translations, and may potentially decrease joint stability (McMahon et al. 2003; Labriola et al. 2005; Konrad et al. 2006); however, the present study suggests that the resultant force created by the combined anterior shear force potential of the pectoralis major and the posterior shear force potential of the deltoid may produce a compressive force in the transverse plane during both abduction and flexion. The role of the pectoralis major in stability of the anatomical shoulder is therefore likely to be dependent on rotator cuff and deltoid muscle activity; dysfunction in these muscles may lead to a force imbalance resulting in increased anterior translations and anterior instability under the action of the pectoralis major.

Muscle activity of the three heads of deltoid during abduction and flexion has been extensively reported in EMG studies (Basmajian & de Luca, 1984; Sigholm et al. 1984; Ringelberg, 1985), and their role in joint mobility has also been well documented (Inman et al. 1944; Poppen & Walker, 1978). The function of the deltoid in glenohumeral joint stability is still debated, however. In the present study, the deltoid provided significant superior shear capacity at the glenohumeral joint during both abduction and flexion. Our results show that the deltoid's greatest potential to sublux the glenohumeral joint superiorly was during early flexion, due principally to the destabilizing capacity of the anterior deltoid.

It is generally accepted that the rotator cuff muscles are ideally aligned for effective compression of the glenohumeral joint at most shoulder positions and thus contribute considerably to its stability. However, as their three-dimensional lines of action have not been documented, their potential contributions to glenohumeral joint stability remain unclear. We found that the lines of action of the posterior rotator cuff (infraspinatus and teres minor) were inclined anteriorly to the glenohumeral joint and have significant compressive capacity. In contrast, the anterior rotator cuff (subscapularis) was inclined posteriorly and also functioned as a prominent stabilizer. These muscle lines of action revealed a greater capacity to stabilize the glenohumeral joint in the transverse plane than in the scapular plane and implicate the importance of these rotator cuff muscles in preventing anterior and posterior joint instability. The results of the present study suggest that the anterior and posterior rotator cuff muscles are unlikely to provide significant superior/inferior stability and resistance against subluxation, for example, in the case of a supraspinatus deficiency.

The anterior supraspinatus was found to have the most significant potential stabilizing function throughout abduction and flexion, as its line of action was closest to the mediolateral axis of the scapula. This result indicates that a full-thickness tear to the anterior supraspinatus may result in joint instability and increased superior migration of the humerus under the superior shear of the deltoid. However, despite the significant potential of the infraspinatus and teres minor to impart inferior shear during abduction and flexion, studies suggest that the adductor and extensor torque-producing capacity of these muscles, in the presence of a supraspinatus tear, may not be able to overcome the superior shear imparted by the deltoid (Weiner & Macnab, 1970; Terrier et al. 2007). Therefore, the role of the supraspinatus in maintaining stability of the glenohumeral joint may be significant and priority should be given to the repair of the anterior sub-region of this muscle for restoration of joint stability in the presence of a massive full-thickness rotator cuff tear.

The present study described the lines of action of 18 major muscles and muscle sub-regions spanning the shoulder joint during abduction and flexion, and their potential contributions to glenohumeral joint stability. These results may be used by physicians in diagnosing glenohumeral joint instability, for example, by assessing muscle weakness and detecting musculature imbalance that may contribute to instability. An understanding of the contributions of individual muscle sub-regions to joint force may also assist surgeons in planning procedures such as tendon transfer and muscle-tendon tensioning. Furthermore, clarifying the roles of the shoulder musculature may aid in the development of rehabilitation protocols that aim to strengthen specific muscles to maximize joint compression or minimize joint translation. It is intended that the dataset presented will serve as a basis for validating a number of existing models of the shoulder complex (Karlsson & Peterson, 1992; Charlton & Johnson, 2001; Garner & Pandy, 2001) and developing realistic computational models to investigate shoulder disease and trauma.

Conflict of interest

The authors do not have any financial or personal relationships with other people or organizations that could inappropriately influence this work.

