Proportional Jerk: A New Measure of Motion as Applied to Eye Movements in Sleep and Waking.

The third derivative of motion or the change in the rate of acceleration (also known as jerk) is examined in terms of its applicability to the study of psychophysiological function. An algorithm of this third derivative is presented to show that jerk can be derived from the arithmetic difference of two slopes which constitute the portion of motion being differentiated. By modifying the algorithm, a new parameter termed "proportional jerk" or PJ is formulated whereby one slope is measured relative to the other slope; this PJ provides information about the smoothness of movement without being influenced by the velocity as is the traditional jerk measure. A practical application of the PJ to waking saccades and REMs in 11 human subjects revealed that REMs are significantly "jerkier" or less smooth than waking calibration eye movements. Whereas the waking eye movements had a well-defined negative phase of the PJ, the REMs did not show such stereotypical behavior. This is in accord with previous work which showed that waking saccade velocity increases to a maximum and then decreases whereas REMs maintain their peak or near peak velocities for varying periods. It was suggested that PJ can be useful in detecting subtle temporal changes in the course of movements and may be used as a parameter of motion even when the absolute amplitude is unknown. [ABSTRACT FROM AUTHOR]

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