EC Kuska, KM Steele (2024) “Does crouch alter the effects of neuromuscular impairments on gait? A simulation study”

Journal Article in Journal of Biomechanics

Cerebral palsy (CP) is a neurologic injury that impacts control of movement. Individuals with CP also often develop secondary impairments like weakness and contracture. Both altered motor control and secondary impairments influence how an individual walks after neurologic injury. However, understanding the complex interactions between and relative effects of these impairments makes analyzing and improving walking capacity in CP challenging.

A sagittal-plane musculoskeletal model and neuromuscular simulation framework that tracked average nondisabled (ND) kinematics and moderate and severe crouch gait. The model contains nine degrees-of-freedom (pelvic tilt and translation, and right and left hip, knee, and ankle flexion) actuated by eight Hill-type musculotendinous units per leg. The objective function minimized deviations from tracked kinematics and the sum of muscle activations squared (a2). We perturbed each gait simulation with multi-modal neuromuscular impairments—altered control, weakness, and contracture—of varying severities. Altered control was simulated by reducing the number of fixed synergies controlling each leg, and weakness and contracture were simulated by reducing a muscle’s maximum isometric force ( ) and tendon slack length ( ), respectively. A Bayesian Additive Regression Trees (BART) model then predicted resultant a2 from the simulated neuromuscular impairments for crouch and ND gait to evaluate the relative effects of each simulated neuromuscular impairment on the muscle activations required to maintain each gait pattern.Aim: The purpose of this study was to investigate the interactions between neuromuscular impairments and gait in CP.

Methods: We used a sagittal-plane musculoskeletal model and neuromuscular control framework to simulate crouch and nondisabled gait. We perturbed each simulation by varying the number of synergies controlling each leg (altered control), and imposed weakness and contracture. A Bayesian Additive Regression Trees (BART) model was also used to parse the relative effects of each impairment on the muscle activations required for each gait pattern.

Results: By using these simulations to evaluate gait-pattern specific effects of neuromuscular impairments, we identified some advantages of crouch gait. For example, crouch tolerated 13 % and 22 % more plantarflexor weakness than nondisabled gait without and with altered control, respectively. Furthermore, BART demonstrated that plantarflexor weakness had twice the effect on total muscle activity required during nondisabled gait than crouch gait. However, crouch gait was also disadvantageous in the presence of vasti weakness: crouch gait increased the effects of vasti weakness on gait without and with altered control.

Interpretation: These simulations highlight gait-pattern specific effects and interactions between neuromuscular impairments. Utilizing computational techniques to understand these effects can elicit advantages of gait deviations, providing insight into why individuals may select their gait pattern and possible interventions to improve energetics.

NL Zaino, Z McKee, CD Caskey, KM Steele, HA Feldner (2024) “Perceptions and experiences of first mobility aid provision for young children with cerebral palsy in the United States: a mixed-methods study”

Journal Article in Disability and Rehabilitation: Assistive Technology 

This research provides insights into the lived experiences of clinicians and caregivers of young children with CP regarding the prescription, provision, use and impact of first mobility aids, specifically ankle foot orthoses and walkers/gait trainers.

Caregiver views of impact of first orthoses (n = 8) and walkers (n = 4). Proportional bar graph depicting caregiver perceptions on the impacts of their child’s ankle foot orthoses and/or walkers on various activities.Aim: The purpose of this study was to establish and understand the provision process and impacts of first mobility aids for children with cerebral palsy (CP) in the United States – specifically orthoses, walkers and gait-trainers.

Methods: We performed a mixed-methods study including surveys and semi-structured interviews of caregivers of young children with CP (n = 10) and clinicians who work with young children with CP (n = 29). We used content analysis for the surveys and inductive coding for the interviews.

Results: Four themes emerged: (1) first mobility aids have mixed impacts and use patterns, (2) there is varied caregiver education and understanding about mobility aids, (3) clinician knowledge, consistency and connection impact care and (4) numerous access barriers exist for families, and there are still opportunities for improvement across all domains.

