Algorithms for exact multi-object muscle wrapping and application to the deltoid muscle wrapping around the humerus

Lines of action of muscle forces imply the function and performance of muscles acting around joints. It is not always possible to determine muscle force lines of action in vivo, and so computational techniques are often used to predict them. It is common to model a muscle as a taut elastic string that follows the shortest geodesic path between attachments over the wrapping geometry. A number of studies have been concerned with wrapping paths over single wrapping objects, and those that have considered more objects have applied the single-object solutions with iterative approaches to the search for a solution. This study presents a more efficient methodology for finding the exact solutions to a certain class of wrapping problems in which the path is constrained by multiple surfaces. It also introduces a more general wrapping technique based on the idea of energy minimization, which has been successfully validated against the exact solution. These methods are applied to the case of an element of the deltoid wrapping around the humerus modelled as a composite sphere-cylinder. Comparison of results with those obtained from approximated single-object solutions demonstrates the need to include correct multi-object wrapping algorithms in biomechanical models.