  Microorganisms, such as E.Coli, are known to display upstream behavior and
respond rheotactically to shear flows. In particular, E.Coli suspensions have
been shown to display strong sensitivity to spatial constrictions, leading to
an anomalous densification past the constriction for incoming fluid velocities
comparable to the microoganism's self propulsion speed. We introduce a Brownian
dynamics model for ellipsoidal self-propelling particles in a confined channel
subject to a constriction. The model allows to identify the relevant parameters
that characterize the relevant dynamical regimes of the accumulation of the
active particles at the constriction, and clarify the mechanisms underlying the
experimental observations. We find that particles are trapped in butterfly-like
attractors in front of the constriction, which is the origin of the symmetry
breaking in the emerging density profiles of active particles passing the
constriction. In addition, the probability of trapping and thus the strength of
asymmetry is affected by size of the particles and geometry of the channel, as
well as the ratio of fluid velocity to propulsion speed.
