A Matlab toolbox for scaled-generic modeling of shoulder and elbow

Abstract

There still remains a barrier ahead of widespread clinical applications of upper extremity musculoskeletal models. This study is a step toward lifting this barrier for a shoulder musculoskeletal model by enhancing its realism and facilitating its applications. To this end, two main improvements are considered. First, the elbow and the muscle groups spanning the elbow are included in the model. Second, scaling routines are developed that scale model's bone segment inertial properties, skeletal morphologies, and muscles architectures according to a specific subject. The model is also presented as a Matlab toolbox with a graphical user interface to exempt its users from further programming. We evaluated effects of anthropometric parameters, including subject's gender, height, weight, glenoid inclination, and degenerations of rotator cuff muscles on the glenohumeral joint reaction force (JRF) predictions. An arm abduction motion in the scapula plane is simulated while each of the parameters is independently varied. The results indeed illustrate the effect of anthropometric parameters and provide JRF predictions with less than 13% difference compared to in vivo studies. The developed Matlab toolbox could be populated with pre/post operative patients of total shoulder arthroplasty to answer clinical questions regarding treatments of glenohumeral joint osteoarthritis.

Figure 1

Modeling the elbow kinematics. (a) MRI scans of the forearm from the same subject are used to define the surface boundaries of the ulna and the radius. The hand is assumed to be rigidly tied to the radius. The elbow consists of 4 anatomical joints including humeroulnar, radioulnar proximal/distal, and humeroradial joints. (b) Two non-perpendicular hinge joints are considered to replicate the elbow motion. To construct the bone-fixed frames, 3 landmarks namely EM, HU, and EL are borrowed from the humerus. Two landmarks namely US and RS are also used from ulna and radius, respectively. $\{\mathit{HU},{\widehat{x}}_u,{\widehat{y}}_u,{\widehat{z}}_u\}$ and $\{\mathit{EL},{\widehat{x}}_r,{\widehat{y}}_r,{\widehat{z}}_r\}$ are the ulna and the radius frames, respectively. The joint coordinates are considered to be coincide with the bone-fixed frames. Two generalized coordinate $q_{10}$ and $q_{11}$ are used to uniquely define elbow flexion/extension and pronation/supination, respectively.

Figure 2

The developed shoulder and elbow model. (a) The anthropometric data of a healthy male subject is used to develop the model. (b) The bone morphologies and muscles origins/insertions are deduced from MRI scans of the same subject. (c) The model consists of thorax, clavicle, scapula, humerus, ulna, radius, and a hand tied to the radius. It has nine DOF represented by eleven generalized coordinates and two holonomic constraints. The model includes 42 muscles that can be represented by up to 20 massless elastic strings. Muscle origins and insertions are denoted by green and blue areas, respectively.

Figure 3

Scaling the ribcage ellipsoid containing AI. A base ellipsoid (blue) is dilated by ${\delta }_{\mathrm{AI}}$ to obtain the ribcage ellipsoid AI (red). The base ellipsoid is centered at ${\mathit{e}}_0$ with axes equal to $e_{{\mathrm{BE}}_x}$, $e_{{\mathrm{BE}}_y}$, and $e_{{\mathrm{BE}}_z}$. The center of the scaled AI ellipsoid is also obtained by scaling ${\mathit{e}}_0$ with S. Scaling the TS ribcage ellipsoid follows the same procedure and results in an ellipsoid centered at $S{\mathit{e}}_0$ and dilated by ${\delta }_{\mathrm{TS}}$.

Figure 4

Scaling and definition of the glenoid inclination/version (${\alpha }_{\mathrm{GI}}$ and ${\alpha }_{\mathrm{GV}}$). The scapula frame $\{{\widehat{x}}_s{\widehat{y}}_s{\widehat{z}}_s\}$ is attached to SN and is defined according to Eq. (15). The ${\alpha }_{\mathrm{GI}}$ is defined in ${\widehat{x}}_s{\widehat{z}}_s$ plane where the two points IG and SG are projected (white circles). It is defined as the angle between the ${\widehat{z}}_s$ and a vector passes through the two projected points of IG and SG. The ${\alpha }_{\mathrm{GV}}$ has a similar definition, but in the ${\widehat{x}}_s{\widehat{y}}_s$ plane and through projections of PG and AG. The adaptation of ${\alpha }_{\mathrm{GI}}$ and ${\alpha }_{\mathrm{GV}}$ results in a scaled GC point that modifies the cone of the stability constraint (Eq. 12).

Figure 5

Evaluations of the effects of subject specific parameters on the JRF predictions during abduction motion in the scapula plane. (a) Gender, (b) weight, (c) height, (d) glenoid inclination, and (e) 50% reduction in PCSAs of RC muscles.