Placental blood flow

A problem presented at the UK MMSG Nottingham 2001.

Presented by:
Dr Penny Gowland (Magnetic Resonance Centre, University of Nottingham)
H Byrne, P Gowland, OE Jensen, T Mayhew, J McGuinness, CP Please, S Wilson

Problem Description

Intrauterine growth restriction is a condition that causes health problems for the fetus from the prenatal period though to late adult life; it is often associated with pre-eclampsia. Adequate oxygen and nutrient supply to the fetus depend on the delivery of oxygenated blood to the placenta via the maternal spiral arteries and on the flow of blood through the maternal intervillous space. Pre eclampsia (PE) and intra uterine growth restriction (IUGR) can cause changes in spiral artery morphology and function that are expected to lead to changes in blood flow, pulsatility and pressure in the placenta. The flow of blood through the maternal intervillous space depends on its geometrical characteristics, including the extent and elasticity or stiffness of the villous trees and the deposition of fibrin-type fibrinoid (blood coagulation product).

It is known that IUGR and PE change the morphology of villous trees and this may alter their elastic or stiffness properties, as well as the nature of the fetal blood flow. Fibrinoid deposition in PE will also alter intervillous porosity. In vivo, the geometry will fluctuate since pulsatile spurting of blood into the intervillous space periodically deforms the villous trees and increases pore sizes. Hence, it is expected that PE/IUGR is not only associated with a decreased blood flow to the placenta, but with changes in intervillous haemodynamics, expressible in terms of transit times, porosity and temporal and spatial heterogeneity of blood flow. It is expected that factors that reduce blood movement throughout the placenta will lead to reduced oxygen transfer and decreased materno-fetal oxygen gradients. However a mathematical model linking blood flow into the placenta with blood movement into the placenta, would clarify the interaction between blood flow to the placenta, villous structure and oxygen delivery to the fetus.

Study Group Report

The Study Group was asked to develop a mathematical model of flow and nutrient delivery within the placenta. Such a model could be used to relate the physical properties of the placenta (such as the morphology and deformability of fetal blood vessels, pressure and flow characteristics of the maternal and fetal circulations) to oxygen delivery, in the overall context of intrauterine growth deficiency. A simple compartmental model was developed to describe the effect of blood jetting out of a maternal spiral artery on a single deformable villous tree (a group of fetal blood vessels). The permeability of the tree was lumped into a single variable that depends on transverse expansion (as neighbouring branches of the tree are moved apart by the flow) and streamwise compression. Accounting also for elastic restoring forces and the tree's inertia, the problem reduced to that of a forced, damped nonlinear oscillator. Simple estimates of nutrient delivery to the fetus may be obtained from this model. The model highlights a number of important and interesting areas for future work.

Download the full report

Follow-Up Activities

The following publications have been written as a result of this problem:

A mathematical model of intervillous blood flow in the human placentone
IL Chernyavsky, OE Jensen, & L Leach (2010)
Placenta 31 (1), 44–52.
Transport in the placenta: homogenizing haemodynamics in a disordered medium
IL Chernyavsky, L Leach, IL Dryden, & OE Jensen (2011)
Philosophical Transactions of the Royal Society A 369 (1954), 4162–4182.

The following funding for further work has been obtained to investigate aspects of this problem:

Mathematical Modelling of Blood Flow in the Human Placenta
S Wilson
Carnegie Trust, three-year scholarship, £45k.
Modelling flow and growth in the placenta
OE Jensen
Medical Research Council, discipline-hopping award, £53k, October 2003 to September 2004.
A multiscale analysis of flow and transport in the human placenta
Igor Chernyavsky
Marie Curie Early Stage Training Network MMBNOTT, PhD fellowship, July 2007 to June 2010.