An equation to calculate individual muscle contributions to joint stability

Abstract 

The purpose of the current paper was to use the energy approach to develop a simplified equation for quantifying individual muscle contributions to mechanical stability about all three axes of a particular joint. Specific examples are provided for muscles acting about the lumbar spine's L4/L5 joint. The stability equation requires input of: (1) origin and insertion coordinates, relative to the joint of interest, (2) muscle force, and (3) muscle stiffness. The muscle force must be derived from a biomechanical analysis that first results in static equilibrium about all axes being studied. The equation can also accommodate muscles with nodes that change the line of action, with respect to a particular joint, as it passes from the origin to insertion. The results from this equation were compared to those from a Moment approach using more than two million simulated muscles with three-dimensional orientations. The differences between approaches were negligible in all cases. The primary advantage of the current method is that it is very easy to implement into any 2D or 3D biomechanical model of any joint, or system of joints. Furthermore, this approach will be useful in dissecting total joint stability into the individual contributions of each muscle for various systems, joints, postures and recruitment patterns.

Keywords: Joint stability, Spine mechanics, Muscle stiffness, Buckling behavior