Computational modeling serves an important role in childbirth-related research. Prescribed fetal descent trajectory is a key characteristic in childbirth simulations. Two major types of fully prescribed fetal descent trajectory can be identified in the literature: straight descent trajectories and curve of Carus. The straight descent trajectory has the advantage of being simpler and could serve as a reasonable approximation for relatively small fetal movements during labor, but it cannot be used to simulate the entire childbirth process. Curve of Carus is the well-recognized fetal descent trajectory with physiological significance. However, no mathematical description of the curve of Carus can be found in the existing computational studies. This status of curve of Carus simulation in the literature hinders the direct comparison of results across different studies and the advancement of computational techniques built upon previous research. The goals of this study are: (1) propose a universal approach to achieve the curve of Carus for the second stage of labor, from the point when the fetal head engages the pelvis to the point when the fetal head is fully delivered. (2) demonstrate its utility when considering various fetal head sizes. The current study provides a detailed formulation of the curve of Carus, considering geometries of both the mother and the fetus. The maternal geometries were obtained from MRI data, and the fetal head geometries were based on laser scanning of a replica of a real fetal head.

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