Velocity profiles in the human ductus venosus: a numerical fluid structure interaction study

Abstract

The veins distributing oxygenated blood from the placenta to the fetal body have been given much attention in clinical Doppler velocimetry studies, in particular the ductus venosus. The ductus venosus is embedded in the left liver lobe and connects the intra-abdominal portion of the umbilical vein (IUV) directly to the inferior vena cava, such that oxygenated blood can bypass the liver and flow directly to the fetal heart. In the current work, we have developed a mathematical model to assist the clinical assessment of volumetric flow rate at the inlet of the ductus venosus. With a robust estimate of the velocity profile shape coefficient (VC), the volumetric flow rate may be estimated as the product of the time-averaged cross-sectional area, the time-averaged cross-sectional maximum velocity and the VC. The time average quantities may be obtained from Doppler ultrasound measurements, whereas the VC may be estimated from numerical simulations. The mathematical model employs a 3D fluid structure interaction model of the bifurcation formed by the IUV, the ductus venosus and the left portal vein. Furthermore, the amniotic portion of the umbilical vein, the right liver lobe and the inferior vena cava were incorporated as lumped model boundary conditions for the fluid structure interaction model. A hyperelastic material is used to model the structural response of the vessel walls, based on recently available experimental data for the human IUV and ductus venous. A parametric study was constructed to investigate the VC at the ductus venosus inlet, based on a reference case for a human fetus at 36 weeks of gestation. The VC was found to be [Formula: see text] (Mean [Formula: see text] SD of parametric case study), which confirms previous studies in the literature on the VC at the ductus venosus inlet. Additionally, CFD simulations with rigid walls were performed on a subsection of the parametric case study, and only minor changes in the predicted VCs were observed compared to the FSI cases. In conclusion, the presented mathematical model is a promising tool for the assessment of ductus venosus Doppler velocimetry.

Maternal Smoking Induced Cardiovascular Risks in Fetuses: How Can in silico Models Help?

“…adverse birth outcomes (Dicke et al, 2009), simulations with an in silico model may be made for normal and abnormal blood flow patterns, similar to that performed for UAs (Wilke et al, 2018), and for ductus venosus (Leinan et al, 2013) but also incorporating nicotine effect data (Dicke et al, 2009). Moreover, it is essential to connect the disparate scales of WSS and signaling dynamics in an overarching model to explore how nicotine may affect vascular wall remodeling in fetuses (Milnerowicz-Nabzdyk and Bizon, 2015).…”

“…Investigating the blood flow in a vasculature proves more computationally feasible with 1D Navier-Stokes equations coupled with a wall constitutive equation (Formaggia et al, 2006;van de Vosse and Stergiopulos, 2011). To our knowledge, this method has not been applied to the fetal CVS yet, but a 3Dlumped parameter model coupled method has been used to simulate the blood flow in the ductus venosus (Leinan et al, 2013). To study pressure wave propagation along the elastic arterial wall, the flow equations are solved from the frequency domain, using methods such as the Transmission Line Theory (Muller et al, 2017), or Fourier series analysis for the velocity waveforms (Sled et al, 2019).…”

Numerical investigation of the haemodynamics in the human fetal umbilical vein/ductus venosus based on the experimental data

“…The present study numerically investigated the velocity of blood flow in DV and interestingly good agreement between the experimental and numerical results are found. For instance, there is high-velocity jet throughout the lower portion of the ductus as is the low velocity in the umbilical vein [ 26 , 35 ] or the umbilical pressure may show little pulsatility, due to relatively high umbilical compliance [ 29 ]. Our numerical results including Figures 6 and 7 were verified by mentioned clinical findings [ 26 , 29 , 35 ].…”

Multiscale Modeling Is Required for the Patent Ductus Arteriosus in Preterm Infants

“…However, neither study included the DA and pulmonary artery in the arterial model. Blood flow simulations have been performed at a single-vessel level for the umbilical artery ( 13 ) and the ductus venosus ( 14 ). In a fetal circulation model, the DA is designed as an electronic component connecting the descending aorta and the pulmonary artery ( 15 ).…”