Orbital stability analysis in biomechanics: a systematic review of a nonlinear technique to detect instability of motor tasks

Enhanced assessment of human dynamic stability by eliminating the effect of body height: modeling and experiment study

Margin of stability (MOS) is one of the essential indices for evaluating dynamic stability. However, there are indications that MOS was affected by body height and its application in identifying factors on dynamic stability other than body height is restricted. An inverted pendulum model was used to simulate human walking and investigate the relevance between MOS and body height. Eventually, a height-independent index in dynamic stability assessment (named as Angled Margin of Stability, AMOS) was proposed. For testing, fifteen healthy young volunteers performed walking trials with normal arm swing, holding arms, and anti-normal arm swing. Kinematic parameters were recorded using a gait analysis system with a Microsoft Kinect V2.0 and instrumented walkway. Both simulation and test results show that MOS had a significant correlation with height during walking with normal arm swing, while AMOS had no such significant correlation. Walking with normal arm swing produced significantly larger AMOS than holding arms and anti-normal arm swing. However, no significant difference showed up in MOS between normal arm swing and holding arms. The results suggest that AMOS is not affected by body height and has the potential to identify the variations in dynamic stability caused by physiological factors other than body height.

Nonlinear Dynamic Measures of Walking in Healthy Older Adults: A Systematic Scoping Review

Background: Maintaining a healthy gait into old age is key to preserving the quality of life and reducing the risk of falling. Nonlinear dynamic analyses (NDAs) are a promising method of identifying characteristics of people who are at risk of falling based on their movement patterns. However, there is a range of NDA measures reported in the literature. The aim of this review was to summarise the variety, characteristics and range of the nonlinear dynamic measurements used to distinguish the gait kinematics of healthy older adults and older adults at risk of falling. Methods: Medline Ovid and Web of Science databases were searched. Forty-six papers were included for full-text review. Data extracted included participant and study design characteristics, fall risk assessment tools, analytical protocols and key results. Results: Among all nonlinear dynamic measures, Lyapunov Exponent (LyE) was most common, followed by entropy and then Fouquet Multipliers (FMs) measures. LyE and Multiscale Entropy (MSE) measures distinguished between older and younger adults and fall-prone versus non-fall-prone older adults. FMs were a less sensitive measure for studying changes in older adults’ gait. Methodology and data analysis procedures for estimating nonlinear dynamic measures differed greatly between studies and are a potential source of variability in cross-study comparisons and in generating reference values. Conclusion: Future studies should develop a standard procedure to apply and estimate LyE and entropy to quantify gait characteristics. This will enable the development of reference values in estimating the risk of falling.

Magnetic Resonance Imaging-based biomechanical simulation of cartilage: A systematic review

MRI-based mathematical and computational modeling studies can contribute to a better understanding of the mechanisms governing cartilage's mechanical performance and cartilage disease. In addition, distinct modeling of cartilage is needed to optimize artificial cartilage production. These studies have opened up the prospect of further deepening our understanding of cartilage function. Furthermore, these studies reveal the initiation of an engineering-level approach to how cartilage disease affects material properties and cartilage function. Aimed at researchers in the field of MRI-based cartilage simulation, research articles pertinent to MRI-based cartilage modeling were identified, reviewed, and summarized systematically. Various MRI applications for cartilage modeling are highlighted, and the limitations of different constitutive models used are addressed. In addition, the clinical application of simulations and studied diseases are discussed. The paper's quality, based on the developed questionnaire, was assessed, and out of 79 reviewed papers, 34 papers were determined as high-quality. Due to the lack of the best constitutive models for various clinical conditions, researchers may consider the effect of constitutive material models on the cartilage disease simulation. In the future, research groups may incorporate various aspects of machine learning into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification, such as gait analysis.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.

