Overset meshing in combination with novel blended weak-strong fluid-structure interactions for simulations of a translating valve in series with a second valve.

Mechanical circulatory support (MCS) devices can bridge the gap to transplant whilst awaiting a viable donor heart. The Realheart Total Artificial Heart is a novel positive-displacement MCS that generates pulsatile flow via bileaflet mechanical valves. This study developed a combined computational fluid dynamics and fluid-structure interaction (FSI) methodology for simulating positive displacement bileaflet valves. Overset meshing discretised the fluid domain, and a blended weak-strong coupling FSI algorithm was combined with variable time-stepping. Four operating conditions of relevant stroke lengths and rates were assessed. The results demonstrated this modelling strategy is stable and efficient for modelling positive-displacement artificial hearts.

Acute regional changes in myocardial strain may predict ventricular remodelling after myocardial infarction in a large animal model.

To identify predictors of left ventricular remodelling (LVR) post-myocardial infarction (MI) and related molecular signatures, a porcine model of closed-chest balloon MI was used along with serial cardiac magnetic resonance imaging (CMRI) up to 5-6 weeks post-MI. Changes in myocardial strain and strain rates were derived from CMRI data. Tissue proteomics was compared between infarcted and non-infarcted territories. Peak values of left ventricular (LV) apical circumferential strain (ACS) changed over time together with peak global circumferential strain (GCS) while peak GLS epicardial strains or strain rates did not change over time. Early LVR post-MI enhanced abundance of 39 proteins in infarcted LV territories, 21 of which correlated with LV equatorial circumferential strain rate. The strongest associations were observed for D-3-phosphoglycerate dehydrogenase (D-3PGDH), cysteine and glycine-rich protein-2, and secreted frizzled-related protein 1 (sFRP1). This study shows that early changes in regional peak ACS persist at 5-6 weeks post-MI, when early LVR is observed along with increased tissue levels of D-3PGDH and sFRP1. More studies are needed to ascertain if the observed increase in tissue levels of D-3PGDH and sFRP1 might be casually involved in the pathogenesis of adverse LV remodelling.

A spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging.

Contrast agent enhanced magnetic resonance (MR) perfusion imaging provides an early, non-invasive indication of defects in the coronary circulation. However, the large variation of contrast agent properties, physiological state and imaging protocols means that optimisation of image acquisition is difficult to achieve. This situation motivates the development of a computational framework that, in turn, enables the efficient mapping of this parameter space to provide valuable information for optimisation of perfusion imaging in the clinical context. For this purpose a single-compartment porous medium model of capillary blood flow is developed which is coupled with a scalar transport model, to characterise the behaviour of both blood-pool and freely-diffusive contrast agents characterised by their ability to diffuse through the capillary wall into the extra-cellular space. A parameter space study is performed on the nondimensionalised equations using a 2D model for both healthy and diseased myocardium, examining the sensitivity of system behaviour to Peclet number, Damköhler number (Da), diffusivity ratio and fluid porosity. Assuming a linear MR signal response model, sample concentration time series data are calculated, and the sensitivity of clinically-relevant properties of these signals to the model parameters is quantified. Both upslope and peak values display significant non-monotonic behaviour with regard to the Damköhler number, with these properties showing a high degree of sensitivity in the parameter range relevant to contrast agents currently in use. However, the results suggest that signal upslope is the more robust and discerning metric for perfusion quantification, in particular for correlating with perfusion defect size. Finally, the results were examined in the context of nonlinear signal response, flow quantification via Fermi deconvolution and perfusion reserve index, which demonstrated that there is no single best set of contrast agent parameters, instead the contrast agents should be tailored to the specific imaging protocol and post-processing method to be used.

A computationally efficient framework for the simulation of cardiac perfusion using a multi-compartment Darcy porous-media flow model.

We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi-compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi-compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N-compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting 'reduced' Darcy formulation leads to a dramatic reduction in algebraic-system size and is therefore computationally cheaper to solve than the full multi-compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject-specific model of the left ventricle.

A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics.

The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.

Mixing through stirring of steady flow in small amplitude helical tubes.

In this paper we numerically simulate flow in a helical tube for physiological conditions using a co-ordinate mapping of the Navier-Stokes equations. Helical geometries have been proposed for use as bypass grafts, arterial stents and as an idealized model for the out-of-plane curvature of arteries. Small amplitude helical tubes are also currently being investigated for possible application as A-V shunts, where preliminary in vivo tests suggest a possibly lower risk of thrombotic occlusion. In-plane mixing induced by the geometry is hypothesized to be an important mechanism. In this work, we focus mainly on a Reynolds number of 250 and investigate both the flow structure and the in-plane mixing in helical geometries with fixed pitch of 6 tube diameters (D), and centerline helical radius ranging from 0.1 D to 0.5 D. High-order particle tracking, and an information entropy measure is used to analyze the in-plane mixing. A combination of translational and rotational reference frames are shown to explain the apparent discrepancy between flow field and particle trajectories, whereby particle paths display a pattern characteristic of a double vortex, though the flow field reveals only a single dominant vortex. A radius of 0.25 D is found to provide the best trade-off between mixing and pressure loss, with little increase in mixing above R=0.25 D, whereas pressure continues to increase linearly.