Loss of fractal gait harmony in Parkinson's Disease

Exploring harmonic walking development in children with unilateral cerebral palsy and typically developing toddlers: Insights from walking experience

This longitudinal study investigated the impact of the first independent steps on harmonic gait development in unilateral cerebral palsy (CP) and typically developing (TD) children. We analysed the gait ratio values (GR) by comparing the duration of stride/stance, stance/swing and swing/double support phases. Our investigation focused on identifying a potential trend towards the golden ratio value of 1.618, which has been observed in the locomotion of healthy adults as a characteristic of harmonic walking. Locomotor ability was assessed in both groups at different developmental stages: before and after the emergence of independent walking. Results revealed that an exponential fit was observed only after the first unsupported steps were taken. TD children achieved harmonic walking within a relatively short period (approximately one month) compared to children with CP, who took about seven months to develop harmonic walking. Converging values for stride/stance and stance/swing gait ratios, averaged on the two legs, closely approached the golden ratio in TD children (R2 = 0.9) with no difference in the analysis of the left vs right leg separately. In contrast, children with CP exhibited a trend for stride/stance and stance/swing (R2 = 0.7), with distinct trends observed for the most affected leg which did not reach the golden ratio value for the stride/stance ratio (GR = 1.5), while the least affected leg exceeded it (GR = 1.7). On the contrary, the opposite trend was observed for the stance/swing ratio. These findings indicate an overall harmonic walking in children with CP despite the presence of asymmetry between the two legs. These results underscore the crucial role of the first independent steps in the progressive development of harmonic gait over time.

Dopamine improves defective cortical and muscular connectivity during bilateral control of gait in Parkinson's disease

Parkinson's Disease (PD)-typical declines in gait coordination are possibly explained by weakness in bilateral cortical and muscular connectivity. Here, we seek to determine whether this weakness and consequent decline in gait coordination is affected by dopamine levels. To this end, we compare cortico-cortical, cortico-muscular, and intermuscular connectivity and gait outcomes between body sides in people with PD under ON and OFF medication states, and in older adults. In our study, participants walked back and forth along a 12 m corridor. Gait events (heel strikes and toe-offs) and electrical cortical and muscular activities were measured and used to compute cortico-cortical, cortico-muscular, and intermuscular connectivity (i.e., coherences in the alpha, beta, and gamma bands), as well as features characterizing gait performance (e.g., the step-timing coordination, length, and speed). We observe that people with PD, mainly during the OFF medication, walk with reduced step-timing coordination. Additionally, our results suggest that dopamine intake in PD increases the overall cortico-muscular connectivity during the stance and swing phases of gait. We thus conclude that dopamine corrects defective feedback caused by impaired sensory-information processing and sensory-motor integration, thus increasing cortico-muscular coherences in the alpha bands and improving gait.

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.

Sensitivity to gait improvement after levodopa intake in Parkinson's disease: A comparison study among synthetic kinematic indices

The synthetic indices are widely used to describe balance and stability during gait. Some of these are employed to describe the gait features in Parkinson's disease (PD). However, the results are sometimes inconsistent, and the same indices are rarely used to compare the individuals affected by PD before and after levodopa intake (OFF and ON condition, respectively). Our aim was to investigate which synthetic measure among Harmonic Ratio, Jerk Ratio, Golden Ratio and Trunk Displacement Index is representative of gait stability and harmony, and which of these are more sensitive to the variations between OFF and ON condition. We found that all indices, except the Jerk Ratio, significantly improve after levodopa. Only the improvement of the Trunk Displacement Index showed a direct correlation with the motor improvement measured through the clinical scale UPDRS-III (Unified Parkinson's Disease Rating Scale-part III). In conclusion, we suggest that the synthetic indices can be useful to detect motor changes induced by, but not all of them clearly correlate with the clinical changes achieved with the levodopa administration. In our analysis, only the Trunk Displacement Index was able to show a clear relationship with the PD clinical motor improvement.

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.

