AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting
of the American Society of Biomechanics
Clemson University, South Carolina
September 24-27, 1997
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| AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting |
Sometimes muscles are resected during oncologic reconstructions of the shoulder, which can have profound affects on arm strength. The purpose of this study was to develop a three-dimensional biomechanical model for predicting arm strength (e.g. push, pull, lift, etc.) from musculoskeletal geometry and muscle physiology. Such a model could be used to pre-operatively evaluate effects of tissue resection.
Three-dimensional biomechanical models of the upper extremity have been developed (van der Helm, 1994; Ho¬gfors et al., 1987; Karlsson and Peterson, 1992, Nieminen et al., 1995). These models have used optimization methods to compute muscle forces. Nieminen et al. (1995) used a 3D model to predict maximal arm strength.
All of these models used an idealized representation of musculoskeletal geometry to determine the moments produced by individual muscles. Specifically, it was assumed that each muscle took the shortest distance between origin and insertion subject to the constraint that the path did not pass through a bone. Hughes et al. (1996) found that this method produces moment arm estimates that can be substantially different from moment arms determined by using the relationship between tendon excursion and joint angle measured in in vitro experiments.
A 3D static biomechanical model of the upper extremity (glenohumeral joint, elbow, and wrist) was formulated. The glenohumeral, ulnohumeral, and radiohumeral joints were modeled as ball-and-socket, revolute, and revolute joints, respectively. The wrist was modeled as a universal joint. Coordinate systems on the hand, ulna, humerus, scapula, and torso were used to specify upper extremity posture. Body segment masses and center of gravity locations were taken from the literature (Chaffin and Andersson, 1984) and scaled to stature and weight. Muscle moment arms were taken from studies that used the tendon excursion-joint angle method: glenohumeral joint (Kuechle, 1994), elbow (Murray et al., 1995; Schuind et al., 1994), and wrist (Horii et al., 1993). Maximum muscle force was modeled as the product of specific tension (Ikai and Fukunaga, 1968) and physiological cross sectional area (An et al., 1981; Veeger et al., 1991; Karlsson and Peterson, 1992). Two external forces were allowed in the model (radial and ulnar side of palm), and the directions were specified. The model was formulated as a linear program, were the objective to be maximized was the sum of the reaction forces acting on the palm of the hand.
Isometric arm strength measurements were made on ten subjects (5 male; 5 female) ages 23 to 66 (median 34) in order to evaluate model predictions. Strength measurements were made using a cylindrical grip attached to 500 lb load cell via a nylon cord. Three repetitions of each test condition were performed, and subjects were given rest between exertions. Each test consisted of a three second exertion, and the middle two seconds were averaged and stored. Three upper arm postures (neutral, flexed 45o, abducted 45o) were tested, and an 85o elbow angle was used in each condition. Maximal lift up and push down forces were measured with the upper arm in neutral (posture 1). Lift up, push down, pull medially, and pull laterally were measured in the flexed posture (posture 2). Lift up, push down, push and pull forces were measured in the abducted posture (posture 3). The order of postures tested were randomized, and the order of exertion directions was randomized within each posture. Anthropometric measurements were taken and used as input for the biomechanical model.
Inter-subject variability was reduced by normalizing strength test data by maximal forces measured in the opposite direction (e.g. ratio of push to pull forces). Wilcoxon signed rank tests were used to test for differences between predicted and measured strength ratios.
The model predicted the ratio of pull up to push down strength when the humerus was in a neutral posture. Statistically significant differences between measured values and model predictions were found in all other test conditions (Figure 1). The largest difference was found in the push/pull forces with the arm abducted 45 degrees.
Figure 1. Measured and predicted hand force exertion ratios. * denotes statistically significant difference (P<0.05) between measured and predicted values.
The biomechanical model predicted the ratio of lift up to push down forces when the upper arm was in a neutral posture. However, the model did not predict forces well when the arm was flexed or abducted. The discrepancies between predictions and measurements may be due to not including the length-tension property of muscle, because the largest differences occurred in flexed or abducted postures. The inability of model to predict push and pull forces in an abducted arm posture may be caused by the representation of the glenohumeral joint, which did not include shear forces and the need for active stabilization by the muscles.
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This study was supported by NIH grants AR41171 and HD07447 and the Musculoskeletal Transplant Foundation.
