Fractal analysis of capacitating human spermatozoa.

While head centroid-derived kinematic values have been determined for the trajectories of hyperactivated human spermatozoa, the definitions are not robust with respect to image sampling frequency and track analysis methods. The determination of the fractal dimension of a trajectory has been suggested as an alternative descriptive parameter for hyperactivated motility. Here, we have investigated two methods for the determination of the fractal dimension of a trajectory. A simple but useful equation was found to be: D = log(n)/[log (n + log (d/L)], where the n is the number of intervals in the trajectory, d is the planar extent of the curve and L is the length of the trajectory. This equation was not influenced by scaling of the trajectory. A fractal dimension (D) >=1.30 was found to define hyperactivated trajectories, and D <= 1.20 defined non-hyperactivated trajetories, reconstructed at both 30 and 60 Hz. However, when circling tracks were studied, all had D > 1.30, even though they were classified as non-hyperactivated by curvilinear velocity and/or amplitude of lateral head displacement values. An analysis of a series of non-ideal track segments suggested a relationship between a track's linearity and its fractal dimension. It was determined by a linear regression analysis that the fractal dimension of a trajectory was inversely proportional to its linearity (r = -0.77, P < 0.001). Although the fractal dimension of a trajectory is a good indicator of its regularity (describing its space-filling properties), it should not be used as the sole criterion for the classification of a trajectory as hyperactivated.