Deciphering the unique inertial focusing behavior of sperm cells

Inertial focusing has been utilized to advance assisted reproductive technologies (ART) for animal breeding and in vitro fertilization (IVF) by separating sperm cells from biofluids with complex cell backgrounds. While existing studies have aimed to design and optimize sperm separation devices, the fundamental mechanism behind the unique focusing behavior of sperm in spiral channels remains largely unknown: sperm cells focus near the outer wall, whereas most other cells focus near the inner wall. This is primarily due to the lack of a direct modelling scheme for capturing the detailed inertial migration of sperm cells in the spiral channels. In this work, we developed a 3D DNS-PT modeling approach that can predict the inertial focusing of sperm cells with long tails. Unlike previous studies that considered rotating spheres, the novelty of our approach is in extracting the inertial lift force for a triaxial ellipsoid (which represents the asymmetric oval-shaped sperm head) and accounting for the tail effect through appropriate boundary conditions, thus capturing their cumulative impact on sperm focusing behavior. Furthermore, we conducted inertial microfluidics experiments with fluorescent images of spermatozoa to validate the modelling results. We discovered that the effect of the tail, rather than the sperm head shape or orientation, is the primary determinant of the unique inertial focusing position of sperm cells in microchannels. The modelling results provided significant insights into the evolution of particle distribution in the channel cross-section along the flow direction, which was previously unknown due to the limitations of imaging techniques. The predicted particle trajectories enabled detailed analysis and explanation of the distinct migration paths of sperm cells and spherical particles. This work bridges the gap in our understanding of the inertial migration of sperm and other flagellated cells, facilitating the better design and optimization of sorting and separation devices.