Computational modeling of the structure-function relationship in human placental terminal villi

Abstract

Placental oxygen transport takes place at the final branches of the villous tree and is dictated by the relative arrangement of the maternal and fetal circulations. Modeling techniques have failed to accurately assess the structure-function relationship in the terminal villi due to the geometrical complexity. Three-dimensional blood flow and oxygen transport was modeled in four terminal villi reconstructed from confocal image stacks. The blood flow was analyzed along the center lines of capillary segments and the effect of the variability in capillary diameter, tortuosity and branching was investigated. Additionally, a validation study was performed to corroborate the simulation results. The results show how capillary variations impact motion of the fetal blood, and how their bends and dilatations can decelerate the flow by up to 80%. Vortical flow is also demonstrated not to develop in the fetal capillaries. The different geometries are shown to dictate the transport of gases with differences of over 100% in the oxygen flux between samples. Capillary variations are key for efficient oxygen uptake by the fetus; they allow the blood to decelerate where the villous membrane is thinnest allowing for a better oxygenation, but also by reducing the vessel diameter they carry the oxygenated blood away fast. The methodology employed herein could become a platform to simulate complicated in-vivo and in-vitro scenarios of pregnancy complications.

Introduction

The importance of placental blood circulation was already noted by Aristotle on the Generation of Animals, ca. 340 B.C., due to its role in the transport of respiratory gases from the mother to her fetus. Because of the in-vivo ethical limitations and the complicated acquisition and manipulation of the ex-vivo organ, placental research has been very challenging. Furthermore, animal models are of limited use due to species differences in structure and biochemistry of the placenta (Battaglia and Meschia, 1986). As a consequence, the functional relationships between the maternal and fetal blood streams, at the level of the terminal villus (microscopic scale), are not well understood.

Maternal blood enters the placenta when it reaches the intervillous space via the uterine arteries, percolates between branches of the villous tree and returns deoxygenated to the maternal circulatory system through the uterine veins. On the other side, fetal blood flows from the umbilical arteries towards the branching trees of the chorionic vasculature, and oxygenated blood returns via the umbilical vein (Fig. 1). The feto-placental capillaries are tortuous, have variable diameters and sharp bends (Plitman Mayo et al., 2016), making their architecture unique. The two circulations are brought into proximity in the villous tree, separated by the villous membrane. Placental gas exchange takes place at the terminal villi where vasculo-syncytial membranes form (Gill et al., 2011). These are localized areas where the membrane is thinnest, often as little as $1–2\mathrm{\mu }\mathrm{m}$ (Burton and Tham, 1992).

Much attention has been paid to the maternal placental circulation, i.e. uterine arteries and intervillous space blood flow (Serov et al., 2015, Chernyavsky et al., 2011, Chernyavsky et al., 2010, Sengupta et al., 1997, Heilmann et al., 1979), because maladaptations such as pre-eclampsia or intrauterine growth restriction (IUGR) are the source of pregnancy complications. The feto-placental circulation was almost neglected until Doppler ultrasound was proposed as an early risk assessment tool (Fitzgerald and Drumm, 1977). The easy and routine acquisition of in-vivo data provided the opportunity to investigate and validate various aspects of the fetal circulation, such as the hemodynamics of the umbilical cord (Bracero et al., 1989, Giles et al., 1986, Trudinger et al., 1985, Gill, 1979, Fitzgerald and Drumm, 1977), insights regarding the villous tree function and development (Guiot et al., 1992, Thompson and Stevens, 1989, Reuwer et al., 1986) and the understanding of the complete fetal circulatory system (Kiserud and Acharya, 2004, Fitzgerald et al., 1984). However, Doppler ultrasound cannot provide in-vivo information on the flow at the terminal vasculature due to limits of resolution. Histology has also failed to identify the flow regimes because the maternal and fetal blood streams are not arranged in parallel. Therefore, mathematical modeling has become the only accessible tool for providing insights regarding the microcirculation in human placental capillaries.

The flow in the terminal villi was initially modeled as a two-dimensional (2D) concurrent, countercurrent, crosscurrent or mixed (partly concurrent and partly countercurrent) system (Moll, 1971, Guilbeau et al., 1971, Bartels et al., 1962). There have been a few attempts to improve the placental microvasculature modeling, such as Reneau et al. (1974) who simulated the three-dimensional (3D) fetal capillary tissue as small cylinders inside a larger cylinder or Costa et al. (1992) who modeled whirling motion in the capillary bends (sinusoids) where blood mixing takes place. Although technological advances offer new modeling tools, computational simulations have been barely used in placental related research possibly due to the geometrical complexity (Reneau et al., 1974, Moll, 1971, Guilbeau et al., 1971, Bartels et al., 1962). Gordon et al. (2007) created a branching model of the chorionic arterial vasculature based on published data and solved the fetal blood flow field. However, the branching model does not reach the terminal villi and only includes a few intraplacental vessels. For a comprehensive review on the role of morphology in mathematical models of placental gas exchange, the reader is referred to Serov et al. (2016). To the best of the authors׳ knowledge, the circulation in feto-placental capillaries has not been satisfactorily simulated by either a mathematical or a computational model.

The main objective of this work was to better understand the structure–function relationship of human placental terminal villi. For that purpose, 3D blood flow simulations were performed in fetal capillaries reconstructed from confocal microscopic image stacks (Plitman Mayo et al., 2016, Plitman Mayo et al., 2014). The impact of the variability in capillary diameter and tortuosity together with the blood flow direction and distribution on the oxygen transport was investigated and corroborated by an experimental validation.