With a view towards reducing the incidence of unnecessary surgical intervention during birth by reaching a better understanding of the mechanics of human birth, we aim to shed light on how amniotic fluid transfers forces from the birth canal onto the fetus during birth. Motivated by a simplified physical model, this work uses a numerical method to explore the forces on the fetus, and their relationship to the successful progression of birth and to strain in the birth canal. The numerical model is based on a physical model which represents the fetus moving through the birth canal using a rigid cylinder (fetus) that moves at a constant velocity through the center of a passive elastic tube (birth canal). The entire system is immersed in a highly viscous fluid; low Reynolds number allows the Stokes equations to approximate fluid behavior.

The pulling force necessary to move the rigid inner cylinder through the tube at a specified velocity is measured, along with the time-evolving geometry of the elastic tube. The discrete tube through which the rigid cylinder passes has macroscopic elasticity that can be matched to the tube. The buckling behavior of the elastic tube, which also occurs in other systems of flow through collapsible tubes, is explored by varying velocity and dimensions of the rigid cylinder, elastic properties and dimensions of the elastic tube, and viscosity of the surrounding fluid. Peristaltic contraction of the elastic tube is also included in the model to provide additional insight into the force and velocity of the fetus and strain in the birth canal during human birth, when the birth canal is highly active.