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The regions of deviation method has been proposed as a technique for identifying regions of the gait cycle where joint motion deviates from normal (Shorter et al., 2008). The original statistical analysis distinguished only peak values during stance and swing. In the current article, we extend the approach by examining deviations from normal throughout the entire gait cycle using pointwise t tests. These methods were demonstrated on hind-limb joint angles of 21 Labrador Retrievers without and with cranial cruciate ligament disease. Results were compared with peak difference analysis previously performed on these subjects. All points in the gait cycle where symmetry deviations were significantly affected by cranial cruciate ligament disease (via pointwise t tests) were defined as regions of deviation from symmetry. Discriminant function analysis was used to consider single subjects and validate that these regions were truly areas of difference between groups. Regions of deviation encompassed previously determined significant peak differences, while extending analysis to additional areas of asymmetry. Discriminant function analysis suggested that the region of deviation method is a viable approach for distinguishing motion pattern differences. This enhanced method may help researchers better understand the mechanisms behind lameness and compensation.

In this paper, we consider model examples of dynamical systems with only a few degrees of freedom, and with desirable symmetry properties, and explore compensating control strategies for retaining robust symmetric system response even under symmetry-breaking defects. The analysis demonstrates the distinct differences between linear versions of these models, in which fault-compensating strategies are always found, and weakly nonlinear counterparts with varying degrees of asymmetry, for which a multitude of locally optimal solutions may coexist. We further formulate a candidate optimization protocol for fault compensation applied to self-healing systems, which respond to symmetry-breaking defects by a continuous process of fault correction. The analysis shows that such a protocol may exhibit discontinuous changes in the control strategy as the self-healing system successively regains its original symmetry properties. In addition, it is argued that upon return to a symmetric configuration, such a protocol may result in a different control strategy from that applied prior to the occurrence of a fault.