New measures of sperm motion. I. Adaptive smoothing and harmonic analysis

Several kinematic measures from computer-aided sperm analysis (CASA) instruments depend critically upon the computation of the spatially averaged path of a sperm's curvilinear swimming trajectory. Presently available instruments compute the average path by smoothing the curvilinear trajectory using a fixed-length running average. We demonstrate that this method significantly distorts the spatially averaged path for irregularly swimming sperm, both within and between trajectories, resulting in inaccurate calculations for the velocity of the average path (VAP), amplitude of lateral head displacement (ALH), beat-cross frequency (BCF), wobble of the curvilinear trajectory (WOB), and straightness of the curvilinear trajectory (STR). The authors introduce an alternative approach, based on engineering signal processing techniques, where the width of the running average is adapted to the changing wavelengths of the major spatial oscillations of each curvilinear trajectory. How this adaptive method results in less distortion of the average path and produces more accurate characterizations of the above measures is shown. This method is implemented in a computer program developed by the authors, called PathTool. It is also demonstrated that the simple methods used to characterize the frequency and amplitude of the major oscillation in a sperm's curvilinear trajectory (ie, BCF and ALH) are only accurate for the most periodic, progressive, and symmetrical trajectories. Three new measures are introduced, based on mathematical harmonic analysis, that are more robust alternatives to the present methods. These new methods and measures are initially evaluated using prototypical sperm trajectories from human semen. Results suggest that adaptive smoothing and harmonic analysis produce more accurate estimates of the frequency and magnitude of oscillations in sperm trajectories than the method based on fixed-length smoothing, BCF, and ALH.