Application of Rational Power Functions in Analyses of Saccadic Velocity Profiles

The relationship between the product of peak velocity and duration (V_mD) and saccadic amplitude is tightly correlated. The velocity profile of a saccade was referred as a triangular profile; whereas the saccadic amplitude is proportional to V_mD. From our observation and derivation, in addition to the triangular profile, the rational power function can also be applied to explain the linear relationship between the saccadic amplitude and V_mD. In this study, rational power functions were used for the analyses of saccadic dynamics. The results show that the rational power functions were fitted very well to the velocity profiles for three different amplitudes, i.e. 10deg, 20deg, and 30deg, with correlation coefficients are all greater than 0.99. Significant differences in shape parameters between experimental and simulated profiles were also observed. Additionally, we have found that the minimum variance model proposed based on the minimization of variance of post-saccadic eye position cannot simulate velocity profiles matched with the experimental results. In conclusion, rational power functions are efficient in describing the saccadic velocity profiles. The shape parameters are also efficient for describing the dynamics of saccadic velocity profiles