Interpretation: This study not only provides researchers and clinicians with an understanding of the current status of the prescription and provision process in the United States, but also offers suggestions for improvements of the process and mobility aids themselves. These results have implications for future research, mobility aid, design and the provision process of first mobility aids.

MC Rosenberg, JL Proctor, KM Steele (2024) “Quantifying changes in individual-specific template-based representations of center-of-mass dynamics during walking with ankle exoskeletons using Hybrid-SINDy”

Journal Article in Scientific Reports

Ankle exoskeletons alter whole-body walking mechanics, energetics, and stability by altering center-of-mass (CoM) motion. Controlling the dynamics governing CoM motion is, therefore, critical for maintaining efficient and stable gait. However, how CoM dynamics change with ankle exoskeletons is unknown, and how to optimally model individual-specific CoM dynamics, especially in individuals with neurological injuries, remains a challenge.

Depictions of walking conditions, phase variables, and example template state variables. (A) Two-dimensional depictions of template model applied to human walking without and with ankle exoskeletons (left). The phase portrait (right) defined a phase variable, , used to cluster kinematically similar measurements for model fitting. Colors denote gait phases corresponding to first and second double-limb support, single-limb support, and swing of the right leg. (B) Stride-averaged global CoM position, velocity, and acceleration for an exemplary unimpaired adult in the anterior–posterior, vertical, and mediolateral directions. The three exoskeleton conditions are shown in panels (B) and (C): shoes-only (solid lines), zero-stiffness exoskeletons (K0; dashed lines), and stiff exoskeletons (KH; dotted lines). (C) Template position and velocity states used to fit the template signatures were defined by sagittal- and frontal-plane leg angles, and leg length.Aim: Evaluate individual-specific changes in CoM dynamics in unimpaired adults and one individual with post-stroke hemiparesis while walking in shoes-only and with zero-stiffness and high-stiffness passive ankle exoskeletons.

Methods: To identify optimal sets of physically interpretable mechanisms describing CoM dynamics, termed template signatures, we leveraged hybrid sparse identification of nonlinear dynamics (Hybrid-SINDy), an equation-free data-driven method for inferring sparse hybrid dynamics from a library of candidate functional forms.

Results: In unimpaired adults, Hybrid-SINDy automatically identified spring-loaded inverted pendulum-like template signatures, which did not change with exoskeletons (p > 0.16), except for small changes in leg resting length (p < 0.001). Conversely, post-stroke paretic-leg rotary stiffness mechanisms increased by 37–50% with zero-stiffness exoskeletons.

Interpretation: While unimpaired CoM dynamics appear robust to passive ankle exoskeletons, how neurological injuries alter exoskeleton impacts on CoM dynamics merits further investigation. Our findings support Hybrid-SINDy’s potential to discover mechanisms describing individual-specific CoM dynamics with assistive devices.

MR Ebers, KM Steele, JN Kutz (2024) “Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects”

Journal Article in SIAM Journal on Applied Dynamical Systems

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms.

Top panel: An approximate dynamical model f(·) provides estimates of system behavior used for both reconstruction and forecasting (shaded region), x(t). However, true behavior x0(t) (without observation noise) deviates from these estimates. The goal of discrepancy modeling is to learn a discrepancy model that recovers the missing physics and augments the approximate dynamics to improve system characterization, ˜x(t). Bottom panel: There are two approaches for building a discrepancy model to estimate missing physics: (i) modeling systematic state-space residual between the approximate state space, x(t), and true state space, x0(t), and (ii) learning the deterministic dynamical error between the true dynamics, x˙ 0(t) = f(x0(t)) + g(x0(t)), and the approximate dynamics, x˙ (t) = f(x(t)). In real-world systems, the true system behavior is noisily observed, yk = x0(tk) + N(μ, σ), model-measurement mismatch contains both deterministic and random effects; measurements yk = y(kΔt) denote a continuous dynamical system’s full state noisily observed at discrete time points.

