Research Papers

A Musculoskeletal Model of the Equine Forelimb for Determining Surface Stresses and Strains in the Humerus—Part I. Mathematical Modeling

[+] Author and Article Information
Sarah Pollock

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.edu

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

Larry D. Galuppo

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


Corresponding author.

J Biomech Eng 130(4), 041006 (May 29, 2008) (7 pages) doi:10.1115/1.2898726 History: Received May 10, 2006; Revised July 10, 2007; Published May 29, 2008

Knowledge of the forces that act upon the equine humerus while the horse is standing and the resulting strains experienced by the bone is useful for the prevention and treatment of fractures and for assessing the proximolateral aspect of the bone as a site for obtaining autogenous bone graft material. The first objective was to develop a mathematical model to predict the loads on the proximal half of the humerus created by the surrounding musculature and ground reaction forces while the horse is standing. The second objective was to calculate surface bone stresses and strains at three cross sections on the humerus corresponding to the donor site for bone grafts, a site predisposed to stress fracture, and the middle of the diaphysis. A three-dimensional mathematical model employing optimization techniques and asymmetrical beam analysis was used to calculate shoulder muscle forces and surface strains on the proximal and mid-diaphyseal aspects of the humerus. The active shoulder muscles, which included the supraspinatus, infraspinatus, subscapularis, and short head of the deltoid, produced small forces while the horse is standing; all of which were limited to 4.3% of their corresponding maximum voluntary contraction. As a result, the strains calculated at the proximal cross sections of the humerus were small, with maximum compressive strains of 104με at the cranial aspect of the bone graft donor cross section. The middle of the diaphysis experienced larger strain magnitudes with compressive strains at the lateral and the caudal aspects and tensile strains at the medial and cranial aspects (377με and 258με maximum values, respectively) while the horse is standing. Small strains at the donor bone graft site do not rule out using this location to harvest bone graft tissue, although strains while rising to a standing position during recovery from anesthesia are unknown. At the site common to stress fractures, small strains imply that the stresses seen by this region while the horse is standing, although applied for long periods of time, are not a cause of fracture in this location. Knowing the specific regions of the middle of the diaphysis of the humerus that experience tensile and compressive strains is valuable in determining optimum placement of internal fixation devices for the treatment of complete fractures.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Lateral CT scan of the scapula, humerus, radius, and ulna embedded with metallic markers to represent muscle origins and insertions, contact points, and other important locations. (X,Y,Z) represent the global CT coordinate system while (x,y,z) represent the local humeral coordinate system. The x axis was defined distal to proximal, the y axis was caudal to cranial, and the z axis was lateral to medial.

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Figure 2

Two-dimensional free body diagram of the equine humerus including forces due to muscles, bone-on-bone contact, and muscle wrapping contact, and transverse cross sections of the humerus corresponding to the bone graft donor site, stress fracture site, and middle of the diaphysis. Only muscles proximal to the middle of the diaphysis of the humerus and active during the middle of the stance phase of walking were used in the optimization procedure.  * Active muscles during the middle of stance phase of walking as indicated by EMG data.  ** Muscle for which no EMG data were available.

Grahic Jump Location
Figure 3

Simplified musculoskeletal preparation for the biceps brachii only model used to calculate the biceps contact force. The large arrow on the scapula indicates the weight of the trunk of the horse (reprinted with permission (40) and biceps contact force added).

Grahic Jump Location
Figure 4

Intersegmental force (F¯e) and couple (C¯e) vectors, and contact forces due to the biceps brachii muscle and the scapula exerted on the proximal humerus

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Figure 5

Transverse cross section of a right humerus at the level of the bone graft donor site viewed from the bottom in the direction of the positive x axis. The positive torsional moment (Mx) and the bending moments (My and Mz) are labeled at the centroid of the cross section, and the shaded region represents cortical bone.




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