Generalized Finite-Length Fibonacci Sequences in Healthy and Pathological Human Walking: Comprehensively Assessing Recursivity, Asymmetry, Consistency, Self-Similarity, and Variability of Gaits

Cristiano Maria Verrelli, Marco Iosa, Paolo Roselli, Antonio Pisani, Franco Giannini, Giovanni Saggio

Research output: Contribution to journalArticlepeer-review

Abstract

Healthy and pathological human walking are here interpreted, from a temporal point of view, by means of dynamics-on-graph concepts and generalized finite-length Fibonacci sequences. Such sequences, in their most general definition, concern two sets of eight specific time intervals for the newly defined composite gait cycle, which involves two specific couples of overlapping (left and right) gait cycles. The role of the golden ratio, whose occurrence has been experimentally found in the recent literature, is accordingly characterized, without resorting to complex tools from linear algebra. Gait recursivity, self-similarity, and asymmetry (including double support sub-phase consistency) are comprehensively captured. A new gait index, named Φ-bonacci gait number, and a new related experimental conjecture—concerning the position of the foot relative to the tibia—are concurrently proposed. Experimental results on healthy or pathological gaits support the theoretical derivations.

Original languageEnglish
Article number649533
JournalFrontiers in Human Neuroscience
Volume15
DOIs
Publication statusPublished - Aug 9 2021

Keywords

  • asymmetry
  • fibonacci sequence
  • gait analysis
  • golden ratio
  • locomotion
  • neuroscience
  • self-similarity
  • walking gait

ASJC Scopus subject areas

  • Neuropsychology and Physiological Psychology
  • Neurology
  • Psychiatry and Mental health
  • Biological Psychiatry
  • Behavioral Neuroscience

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