  The migratory abilities of motile human spermatozoa in vivo are essential for
natural fertility, but it remains a mystery what properties distinguish the
tens of cells which find an egg from the millions of cells ejaculated. To reach
the site of fertilization, sperm must traverse narrow and convoluted channels,
filled with viscous fluids. To elucidate individual and group behaviors that
may occur in the complex three-dimensional female tract environment, we examine
the behavior of migrating sperm in assorted micro-channel geometries. Cells
rarely swim in the central part of the channel cross-section, instead traveling
along the intersection of the channel walls (`channel corners'). When the
channel turns sharply, cells leave the corner, continuing ahead until hitting
the opposite wall of the channel, with a distribution of departure angles, the
latter being modulated by fluid viscosity. If the channel bend is smooth, cells
depart from the inner wall when the curvature radius is less than a threshold
value close to 150 micron. Specific wall shapes are able to preferentially
direct motile cells. As a consequence of swimming along the corners, the domain
occupied by cells becomes essentially 1-dimensional. This leads to frequent
collisions and needs to be accounted for when modeling the behavior of
populations of migratory cells and considering how sperm populate and navigate
the female tract. The combined effect of viscosity and three-dimensional
architecture should be accounted for in future in vitro studies of sperm
chemoattraction.