Appendix

The scapular reference frame was positioned at the centre of the glenohumeral joint (i.e. the centre of the head of the humerus for a congruent joint), with the x axis defined by a vector parallel to the line passing from the triangular surface of the medial border of the scapula to the centre of the aromioclavicular joint; the z axis was defined by a line passing upward from the centre of the glenohumeral joint and through the acromioclavicular joint, and the y axis was perpendicular to the x and z axes. The humeral reference frame was positioned at the centre of the head of the humerus, with the x axis defined by the vector parallel to the line passing from the medial epicondyle to the lateral epicondyle; the z axis was defined by a line passing upward through the centre of the long axis of the humerus and the y axis was perpendicular to the x and z axes. The scapular and humeral reference frames were aligned when the shoulder was positioned at zero degrees of abduction and flexion.

Regression coefficients used to describe the projected angles of the three-dimensional muscle lines of action in the scapular and transverse planes as a function of joint angle are presented in Table A1. The projected angles are defined by the variable θ, illustrated in Fig. 2B,C.

Direction cosines were used to describe the line of action measured for each muscle. Each three-dimensional unit muscle-force vector,

, was expressed in the scapular reference frame and represented by its three components as follows

where f_x, f_y and f_zare the direction cosines (given in Tables A2, A3) and i, j and k are unit vector directions of the x, y and z axes of the scapular reference frame (shown in Fig. 2A).

Table A1.

Regression coefficients (A0–A3) for third-order polynomial equations used to describe the lines of action of the shoulder muscles in the transverse and scapular planes as a function of humeral elevation angle [joint angle (JA) (degrees)] during abduction and flexion

