Obtaining correlation between orientation of sperm and the direction of the movement using machine learning

In polar active matter, the orientation of the front-aft asymmetric body and the direction of the velocity that the body is moving toward are typically assumed to be the same. Here, we use swimming sperm as an experimental model to examine how good this assumption is. We utilize SLEAP (Social LEAP Estimates Animal Pose), a deep learning image processing tool, to obtain sperm location and orientation from experimental video data. At each frame, the machine learning algorithm tracks the head (acrosome), the body (the flagellum meets the head or centriole), the mid-piece of the flagellum meets the principal piece, and one point on the principal piece of the flagellum. The position of the cell is defined as the head position and the orientation is given by the vector direction from the body to the head. Direction of the sperm moving velocity is calculated using the position time series between consecutive frames. We found the deviation between the two measures to be (7± 6)°. We conclude that the two directions are highly correlated and only differ from each other minimally, while the origin and influence of the small difference need to be explored in further study.