Physical and geometric determinants of transport in fetoplacental microvascular networks

Abstract

Across mammalian species, solute exchange takes place in complex microvascular networks. In the human placenta, the primary exchange units are terminal villi that contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. We show how the irregular internal structure of a terminal villus determines its exchange capacity for diverse solutes. Distilling geometric features into three parameters, obtained from image analysis and computational fluid dynamics, we capture archetypal features of the structure-function relationship of terminal villi using a simple algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. Our theory accommodates countercurrent effects, incorporates nonlinear blood rheology, and offers an efficient method for testing network robustness. Our results show how physical estimates of solute transport, based on carefully defined geometrical statistics, provide a viable method for linking placental structure and function and offer a framework for assessing transport in other microvascular systems.

Homogenization approximations for unidirectional transport past randomly distributed sinks

“…In practical applications it can be important to understand not only large-scale concentration distributions across a region but also small-scale variations across unit cells. In the placenta, for example, transfer between fetal and maternal circulation takes place at the lengthscale of individual terminal villi, where individual fetal capillary loops within a branch come into close proximity to maternal blood outside the branch (Erlich et al, 2018). The size of solute fluctuations across an individual branch can be expected to influence the transport across the surface of the branch.…”

“…The size of solute fluctuations across an individual branch can be expected to influence the transport across the surface of the branch. Given the high degree of spatial disorder in branches (Chernyavsky et al, 2011;Erlich et al, 2018), the fluctuations associated with spatial disorder (reflected by the standard deviation ofĈ b in Table 2) deserve particular attention, particularly if there are correlations between the orientation of capillary loops within the villous branch and the position of the branch with respect to its neighbours.…”

Quantifying the impact of tissue metabolism on solute transport in feto-placental microvascular networks

“…As explained by Jensen & Chernyavsky [7], this expression is naturally expressed in terms of suitable dimensionless parameters, namely a Damköhler number Da that measures solute transit time across the villous tissue due to diffusion relative to transit time through the villus due to flow, and a parameter μ that measures the relative diffusive capacities of the villous tissue and the intravillous capillary network. Erlich et al [9] added a further refinement to the regression equation and then validated it using computational simulations of four villus specimens, each having complex internal structure. The significant physical parameters in their analysis were the solute diffusivities in tissue and plasma ( D t and D p , respectively), the effective viscosity of blood η (based on an assumption of Newtonian flow), a dimensionless parameter B that captures the advective boost that oxygen acquires from binding to haemoglobin [10], and the imposed pressure drop Δ P driving blood through the vessel network.…”

“…This analysis also revealed some of the key geometric parameters determining the transport capacity of a villus for most solutes: the flow resistance of the capillary network per unit viscosity (R/η, which has dimensions of inverse volume); the total length of capillary vessels within the villus L c ; and a lengthscale L capturing the diffusive capacity of villous tissue (a normalized diffusive flux integrated over an exchange area). A key finding from [9] is that, for the majority of physiologically relevant solutes studied, the diffusive capacity ratio μ =DtscriptL/D pLc was sufficiently small among all specimens studied for the effects of concentration boundary layers within capillaries to be a secondary factor. Then, assuming the solute is not absorbed by villous tissue, transport was predicted to be flow-limited when Da ≫ 1 and diffusion-limited when Da ≪ 1, where Da=DtscriptLscriptRBΔP.The solute flux N is well approximated [5,9] by N=Nmax1+ Da +DanormalF1/3,where Ntruemax=DnormaltnormalΔcL represents the maximum diffusive capacity of the villus under a solute concentration difference Δ c between maternal and fetal blood.…”

“…A key finding from [9] is that, for the majority of physiologically relevant solutes studied, the diffusive capacity ratio μ =DtscriptL/D pLc was sufficiently small among all specimens studied for the effects of concentration boundary layers within capillaries to be a secondary factor. Then, assuming the solute is not absorbed by villous tissue, transport was predicted to be flow-limited when Da ≫ 1 and diffusion-limited when Da ≪ 1, where Da=DtscriptLscriptRBΔP.The solute flux N is well approximated [5,9] by N=Nmax1+ Da +DanormalF1/3,where Ntruemax=DnormaltnormalΔcL represents the maximum diffusive capacity of the villus under a solute concentration difference Δ c between maternal and fetal blood. Setting aside the term involving Da F ≡ μ 2 Da/166.4 (a correction accounting for concentration boundary layers), (1.2) captures the transition from flow-limited transport (N≈Ntruemax/ Da =Bfalse(normalΔP/Rfalse)normalΔc) to diffusion-limited transport ( N ≈ N max ) as flow strength (Da −1 ) increases from low to high values.…”