		Transverse plane					Scapular plane
A3	A2	A1	A0	R2	A3	A2	A1	A0	R2
Abduction	A. deltoid	–9.847E–06	3.061E–03	–3.081E–01	1.803E+02	9.930E–01	–1.014E–04	2.050E–02	–1.383E+00	2.427E+02	9.988E–01
	M. deltoid	2.859E–05	–5.712E–03	–3.136E–02	2.231E+02	9.885E–01	1.267E–05	–1.113E–03	–4.065E–01	2.271E+02	9.956E–01
	P. deltoid	1.142E–05	–2.489E–03	1.588E–01	1.837E+02	1.000E+00	–9.714E–05	1.818E–02	–1.053E+00	2.171E+02	1.000E+00
	S. pec major	5.094E–05	–1.420E–02	1.176E+00	1.176E+02	9.980E–01	–1.331E–05	3.008E–03	–6.414E–01	2.576E+02	9.998E–01
	M. pec major	1.873E–06	–2.154E–03	3.349E–01	1.134E+02	9.882E–01	–2.865E–05	4.685E–03	–6.348E–01	2.307E+02	1.000E+00
	I. pec major	–2.411E–05	4.998E–03	–1.514E–01	1.108E+02	9.988E–01	–3.559E–05	6.724E–03	–3.478E–01	1.477E+02	8.770E–01
	S. lat dorsi	4.889E–06	–3.159E–03	1.508E–01	1.809E+02	9.999E–01	–4.021E–05	7.276E–03	–2.829E–01	1.719E+02	9.993E–01
	M. lat dorsi	5.440E–06	–5.276E–04	1.706E–02	1.764E+02	9.875E–01	–3.622E–05	7.475E–03	–2.085E–01	1.358E+02	9.997E–01
	I. lat dorsi	–2.870E–06	1.114E–03	–3.970E–02	1.732E+02	9.786E–01	–4.017E–05	8.613E–03	–2.663E–01	1.237E+02	9.998E–01
	A. supra	1.111E–05	–1.927E–03	2.360E–02	1.854E+02	9.881E–01	8.125E–06	–2.029E–06	–3.692E–02	1.787E+02	9.999E–01
	P. supra	9.128E–06	–1.727E–03	6.898E–02	1.922E+02	9.999E–01	1.608E–05	–1.890E–03	7.692E–02	1.683E+02	9.995E–01
	S. subscap	9.597E–06	–1.376E–03	–1.866E–02	1.951E+02	9.940E–01	3.012E–05	–6.152E–03	4.749E–01	1.675E+02	9.974E–01
	M. subscap	1.599E–05	–2.636E–03	5.409E–02	1.980E+02	9.955E–01	1.831E–05	–4.197E–03	3.382E–01	1.482E+02	9.899E–01
	I. subscap	–6.487E–06	1.573E–03	–1.432E–01	1.962E+02	9.975E–01	1.076E–05	–3.205E–03	3.071E–01	1.317E+02	9.951E–01
	S. infra	3.039E–06	–3.906E–04	–4.249E–02	1.839E+02	9.995E–01	4.177E–06	–5.106E–04	9.570E–03	1.533E+02	9.803E–01
	I. infra	1.215E–05	–2.362E–03	8.175E–02	1.747E+02	9.962E–01	–1.138E–06	–3.564E–05	9.025E–03	1.386E+02	9.110E–01
	Teres minor	1.117E–05	–1.650E–03	1.564E–02	1.760E+02	9.506E–01	–2.346E–05	4.593E–03	–2.733E–01	1.383E+02	9.865E–01
	Teres major	6.337E–06	–1.685E–04	–7.834E–02	1.901E+02	9.888E–01	2.463E–06	–1.241E–03	5.776E–02	1.554E+02	9.807E–01
Flexion	A. deltoid	3.548E–05	–1.176E–02	1.231E+00	1.804E+02	9.996E–01	–1.956E–05	–2.876E–04	–3.819E–02	2.428E+02	9.958E–01
	M. deltoid	1.859E–05	–4.733E–03	4.306E–01	2.227E+02	9.999E–01	–2.729E–05	8.535E–03	–8.849E–01	2.271E+02	9.907E–01
	P. deltoid	1.484E–06	7.796E–04	–2.410E–02	1.837E+02	9.990E–01	–3.643E–05	9.757E–03	–8.139E–01	2.172E+02	9.965E–01
	S. pec major	7.557E–05	–2.121E–02	1.738E+00	1.176E+02	9.992E–01	–9.745E–06	1.507E–03	–5.289E–01	2.575E+02	1.000E+00
	M. pec major	3.882E–06	–2.677E–03	4.157E–01	1.133E+02	9.999E–01	3.393E–05	–6.254E–03	–2.102E–01	2.308E+02	9.998E–01
	I. pec major	–3.020E–05	5.468E–03	–1.099E–01	1.107E+02	9.984E–01	–1.956E–05	4.355E–03	–3.061E–01	1.479E+02	9.918E–01
	S. lat dorsi	–1.426E–05	4.185E–04	8.196E–02	1.811E+02	9.876E–01	–1.920E–05	2.136E–03	6.450E–02	1.720E+02	9.953E–01
	M. lat dorsi	–1.487E–05	2.954E–03	–1.013E–01	1.764E+02	9.982E–01	–2.017E–05	2.679E–03	1.240E–01	1.358E+02	1.000E+00
	I. lat dorsi	–1.800E–05	3.739E–03	–1.293E–01	1.731E+02	1.000E+00	–2.570E–05	3.930E–03	7.797E–02	1.237E+02	9.997E–01
	A. supra	2.119E–05	–4.177E–03	1.381E–02	1.820E+02	9.977E–01	–3.777E–06	3.529E–03	–3.366E–01	1.787E+02	1.000E+00
	P. supra	1.824E–05	–3.469E–03	1.852E–02	1.922E+02	9.985E–01	2.386E–05	–1.253E–03	–1.131E–01	1.684E+02	9.947E–01
	S. subscap	–7.706E–06	2.924E–03	–3.748E–01	1.950E+02	9.990E–01	–2.591E–06	2.704E–04	6.622E–02	1.673E+02	9.911E–01
	M. subscap	–3.304E–06	1.518E–03	–1.934E–01	1.979E+02	9.908E–01	–1.279E–05	2.395E–03	–1.355E–01	1.479E+02	8.312E–01
	I. subscap	–8.639E–06	2.531E–03	–2.167E–01	1.961E+02	9.816E–01	–1.556E–05	2.919E–03	–1.588E–01	1.315E+02	8.384E–01
	S. infra	–2.148E–05	5.102E–03	–3.838E–01	1.838E+02	9.876E–01	1.315E–05	–2.337E–03	1.612E–01	1.532E+02	9.715E–01
	I. infra	2.950E–06	–5.288E–04	3.709E–02	1.747E+02	9.820E–01	8.716E–06	–1.577E–03	1.107E–01	1.386E+02	9.952E–01
	Teres minor	2.005E–06	–3.672E–04	5.092E–02	1.732E+02	9.980E–01	4.536E–06	–8.542E–04	7.841E–02	1.382E+02	8.371E–01
	Teres major	1.419E–05	–4.164E–03	4.479E–01	1.904E+02	9.872E–01	–3.744E–05	7.920E–03	–5.639E–01	1.550E+02	9.717E–01

The following equation was used: line of action = A0 + A1(JA) + A2(JA)²+ A3(JA)³.

