The Golden Ratio of Gait Harmony: Repetitive Proportions of Repetitive Gait Phases

Abstract

In nature, many physical and biological systems have structures showing harmonic properties. Some of them were found related to the irrational number ϕ known as the golden ratio that has important symmetric and harmonic properties. In this study, the spatiotemporal gait parameters of 25 healthy subjects were analyzed using a stereophotogrammetric system with 25 retroreflective markers located on their skin. The proportions of gait phases were compared with ϕ, the value of which is about 1.6180. The ratio between the entire gait cycle and stance phase resulted in 1.620 ± 0.058, that between stance and the swing phase was 1.629 ± 0.173, and that between swing and the double support phase was 1.684 ± 0.357. All these ratios did not differ significantly from each other (F = 0.870, P = 0.422, repeated measure analysis of variance) or from ϕ (P = 0.670, 0.820, 0.422, resp., t-tests). The repetitive gait phases of physiological walking were found in turn in repetitive proportions with each other, revealing an intrinsic harmonic structure. Harmony could be the key for facilitating the control of repetitive walking. Harmony is a powerful unifying factor between seemingly disparate fields of nature, including human gait.

The contribution of a central pattern generator in a reflex-based neuromuscular model

“…As demonstrated in Iosa et al (2013), the ratios between cycle/stance durations (noted GR0, commonly referred to as the duty factor), stance/swing durations (noted GR1), and swing/“double stance support” durations (noted GR2) is similar in healthy humans of different size, corpulence and age walking at preferred (self-chosen) speed, and satisfy the golden ratio ($\sigma =\frac{1+\sqrt{5}}{2}$). Note that the variability of GR1 is higher than GR0, and the variability of the GR2 is higher than GR1.…”

Assessment of gait stability, harmony, and symmetry in subjects with lower-limb amputation evaluated by trunk accelerations

“…In training people with amputation to use prostheses, researchers should focus interventions on the most impaired aspect of walking, i.e., harmony, a feature recently shown to be crucial for optimizing physiological gait [38][39].…”

“…A low value of the HR of trunk acceleration has been highlighted as a prognostic factor for the risk of falling in the elderly [38]. Moreover, harmony has recently been shown to be a fundamental feature of physiological human gait, with specific iterative proportions among repetitive gait phases related to the so-called golden ratio [39].…”

Wearable inertial sensors for human movement analysis

“…The relationship between upright gait stability assessment performed with IMUs and risk of falls needs further studies, however it has recently been suggested that the involuntary control of locomotion can be favoured by the intrinsic gait temporal harmony, implying that its loss can increase the difficulties in controlling gait [51].…”