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Research Papers

# A Musculoskeletal Model of the Equine Forelimb for Determining Surface Stresses and Strains in the Humerus—Part II. Experimental Testing and Model Validation

[+] Author and Article Information
Sarah Pollock

Biomedical Engineering Program,  University of California, One Shields Avenue, Davis, CA 95616

Susan M. Stover

Department of Anatomy, Physiology and Cell Biology, School of Veterinary Medicine, and Biomedical Engineering Program,  University of California, One Shields Avenue, Davis, CA 95616

M. L. Hull1

Department of Mechanical Engineering, and Biomedical Engineering Program,  University of California, One Shields Avenue, Davis, CA 95616mlhull@ucdavis.com

Larry D. Galuppo

Department of Anatomy, Physiology, and Cell Biology, School of Veterinary Medicine,  University of California, One Shields Avenue, Davis, CA 95616

1

Corresponding author.

J Biomech Eng 130(4), 041007 (May 29, 2008) (6 pages) doi:10.1115/1.2898729 History: Received May 10, 2006; Revised July 10, 2007; Published May 29, 2008

## Abstract

The first objective of this study was to experimentally determine surface bone strain magnitudes and directions at the donor site for bone grafts, the site predisposed to stress fracture, the medial and cranial aspects of the transverse cross section corresponding to the stress fracture site, and the middle of the diaphysis of the humerus of a simplified in vitro laboratory preparation. The second objective was to determine whether computing strains solely in the direction of the longitudinal axis of the humerus in the mathematical model was inherently limited by comparing the strains measured along the longitudinal axis of the bone to the principal strain magnitudes and directions. The final objective was to determine whether the mathematical model formulated in Part I [Pollock, 2008, ASME J. Biomech. Eng., 130, p. 041006] is valid for determining the bone surface strains at the various locations on the humerus where experimentally measured longitudinal strains are comparable to principal strains. Triple rosette strain gauges were applied at four locations circumferentially on each of two cross sections of interest using a simplified in vitro laboratory preparation. The muscles included the biceps brachii muscle in addition to loaded shoulder muscles that were predicted active by the mathematical model. Strains from the middle grid of each rosette, aligned along the longitudinal axis of the humerus, were compared with calculated principal strain magnitudes and directions. The results indicated that calculating strains solely in the direction of the longitudinal axis is appropriate at six of eight locations. At the cranial and medial aspects of the middle of the diaphysis, the average minimum principal strain was not comparable to the average experimental longitudinal strain. Further analysis at the remaining six locations indicated that the mathematical model formulated in Part I predicts strains within $±2$ standard deviations of experimental strains at four of these locations and predicts negligible strains at the remaining two locations, which is consistent with experimental strains. Experimentally determined longitudinal strains at the middle of the diaphysis of the humerus indicate that tensile strains occur at the cranial aspect and compressive strains occur at the caudal aspect while the horse is standing, which is useful for fracture fixation.

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## Figures

Figure 1

Lateral view of a simplified preparation of a left equine forelimb in the materials testing machine. The subscapularis (not visible due to its medial origin and insertion sites), infraspinatus, and the lateral and medial head of the supraspinatus were clamped and weighted to simulate active force production as predicted with optimization. The biceps brachii muscle was left intact. Flexion of the elbow joint was due to the rotation of the humerus in relation to the fixed radius and ulna.

Figure 2

The longitudinal axis along the lateral aspect of the equine humerus was defined as running from the proximal aspect of the major tubercle to the distal aspect of the lateral epicondyle. The midpoint of this line was used to define the mid-diaphysis of the humerus and the middle gauge of each rosette strain gauge was aligned with the longitudinal axis of the humerus.

Figure 3

Right humerus with locations of applied strain gauges at the mid-diaphysis and the proximal cross sections including the specific stress fracture and bone graft donor sites. The gauge located on the medial mid-diaphysis was positioned just distal to the muscular attachment of the teres major and the latissimus dorsi muscles.

Figure 4

The three grids of the triple rosette strain gauge labeled in the counterclockwise direction produce the three strains ε1, ε2, and ε3, which were used to calculate the principal strains and corresponding directions. εP and εQ are the maximum and minimum principal strains respectively. θ represents the principal angle measured from the axis of maximum principal strain to Grid 1. Note the axis of Grid 2 points along the longitudinal axis of the humerus.

Figure 5

Comparison of the distribution of longitudinal strains (from Grid 2) with the predicted strains from the mathematical model formulated in Part I of this two-part article at the middle of the diaphysis and the proximal humerus. The caudal and lateral aspects of the proximal humerus represent the stress fracture and bone graft donor sites, respectively. The top and bottom lines of each box represent the 75th and 25th percentile of data, respectively, the middle line represents the median, and the outlying lines represent ±2 standard deviations from the mean. Compressive values are negative and tensile values are positive.

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