Table A2.

Direction cosines (f_x, f_y, f_z) of unit muscle-force vectors for the prime mover muscles during abduction and flexion¹

		A. deltoid		M. deltoid		P. deltoid		S. pec major		M pec major		I. pec major		S. lat dorsi		M. lat dorsi		I. lat dorsi
	JA	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F
fx	0	–0.461	–0.461	–0.574	–0.574	–0.797	–0.797	–0.200	–0.200	–0.355	–0.355	–0.347	–0.347	–0.990	–0.990	–0.716	–0.716	–0.554	–0.554
	30	–0.790	–0.455	–0.690	–0.591	–0.939	–0.931	–0.454	–0.446	–0.498	–0.501	–0.328	–0.350	–0.980	–0.995	–0.708	–0.780	–0.533	–0.624
	60	–0.851	–0.534	–0.848	–0.553	–0.943	–0.962	–0.628	–0.639	–0.560	–0.612	–0.401	–0.435	–0.992	–0.998	–0.793	–0.853	–0.645	–0.732
	90	–0.848	–0.604	–0.947	–0.544	–0.942	–0.946	–0.719	–0.776	–0.612	–0.666	–0.468	–0.497	–0.989	–0.999	–0.874	–0.898	–0.766	–0.806
	120	–0.946	–0.738	–0.991	–0.518	–0.990	–0.928	–0.756	–0.839	–0.581	–0.658	–0.500	–0.509	–0.945	–0.990	–0.912	–0.902	–0.833	–0.822
fy	0	–0.003	–0.003	–0.530	–0.530	–0.052	–0.052	0.385	0.385	0.827	0.827	0.913	0.913	–0.016	–0.016	0.045	0.045	0.067	0.067
	30	0.095	–0.243	–0.566	–0.751	–0.108	–0.058	0.355	0.226	0.793	0.756	0.908	0.896	–0.045	–0.070	0.040	0.061	0.062	0.087
	60	0.132	–0.434	–0.386	–0.807	–0.112	–0.094	0.404	0.219	0.793	0.749	0.871	0.830	0.004	–0.063	0.049	0.032	0.072	0.065
	90	0.152	–0.546	–0.279	–0.825	–0.102	–0.146	0.484	0.318	0.782	0.742	0.816	0.769	0.132	–0.034	0.033	–0.004	0.041	0.019
	120	0.159	–0.619	–0.106	–0.841	–0.116	–0.242	0.588	0.463	0.810	0.750	0.770	0.749	0.307	0.136	–0.004	–0.017	0.008	–0.005
fz	0	0.888	0.888	0.625	0.625	0.602	0.602	0.901	0.901	0.435	0.435	–0.217	–0.217	–0.141	–0.141	–0.697	–0.697	–0.830	–0.830
	30	0.606	0.857	0.451	0.293	0.327	0.359	0.817	0.866	0.350	0.422	–0.261	–0.275	–0.194	–0.077	–0.705	–0.623	–0.844	–0.777
	60	0.508	0.726	0.363	0.209	0.313	0.255	0.665	0.737	0.242	0.254	–0.284	–0.348	–0.130	–0.017	–0.607	–0.521	–0.761	–0.678
	90	0.508	0.581	0.161	0.151	0.319	0.288	0.500	0.544	0.115	0.074	–0.339	–0.401	–0.069	0.023	–0.485	–0.440	–0.641	–0.592
	120	0.282	0.269	0.078	0.158	0.079	0.283	0.288	0.287	–0.076	–0.068	–0.396	–0.425	–0.112	–0.048	–0.409	–0.432	–0.553	–0.569

JA, joint angle (degrees); A, abduction; F, flexion.

