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

Is human height based on a Lucas sequence relationship between the foot height, tibial length, femur length and upper body length?

This is a retrospective chart and radiographic review of 145 patients who underwent full-body EOS imaging; 109 males and 36 females. The mean ages of the female and male subsets are 28.8 (SD = 11.6) years and 29.5 (SD = 11.8) years, respectively. The sum of the foot height (Ft) and the tibial length (T) for each subject was compared to their femur length (Fe). Subsequently, the sum of the tibial (T) and femoral lengths (Fe) were compared to their respective upper body lengths (UB), as measured from the tops of the femoral heads. A linear regression test was performed to determine whether a Lucas sequence-based relationship exists between Ft + T and Fe, and between T + Fe and UB. The regression for the relationship between Ft + T and Fe for the entire cohort (R = 0.82, R2 = 0.70), the female subset (R = 0.94, R2 = 0.88) and the male subset (R = 0.75, R2 = 0.57), all demonstrated a strong positive correlation between Ft + T and Fe and showed that Ft + T is a likely predictor of Fe. The regression test for the entire cohort demonstrated a moderately positive correlation between T + Fe and UB (R = 0.41, R2 = 0.17, F(1, 145) = 29.42, p = 2.4E-07). A stronger correlation was found for the relationship between T + Fe and UB (R = 0.57, R2 = 0.32, F(1, 35) = 16.64, p = 2.5E-05) for the female subset relative to the male subset (R = 0.20, R2 = 0.038, F(1, 35) = 4.37, p = 0.04). There appears to be a Lucas sequence relationship between the lengths of the foot height, tibial length, femoral length and upper body length, which together make up standing height. This mathematical proportion relationship is stronger in females than males.

Golden ratio and self-similarity in swimming: breast-stroke and the back-stroke

INTRODUCTION

Dynamics-on-graph concepts and generalized finite-length Fibonacci sequences have been used to characterize, from a temporal point of view, both human walking & running at a comfortable speed and front-crawl & butterfly swimming strokes at a middle/long distance pace. Such sequences, in which the golden ratio plays a crucial role to describe self-similar patterns, have been found to be subtly experimentally exhibited by healthy (but not pathological) walking subjects and elite swimmers, in terms of durations of gait/stroke-subphases with a clear physical meaning. Corresponding quantitative indices have been able to unveil the resulting hidden time-harmonic and self-similar structures.

RESULTS

In this study, we meaningfully extend such latest findings to the remaining two swimming strokes, namely, the breast-stroke and the back-stroke: breast-stroke, just like butterfly swimming, is highly technical and involves the complex coordination of the arm and leg actions, while back-stroke is definitely similar to front-crawl swimming. An experimental validation with reference to international-level swimmers is included.

Performance Index for in Home Assessment of Motion Abilities in Ataxia Telangiectasia: A Pilot Study

Background. It has been shown in the very recent literature that human walking generates rhythmic motor patterns with hidden time harmonic structures that are represented (at the subject’s comfortable speed) by the occurrence of the golden ratio as the the ratio of the durations of specific walking gait subphases. Such harmonic proportions may be affected—partially or even totally destroyed—by several neurological and/or systemic disorders, thus drastically reducing the smooth, graceful, and melodic flow of movements and altering gait self-similarities. Aim. In this paper we aim at, preliminarily, showing the reliability of a technologically assisted methodology—performed with an easy to use wearable motion capture system—for the evaluation of motion abilities in Ataxia-Telangiectasia (AT), a rare infantile onset neurodegenerative disorder, whose typical neurological manifestations include progressive gait unbalance and the disturbance of motor coordination. Methods. Such an experimental methodology relies, for the first time, on the most recent accurate and objective outcome measures of gait recursivity and harmonicity and symmetry and double support subphase consistency, applied to three AT patients with different ranges of AT severity. Results. The quantification of the level of the distortions of harmonic temporal proportions is shown to include the qualitative evaluations of the three AT patients provided by clinicians. Conclusions. Easy to use wearable motion capture systems might be used to evaluate AT motion abilities through recursivity and harmonicity and symmetry (quantitative) outcome measures.

Gaming Technology for Pediatric Neurorehabilitation: A Systematic Review

INTRODUCTION

The emergence of gaming technologies, such as videogames and virtual reality, provides a wide variety of possibilities in intensively and enjoyably performing rehabilitation for children with neurological disorders. Solid evidence-based results are however required to promote the use of different gaming technologies in pediatric neurorehabilitation, while simultaneously exploring new related directions concerning neuro-monitoring and rehabilitation in familiar settings.

AIM OF THE STUDY AND METHODS

In order to analyze the state of the art regarding the available gaming technologies for pediatric neurorehabilitation, Scopus and Pubmed Databases have been searched by following: PRISMA statements, PICOs classification, and PEDro scoring.

RESULTS

43 studies have been collected and classified as follows: 11 feasibility studies; six studies proposing home-system solutions; nine studies presenting gamified robotic devices; nine longitudinal intervention trials; and eight reviews. Most of them rely on feasibility or pilot trials characterized by small sample sizes and short durations; different methodologies, outcome assessments and terminologies are involved; the explored spectrum of neurological conditions turns out to be scanty, mainly including the most common and wider debilitating groups of conditions in pediatric neurology: cerebral palsy, brain injuries and autism.

CONCLUSION

Even though it highlights reduced possibilities of drawing evidence-based conclusions due to the above outlined biases, this systematic review raises awareness among pediatricians and other health professionals about gaming technologies. Such a review also points out a definite need of rigorous studies that clearly refer to the underlying neuroscientific principles.