arXiv subjects

F. Dierick

Publications and source records attributed to F. Dierick.

9 recordsLinked to original sources

arXiv2026

A higher-derivative model predicts a smoothness vs duration relationship in head-pointing movements

Head movements require integration of visual, proprioceptive, vestibular, and cervical motor signals. The dynamical principles governing their temporal organization remain unclear. We tested whether a Pais-Uhlenbeck oscillator -- a higher-derivative model with one internal frequency parameter $\omega$ -- can model head kinematics during virtual-reality-based head pointing. Our model predicts a parabolic relationship between movement duration ($T$) and smoothness (log-dimensionless jerk, $LDLJ$) that we have experimentally checked. Sixty-two healthy young adults performed horizontal and vertical head movements with an amplitude of 30{\deg}. Movement duration, endpoint accuracy, peak angular velocity, overshoot, and $LDLJ$ were extracted from headset kinematics. A mixed-effects parabolic regression confirmed the predicted $LDLJ$ vs $T$ parabolic relation ($R^2 = 0.851$). The quadratic coefficient was not significantly modified by direction or participant, but the intercept and linear coefficient differed between horizontal and vertical movements. As an internal consistency check of the model, we find that the parameter $\omega$, as estimated from the regressions, gives time durations that closely match the measured ones. These findings outline a nonlinear temporal organization of head pointing modulated by direction-specific biomechanical constraints, and suggest that higher-derivative mechanics may provide a principled, non-invasive framework for quantifying cervical motor planning, warranting further validation in clinical populations.

physics.bio-ph↗

arXiv2025

From Brain to Motion: Harnessing Higher-Derivative Mechanics for Neural Control

Optimal Feedback Control (OFC) provides a theoretical framework for goal-directed movements, where the nervous system adjusts actions based on sensory feedback. In OFC, the central nervous system (CNS) not only reacts to stimuli but proactively predicts and adjusts motor commands, minimizing errors and (often energetic) costs through internal models. OFC theory assumes that there exists a cost function that is optimized throughout one's movement. It is natural to assume that mechanical quantities should be involved in cost functions. This does not imply that the mechanical principles that govern human voluntary movements are necessarily Newtonian. Indeed, the undisputed efficiency of Newtonian mechanics to model and predict the motion of non-living systems does not guarantee its relevance to model human behavior. We propose that integrating principles from Lagrangian and Hamiltonian higher-derivative mechanics, i.e. dynamical models that go beyond Newtonian mechanics, provides a more natural framework to study the constraints hidden in human voluntary movement within OFC theory.

q-bio.NC↗

arXiv2024

The two-thirds power law derived from an higher-derivative action

The two-thirds power law is a link between angular speed $\omega$ and curvature $\kappa$ observed in voluntary human movements: $\omega$ is proportional to $\kappa^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law. We propose that a broader class of higher-derivative Lagrangians leads to the two-thirds power law and we perform the Hamiltonian analysis leading to action-angle variables through Ostrogradski's procedure. In this framework, squared jerk appears as an action variable and its minimization may be related to power expenditure minimization during motion. The identified higher-derivative Lagrangians are therefore natural candidates for cost functions, i.e. movement functions that are targeted to be minimal when one individual performs a voluntary movement.

physics.class-ph↗

arXiv2023

Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion During Long-Range Walking

When a Hamiltonian system undergoes a stochastic, time-dependent anharmonic perturbation, the values of its adiabatic invariants as a function of time follow a distribution whose shape obeys a Fokker-Planck equation. The effective dynamics of the body's centre-of-mass during human walking is expected to represent such a stochastically perturbed dynamical system. By studying, in phase space, the vertical motion of the body's centre-of-mass of 25 healthy participants walking for 10-minutes at spontaneous speed, we show that the distribution of the adiabatic invariant is compatible with the solution of a Fokker-Planck equation with constant diffusion coefficient. The latter distribution appears to be a promising new tool for studying the long-range kinematic variability of walking.