Artificial Neural Network Detects Hip Muscle Forces as Determinant for Harmonic Walking in People after Stroke

Many recent studies have highlighted that the harmony of physiological walking is based on a specific proportion between the durations of the phases of the gait cycle. When this proportion is close to the so-called golden ratio (about 1.618), the gait cycle assumes an autosimilar fractal structure. In stroke patients this harmony is altered, but it is unclear which factor is associated with the ratios between gait phases because these relationships are probably not linear. We used an artificial neural network to determine the weights associable to each factor for determining the ratio between gait phases and hence the harmony of walking. As expected, the gait ratio obtained as the ratio between stride duration and stance duration was found to be associated with walking speed and stride length, but also with hip muscle forces. These muscles could be important for exploiting the recovery of energy typical of the pendular mechanism of walking. Our study also highlighted that the results of an artificial neural network should be associated with a reliability analysis, being a non-deterministic approach. A good level of reliability was found for the findings of our study.

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

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.

Effects of a posture shirt with back active correction keeper on static and dynamic balance in Parkinson's disease

BACKGROUND

Patients with Parkinson's disease (PD) suffer from postural disorders. This study aims at investigating the short- and medium-term effects of a shirt with appropriate tie-rods that allows to correct the posture of the trunk.

METHODS

This is a longitudinal clinical study in which a pressure platform was used to assess the static and dynamic baropodometry and the static stabilometry of 20 patients with PD (70.95 ± 8.39 years old; 13 males, time from the onset of symptoms: 6.95 ± 4.04 years, Unified Parkinson's Disease Rating Scale score: UPDRS = 7.25 ± 6.26) without and with a shirt, specifically designed for improving posture, at baseline and after one month of wearing.

RESULTS

The results showed a significant improvement in symmetry of loads (p = 0.015) and an enlargement of the foot contact surface (p = 0.038). A significant correlation was found between the change in forefoot load and time spent daily in wearing the shirt (R = 0.575, p = 0.008), with an optimal value identified at 8 h per day.

CONCLUSION

The use of a postural shirt in patients with PD symmetrized the postural load and enlarged the foot contact surface improving their balance.

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

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.

Artificial Neural Network Analyzing Wearable Device Gait Data for Identifying Patients With Stroke Unable to Return to Work

A potential dramatic effect of long-term disability due to stroke is the inability to return to work. An accurate prognosis and the identification of the parameters inflating the possibility of return to work after neurorehabilitation are crucial. Many factors may influence it, such as mobility and, in particular, walking ability. In this pilot study, two emerging technologies have been combined with the aim of developing a prognostic tool for identifying patients able to return to work: a wearable inertial measurement unit for gait analysis and an artificial neural network (ANN). Compared with more conventional statistics, the ANN showed a higher accuracy in identifying patients with respect to healthy subjects (90.9 vs. 75.8%) and also in identifying the subjects unable to return to work (93.9 vs. 81.8%). In this last analysis, the duration of double support phase resulted the most important input of the ANN. The potentiality of the ANN, developed also in other fields such as marketing on social networks, could allow a powerful support for clinicians that today should manage a large amount of instrumentally recorded parameters in patients with stroke.

A synthetic kinematic index of trunk displacement conveying the overall motor condition in Parkinson's disease

Parkinson's disease (PD) is characterized by motor impairment, affecting quality of life and increasing fall risk, due to ineffective postural control. To this day, the diagnosis remains based on clinical approach. Similarly, motor evaluation is based on heterogeneous, operator-dependent observational criteria. A synthetic, replicable index to quantify motor impairment is still lacking. Hence, we have designed a new measure of postural stability which assesses the trunk displacement in relation to the center of mass, that we named trunk displacement index (TDI). Twenty-three PD patients and twenty-three healthy controls underwent motor examination through a stereophotogrammetric system. A correlation analysis was performed to assess the relationship of TDI with gait parameters and clinical motor scale (UPDRS-III). The TDI sensitivity was estimated, comparing pre- and post- L-DOPA subclinical dose intake. The TDI showed significant correlations with many gait parameters and with the UPDRS-III. Furthermore, the TDI resulted capable in discriminating between off and on state in PD, whereas gait parameters failed two show any difference between those two conditions. Our results suggest that the TDI may be considered a highly sensitive biomechanical index, reflecting the overall motor condition in PD, and provided of clinical relevance due to the correlation with the clinical evaluation.

