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

Abstract

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.

Effect of non-linearity in predicting doppler waveforms through a novel model

“…Moreover, wide availability of several MOS models and extensive research in MOS fabrication justifies its selection as an ideal and a better model than the TL model. The simulation outputs are similar to the actual Doppler FVW's profiles obtained for some of the non-linear parameters by various authors [4,9]. However, we expect the present model and the simulation results to initiate extensive clinical or experimental studies involving various non-linear parameters in the near future.…”

“…We proposed the mathematical model for uteroplacental artery, which contributes to the load at the end of the transmission line [4]. Various inputs used in the model representing the non-linear parameters such as elastic parameters, viscosity, wall density, womersley parameters are taken from the known experimental and histopathological studies and are further modified for specific conditions by using standard formula [4]. Based on the accumulated knowledge, the entire system has been simplified to develop a novel MOSFET model.…”

“…Modeling is a known tool in the physiological fluid dynamics study. A validated non-linear mathematical model of the uteroplacental system has been developed which has also opened up a new frontier of research in the field of Doppler velocimetry analysis, modelling and image processing [4]. An electrical model can be easily simulated which can also incorporate various non-linearities present in the actual system.…”

Re-Evaluate the Effect of Hyperbaric Oxygen Therapy in Cancer - A Preclinical Therapeutic Small Animal Model Study

“…The basis of modulating pressure and oxygen concentration is to regulate cellular metabolism or tumor microenvironment. High external pressure exerted on the arterioles or capillaries results in reduction in tumor microcirculation, compromising oxygen perfusion as well as glucose & micronutrient supply to the proliferating cell [10], [11]. The net effect on the tissue oxygen level during HBO therapy remains positive thus eliminating tumor hypoxia.…”

“…Theoretical model and physiological fluid dynamic studies have also documented alteration in blood flow volume and tissue perfusion due to change in the extra-luminal vascular pressure [12], [13]. Hypoxia drives angiogenesis and facilitates tumor growth [10], [14]. At molecular or cellular level, reduced blood flow & micronutrient may inhibit cell proliferation and tumor growth.…”