Transport in the placenta: homogenizing haemodynamics in a disordered medium

Area of Science:

• Physiology
• Biomedical Engineering
• Computational Biology

Background:

• The placenta facilitates vital nutrient and waste exchange between mother and fetus.
• Maternal blood circulates within villous trees containing fetal vessels.
• Accurate modeling of maternal hemodynamics is essential for understanding placental function.

Purpose of the Study:

• To explore challenges in modeling maternal hemodynamic transport using homogenization techniques.
• To assess the accuracy of homogenization approximations under varying physiological parameters.
• To quantify errors introduced by spatial disorder in multi-scale physiological models.

Main Methods:

• Developed measures to estimate the statistical homogeneity of villous branch distribution.
• Analyzed a simplified model of solute transport with point sinks.
• Evaluated homogenization accuracy based on Péclet and Damköhler numbers and sink distribution properties.

Main Results:

• Identified minimum distances for statistical homogeneity in villous branching.
• Characterized differences between homogenization approximations and exact solute distribution.
• Observed large spatial gradients and correlated fluctuations at various scales.

Conclusions:

• Homogenization approximations can introduce significant errors in modeling placental transport.
• Spatial disorder significantly impacts the accuracy of multi-scale approximations.
• Quantifying these errors is crucial for reliable physiological modeling.