A systematic review of center of pressure measures to quantify gait changes in older adults

Measures of gait center of pressure (COP) can be recorded using simple available technologies in clinical settings and thus can be used to characterize gait quality in older adults and its relationship to falls. The aim of this systematic review was to investigate the association between measures of gait COP and aging and falls. A comprehensive search of electronic databases including MEDLINE, Embase, Cochrane Central Register of Controlled Trials, CINAHL (EBSCO), Ageline (EBSCO) and Scopus was performed. The initial search yielded 2809 papers. After removing duplicates and applying study inclusion/exclusion criteria, 34 papers were included in the review. Gait COP has been examined during three tasks: normal walking, gait initiation, and obstacle negotiation. The majority of studies examined mean COP position and velocity as outcome measures. Overall, gait in older adults was characterized by more medial COP trajectory in normal walking and lower average anterior-posterior and medio-lateral COP displacements and velocity in both gait initiation and obstacle crossing. Moreover, findings suggest that Tai chi training can enhance older adults' balance control during gait initiation as demonstrated by greater COP backward, medial and forward shift in all three phases of gait initiation. These findings should be interpreted cautiously due to inadequacy of evidence as well as methodological limitations of the studies such as small sample size, limited numbers of 'fallers', lack of a control group, and lack of interpretation of COP outcomes with respect to fall risk. COP measures can be adopted to assess fall-related gait changes in older adults but more complex measures of COP that reveal the dynamic nature of COP behavior in step-to-step variations are needed to adequately characterize gait changes in older adults.

Mediolateral damping of an overhead body weight support system assists stability during treadmill walking

BACKGROUND

Body weight support systems with three or more degrees of freedom (3-DoF) are permissive and safe environments that provide unloading and allow unrestricted movement in any direction. This enables training of walking and balance control at an early stage in rehabilitation. Transparent systems generate a support force vector that is near vertical at all positions in the workspace to only minimally interfere with natural movement patterns. Patients with impaired balance, however, may benefit from additional mediolateral support that can be adjusted according to their capacity. An elegant solution for providing balance support might be by rendering viscous damping along the mediolateral axis via the software controller. Before use with patients, we evaluated if control-rendered mediolateral damping evokes the desired stability enhancement in able-bodied individuals.

METHODS

A transparent, cable-driven robotic body weight support system (FLOAT) was used to provide transparent body weight support with and without mediolateral damping to 21 able-bodied volunteers while walking at preferred gait velocity on a treadmill. Stability metrics reflecting resistance to small and large perturbations were derived from walking kinematics and compared between conditions and to free walking.

RESULTS

Compared to free walking, the application of body weight support per-se resulted in gait alterations typically associated with body weight support, namely increased step length and swing phase. Frontal plane dynamic stability, measured by kinematic variability and nonlinear dynamics of the center of mass, was increased under body weight support, indicating reduced balance requirements in both damped and undamped support conditions. Adding damping to the body weight support resulted in a greater increase of frontal plane stability.

CONCLUSION

Adding mediolateral damping to 3-DoF body weight support systems is an effective method of increasing frontal plane stability during walking in able-bodied participants. Building on these results, adjustable mediolateral damping could enable therapists to select combinations of unloading and stability specifically for each patient and to adapt this in a task specific manner. This could extend the impact of transparent 3-DoF body weight support systems, enabling training of gait and active balance from an early time point onwards in the rehabilitation process for a wide range of mobility activities of daily life.

Towards an objective assessment of motor function in sub-acute stroke patients: Relationship between clinical rating scales and instrumental gait stability indexes

The assessment of walking function alterations is a key issue to design effective rehabilitative interventions in sub-acute stroke patients. Nevertheless, the objective quantification of these alterations remains a challenge. Clinical rating scales are commonly used in clinical practice, but have been proven prone to errors associated to the evaluator subjective perception. On the other hand, instrumental measurement of trunk acceleration can be exploited for an objective quantitative characterization of gait function, but it is not applied in routine clinical practice, because the resulting quantitative indexes have not been related to the clinically information, conventionally provided by the rating scales. To overcome this limitation, the relationship between the indexes, in specific clinical conditions, and rating scale must be better investigated, to support their exploitability in the clinical practice as a fast and reliable screening tool. Thirty-one sub-acute stroke patients (17 with and 14 without cane) participated in the study. All were assessed with 6 rating scales (MI, TCT, MRI, FAC, WHS, CIRS) and 2 functional tests (2MWT and TUG). Sample Entropy (SEN) and Recurrence Quantification Analysis (RQA) in AP, ML and V directions were calculated over 2MWT and walking section of TUG. The influence of assessment task and cane was analysed, as well as correlation of SEN and RQA indexes with clinical rating scales. SEN and RQA on the medio-lateral plane resulted influenced by the use of the cane, while the correlations between indexes and clinical scales showed that SEN and RQA for antero-posterior direction correlate positively with WHS.

