Multifractal Nonlinearity Moderates Feedforward and Feedback Responses to Suprapostural Perturbations

Abstract

An adaptive response to unexpected perturbations requires near-term and long-term adjustments over time. We used multifractal analysis to test how nonlinear interactions across timescales might support an adaptive response following an unpredictable perturbation. We reanalyzed torque data from 44 young and 24 older adults who performed a single-leg squat task challenged by an unexpected mechanical perturbation and a secondary visual-cognitive task. We report three findings: (a) multifractal nonlinearity interacted with pre-perturbation torque production and task error to presage greater pre-voluntary feedforward increases and greater voluntary reductions, respectively, in post-perturbation task error; (b) multifractal nonlinearity presaged relatively smaller task error than standard deviations of both pre-perturbation torques and pre-perturbation task error; and (c) increased task demand (e.g., age-related changes in dexterity and dual-task settings) led to multifractal nonlinearity presaging reduced task error. All these results were consistent with our expectations, except that a pre-perturbation knee torque-dependent increase in post-perturbation task error appeared later for older than for younger participants. This correlational multifractal modeling offered theoretical clarity on the possible roles of nonlinear interactions across timescales, moderating both feedforward and feedback processes, and presaging greater stability when the standard deviation is relatively large and task demands are strong. Thus, multifractal nonlinearity usefully describes movement variability even when paired with classical descriptors like the standard deviation. We discuss potential insights from these findings for understanding suprapostural dexterity and developing rehabilitative interventions.

Spatial variability and directional shifts in postural control in Parkinson’s disease

“…Significantly, the potential role of fractal scaling as a control parameter is pivotal in theory-driven approaches aimed at comprehending empirical evidence concerning cascade dynamics [82] . This approach would also align with recent findings suggesting that multifractal dynamics within postural and suprapostural variability play a pivotal role in facilitating the subsequent response to visual stimuli and mechanical perturbations [59] , [56] , [60] . We posit that the concept of OFSCA propels us to a heightened analytical plane, making this notion of H as a control parameter testable.…”

Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation

“…The more forward-looking second point of the MFT hypothesis was that the empirically estimable multifractal profile of bodily coordination might provide an empirical means for modeling the control of dexterous action. This latter point has received extensive support through the correlational study of postural, suprapostural, perceptual, and cognitive performance ( Bell et al, 2019 ; Booth et al, 2018 ; Carver et al, 2017 ; Dixon and Kelty-Stephen, 2012 ; Hajnal et al, 2018 ; Kelty-Stephen and Dixon, 2014 ; Kelty-Stephen et al, 2021b ; Mangalam et al, 2020a ; Mangalam et al, 2020b ; Mangalam and Kelty-Stephen, 2021a ; Mangalam et al, 2021 ; Stephen et al, 2012a ; Teng et al, 2016 ) as well as through experimental tests of multifractal stimulation on some of the same performance measures ( Stephen and Dixon, 2011 ; Ward and Kelty-Stephen, 2018 ; Bloomfield et al, 2021 ; Kelty-Stephen et al, 2023 ).…”

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

“…We have provided a theoretical roadmap to study the statistical aspects of movement coordination and then use cascade-dynamical parameters that match these movement structures. This research framework could help identifying the relative contributions of feedforward and feedback control in post-perturbation motor outputs during and after locomotor performance following degrading sensory feedback [ 152 ]. The methods we used to assess ergodicity breaking (the Thirumalai-Mountain metric), persistence ( H fGn , computed using the detrended fluctuation analysis), and cascade-like intermittency ( t MF , computed using the multifractal analysis) can also help investigate altered sensorimotor control of locomotion in older adults and clinical populations.…”