A computer‑based simulation of childbirth using the partial Dirichlet–Neumann contact method with total Lagrangian explicit dynamics on the GPU

During physiological or ‘natural’ childbirth, the fetal head follows a distinct motion pattern—often referred to as the cardinal movements or ‘mechanisms’ of childbirth—due to the biomechanical interaction between the fetus and maternal pelvic anatomy. The research presented in this paper introduces a virtual reality-based simulation of physiological childbirth. The underpinning science is based on two numerical algorithms including the total Lagrangian explicit dynamics method to calculate soft tissue deformation and the partial Dirichlet–Neumann contact method to calculate the mechanical contact interaction between the fetal head and maternal pelvic anatomy. The paper describes the underlying mathematics and algorithms of the solution and their combination into a computer-based implementation. The experimental section covers first a number of validation experiments on simple contact mechanical problems which is followed by the main experiment of running a virtual reality childbirth. Realistic mesh models of the fetus, bony pelvis and pelvic floor muscles were subjected to the intra-uterine expulsion forces which aim to propel the virtual fetus through the virtual birth canal. Following a series of simulations, taking variations in the shape and size of the geometric models into account, we consistently observed the cardinal movements in the simulator just as they happen in physiological childbirth. The results confirm the potential of the simulator as a predictive tool for problematic childbirths subject to patient-specific adaptations.