physics.class-ph↗

arXiv2021

Motor strategies and adiabatic invariants: The case of rhythmic motion in parabolic flights

The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal nearly-conserved quantities in human voluntary rhythmic motion, an individual being seen as a complex time-dependent dynamical system with bounded motion in phase-space. We study an explicit realization of our proposal: An experiment in which we asked participants to perform $\infty-$ shaped motion of their right arm during a parabolic flight, either at self-selected pace or at a metronome's given pace. Gravity varied between $0$ and $1.8$ $g$ during a parabola. We compute the adiabatic invariants in participant's frontal plane assuming a separable dynamics. It appears that the adiabatic invariant in vertical direction increases linearly with $g$, in agreement with our model. Differences between the free and metronome-driven conditions show that participants' adaptation to variable gravity is maximal without constraint. Furthermore, motion in the participant's transverse plane induces trajectories that may be linked to higher-derivative dynamics. Our results show that adiabatic invariants are relevant quantities to show the changes in motor strategy in time-dependent environments.

physics.class-ph↗

arXiv2019

Adiabatic invariants drive rhythmic human motion in variable gravity

Natural human movements are stereotyped. They minimise cost functions that include energy, a natural candidate from mechanical and physiological points of view. In time-changing environments, however, motor strategies are modified since energy is no longer conserved. Adiabatic invariants are relevant observables in such cases, although they have not been investigated in human motor control so far. We fill this gap and show that the theory of adiabatic invariants explains how humans move when gravity varies.

physics.med-ph↗

arXiv2017

Ergonomic risk assessment of developing musculoskeletal disorders in workers with the Microsoft Kinect: TRACK TMS

Routine ergonomic assessment of postures and gestures in the workplace are mostly conducted by visual observations, either direct or based on video recordings. Nowadays, low-cost three-dimensional cameras like Microsoft Kinect open the possibility of recording the full kinematics of workers in a non-intrusive way, providing a more precise, and reliable assessment of their motor strategies. As an illustration, we focus on a peculiar kind of workers: professional musicians (violinists), whose playing is representative of a work situation involving repeated gestures and postures that can be described as non-ergonomic. We show that the Microsoft Kinect can be efficiently used to quantify the motion performed by these musicians. Moreover, we argue that low-cost three-dimensional cameras can be a useful aid in ergonomic risk assessment of developing musculoskeletal disorders and give the example of the repetition of movements and postural items included in the OCRA checklist, whose scoring can be facilitated by such a device, as addressed in our TRACK TMS research project.

physics.med-ph↗

arXiv2017

Fractal Analyses Reveal Independent Complexity and Predictability of Gait

Locomotion is a natural task that has been assessed since decades and used as a proxy to highlight impairments of various origins. Most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent $\alpha$ and the Minkowski fractal dimension $D$ were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. We show that $\alpha$ and $D$ accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity ($D$) and hence, adaptability. In contrast, any perturbation (walking backward and/or stimulation of the vestibular system) decreased it. Furthermore, walking backward increased predictability ($\alpha$) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures.

physics.med-ph↗

arXiv2017

Unstable Footwear as a Speed-Dependent Noise-Based Training Gear to Exercise Inverted Pendulum Motion During Walking

Previous research on unstable footwear has suggested that it may induce plantar mechanical noise during walking. The purpose of this study was to explore whether unstable footwear could be considered as a noise-based training gear to exercise body center of mass (CoM) motion during walking or not. Ground reaction forces were collected among 24 healthy young women walking at speeds between 3 and 6 km h-1 with control running shoes and unstable rocker-bottom shoes. The external mechanical work, the recovery of mechanical energy of the CoM during and within the step cycles, and the phase shift between potential and kinetic energy curves of the CoM were computed. Our findings support the idea that unstable rocker-bottom footwear could serve as a speed-dependent noise- based training gear to exercise CoM motion during walking. At slow speed, it acts as a stochastic resonance or facilitator, whereas at brisk speed it acts as a constraint.

physics.med-ph↗