Aim: Introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used.

Method: Specifically, we use four fundamentally different methods to demonstrate the mathematical implementations of discrepancy modeling: (i) the sparse identification of nonlinear dynamics (SINDy), (ii) dynamic mode decomposition (DMD), (iii) Gaussian process regression (GPR), and (iv) neural networks (NN). The choice of method depends on one’s intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., state- or dynamical-space operability).

Results: We demonstrate the utility and suitability for both discrepancy modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type.

Interpretation: In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.

AM Spomer, BC Conner, MH Schwartz, ZF Lerner, KM Steele (2023) “Audiovisual biofeedback amplifies plantarflexor adaptation during walking among children with cerebral palsy”

Journal Article in Journal of NeuroEngineering and Rehabilitation

Biofeedback is a promising noninvasive strategy to enhance gait training among individuals with cerebral palsy (CP). Commonly, biofeedback systems are designed to guide movement correction using audio, visual, or sensorimotor (i.e., tactile or proprioceptive) cues, each of which has demonstrated measurable success in CP.

Figure 1. Experimental Protocol. Audiovisual (AV) biofeedback on soleus activity was provided for the more-affected limb alongside an auto-adjusting target score. Sensorimotor (SM) biofeedback was provided for the more-affected limb using an untethered ankle exoskeleton designed to impart a resistive ankle torque through stance, proportional to baseline values. Participants completed three data collection visits (pre-acclimation, post-acclimation, and follow-up), during which they walked with both biofeedback systems independently and in combination. Trials were pseudo-randomized within and between visits to ensure that feedback modalities were presented to each participant in a different order and control for fatigue and learning effects. Each trial was 10 min long and separated into baseline, feedback, and washout phases. All data analysis was performed for early (strides 1–30), mid (strides 91–110), and late (strides 181–210) feedback phases and washout (strides 1–30). Mean soleus activity for individual strides (purple dots) was normalized to baseline activity. Between the pre-acclimation and post-acclimation visits, participants completed four, 20-min acclimation sessions where they received additional practice with both systems

Aim: The aim of this study is to evaluate how the modality of biofeedback may influence user response which has significant implications if systems are to be consistently adopted into clinical care.

Method: In this study, we evaluated the extent to which adolescents with CP (7M/1F; 14 [12.5,15.5] years) adapted their gait patterns during treadmill walking (6 min/modality) with audiovisual (AV), sensorimotor (SM), and combined AV + SM biofeedback before and after four acclimation sessions (20 min/session) and at a two-week follow-up. Both biofeedback systems were designed to target plantarflexor activity on the more-affected limb, as these muscles are commonly impaired in CP and impact walking function. SM biofeedback was administered using a resistive ankle exoskeleton and AV biofeedback displayed soleus activity from electromyography recordings during gait. At every visit, we measured the time-course response to each biofeedback modality to understand how the rate and magnitude of gait adaptation differed between modalities and following acclimation.

Results: Participants significantly increased soleus activity from baseline using AV + SM (42.8% [15.1, 59.6]), AV (28.5% [19.2, 58.5]), and SM (10.3% [3.2, 15.2]) biofeedback, but the rate of soleus adaptation was faster using AV + SM biofeedback than either modality alone. Further, SM-only biofeedback produced small initial increases in plantarflexor activity, but these responses were transient within and across sessions (p > 0.11). Following multi-session acclimation and at the two-week follow-up, responses to AV and AV + SM biofeedback were maintained.

Interpretation: This study demonstrated that AV biofeedback was critical to increase plantarflexor engagement during walking, but that combining AV and SM modalities further amplified the rate of gait adaptation. Beyond improving our understanding of how individuals may differentially prioritize distinct forms of afferent information, outcomes from this study may inform the design and selection of biofeedback systems for use in clinical care.