Exploring musculoskeletal redundancy using null space projection for evaluation of knee reaction loads

It is an undeniable fact that musculoskeletal systems are inherently redundant, i.e., there are more degrees of freedom than those required to perform certain tasks and each degree of freedom is actuated by multiple muscles. This over-availability poses numerous challenges in the process of modeling and simulation that can negatively affect the validity of the models and the obtained results, rendering their application frequently inappropriate for clinical practice. The projection from a low- to a high-dimensional space is not uniquely defined (e.g., muscle sharing problem), however, this indeterminacy can be captured mathematically using the notion of null space. This study presents a method for calculating the feasible muscle forces that satisfy the movement and physiological muscle constraints. Its importance is demonstrated in the context of joint reaction analysis, where it is shown that misinterpretation of the results is possible if the null space solutions are ignored.