Minimum sperm trajectory length for reliable determination of the fractal dimension

The aim of this study was to determine the minimum track length required for the reliable calculation of the fractal dimension of trajectories of capacitating human spermatozoa. Manually reconstructed trajectories classified previously as hyperactivated or non-hyperactivated were re-analyzed. The trajectories were reconstructed at 60 Hz, and each comprised 61 points (corresponding to 1 s movement). The trajectories were 'split' to give the equivalent of 2 x 31 point, 3 x 21 point, 4 x 16 point and 6 x 11 point track segments and the fractal dimension determined for each. The fractal dimensions of each track segment within each trajectory were compared using paired t-tests. No significant difference was observed between the fractal dimensions of track segments of equal length, irrespective of the motility pattern. However, significant differences in fractal dimension values were observed when segments of different lengths were compared (P<0.01). For the non-hyperactivated tracks, the fractal dimension was consistently below the hyperactivation threshold level for only the 31 point segments. The hyperactivated tracks consistently had fractal dimension values above the threshold level when segments of 16 points or longer were analysed. Therefore, the minimum track length for the determination of reliable fractal dimension values was 31 points, corresponding to an image sampling time of 0.5 s at 60 Hz, although it could be used as a screening method for the identification of hyperactivated motility for track segments of greater than 11 points (corresponding to 0.17 s movement).