An Optimization Approach to Inverse Dynamics Provides Insight as to the Function of the Biarticular Muscles During Vertical Jumping

Abstract

Traditional inverse dynamics approaches to calculating the inter-segmental moments are limited in their ability to accurately reflect the function of the biarticular muscles. In particular they are based on the assumption that the net inter-segmental moment is zero and that total joint moments are independent of muscular activity. Traditional approaches to calculating muscular forces from the inter-segmental moments are based on a consideration of joint moments which do not encapsulate the potential moment asymmetry between segments. In addition, traditional approaches may artificially constrain the activity of the biarticular muscles. In this study, an optimization approach to the simultaneous inverse determination of inter-segmental moments and muscle forces (the 1-step method) based on a consideration of segmental rotations was employed to study vertical jumping and contrasted with the more traditional 2-step approach of determining inter-segmental moments from an inverse dynamics analysis then muscle forces using optimization techniques. The 1-step method resulted in significantly greater activation of both the monoarticular and biarticular musculature which was then translated into significantly greater joint contact forces, muscle powers, and inter-segmental moments. The results of this study suggest that traditional conceptions of inter-segmental moments do not completely encapsulate the function of the biarticular muscles and that joint function can be better understood by recognizing the asymmetry in inter-segmental moments.

An Optimization-Based Simultaneous Approach to the Determination of Muscular, Ligamentous, and Joint Contact Forces Provides Insight into Musculoligamentous Interaction

“…It is important to recognize that in the previous work of Cleather and colleagues, 11 in order for the optimization to produce a solution it was necessary to increase the upper bounds for 6 of the 12 subjects, and for some subjects the necessary upper bound was over double that used in this study. The increased upper bounds were utilized solely by the small muscle groups and represented the difficulty in finding an equilibrium solution in 3D (and in particular in the non-sagittal planes).…”

“…Further details as to the description of musculoskeletal geometry in the lower limb model are described in more detail elsewhere. 9,11 The method of Dumas and colleagues 18 is used to formulate the equations of motion of the lower limb model. First, the inter-segmental forces can be calculated based on the traditional Newtonian iterative approach (Fig.…”

“…Recent research has demonstrated that the method of Dumas and colleagues is computationally equivalent to the traditional approach 8 and thus this alternative formulation presents new opportunities for the analysis of movement. For instance, Cleather and colleagues 10, 11 have recently demonstrated that the equations of motion describing moment equilibrium given by Dumas and colleagues can be modified to include the muscle forces in a musculoskeletal model of the lower limb. This results in an indeterminate problem that can be solved using optimization techniques and gives a more accurate representation as to the function of the biarticular muscles.…”

“…Parameters used within the optimization cost function for the four different cases considered in this study (Cases 1-5), and for the previous work of Cleather and colleagues 11. …”

Erratum to: An Optimization Approach to Inverse Dynamics Provides Insight as to the Function of the Biarticular Muscles During Vertical Jumping

“…(6) of Ann Biomed Eng, 2011; 39:147-160 1 did not include the moment created by the joint contact forces arising due to the action of the biarticular muscles. 2 The correct equation should read:…”