A computational model of a human placentone: simulating uteroplacental hemodynamics

Introduction:: The placenta is a vital organ that connects the mother and fetus, facilitating the exchange of oxygen and nutrients. This whole system undergoes significant changes during pregnancy, including the remodeling of the spiral arteries to establish uteroplacental circulation and the development of the villous trees, the main structure of the placenta. A better understanding of the placenta and the factors affecting its development and function is essential for predicting and detecting pregnancy pathologies. However, placentation remains understudied, partly due to the limitations of current technology in studying the placenta in vivo. The pregnant uterus is not accessible to invasive measurements, and there are limitations in the resolution of the standard of care clinical imaging that can be safely utilized during the pregnancy. Therefore, computational modeling can provide valuable insights into healthy and abnormal pregnancies. Results from computational simulations could inform metrics for the early detection of pregnancy complications and help identify therapeutic targets. Here, we present a computational model of uteroplacental hemodynamics. The model parameters are informed by data from histological studies and Doppler ultrasound measurements at the uteroplacental interface in healthy pregnancies [1]. Given the limited experimental data available and the uncertainty associated with placenta structure and function measurements, we examine the effect of different parameters on local hemodynamics in the intervillous space, including variations related to abnormal pregnancy.


Materials and Methods:: We constructed a three-dimensional model of a placentone, the basic functional unit of the placenta (its schematic picture in Fig.1A). This model consists of a spiral artery (SA), decidual veins, and intervillous space (Figs.1B&C). We modeled the placentone at the end of the gestational age. The intervillous space is defined as an open cavity and a porous medium region representing the volume occupied by the villous tree. The cavity represents the free-of-villous-trees space at the center of the lobule, as reported in MRI studies [2]. The porous medium was divided into two regions with different porosities. Based on data from MRI, we defined higher porosity in the peripheral region [2]. The length of the SA, its opening width and the length of the remodeled section were defined based on data from the literature [3,4,5]. The length, depth and width of the lobule were chosen according to [3,5]. Blood was modeled as a Newtonian fluid. We used the finite element method (FEM) to solve the Navier-Stokes and continuity equations that govern blood flow in the non-porous regions (SA, cavity, and veins), and the continuity and Darcy-Brinkman equations in the porous region. In each simulation case, a mesh independence study was conducted to determine the optimal number of elements. The Newton method was implemented to linearize the nonlinear equations, and we used Generalized Minimal Residual algorithm to solve the resulting linear system. We examined the effect of model parameters on uteroplacental hemodynamics which are explained in the “Results and Discussion” section.

Results, Conclusions, and Discussions:: We performed computational simulations to study the effect of model parameters, including vein location, cavity length, and simulation boundary conditions (BCs), on uteroplacental hemodynamics. Our results show as the veins come close to the SA, jet length decreases (Fig.2). Unless the veins are far enough from the SA, the jet length does not reach physiological values, even if the cavity length is increased to a value as high as half of the placentone. The jet shape is also affected if the veins are too close to the SA (Fig.2A). Our simulations suggest veins are in the lobule periphery. Cavity length also has a significant impact on jet length. We observe that jet length increases with cavity length. However, the rate of increase gradually diminishes until increasing cavity length no longer increases the jet length. A cavity length of 7mm (veins in the periphery) produces a jet length of 4.95mm, comparable to ultrasound measurements (5.3 mm) [1]. In the absence of a cavity, no jet gets formed (Fig.3A). Hence, our results confirm that there should exist a free-of-villous-trees space at the lobule center. In all the above-mentioned results, a no-slip BC was set on the lobule side surfaces to represent the septa. However, septa usually do not extend to the end of the lobule [2]. To model this, we applied zero-pressure BCs on the distal sections. In this case, we obtain a jet length of 5.3mm with a shorter cavity length(6.4mm). Defective or incomplete SA remodeling is the underlying cause of many pregnancy disorders. In the case of un-remodeled or partially remodeled SA, our simulations reveal circular vortices generated close to the SA opening and higher intervillous velocities. High velocities can damage the delicate structure of the villous trees (because of higher shear stresses) and limit the diffusion of oxygen and nutrients to the fetus. In conclusion, we developed a computational model of a human placentone and validated our results against experimental data. Our simulations suggest a cavity is critical to obtain realistic entry jets, veins are in the lobule periphery, and the extension length of the septa should be considered.

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References (Optional): : [1] Collins, S.L., Stevenson, G.N., Noble, J.A. and Impey, L., 2012. Developmental changes in spiral artery blood flow in the human placenta observed with colour Doppler ultrasonography. Placenta, 33(10), pp.782-787.

[2] Kliewer, M.A., Bockoven, C.G., Reeder, S.B., Bagley, A.R. and Fritsch, M.K., 2023. Ferumoxytol-enhanced magnetic resonance imaging with volume rendering: a new approach for the depiction of internal placental structure in vivo. Placenta, 131, pp.104-110.


[3] Benirschke, K. and Driscoll, S.G., Sixth Edition. The pathology of the human placenta. Springer Berlin Heidelberg.

[4] Burton, G.J., Woods, A.W., Jauniaux, E. and Kingdom, J.C.P., 2009. Rheological and physiological consequences of conversion of the maternal spiral arteries for uteroplacental blood flow during human pregnancy. Placenta, 30(6), pp.473-482.

[5] Saghian, R., James, J.L., Tawhai, M.H., Collins, S.L. and Clark, A.R., 2017. Association of placental jets and mega-jets with reduced villous density. Journal of Biomechanical Engineering, 139(5).