Kadar E E, Schmidt R C, Turvey M T
Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs 06268.
Biol Cybern. 1993;68(5):421-30. doi: 10.1007/BF00198774.
When an animal increases or decreases the frequency of its limb motions, how should the transformation in timing be characterized? It has been hypothesized that the transformation is adiabatic, even though the biological conditions are nonconservative and non-rate-limited (Kugler and Turvey 1987). An adiabatic transformation requires that the rhythmic system's action (energy/frequency) and entropy production remain time-invariant throughout the transformation. The non-conservative adiabatic hypothesis was evaluated through an experiment on human rhythmic hand movements. On each trial, a subject began at a prescribed frequency and then, over a 30 s interval, increased (or decreased) the frequency continuously at will. For each subject, on each increasing and decreasing trial, cycle kinetic energy was a linear function of cycle frequency with a negative energy intercept. By the adiabatic hypothesis, the slope of the function defines the constant action and the intercept defines the constant dissipation - changes in cycle frequency incur no changes in energy dissipated per cycle. Slopes and intercepts were correlated suggesting a common basis for the two constants, and the variety of cycle amplitude-cycle duration relations were in agreement with the nonmonotonic, nonlinear space-time function predicted by the hypothesis. The possibilities of addressing aspects of the data through (a) muscle modeled as a continuum of Kelvin bodies with a continuous relaxation spectrum, and (b) various classes of autonomous differential equations, were discussed. Most importantly, the discussion focused on the puzzling independence of energy cost and speed exhibited by locomoting animals differing in morphology, physiology, size, and taxa. It was suggested that the independence may reflect a very general principle - adiabatic transformability of biological movement systems.
当动物增加或减少其肢体运动频率时，时间上的变化应如何表征？尽管生物条件是非保守且非速率限制的，但有人假设这种变化是绝热的（库格勒和特维1987）。绝热变化要求节律系统的作用（能量/频率）和熵产生在整个变化过程中保持时间不变。通过一项关于人类有节奏手部运动的实验对非保守绝热假设进行了评估。在每次试验中，受试者从规定频率开始，然后在30秒的时间间隔内随意连续增加（或减少）频率。对于每个受试者，在每次增加和减少频率的试验中，周期动能是周期频率的线性函数，能量截距为负。根据绝热假设，该函数的斜率定义了恒定作用，截距定义了恒定耗散——周期频率的变化不会导致每个周期耗散能量的变化。斜率和截距相关，表明这两个常数有共同的基础，并且各种周期幅度-周期持续时间关系与该假设预测的非单调、非线性时空函数一致。讨论了通过（a）建模为具有连续松弛谱的开尔文体连续统的肌肉，以及（b）各类自治微分方程来处理数据方面的可能性。最重要的是，讨论集中在形态、生理、大小和分类群不同的运动动物所表现出的能量消耗与速度令人困惑的独立性上。有人认为这种独立性可能反映了一个非常普遍的原则——生物运动系统的绝热可变换性。
