Deep learning reduced order models of vaginal tear propagation

Childbirth often has traumatic consequences that profoundly affect the mother's health. The passage of a baby through the vagina causes tissue lacerations, such as vaginal tears, which lead to pelvic floor disorders later in life. Despite advances in obstetrics, accurately predicting the possible complications of vaginal delivery remains challenging with current clinical methods. This paper introduces new computational methods that integrate finite element (FE) analysis, proper orthogonal decomposition (POD), and machine learning (ML) to predict vaginal deformations and tearing. Based on ex vivo micro-mechanical data collected from rodents, FE models of the vaginal canal subjected to increasing pressure with propagating tears are created. Snapshots of the FE displacement fields at increasing pressures and with different collagen fiber organization in the proximal, mid, and distal regions of the vagina are then used to develop (a) full-order ML models and (b) POD-based reduced order models with coefficients computed using ML. Both the full-order ML models and POD-ML models with POD bases of dimension l≥2 approximated the FE results with root squared mean errors of O(10^-2). Training (offline) times for the ML and POD-ML models were O(10²) and O(10) seconds, respectively, whereas prediction (online) times for both ML and POD-ML models were O(10^-3) seconds. Thus, the POD-ML models outperformed the ML models in terms of training efficiency while achieving similar prediction accuracy. Our findings demonstrate that the integration of these techniques can lead to faster computations of vaginal delivery outcomes. POD-based reduced order models and ML-based computational tools emerge as non-invasive methods for quantifying vaginal tissue deformations and tears.