Rethinking Margin of Stability: Incorporating Step-To-Step Regulation to Resolve the Paradox

ABSTRACTMaintaining frontal-plane stability is a major objective of human walking. Derived from inverted pendulum dynamics, the mediolateral Margin of Stability (MoSML) is frequently used to measure people’s frontal-plane stability on average. However, typical MoSML-based analyses deliver paradoxical interpretations of stability status. To address mediolateral stability using MoSML, we must first resolve this paradox. Here, we developed a novel framework that unifies the well-established inverted pendulum model with Goal-Equivalent Manifold (GEM)-based analyses to assess how humans regulate step-to-step balance dynamics to maintain mediolateral stability. We quantified the extent to which people corrected fluctuations in mediolateral center-of-mass state relative to a MoSML-defined candidate stability GEM in the inverted pendulum phase plane. Participants’ variability and step-to-step correction of tangent and perpendicular deviations from the candidate stability GEM demonstrate that regulation of balance dynamics involves more than simply trying to execute a constant-MoSML balance control strategy. Participants adapted these step-to-step corrections to mediolateral sensory and mechanical perturbations. How participants regulated mediolateral foot placement strongly predicted how they regulated center-of-mass state fluctuations, suggesting that regulation of center-of-mass state occurs as a biomechanical consequence of foot placement regulation. We introduce the Probability of Instability (PoI), a convenient statistic that accounts for step-to-step variance to properly predict instability likelihood on any given future step. Participants increased lateral PoI when destabilized, as expected. These lateral PoI indicated an increased risk of lateral instability, despite larger (i.e., more stable) average MoSML. PoI thereby explicitly predicts instability risk to decisively resolve the existing paradox that arises from conventional MoSML implementations.

Increased Arm Swing and Rocky Surfaces Reduces Postural Control in Healthy Young Adults

Fall-induced injuries can stem from a disruption in the postural control system and place a financial burden on the healthcare system. Most gait research focused on lower extremities and neglected the contribution of arm swing, which have been shown to affect the movement of the center of mass when walking. This study evaluated the effect of arm swing on postural control and stability during regular and rocky surface walking. Fifteen healthy young adults (age = 23.4 ± 2.8) walked on these two surfaces with three arm motions (normal, held, and active) using the CAREN Extended-System (Motek Medical, Amsterdam, NL). Mean, standard deviation and maximal values of trunk linear and angular velocity were calculated in all three axes. Moreover, step length, time and width mean and coefficient of variation as well as margin of stability mean and standard deviation were calculated. Active arm swing increased trunk linear and angular velocity variability and peak values compared to normal and held arm conditions. Active arm swing also increased participants’ step length and step time, as well as the variability of margin of stability. Similarly, rocky surface walking increased trunk kinematics variability and peak values compared to regular surface walking. Furthermore, rocky surface increased the average step width while reducing the average step time. Though this surface type increased the coefficient of variation of all spatiotemporal parameters, rocky surface also led to increased margin of stability mean and variation. The spatiotemporal adaptations showed the use of “cautious” gait to mitigate the destabilizing effects of both the active arm swing and rocky surface walking and, ultimately, maintain dynamic stability.

Small Directional Treadmill Perturbations Induce Differential Gait Stability Adaptation

Introducing unexpected perturbations to challenge gait stability is an effective approach to investigate balance control strategies. Little is known about the extent to which people can respond to small perturbations during walking. This study aimed to determine how subjects adapted gait stability to multidirectional perturbations with small magnitudes applied on a stride-by-stride basis. Ten healthy young subjects walked on a treadmill that either briefly decelerated belt speed ("stick"), accelerated belt speed ("slip"), or shifted the platform medial-laterally at right leg mid-stance. We quantified gait stability adaptation in both anterior-posterior and medial-lateral directions using margin of stability and its components, base of support and extrapolated center of mass. Gait stability was disrupted upon initially experiencing the small perturbations as margin of stability decreased in the stick, slip, and medial shift perturbations and increased in the lateral shift perturbation. Gait stability metrics were generally disrupted more for perturbations in the coincident direction. Subjects employed both feedback and feedforward strategies in response to the small perturbations, but mostly used feedback strategies during adaptation. Subjects primarily used base of support (foot placement) control in the lateral shift perturbation and extrapolated center of mass control in the slip and medial shift perturbations. These findings provide new knowledge about the extent of gait stability adaptation to small magnitude perturbations applied on a stride-by-stride basis and reveal potential new approaches for balance training interventions to target foot placement and center of mass control.

