Computational analysis of the ductus venosus fluid dynamics based on Doppler measurements

The simplified Bernoulli equation is currently used to evaluate pressure gradients on the basis of Doppler velocity measurements when direct pressure data require highly invasive procedures. Recently, this method was applied to the ductus venosus (DV) in order to estimate the fetal central venous pressure. The complex geometry - and consequently hemodynamics - of this fetal region suggests caution in automatically converting Doppler velocity measurements to pressure data. To investigate the reliability of the Bernoulli equation for this practice, we simulated the hemodynamics of the branching between the umbilical vein (UV) and the DV on the basis of ultrasonographic data from a normal fetus, using a simplified parametric 3D numerical model of a bent tube with varying cross section (UV) and a smaller trumpet-shaped branch (DV). A finite element formulation has been adopted to solve the governing Navier-Stokes equations. The results show that the simplified Bernoulli equation, despite of its simplicity, provides a good estimation of the pressure drop between the UV and the DV outlet section (with an error of about 0.25; mmHg, equal to 15%, compared with the model results). Nevertheless, attention must be paid to the velocity measurement sites, as discussed in this paper. In turn, the error becomes notable (2.8 mmHg, i.e., 34%) for high velocity values, thus suggesting that the error in evaluating the pressure drop with the simplified Bernoulli equation during fetal inspiratory movements may be substantial.