Synchronicity Rectangle for temporal gait analysis: Application to Parkinson's Disease

Human walking and running gaits are represented by the same temporal model. The golden ratio phi - namely, the largest solution to the equation x(2) = 1 + x - is associated with all of the four eigenvalues of such a model. An eigenspace of dimension two, named symmetry plane, is determined. It contains an eigenspace of dimension one, named golden line, on which the ratio between stance and swing durations is equal to phi for walking and to phi(-1) for running. The Synchronicity Rectangle is defined, whose sides are: the normalized distance of the gait from the symmetry plane and the normalized distance from the golden line of the gait projection on the symmetry plane. It constitutes a new comprehensive geometric representation of walking and running gaits. The area of such a rectangle computed for an averaged gait is illustratively shown to discriminate between patients affected by Parkinson's Disease and healthy subjects: its mean value is significantly higher for patients affected by Parkinson's Disease; high Sensitivity and moderate Specificity, along with relatively large likelihood and odds ratios, are obtained.