¹Corrections added after publication 28 May 2009. The sign convention of f_x in Table A2 was changed so that the negative direction represents the medial (compressive) direction. Directional cosines at 0 degrees of abduction and flexion were adjusted to represent unit vector values, consistent with all other joint angles.

Table A3.

Direction cosines (f_x, f_y, f_z) of unit muscle-force vectors for the rotator cuff muscles and teres major during abduction and flexion²

		A. supra		P. supra		S. Subscap		M. Subscap		I. Subscap		S. infra		I. infra		Teres minor		Teres major
	JA	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F
fx	0	–0.995	–0.999	–0.958	–0.958	–0.944	–0.944	–0.818	–0.818	–0.652	–0.652	–0.892	–0.892	–0.748	–0.748	–0.746	–0.744	–0.896	–0.896
30	–0.996	–0.989	–0.959	–0.951	–0.970	–0.977	–0.873	–0.805	–0.738	–0.615	–0.892	–0.910	–0.748	–0.771	–0.685	–0.754	–0.910	–0.763
60	–0.999	–0.976	–0.962	–0.947	–0.982	–0.990	–0.892	–0.822	–0.762	–0.637	–0.891	–0.925	–0.752	–0.782	–0.690	–0.786	–0.896	–0.754
90	–1.000	–0.962	–0.972	–0.970	–0.985	–0.993	–0.908	–0.812	–0.773	–0.623	–0.891	–0.923	–0.740	–0.786	–0.685	–0.774	–0.885	–0.709
120	–0.990	–0.939	–0.980	–0.997	–0.977	–0.996	–0.914	–0.801	–0.768	–0.607	–0.901	–0.945	–0.729	–0.810	–0.657	–0.801	–0.845	–0.679
fy	0	–0.092	–0.032	–0.206	–0.206	–0.254	–0.254	–0.265	–0.265	–0.190	–0.190	–0.061	–0.061	0.070	0.070	0.052	0.089	–0.161	–0.161
30	–0.086	0.007	–0.220	–0.175	–0.237	–0.102	–0.280	–0.187	–0.174	–0.124	–0.038	0.066	0.060	0.061	0.061	0.074	–0.122	–0.297
60	–0.032	0.143	–0.205	–0.073	–0.188	–0.029	–0.239	–0.167	–0.158	–0.122	–0.009	0.078	0.085	0.061	0.074	0.062	–0.102	–0.338
90	–0.004	0.254	–0.189	0.011	–0.164	0.015	–0.215	–0.144	–0.157	–0.116	0.012	0.089	0.106	0.055	0.099	0.051	–0.096	–0.379
120	0.007	0.342	–0.196	0.071	–0.165	0.020	–0.230	–0.154	–0.142	–0.126	0.025	0.096	0.110	0.048	0.075	0.035	–0.139	–0.369
fz	0	–0.023	–0.023	–0.198	–0.198	–0.211	–0.211	–0.510	–0.510	–0.734	–0.734	–0.448	–0.448	–0.660	–0.660	–0.663	–0.662	–0.413	–0.413
30	–0.040	–0.145	–0.179	–0.255	–0.044	–0.186	–0.399	–0.563	–0.652	–0.779	–0.451	–0.409	–0.661	–0.634	–0.726	–0.653	–0.396	–0.574
60	–0.030	–0.166	–0.178	–0.314	–0.004	–0.137	–0.385	–0.544	–0.628	–0.761	–0.453	–0.373	–0.653	–0.620	–0.720	–0.615	–0.432	–0.563
90	0.021	–0.097	–0.141	–0.243	0.047	–0.116	–0.360	–0.565	–0.615	–0.773	–0.454	–0.375	–0.665	–0.615	–0.722	–0.631	–0.456	–0.595
120	0.144	0.042	–0.032	–0.036	0.135	–0.091	–0.335	–0.578	–0.624	–0.785	–0.433	–0.312	–0.675	–0.584	–0.751	–0.597	–0.516	–0.634

JA, joint angle (degrees); A, abduction; F, flexion.

²Corrections added after publication 28 May 2009. The sign convention of f_x in Table A3 was changed so that the negative direction represents the medial (compressive) direction. Directional cosines at 0 degrees of abduction and flexion were adjusted to represent unit vector values, consistent with all other joint angles.