Auditory Cue Based on the Golden Ratio Can Improve Gait Patterns in People with Parkinson's Disease

The harmonic structure of walking relies on an irrational number called the golden ratio (ϕ): in healthy subjects, it coincides with the stride-to-stance ratio, and it is associated with a smooth gait modality. This smoothness is lost in people with Parkinson’s disease (PD), due to deficiencies in the execution of movements. However, external auditory cues seem to facilitate movement, by enabling the timing of muscle activation, and helping in initiating and modulating motor output. Based on a harmonic fractal structure of gait, can the administration of an auditory cue based on individual’s ϕ-rhythm improve, in acute, gait patterns in people with PD? A total of 20 participants (16 males, age 70.9 ± 8.4 years, Hoehn and Yahr stage-II) were assessed through stereophotogrammetry: gait spatio-temporal parameters, and stride-to-stance ratio were computed before, during, and after the ϕ-rhythm administration. Results show improvements in terms of stride length (p = 0.018), walking speed (p = 0.014), and toe clearance (p = 0.013) when comparing gait patterns before and after the stimulus. Furthermore, the stride-to-stance ratio seems to correlate with almost all spatio-temporal parameters, but it shows the main changes in the before–during rhythm comparison. In conclusion, ϕ-rhythm seems an effective cue able to compensate for defective internal rhythm of the basal ganglia in PD.

Testing the Performance of an Innovative Markerless Technique for Quantitative and Qualitative Gait Analysis

Gait abnormalities such as high stride and step frequency/cadence (SF-stride/second, CAD-step/second), stride variability (SV) and low harmony may increase the risk of injuries and be a sentinel of medical conditions. This research aims to present a new markerless video-based technology for quantitative and qualitative gait analysis. 86 healthy individuals (mead age 32 years) performed a 90 s test on treadmill at self-selected walking speed. We measured SF and CAD by a photoelectric sensors system; then, we calculated average ± standard deviation (SD) and within-subject coefficient of variation (CV) of SF as an index of SV. We also recorded a 60 fps video of the patient. With a custom-designed web-based video analysis software, we performed a spectral analysis of the brightness over time for each pixel of the image, that reinstituted the frequency contents of the videos. The two main frequency contents (F1 and F2) from this analysis should reflect the forcing/dominant variables, i.e., SF and CAD. Then, a harmony index (HI) was calculated, that should reflect the proportion of the pixels of the image that move consistently with F1 or its supraharmonics. The higher the HI value, the less variable the gait. The correspondence SF-F1 and CAD-F2 was evaluated with both paired t-Test and correlation and the relationship between SV and HI with correlation. SF and CAD were not significantly different from and highly correlated with F1 (0.893 ± 0.080 Hz vs. 0.895 ± 0.084 Hz, p < 0.001, r² = 0.99) and F2 (1.787 ± 0.163 Hz vs. 1.791 ± 0.165 Hz, p < 0.001, r² = 0.97). The SV was 1.84% ± 0.66% and it was significantly and moderately correlated with HI (0.082 ± 0.028, p < 0.001, r² = 0.13). The innovative video-based technique of global, markerless gait analysis proposed in our study accurately identifies the main frequency contents and the variability of gait in healthy individuals, thus providing a time-efficient, low-cost means to quantitatively and qualitatively study human locomotion.