Motor equivalence and structure of variance: multi-muscle postural synergies in Parkinson's disease

We explored posture-stabilizing multi-muscle synergies with two methods of analysis of multi-element, abundant systems: (1) Analysis of inter-cycle variance; and (2) Analysis of motor equivalence, both quantified within the framework of the uncontrolled manifold (UCM) hypothesis. Data collected in two earlier studies of patients with Parkinson's disease (PD) were re-analyzed. One study compared synergies in the space of muscle modes (muscle groups with parallel scaling of activation) during tasks performed by early-stage PD patients and controls. The other study explored the effects of dopaminergic medication on multi-muscle-mode synergies. Inter-cycle variance and absolute magnitude of the center of pressure displacement across consecutive cycles were quantified during voluntary whole-body sway within the UCM and orthogonal to the UCM space. The patients showed smaller indices of variance within the UCM and motor equivalence compared to controls. The indices were also smaller in the off-drug compared to on-drug condition. There were strong across-subject correlations between the inter-cycle variance within/orthogonal to the UCM and motor equivalent/non-motor equivalent displacements. This study has shown that, at least for cyclical tasks, analysis of variance and analysis of motor equivalence lead to metrics of stability that correlate with each other and show similar effects of disease and medication. These results show, for the first time, intimate links between indices of variance and motor equivalence. They suggest that analysis of motor equivalence, which requires only a handful of trials, could be used broadly in the field of motor disorders to analyze problems with action stability.

Sit-to-Stand Transition Reveals Acute Fall Risk in Activities of Daily Living

The focus of this paper was on finding wrist sensor-derived features for detecting highly acute fall risk from the sit-to-stand transitions performed in a non-ambulatory environment. Furthermore, the influence of the dominant and non-dominant hand on these features was investigated. A cohort of 174 older subjects was monitored for seven consecutive days in their home setting by using inertial sensors attached at the wrist. Based on the reported falls during a one-month follow-up phase, two groups were defined. Twenty-one time and frequency domain features were implemented for the quantitative assessment of extracted sit-to-stand transitions. The statistical analysis yielded two features that could convincingly distinguish fallers from non-fallers for the dominant hand, and six for the non-dominant hand. A novel feature, energy of the applied support during standing up, showed statistically good performance independently of on which hand the sensor node was worn, as well as for the dominant and non-dominant hand ([Formula: see text], [Formula: see text], and [Formula: see text], respectively). This paper overcomes limitations of clinical tests and shows a reliable application of wrist-worn bands in terms of assessment of highly acute fall risk. In addition, it reveals the sit-to-stand transition as a potential assessment source for the wrist-worn devices in the elderly population. Early assessment of the risk of falling in a widely accepted and non-stigmatized manner has the ability to bring crucial changes in fall prevention strategies, reducing the number of falls and the fall rate.

Body Acceleration as Indicator for Walking Economy in an Ageing Population

BACKGROUND

In adults, walking economy declines with increasing age and negatively influences walking speed. This study aims at detecting determinants of walking economy from body acceleration during walking in an ageing population.

METHODS

35 healthy elderly (18 males, age 51 to 83 y, BMI 25.5±2.4 kg/m2) walked on a treadmill. Energy expenditure was measured with indirect calorimetry while body acceleration was sampled at 60Hz with a tri-axial accelerometer (GT3X+, ActiGraph), positioned on the lower back. Walking economy was measured as lowest energy needed to displace one kilogram of body mass for one meter while walking (WCostmin, J/m/kg). Gait features were extracted from the acceleration signal and included in a model to predict WCostmin.

RESULTS

On average WCostmin was 2.43±0.42 J/m/kg and correlated significantly with gait rate (r2 = 0.21, p<0.01) and regularity along the frontal (anteroposterior) and lateral (mediolateral) axes (r2 = 0.16, p<0.05 and r2 = 0.12, p<0.05 respectively). Together, the three variables explained 46% of the inter-subject variance (p<0.001) with a standard error of estimate of 0.30 J/m/kg. WCostmin and regularity along the frontal and lateral axes were related to age (WCostmin: r2 = 0.44, p<0.001; regularity: r2 = 0.16, p<0.05 and r2 = 0.12, p<0.05 respectively frontal and lateral).

