Automated methods for estimation of sperm flagellar bending parameters

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Abstract
Parameters to describe flagellar bending patterns can be obtained by a microcomputer procedure that uses a set of parameters to synthesize model bending patterns, compares the model bending patterns with digitized and filtered data from flagellar photographs, and uses the Simplex method to vary the parameters until a solution with minimum root mean square differences between the model and the data is found. Parameters for Chlamydomonas bending patterns have been obtained from comparison of shear angle curves for the model and the data. To avoid the determination of the orientation of the basal end of the flagellum, which is required for calculation of shear angles, parameters for sperm flagella have been obtained by comparison of curves of curvature as a function of length for the model and for the data. A constant curvature model, modified from that originally used for Chlamydomonas flagella, has been used for obtaining parameters from sperm flagella, but the methods can be applied using other models for synthesizing the model bending patterns.