Gait phase proportions in different locomotion tasks: The pivot role of golden ratio

Iosa, Marco; Bartolo, Daniela De; Morone, Giovanni; Boffi, Tommaso; Mammucari, Elisa; Vannozzi, Giuseppe; Bini, Fabiano; Marinozzi, Franco; Antonucci, Gabriella; Paolucci, Stefano

doi:10.1016/j.neulet.2019.01.052

Cited by 18 publications

(16 citation statements)

References 25 publications

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“…During typical development, stance phase is directly correlated with walking speed but not significantly dependent on the age of the children [ 20 ]. Moreover, in different walking conditions, such as walking on a steeply inclined surface [ 21 ], the foot-off timing undergoes a low variability, suggesting the possibility that the proportion between stance and swing (60–62% versus 40–38%) is largely unaffected by external conditions [ 20 , 21 , 22 ]. It has been noted that this proportion is close to the irrational numbers phi (φ), that is 1.6180… [ 23 ].…”

Section: Introductionmentioning

confidence: 99%

The Role of Walking Experience in the Emergence of Gait Harmony in Typically Developing Toddlers

et al. 2022

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The ability to walk without support usually develops in the first year of a typically developing toddler’s life and matures further in the following years. Mature walking is characterized by the correct timing of the different gait phases that make up a full gait cycle formed by stance, swing, and double support phases. The harmony of mature walking is given by a specific self-similar structure of the ratios between the durations of these phases (stride/stance, stance/swing, swing/double support), that in adults all converge to the golden ratio (phi, about 1.618). The aim of this longitudinal, prospective, experimental study was to investigate the evolution of this gait harmonic structure in the transition from supported to independent walking. In total, 27 children were recruited and recorded at various stages of locomotor development, ranging from neonatal stepping up to an independent walking experience of about six months. Differently from walking speed that progressively increased with age, the gait phase ratios started to converge to golden value only after the first independent steps, suggesting a relation to the maturation of the walking experience. The independent walking experience seems to represent a trigger for the evolution of a locomotor harmonic pattern in toddlers learning to walk.

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Section: Introductionmentioning

confidence: 99%

The Role of Walking Experience in the Emergence of Gait Harmony in Typically Developing Toddlers

et al. 2022

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“…In fact, it has been shown that healthy subjects could have difficulties in reproducing harmonic behaviors usually implemented unconsciously [ 43 ]. Gait is characterized by a rhythmic behavior with phases and sub-phases alternated at a certain frequency [ 44 , 45 , 46 ] and depends on the activations produced by autonomous central pattern generators (CPGs) probably located in the spinal cord [ 47 , 48 ]. Despite some studies reporting that CPGs guarantee the necessary muscle activation patterns independently from peripheral feedback [ 49 ], other results supported the importance of sensory feedback and stretch reflexes in walking models [ 50 ].…”

Section: Discussionmentioning

confidence: 99%

Sensorized Assessment of Dynamic Locomotor Imagery in People with Stroke and Healthy Subjects

Bartolo

Belluscio

Vannozzi

et al. 2020

Sensors

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Dynamic motor imagery (dMI) is a motor imagery task associated with movements partially mimicking those mentally represented. As well as conventional motor imagery, dMI has been typically assessed by mental chronometry tasks. In this paper, an instrumented approach was proposed for quantifying the correspondence between upper and lower limb oscillatory movements performed on the spot during the dMI of walking vs. during actual walking. Magneto-inertial measurement units were used to measure limb swinging in three different groups: young adults, older adults and stroke patients. Participants were tested in four experimental conditions: (i) simple limb swinging; (ii) limb swinging while imagining to walk (dMI-task); (iii) mental chronometry task, without any movement (pure MI); (iv) actual level walking at comfortable speed. Limb swinging was characterized in terms of the angular velocity, frequency of oscillations and sinusoidal waveform. The dMI was effective at reproducing upper limb oscillations more similar to those occurring during walking for all the three groups, but some exceptions occurred for lower limbs. This finding could be related to the sensory feedback, stretch reflexes and ground reaction forces occurring for lower limbs and not for upper limbs during walking. In conclusion, the instrumented approach through wearable motion devices adds significant information to the current dMI approach, further supporting their applications in neurorehabilitation for monitoring imagery training protocols in patients with stroke.

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“…Such an irrational number φ is the positive solution to the equation x 2 = 1 + x. It is related to the Euclid's problem of cutting in a self-proportional way a given straight segment (Iosa et al, 2017(Iosa et al, , 2019. In this light, φ turns out to describe self-similarity in symmetric walking (Iosa et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

“…It is related to the Euclid's problem of cutting in a self-proportional way a given straight segment (Iosa et al, 2017(Iosa et al, , 2019. In this light, φ turns out to describe self-similarity in symmetric walking (Iosa et al, 2019). Indeed, most of the literature agrees that the foot off reliably occurs at 60-62% of a physiological gait when the subject is (symmetrically and recursively) walking at comfortable speed 2 .…”

Section: Introductionmentioning

confidence: 99%

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

Verrelli

Iosa

Roselli

et al. 2021

Front. Hum. Neurosci.

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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.

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Gait phase proportions in different locomotion tasks: The pivot role of golden ratio

Cited by 18 publications

References 25 publications

The Role of Walking Experience in the Emergence of Gait Harmony in Typically Developing Toddlers

The Role of Walking Experience in the Emergence of Gait Harmony in Typically Developing Toddlers

Sensorized Assessment of Dynamic Locomotor Imagery in People with Stroke and Healthy Subjects

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

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