CONCLUSIONS

The age associated decline in walking economy is induced by the adoption of an increased gait rate and by irregular body acceleration in the horizontal plane.

Measures of gait stability: performance on adults and toddlers at the beginning of independent walking

BACKGROUND

Quantifying gait stability is a topic of high relevance and a number of possible measures have been proposed. The problem in validating these methods is the necessity to identify a-priori unstable individuals. Since proposed methods do not make any assumption on the characteristics of the subjects, the aim of the present study was to test the performance of gait stability measures on individuals whose gait is a-priori assumed unstable: toddlers at the onset of independent walking.

METHODS

Ten toddlers, ten adults and ten elderly subjects were included in the study. Data from toddlers were acquired longitudinally over a 6-month period to test if the methods detected the increase in gait stability with experience, and if they could differentiate between toddlers and young adults. Data from elderly subjects were expected to indicate a stability value in between the other two groups. Accelerations and angular velocities of the trunk and of the leg were measured using two tri-axial inertial sensors. The following methods for quantifying gait stability were applied: stride time variability, Poincaré plots, harmonic ratio, short term Lyapunov exponents, maximum Floquet multipliers, recurrence quantification analysis and multiscale entropy. An unpaired t-test (level of significance of 5%) was performed on the toddlers and the young adults for each method and, for toddlers, for each evaluated stage of gait development.

RESULTS

Methods for discerning between the toddler and the adult groups were: stride time variability, Poincaré plots, harmonic ratio, short term Lyapunov exponents (state space composed by the three linear accelerations of the trunk), recurrence quantification analysis and multiscale entropy (when applied on the vertical or on the antero-posterior L5 accelerations).

CONCLUSIONS

Results suggested that harmonic ratio and recurrence quantification analysis better discern gait stability in the analyzed subjects, differentiating not only between unstable toddlers and stable healthy adults, but also evidencing the expected trend of the toddlers towards a higher stability with walking experience, and indicating elderly subjects as stable as or less stable than young adults.

A new perspective on the walking margin of stability

There remains a pressing need for a stability metric that can reliably identify fall susceptibility during walking, enabling more effective gait rehabilitation for reduced fall incidence. One available metric is the maximum margin of stability (MOS(max)), which is calculated using the body's center of mass (COM) position and velocity along with the location of the maximum center of pressure (COP(max)). However, MOS(max) has several limitations that may limit stability assessment. Specifically, the assumptions of a fixed COP and constant ground reaction force (GRF) are not applicable to gait. To address these limitations, a modified MOS equation that allows for a variable COP and is not dependent on a constant GRF is presented here. The modified MOS was significantly lower than MOS(max) throughout a significant portion of single limb support for normal walking gait. This finding indicates the MOS(max) metric may lack sensitivity to instability as it may still be positive when the actual MOS indicates existing or impending instability. This comparison also showed that the MOS might offer additional information about walking stability relevant to gait assessment for fall prevention and rehabilitation. However, like other stability metrics, this capability must be established with further investigations of perturbed and pathological gait.

Gait variability and stability measures: minimum number of strides and within-session reliability

BACKGROUND

Several methods are proposed in the literature for the quantification of gait variability/stability from trunk accelerations. Since outputs can be influenced by implementation differences, reliability assessment and standardization of implementation parameters are still an issue. The aim of this study is to assess the minimum number of required strides and the within-session reliability of 11 variability/stability measures.

METHOD

Ten healthy participants walked in a straight line at self-selected speed wearing two synchronized tri-axial Inertial Measurement Units. Five variability measures were calculated based on stride times namely Standard deviation, Coefficient of variation, Inconsistency of variance, Nonstationary index and Poincaré plot. Six stability measures were calculated based on trunk accelerations namely Maximum Floquet multipliers, Short term/long term Lyapunov exponents, Recurrence quantification analysis, Multiscale entropy, Harmonic ratio and Index of harmonicity. The required minimum number of strides and the within-session reliability for each measure were obtained based on the interquartile range/mean ratio. Measures were classified in five categories (namely excellent, good, average, poor, and very poor) based on their reliability.