Perturbation-Based Balance Training Using Repeated Trips on a Walkway vs. Belt Accelerations on a Treadmill: A Cross-Over Randomised Controlled Trial in Community-Dwelling Older Adults

Background: Walkway and treadmill induced trips have contrasting advantages, for instance walkway trips have high-ecological validity whereas belt accelerations on a treadmill have high-clinical feasibility for perturbation-based balance training (PBT). This study aimed to (i) compare adaptations to repeated overground trips with repeated treadmill belt accelerations in older adults and (ii) determine if adaptations to repeated treadmill belt accelerations can transfer to an actual trip on the walkway.Method: Thirty-eight healthy community-dwelling older adults underwent one session each of walkway and treadmill PBT in a randomised crossover design on a single day. For both conditions, 11 trips were induced to either leg in pseudo-random locations interspersed with 20 normal walking trials. Dynamic balance (e.g., margin of stability) and gait (e.g., step length) parameters from 3D motion capture were used to examine adaptations in the walkway and treadmill PBT and transfer of adaptation from treadmill PBT to a walkway trip.Results: No changes were observed in normal (no-trip) gait parameters in both training conditions, except for a small (0.9 cm) increase in minimum toe elevation during walkway walks (P < 0.01). An increase in the margin of stability and recovery step length was observed during walkway PBT (P < 0.05). During treadmill PBT, an increased MoS, step length and decreased trunk sway range were observed (P < 0.05). These adaptations to treadmill PBT did not transfer to a walkway trip.Conclusions: This study demonstrated that older adults could learn to improve dynamic stability by repeated exposure to walkway trips as well as treadmill belt accelerations. However, the adaptations to treadmill belt accelerations did not transfer to an actual trip. To enhance the utility of treadmill PBT for overground trip recovery performance, further development of treadmill PBT protocols is recommended to improve ecological authenticity.

Margins of Postural Stability in Parkinson’s Disease: An Application of Control Theory

Background: Postural instability is a restrictive feature in Parkinson’s disease (PD), usually assessed by clinical or laboratory tests. However, the exact quantification of postural stability, using stability theorems that take into account the human dynamics, is still lacking. We investigated the feasibility of control theory, Nyquist stability criterion (Gain Margin – GM –, and Phase Margin – PM –), in discriminating postural instability in PD; as well as the effects of a balance-training program. Methods: Center-of-pressure (COP) data of 40 PD patients before and after a 4-week balance-training program, and 20 healthy control subjects (HCs) (Study1); as well as COP data of 20 other PD patients at four time points during a 6-week balance-training program (Study2), collected in two earlier studies, were used. COP was recorded in four tasks, two on rigid surface and two on foam, eyes-open and closed. A postural control model (an inverted-pendulum with PID controller and time delay) was fitted to the COP data, to subject-specifically identify the model parameters; thereby calculating |GM| and PM for each subject in each task.Results: Patients had smaller margin of stability (|GM|, PM) compared to HCs. Particularly, patients, unlike HCs, showed drastic drop in PM on foam. Clinical outcomes and margin of stability improved in patients after balance training. |GM| improved early at week 4, followed by a plateau in the rest of the training. In contrast, PM improved late (week 6), in a relatively continuous-progression form. Conclusions: Using fundamental stability theorems is a promising technique for standardized quantification of postural stability in various tasks.

Use of the margin of stability to quantify stability in pathologic gait – a qualitative systematic review

Background The Margin of Stability (MoS) is a widely used objective measure of dynamic stability during gait. Increasingly, researchers are using the MoS to assess the stability of pathological populations to gauge their stability capabilities and coping strategies, or as an objective marker of outcome, response to treatment or disease progression. The objectives are; to describe the types of pathological gait that are assessed using the MoS, to examine the methods used to assess MoS and to examine the way the MoS data is presented and interpreted. Methods A systematic review was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Guidelines (PRISMA) in the following databases: Web of Science, PubMed, UCL Library Explore, Cochrane Library, Scopus. All articles measured the MoS of a pathologically affected adult human population whilst walking in a straight line. Extracted data were collected per a prospectively defined list, which included: population type, method of data analysis and model building, walking tasks undertaken, and interpretation of the MoS. Results Thirty-one studies were included in the final review. More than 15 different clinical populations were studied, most commonly post-stroke and unilateral transtibial amputee populations. Most participants were assessed in a gait laboratory using motion capture technology, whilst 2 studies used instrumented shoes. A variety of centre of mass, base of support and MoS definitions and calculations were described. Conclusions This is the first systematic review to assess use of the MoS and the first to consider its clinical application. Findings suggest the MoS has potential to be a helpful, objective measurement in a variety of clinically affected populations. Unfortunately, the methodology and interpretation varies, which hinders subsequent study comparisons. A lack of baseline results from large studies mean direct comparison between studies is difficult and strong conclusions are hard to make. Further work from the biomechanics community to develop reporting guidelines for MoS calculation methodology and a commitment to larger baseline studies for each pathology is welcomed.

Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

This paper considers a relevant issue related to the influence exerted by the fuzziness in linear dynamic system parameters on its stability. It is known that the properties of automated control systems can change under the influence of parametric disturbances. To describe the change in such properties of the system, the concept of roughness is used. It should be noted that taking into consideration the fuzziness in the parameters of mathematical models could make it possible at the design stage to assess all the risks that may arise as a result of an uncontrolled change in the parameters of dynamic systems during their operation. To prevent negative consequences due to variance in the parameters of mathematical models, automated control systems are designed on the basis of the requirement for ensuring a certain margin of stability of the system in terms of its amplitude and phase. At the same time, it remains an open question whether such a system would satisfy the conditions of roughness. Parameters of the mathematical model of a system are considered as fuzzy quantities that have a triangular membership function. This function is inconvenient for practical use, so it is approximated by the Gaussian function. That has made it possible to obtain formulas for calculating the characteristic polynomial and the transfer function of the open system, taking into consideration the fuzziness of their parameters. When investigating the system according to Mikhailov’s criterion, it was established that the dynamic system retains stability in the case when the parameters of the characteristic equation are considered as fuzzy quantities. It has been determined that the quality of the system significantly deteriorated in terms of its stability that could make it enter a non-steady state. When using the Nyquist criterion, it was established that taking into consideration the fuzziness in the parameters of the transfer function did not affect the stability of the closed system but there was a noticeable decrease in the system stability reserve both in terms of phase and amplitude. The relative decrease in the margin of stability for amplitude was 16 %, and for phase ‒ 17.4 %.

Recovery of dynamic stability during slips unaffected by arm swing in people with Parkinson’s Disease

The arm elevation strategy assists in recovering stability during slips in healthy young and elderly individuals. However, in people with Parkinson’s Disease, one of the main motor symptoms affecting the upper limbs is reduced arm swing which intensifies throughout the course of the disease before becoming absent. This holds direct implications for these individuals when encountering slips as the arm elevation strategy is an integral component in the interlimb slip response to restore stability. Arm swing’s effect in recovering from slips in people with Parkinson’s Disease though remains unexamined. Twenty people with Parkinson’s Disease (63.78 ± 8.97 years) walked with restricted and unrestricted arm swing conditions on a dual-belt treadmill where slips were induced on the least and most affected sides. Data were collected on the CAREN Extended System (Motek Medical, Amsterdam, NL). The Margin of Stability, linear and angular trunk velocities, as well as step length, time, and width were calculated. Data were examined during the slipped step and recovery step. The restricted arm swing condition, compared to unrestricted, caused a faster step time during the slipped step. Compared to the most affected leg, the least affected had a wider step width during the slipped step. During the recovery step, the least affected leg had a larger anteroposterior Margin of Stability and longer step time than the most affected. No differences between our arm swing conditions suggests that the normal arm swing in our participants was not more effective at restoring stability after an induced slip compared to when their arm motion was restricted. This may be due to the arm elevation strategy being ineffective in counteracting the slip’s backward destabilization in these individuals. Differences between the legs revealed that our participants were asymmetrically impaired in their slip recovery response.

Kinect V2-Based Gait Analysis for Children with Cerebral Palsy: Validity and Reliability of Spatial Margin of Stability and Spatiotemporal Variables

Children with cerebral palsy (CP) have high risks of falling. It is necessary to evaluate gait stability for children with CP. In comparison to traditional motion capture techniques, the Kinect has the potential to be utilised as a cost-effective gait stability assessment tool, ensuring frequent and uninterrupted gait monitoring. To evaluate the validity and reliability of this measurement, in this study, ten children with CP performed two testing sessions, of which gait data were recorded by a Kinect V2 sensor and a referential Motion Analysis system. The margin of stability (MOS) and gait spatiotemporal metrics were examined. For the spatiotemporal parameters, intraclass correlation coefficient (ICC2,k) values were from 0.83 to 0.99 between two devices and from 0.78 to 0.88 between two testing sessions. For the MOS outcomes, ICC2,k values ranged from 0.42 to 0.99 between two devices and 0.28 to 0.69 between two test sessions. The Kinect V2 was able to provide valid and reliable spatiotemporal gait parameters, and it could also offer accurate outcome measures for the minimum MOS. The reliability of the Kinect V2 when assessing time-specific MOS variables was limited. The Kinect V2 shows the potential to be used as a cost-effective tool for CP gait stability assessment.