The theory

The theory behind this model is based on the integration of models described in detail in:

Please remember to cite these papers if using our softwares.

The basics

The model aims to connect macro-scale perfusion simulations (e.g. Clark et al 2015) with micro-scale models that define geometric determinants of terminal villous exchange capacity (e.g. Erlich et al 2019a/b).

The theory behind the perfusion model is detailed in Models of steady flow in the feto-placental circulation. However, in this model there are some modifications:

  • First, ‘capillary convolutes’ as defined by Clark et al. are replaced by \(n_S\) series and \(n_P\) parallel terminal villi units as defined by Erlich et al. These terminal villous units have a resistance associated with them which reflects their geometric structure.

  • Second, vessels were assumed to be compliant: \(r=r_0(1+3r_0 P_{tm}/4Eh_0)\) (where r is radius, h is wall thickness, E is elastic modulus and \(P_{tm}\) is transmural pressure.

  • Finally a non-linear rheology model is employed (Pries, A., TW, S., Gaehtgens, P., and JF, G. (1990). Blood flow in microvascular networks: experiments and simulations. Circ Res, 67:826–834)

Nutrient exchange is assumed to occur only in the terminal villi, and exchange modelling follows Erlich et al. Sci Adv 2019 directly. This model provides an exchange flux and nutrient concentration supplied to each terminal villous which is then summed over the anatomical tree network to provide a total nutrient delivery/update to the fetal circulation via the placenta.