An increased interest towards the feto-placental venous circulation has
been recently devoted by clinicians, mainly regarding the umbilical
cord (morphological structure and feasibility of quantitative
measurements of the venous blood flow with Doppler US), the Ductus
Venosus and the inferior vena cava.
To investigate the haemodynamic changes leading to pathologies we
have developed a lumped mathematical model (implemented using SIMULINK ™)
simulating the feto-placental circulation from the inlet of
the umbilical artery (where the pressure waveform is assumed to be
known) across the placenta, the intraamniotic and intrahepatic umbilical
vein, the ductus venosus and the inferior vena cava until the fetal
atrium, where again a pressure waveform is assumed.
The main original assumptions of the lumped model are that the
umbilical vein behaves as a collapsible tube subject to an external
pressure exerted by the arteries which are coiled together inside the
cord and that the ductus venosus can dilate and, being in parallel with
the portal-hepatic system, can actively modify the outlet resistance
for the umbilical vein. All these features, however, could be described
with greater detail provided more sophisticated mathematical and numerical
treatments are properly included in the basic model.
The potential for model improvements due to a multiscale approach will
be discussed and evaluated.