A microtubule-sliding–based sperm model for near-wall swimming dynamics

This paper presents a three-dimensional model for simulating human sperm motility using the lattice Boltzmann method. Systematic numerical investigations into the motion modes of sperm in viscous fluids were conducted. Based on the actual microscopic morphology of sperm, the model is simplified as an ellipsoidal head and a slender cylindrical tail. The tail, referencing the 9 + 2 microstructure, was modeled using the immersed boundary method combined with a node-spring connection approach. The spatial motion patterns of sperm observed in the experiment were achieved as both planar motion and helical motion through an internal-force-driven strategy. Specifically, the variation patterns of microtubule structure lengths and angles were extracted and served as critical bases for regulating sperm motility. Based on the internal-force-driven mechanism, a three-dimensional sperm motility model capable of free swimming was successfully developed. By model validation and experimental comparison, it was demonstrated that the model can accurately capture the fluid-solid coupling characteristics of sperm motility. The study focused extensively on the helical mode and the factors influencing helical propulsion performance. As an application of this model, the near-wall swimming dynamics of sperm in a square microchannel was systematically investigated. The results indicate that when sperm move near the microchannel corners, they generate different pressure effects on the surrounding fluid. The cumulative impact of these pressure effects causes sperm to migrate toward the nearby corners and ultimately stabilize in wall-following behavior. The three-dimensional sperm motility model capable of free swimming quantitatively verifies the microtubule sliding mechanisms underlying flagellar bend formation. Across scales, the sperm model demonstrates macroscopic fluid-solid coupling phenomena through the evolution of microstructural deformation. Therefore, this model offers a novel research avenue for scientists to investigate and understand sperm motility.