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

Abstract

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 -104microepsilon 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 (-377microepsilon and 258microepsilon 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.