RESULTS

The number of strides required to obtain a reliable measure was generally larger than those conventionally used. Variability measures showed average to poor reliability, while stability measures ranged from excellent to very poor reliability.

CONCLUSION

Recurrence quantification analysis and multiscale entropy of trunk accelerations showed excellent reliability and a reasonable number of required strides. Based on these results, these measures should be taken into consideration in the assessment of fall risk.

Influence of input parameters on dynamic orbital stability of walking: in-silico and experimental evaluation

Many measures aiming to assess the stability of human motion have been proposed in the literature, but still there is no commonly accepted way to define or quantify locomotor stability. Among these measures, orbital stability analysis via Floquet multipliers is still under debate. Some of the controversies concerning the use of this technique could lie in the absence of a standard implementation. The aim of this study was to analyse the influence of i) experimental measurement noise, ii) variables selected for the construction of the state space, and iii) number of analysed cycles on the outputs of orbital stability applied to walking. The analysis was performed on a 2-dimensional 5-link walking model and on a sample of 10 subjects performing long over-ground walks. Noise resulting from stereophotogrammetric and accelerometric measurement systems was simulated in the in-silico analysis. Maximum Floquet multipliers resulted to be affected by both number of analysed strides and state space composition. The effect of experimental noise was found to be slightly more potentially critical when analysing stereophotogrammetric data then when dealing with acceleration data. Experimental and model results were comparable in terms of overall trend, but a difference was found in the influence of the number of analysed cycles.

Estimating fall risk with inertial sensors using gait stability measures that do not require step detection

Falls have major consequences both at societal (health-care and economy) and individual (physical and psychological) levels. Questionnaires to assess fall risk are commonly used in the clinic, but their predictive value is limited. Objective methods, suitable for clinical application, are hence needed to obtain a quantitative assessment of individual fall risk. Falls in older adults often occur during walking and trunk position is known to play a critical role in balance control. Therefore, analysis of trunk kinematics during gait could present a viable approach to the development of such methods. In this study, nonlinear measures such as harmonic ratio (HR), index of harmonicity (IH), multiscale entropy (MSE) and recurrence quantification analysis (RQA) of trunk accelerations were calculated. These measures are not dependent on step detection, a potentially critical source of error. The aim of the present study was to investigate the association between the aforementioned measures and fall history in a large sample of subjects (42 fallers and 89 non - fallers) aged 50 or older. Univariate associations with fall history were found for MSE and RQA parameters in the AP direction; the best classification results were obtained for MSE with scale factor τ = 2 and for maximum length of diagonals in RQA (72.5% and 71% correct classifications, respectively). MSE and RQA were found to be positively associated with fall history and could hence represent useful tools in the identification of subjects for fall prevention programs.

Assessing the stability of human locomotion: a review of current measures

Falling poses a major threat to the steadily growing population of the elderly in modern-day society. A major challenge in the prevention of falls is the identification of individuals who are at risk of falling owing to an unstable gait. At present, several methods are available for estimating gait stability, each with its own advantages and disadvantages. In this paper, we review the currently available measures: the maximum Lyapunov exponent (λS and λL), the maximum Floquet multiplier, variability measures, long-range correlations, extrapolated centre of mass, stabilizing and destabilizing forces, foot placement estimator, gait sensitivity norm and maximum allowable perturbation. We explain what these measures represent and how they are calculated, and we assess their validity, divided up into construct validity, predictive validity in simple models, convergent validity in experimental studies, and predictive validity in observational studies. We conclude that (i) the validity of variability measures and λS is best supported across all levels, (ii) the maximum Floquet multiplier and λL have good construct validity, but negative predictive validity in models, negative convergent validity and (for λL) negative predictive validity in observational studies, (iii) long-range correlations lack construct validity and predictive validity in models and have negative convergent validity, and (iv) measures derived from perturbation experiments have good construct validity, but data are lacking on convergent validity in experimental studies and predictive validity in observational studies. In closing, directions for future research on dynamic gait stability are discussed.