IMU-Based Classification of Parkinson's Disease From Gait: A Sensitivity Analysis on Sensor Location and Feature Selection

Inertial measurement units (IMUs) have a long-lasting popularity in a variety of industrial applications from navigation systems to guidance and robotics. Their use in clinical practice is now becoming more common, thanks to miniaturization and the ability to integrate on-board computational and decision-support features. IMU-based gait analysis is a paradigm of this evolving process, and in this study its use for the assessment of Parkinson's disease (PD) is comprehensively analyzed. Data coming from 25 individuals with different levels of PD symptoms severity and an equal number of age-matched healthy individuals were included into a set of 6 different machine learning (ML) techniques, processing 18 different configurations of gait parameters taken from 8 IMU sensors. Classification accuracy was calculated for each configuration and ML technique, adding two meta-classifiers based on the results obtained from all individual techniques through majority of voting, with two different weighting schemes. Average classification accuracy ranged between 63% and 80% among classifiers and increased up to 96% for one meta-classifier configuration. Configurations based on a statistical preselection process showed the highest average classification accuracy. When reducing the number of sensors, features based on the joint range of motion were more accurate than those based on spatio-temporal parameters. In particular, best results were obtained with the knee range of motion, calculated with four IMUs, placed bilaterally. The obtained findings provide data-driven evidence on which combination of sensor configurations and classification methods to be used during IMU-based gait analysis to grade the severity level of PD.

Golden Gait: An Optimization Theory Perspective on Human and Humanoid Walking

Human walking is a complex task which includes hundreds of muscles, bones and joints working together to deliver harmonic movements with the need of finding equilibrium between moving forward and maintaining stability. Many different computational approaches have been used to explain human walking mechanisms, from pendular model to fractal approaches. A new perspective can be gained from using the principles developed in the field of Optimization theory and in particularly the branch of Game Theory. In particular we provide a new insight into human walking showing as the trade-off between advancement and equilibrium managed during walking has the same solution of the Ultimatum game, one of the most famous paradigms of game theory, and this solution is the golden ratio. The golden ratio is an irrational number that was found in many biological and natural systems self-organized in a harmonic, asymmetric, and fractal structure. Recently, the golden ratio has also been found as the equilibrium point between two players involved into the Ultimatum Game. It has been suggested that this result can be due to the fact that the golden ratio is perceived as the fairest asymmetric solution by the two players. The golden ratio is also the most common proportion between stance and swing phase of human walking. This approach may explain the importance of harmony in human walking, and provide new perspectives for developing quantitative assessment of human walking, efficient humanoid robotic walkers, and effective neurorobots for rehabilitation.

Brain lesions affecting gait recovery in stroke patients

OBJECTIVES

Gait recovery is an important goal in stroke patients. Several studies have sought to uncover relationships between specific brain lesions and the recovery of gait, but the effects of specific brain lesions on gait remain unclear. Thus, we investigated the effects of stroke lesions on gait recovery in stroke patients.

MATERIALS AND METHODS

In total, 30 subjects with stroke were assessed in a retrograde longitudinal observational study. To assess gait function, the functional ambulation category (FAC) was tested four times: initially (within 2 weeks) and 1, 3, and 6 months after the onset of the stroke. Brain lesions were analyzed via overlap, subtraction, and voxel-based lesion symptom mapping (VLSM).

RESULTS

Ambulation with FAC improved significantly with time. Subtraction analysis showed that involvement of the corona radiata, internal capsule, globus pallidus, and putamen were associated with poor recovery of gait throughout 6 months after onset. The caudate nucleus did influence poor recovery of gait at 6 months after onset. VLSM revealed that corona radiata, internal capsule, globus pallidus, putamen and cingulum were related with poor recovery of gait at 3 months after onset. Corona radiata, internal capsule, globus pallidus, putamen, primary motor cortex, and caudate nucleus were related with poor recovery of gait at 6 months after onset.

CONCLUSION

Results identified several important brain lesions for gait recovery in patients with stroke. These results may be useful for planning rehabilitation strategies for gait and understanding the prognosis of gait in stroke patients.

