In silico prediction of maximum perineal muscle strain during vaginal delivery by design of experiment

The prevalence of pelvic floor muscle injuries induced by childbirth is higher than 23 % in the general women population. Such injuries can lead to prolapses and other pathologies in future female life. Leveraging computational biomechanics, the study implements an advanced female pelvic floor model for computing the maximum pelvic muscle strain, which serves as an injury risk indicator. The design of experiment method, abbreviated as DoE, is used to compute the maximum strain for boundary values of bony pelvis dimensions, namely the anterior-posterior diameter (abbreviated as APD) and the transverse diameter (abbreviated as TD). This is done in combination with small, medium and large percentiles of fetal head circumference (abbreviated as HC).

We utilized a previously developed finite element model of a female pelvic floor, as a reference, and enhanced it with new features, including a more detailed tissue geometry and advanced constitutive material models. The APD and TD dimensions were sourced from the set of MRI of 64 nulliparous women. This data was used to estimate the boundary dimensions of the female bony pelvis, combining both small and large values of APD and TD. Together with the 10th and the 95th percentiles for HC, a three-dimensional domain was constructed to assess the maximum pelvic muscle strain. In boundary cases, the maximum pelvic muscle strain was computed across 8 full-factorial design models (each situated at one corner of the domain, thereby combining the minimum and the maximum values of APD, TD and HC). This was done to define a response surface that predicts the maximum pelvic muscle strain within the domain. The accuracy of this response surface prediction was validated using 15 additional intermediate design models. These models were placed at the center of the domain (1 point), the centres of the domain boundary surfaces (6 points), and midway along each domain boundary edge (8 points).

The maximum strain results for 8 combinations of APD, TD, and HC were employed to construct a linear response surface as a function of APD, TD, and HC. Tests at an additional 19 domain points served to evaluate the efficiency of the response surface prediction. The response surface demonstrated strong predictability, with an absolute average error of 1.52 %, an absolute median error of 1.52 %, and an absolute maximum error of 11.11 %. HC emerged as the most influencing dimension, accounting for 16 % of influence.

The reference finite element pelvic floor model was scaled to 8 full-factorial female-specific pelvic floor models, which represent the combination of boundary values for APD, TD, and HC. The maximum pelvic floor muscle strain from these 8 models was used to design a response surface. When implementing the DoE approach to construct the response, there was consistent predictability for the maximum perineal muscle strain, as validated by the additional 19 intermediate design models. As a result, the response surface methodology can serve as an initial predictor for potential childbirth-induced pelvic floor muscle injury.