Understanding utero-placental blood flow in normal and hypertensive pregnancy through a mathematical model.

Normal development of utero-placental circulation is crucial not only for the survival and growth of the fetus in utero, but also for maternal well-being. Any disturbance or abnormality may reflect underlying pathology. Geometric conversion of a pre-pregnant spiral vessel into a divergent low-resistance vessel is believed to be responsible for the increased utero-placental blood flow in normal pregnancy. Known biomedical investigative techniques have failed to explain many such underlying haemodynamic changes taking place in the utero-placental system. Therefore, proper understanding of the system using a mathematical model has been found to be useful. The physiological fluid dynamic study is the first in this branch of physiology. Abnormal pressure gradient, axial velocity, volume flow and shear rate are obtained for various slowly changing geometries such as, tapering, divergence, local constrictions and sinusoidal tube for low Womersley parameters. The model can explain many enhanced patho-physiological changes, such as persistence or the appearance of local constriction in the utero-placental vessels. Such pathological changes are considered to be responsible for very high utero-placental resistance, leading to blood flow insufficiency in pre-eclampsia or intra-uterine growth retardations. It is believed that these changes may be caused by low shear rate on the pre-existing deranged or abnormal endothelium. Furthermore, this derangement is caused by an abnormal proliferation of either spiral vessels or the invading non-villous trophoblasts. Doppler flow study can explain and validate some of the theoretically derived flow velocity results. The study opens up a new area of research into utero-placental physiological fluid dynamics.