Machine Learning

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

Katie Landwehr JournalArticle, MotorControl, Publications , , , ,

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.

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”

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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.

UW Data Science Seminar with Megan Ebers

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Title slide from the UW eScience Data Science seminar that says "Mobile sensing with shallow recurrent decoder networks. Megan R. Ebers"

Steele lab member and postdoctoral scholar, Megan Ebers, was featured in the Winter 2024 UW Data Science Seminar series. You can watch her full presentation on “Mobile sensing with shallow recurrent decoder networks” linked HERE on UW eScience Institute’s YouTube channel.

Abstract: Sensing is a fundamental task for the monitoring, forecasting, and control of complex systems. In many applications, a limited number of sensors are available and must move with the dynamics, such as with wearable technology or ocean monitoring buoys. In these dynamic systems, the sensors’ time history encodes a significant amount of information that can be extracted for critical tasks. We show that by leveraging the time-history of a sparse set of sensors, we can encode global information of the measured high-dimensional system using shallow recurrent decoder networks. This paradigm has important applications for technical challenges in climate modeling, natural disaster evaluation, and personalized health monitoring; we focus especially on how this paradigm has the potential to transform the way we monitor and manage movement-related health outcomes.

Bio: Megan Ebers is a postdoctoral scholar in applied mathematics with UW’s NSF AI Institute in Dynamic Systems. In her PhD research, she developed and applied machine learning methods for dynamics systems to understand and enable human mobility. Her postdoctoral research focuses on data-driven and reduced-order methods for complex systems, so as to continue her work in human-centered research challenges, as well as to extend her research to a broader set of technical challenges, including turbulent flow modeling, natural disaster monitoring, and acoustic object detection.

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

Katie Landwehr JournalArticle, News, Publications ,

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.

SWE 2023

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Tori and Charlotte are standing with a large sign that says "Heart LA"

Congratulations to Charlotte Caskey and Victoria (Tori) Landrum for presenting as finalists in the Collegiate Poster Competition at the Society of Women Engineer’s Annual Conference in LA this weekend.

Tori placed 3rd in the undergraduate student division for her poster titled “Spinal Stimulation Improves Spasticity and Motor Control in Children with Cerebral Palsy”. Charlotte placed 1st in the graduate student division for her work titled “Machine Learning for Quantifying Rehabilitation Response in Children with Cerebral Palsy.

Congratulations, Charlotte and Tori!

Tori and Charlotte are standing outside of a convention center with a large sign that says "Welcome to SWE 23"
Charlotte has long brown hair and is wearing glasses, a black blazer and black pants. She is standing in front of her poster at SWE.
Vitoria (Tori) has short blonde hair and is wearing a black shirt and grey pant. Tori is standing in front of a poster at SWE 2023.