Harmony as a convergence attractor that minimizes the energy expenditure and variability in physiological gait and the loss of harmony in cerebellar ataxia

BACKGROUND

The harmony of the human gait was recently found to be related to the golden ratio value (ϕ). The ratio between the duration of the stance and that of the swing phases of a gait cycle was in fact found to be close to ϕ, which implies that, because of the fractal property of autosimilarity of that number, the gait ratios stride/stance, stance/swing, swing/double support, were not significantly different from one another. We studied a group of patients with cerebellar ataxia to investigate how the differences between their gait ratios and the golden ratio are related to efficiency and stability of their gait, assessed by energy expenditure and stride-to-stride variability, respectively.

METHODS

The gait of 28 patients who were affected by degenerative cerebellar ataxia and of 28 healthy controls was studied using a stereophotogrammetric system. The above mentioned gait ratios, the energy expenditure estimated using the pelvis reconstructed method and the gait variability in terms of the stride length were computed, and their relationships were analyzed. Matching procedures have also been used to avoid multicollinearity biases.

FINDINGS

The gait ratio values of the patients were farther from the controls (and hence from ϕ), even in speed matched conditions (P=0.011, Cohen's D=0.76), but not when the variability and energy expenditure were matched between the two groups (Cohen's D=0.49). In patients with cerebellar ataxia, the farther the stance-swing ratio was from ϕ, the larger the total mechanical work (R²_adj=0.64). Further, a significant positive correlation was observed between the difference of the gait ratio from the golden ratio and the severity of the disease (R=0.421, P=0.026).

INTERPRETATION

Harmony of gait appears to be a benchmark of physiological gait leading to physiological energy recovery and gait reliability. Neurorehabilitation of patients with ataxia might benefit from the restoration of harmony of their locomotor patterns.

Stability and Harmony of Gait in Patients with Subacute Stroke

Stroke affects many gait features, such as gait stability, symmetry, and harmony. However, it is still unclear which of these features are directly altered by primary damage, and which are affected by the reduced walking speed. The aim of this study was to analyze the above gait features in patients with subacute stroke with respect to the values observed in age- and speed-matched healthy subjects. A wearable triaxial accelerometer and an optoelectronic device were used for assessing the upright gait stability, symmetry of trunk movements, and harmonic structure of gait phases by means of the root-mean-square (RMS) acceleration of the trunk, harmonic ratio (HR), and gait ratios (GRs), respectively. For healthy subjects, results showed that RMS acceleration increased with speed, HR peaked at a comfortable speed, and GRs tended towards the theoretical value of the golden ratio for speeds >1 m/s. At matched speed conditions, patients showed higher instabilities in the latero-lateral axis (p = 0.001) and reduced symmetry of trunk movements (p = 0.002). Different from healthy subjects, antero-posterior and latero-lateral acceleration harmonics were coupled in patients (R = 0.507, p = 0.023). Conversely, GRs were not more altered in patients than in slow-walking healthy subjects. In conclusion, patients with stroke showed some characteristics similar to those of the elderly when the latter subjects walk slowly, and some altered characteristics, such as increased latero-lateral instabilities coupled with movements performed along the antero-posterior axis.

The connection between anthropometry and gait harmony unveiled through the lens of the golden ratio

In nature, many systems have a harmonic organization due to their fractal structure related to an irrational number called golden ratio. That is a constant proportion found in phases of human gait cycle, and is also found in the lengths of human body segments. In this study we tested if artificial alterations in anthropometric proportions may alter gait proportions. Twenty healthy subjects (29.15±5.66years) were enrolled in this study and asked to walk normally and with special shoes altering their anthropometric proportions. Further, to test if the relationship between gait phases and anthropometry could be due to the pendular mechanism of walking, subjects were also asked to walk with extra masses located on their shanks. Results showed that the artificial alteration of body segment proportions affected the gait ratio based on the proportion of time between stance and swing (p=0.015). Conversely, no changes occurred during walking in weighted condition (p=0.394). These results confirm the connection between anthropometric proportions and gait ratio, and suggest the idea that humans may have evolved into the actual anthropometric proportions for favoring a walking having a golden ratio based harmony, but research is required to verify this hypothesis.