Philip Pearce

Image-Based Modeling of Blood Flow and Oxygen Transfer in Feto-Placental Capillaries

During pregnancy, oxygen diffuses from maternal to fetal blood through villous trees in the placenta. In this paper, we simulate blood flow and oxygen transfer in feto-placental capillaries by converting three-dimensional representations of villous and capillary surfaces, reconstructed from confocal laser scanning microscopy, to finite-element meshes, and calculating values of vascular flow resistance and total oxygen transfer. The relationship between the total oxygen transfer rate and the pressure drop through the capillary is shown to be captured across a wide range of pressure drops by physical scaling laws and an upper bound on the oxygen transfer rate. A regression equation is introduced that can be used to estimate the oxygen transfer in a capillary using the vascular resistance. Two techniques for quantifying the effects of statistical variability, experimental uncertainty and pathological placental structure on the calculated properties are then introduced. First, scaling arguments are used to quantify the sensitivity of the model to uncertainties in the geometry and the parameters. Second, the effects of localized dilations in fetal capillaries are investigated using an idealized axisymmetric model, to quantify the possible effect of pathological placental structure on oxygen transfer. The model predicts how, for a fixed pressure drop through a capillary, oxygen transfer is maximized by an optimal width of the dilation. The results could explain the prevalence of fetal hypoxia in cases of delayed villous maturation, a pathology characterized by a lack of the vasculo-syncytial membranes often seen in conjunction with localized capillary dilations.

Flame balls in non-uniform mixtures: existence and finite activation energy effects

The papers broad motivation, shared by a recent theoretical investigation [Daou and Daou, “Flame balls in mixing layers,” Combustion and Flame, Vol. 161 (2014), pp. 2015–2024], is a fundamental but apparently untouched combustion question; specifically, ‘What are the critical conditions insuring the successful ignition of a diffusion flame by means of an external energy deposit (spark), after mixing of cold reactants has occurred in a mixing layer?’ The approach is based on a generalisation of the concept of Zeldovich flame balls, well known in premixed reactive mixtures, to non-uniform mixtures. This generalisation leads to a free boundary problem (FBP) for axisymmetric flame balls in a two-dimensional mixing layer in the distinguished limit β → ∞ with εL = O(1); here β is the Zeldovich number and εL is a non-dimensional measure of the stoichiometric premixed flame thickness. The existence of such flame balls is the main object of current investigation. Several original contributions are presented. First, an analytical contribution is made by carrying out the analysis of Daou and Daou (2014) in the asymptotic limit εL → 0 to higher order. The results capture, in particular, the dependence of the location of the flame ball centre (argued to represent the optimal ignition location which differs from the stoichiometric location) on εL. Second, two detailed numerical studies of the axisymmetric flame balls are presented for arbitrary values of εL. The first study addresses the infinite-β FBP and the second one the original finite-β problem based on the constant density reaction–diffusion equations. In particular, it is shown that solutions to the FBP exist for arbitrary values of εL while actual finite-β flame balls exist in a specific domain of the β–εL plane, namely for εL less than a maximum value proportional to ; this scaling is consistent with the existence of solutions to the FBP for arbitrary εL. In fact, the flame ball existence domain is found to have little dependence on the stoichiometry of the reaction and to coincide, to a good approximation, with the domain of existence of the positively-propagating two-dimensional triple flames in the mixing layer. Finally, we confirm that the flame balls are typically unstable, as one expects in the absence of heat losses.

Learning dynamical information from static protein and sequencing data

Many complex processes, from protein folding and virus evolution to brain activity and neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. While efficient algorithms for cluster detection and data completion in high-dimensional spaces have been developed and applied over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here, we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. Our approach combines Gaussian mixture approximations and self-consistent dimensionality reduction with minimal-energy path estimation and multi-dimensional transition-state theory. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein folding transitions and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data and phylogenetic trees. The underlying numerical protocol thus allows the recovery of relevant dynamical information from instantaneous ensemble measurements, effectively alleviating the need for time-dependent data in many situations. Owing to its generic structure, the framework introduced here will be applicable to modern cryo-electron-microscopy and high-throughput single-cell RNA sequencing data and can guide the design of new experimental approaches towards studying complex multiphase phenomena.