一个高阶导数模型预测头部指向运动中平滑度与持续时间的关系
A higher-derivative model predicts a smoothness vs duration relationship in head-pointing movements
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中文总结 AI 辅助
该研究采用Pais-Uhlenbeck振子模型，通过实验证实头部指向运动的平滑度与持续时间呈抛物线关系，为量化颈部运动规划提供非侵入性框架。
中文摘要 AI 辅助
头部运动需要整合视觉、本体感觉、前庭和颈部运动信号，支配其时间组织的动力学原理仍不明确。我们测试了Pais-Uhlenbeck振子（一种带有一个内部频率参数ω的高阶导数模型）是否能模拟基于虚拟现实的头部指向过程中的头部运动学。我们的模型预测了运动持续时间（T）与平滑度（对数无量纲加加速度，LDLJ）之间存在抛物线关系，这一关系已通过实验验证。62名健康年轻人完成了幅度为30°的水平和垂直头部运动，从头戴设备的运动学数据中提取了运动持续时间、终点精度、峰值角速度、超调量和LDLJ。混合效应抛物线回归证实了预测的LDLJ与T的抛物线关系（R²=0.851）。二次系数未被方向或受试者显著改变，但截距和线性系数在水平与垂直运动间存在差异。作为模型的内部一致性检验，我们发现通过回归估计的参数ω给出的时间持续时间与测量值高度匹配。这些发现揭示了由特定方向生物力学约束调节的头部指向的非线性时间组织，并表明高阶导数力学可能为量化颈部运动规划提供一个有原则的、非侵入性的框架，值得在临床人群中进一步验证。
英文摘要
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 $ω$ -- 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°. 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 $ω$, 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.
