Trajectory Variance and Autocorrelations Within Single‐Sperm Tracks as Population‐Level Descriptors of Sperm Track Complexity, Predictability, and Energy‐Generating Ability

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Abstract
The objectives of the present study were to develop an alternative theoretical approach to the analysis of sperm motility and to develop motility parameters that would complement those more commonly used in current computer‐assisted semen analysis procedures. We have defined a set of parameters and have tested them using boar spermatozoa undergoing bicarbonate‐induced motility activation. The new parameters were calculated for a series of (x,y) coordinates of sperm head positions recorded at each move along the trajectory. The parameters were: mean velocity (MV), immobility ratio, fractal dimension (FD), the variance of the steplengths (VAR), and 2 autocorrelation function coefficients of the step‐length time series for lags 1 and 2 (C1 and C2). MV measures the average speed along the trajectory, and VAR is a measure of displacement variability that can be related to the specific mean (per step) kinetic energy of the spermatozoon. All of the parameters except MV and FD were affected by the sampling frequency (25 vs 50 Hz); inappropriately high sampling frequency in relation to magnification resulted in step‐lengths between successive frames that were below the resolution threshold of the imaging system. The autocorrelation functions were especially informative; discrimination between sperm subpopulations was obvious within simple histogram formats, and complex statistical analyses were not needed for their identification.