Z34 - Finite element model predicts decreased umbilical coiling due to vessel thickening in gestational diabetes

Introduction: : The umbilical cord is a unique vascular structure that connects the growing fetus to the placenta (Heil, Bordoni, StatPearls, 2023). At term, the cord’s vasculature is comprised of two umbilical arteries coiled around an umbilical vein and all surrounded by a layer of connective tissue, the Wharton’s Jelly (WJ). The umbilical arteries begin as straight vessels but adopt a helical structure in the early stages of human pregnancy (~7 weeks) that continues throughout gestation. Abnormal coiling resulting in under- or over-coiled umbilical arteries is associated with adverse fetal outcomes, including an increased risk of fetal death and structural abnormalities (Heil, Bordoni, StatPearls, 2023). Some studies have shown a correlation between conditions such as gestational diabetes (GDM) and abnormal coiling (Hoseinalipour et al., J Neonatal-Périnat Med, 2024) whereas others show no correlation (Laat et al., Eur J Obstet Gynecol Reprod Biol, 2007). Even in otherwise “healthy” pregnancies, the mechanisms driving abnormal coiling are not fully understood.
Computational fluid dynamic models have shown vessel coiling and diameter can affect umbilical hemodynamics (Shah et al., Placenta, 2017; Wilke et al., J Biomech, 2018). No computational studies thus far have considered how vessel shape would affect vessel coiling. Here, we developed a finite element model of a coiling umbilical cord to explore how changes in vessel dimensions due to GDM affected the extent of coiling and resulting tissue stress.

Materials and

Methods: : Tissue characterization: Human umbilical cords from healthy and GDM term pregnancies were collected after Cesarean birth. GDM samples were collected from pregnant individuals diagnosed with GDM (ACOG, Obstet & Gynecol, 2018) who use insulin to manage their blood glucose. Dissected umbilical arteries (UA) and veins (UV) were imaged. Wall thickness (h) and inner diameter (d_o ) were measured in ImageJ and significance determined using a Students’ t-test.
Finite element models: Finite element models were created based on measured umbilical dimensions using FEBio (Maas et al., J Biomech Eng, 2012). Pressure loads were applied to the inner UA and UV surfaces to mimic in utero blood pressure at term. The bottom surface was fixed and a tied-elastic contact was added between the vessels and WJ. A rigid body moment was prescribed to induce coiling. The WJ was assumed to behave as a nearly-incompressible, hyperelastic solid with a neo-Hookean material model
W= μ/2 (I_1-3)-μln⁡〖J+〗 λ/2 (ln⁡J )^2 (1)
where W is the strain-energy density function, μ and λ are the Lamé parameters, I_1 is the first invariant of the right Cauchy-Green tensor, and J is the determinant of the deformation gradient tensor (Eq. 1).
The UAs and UV were assumed to behave as nearly-incompressible, hyperelastic solids with Mooney-Rivlin material models
W= C_1 (I_1-3)+C_2 (I_2-3)+κ/2 (ln⁡J )^2 (2)
where C_1 and C_2 are the Mooney Rivlin material coefficients, I_2 is the second invariant of the right Cauchy-Green tensor, and κ is the bulk modulus (Eq. 2). Model parameters are listed in Figure 1D.

Results, Conclusions, and Discussions::

Results: GDM cords had slightly thicker UAs and UVs than healthy (Fig. 1-2), which led to a modest reduction (~10%) in the extent of coiling within GDM cords (Fig. 3A-C). After rotation, UAs had larger tensile 1st Principal stress (s1) values than the UV (Fig. 3A,D-E). The outer curvature of the UAs exhibited stresses at a higher magnitude than the inner curvature (Fig. 3A). All stress increased in magnitude with increasing coiling (Fig. 3A, D-E). Due to lessened coiling, GDM vessels experienced reduced stress values (~10-20%) as compared to healthy (Fig. 3F).

Discussion and

Conclusion: Reduced blood flow in GDM cords has been measured in utero (Wei et al., Am J Transl Res, 2020), but it is unclear why this occurs. Previous computational fluid dynamic studies have shown umbilical artery inner diameter and extent of coiling can impact blood flow (Shah et al., Placenta, 2017; Wilke et al., J Biomech, 2018). The umbilical artery inner diameter between healthy and GDM cords is similar (Fig. 2), so this is unlikely to cause the observed hemodynamic differences. Here, our model predicted vessel thickening due to GDM can cause reduced coiling as compared to healthy cords (Fig. 3). Previous fluid dynamic models have predicted a less-coiled cord will have increased blood flow compared to a normo-coiled cord (Shah et al., Placenta, 2017; Wilke et al., J Biomech, 2018). With this in mind, reduced coiling due to arterial thickening in GDM does not appear to be the mechanism behind reduced blood flow measured in utero (Wei et al., Am J Transl Res, 2020).
Tissue stress plays an important role in cellular mechanotransductive pathways, including maintenance of vascular tone (Humphrey et al., Annu Rev Biomed Eng, 2021). The 1st Principal stresses differed spatially along the UAs as well as in magnitude between healthy and GDM cords (Fig. 3), but the effect these variations could have on cellular behaviors and signaling pathways was not considered in the model. A future multiscale model combining the current model and a cellular signaling model could be used to explore how cell and tissue-level changes affect umbilical coiling and function.

Acknowledgements and/or References (Optional):: This work was supported by the University of Minnesota Obstetric Measures: Gestational Outcomes and Pediatric Health Repository (UMOMs:GOPHER), American Heart Association Postdoctoral Fellowship 25POST1357478 and CAREER Development Award 23CDA1048434, National Institutes of Health grant R01 HL164800, and the National Institutes of Health’s National Center for Advancing Translational Sciences, grant UL1TR002494. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health’s National Center for Advancing Translational Sciences.