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Register a new userEffects of stenotic aortic valve on the left heart hemodynamics: a fluid-structure-electrophysiology approach
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The aortic valve is a three-leaflet passive structure that, driven by pressure differences between the left ventricle and the aorta, opens and closes during the heartbeat to ensure the correct stream direction and flow rate. In elderly individuals or because of particular pathologies, the valve leaflets can stiffen thus impairing the valve functioning and, in turn, the pumping efficiency of the heart. Using a multi-physics left heart model accounting for the electrophysiology, the active contraction of the myocardium, the hemodynamics and the related fluid-structure-interaction, we have investigated the changes in the flow features for different severities of the aortic valve stenosis. We have found that, in addition to the increase of the transvalvular pressure drop and of the systolic jet velocity, a stenotic aortic valve significantly alters the wall shear stresses and their spatial distribution over the aortic arch and valve leaflets, which may induce a remodelling process of the ventricular myocardium. The numerical results from the multi-physics model are fully consistent with the clinical experience, thus further opening the way for computational engineering aided medical diagnostic.
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The reliability of cardiovascular computational models depends on the accurate solution of the hemodynamics, the realistic characterization of the hyperelastic and electric properties of the tissues along with the correct description of their interaction. The resulting fluid-structure-electrophysiology interaction (FSEI) thus requires an immense computational power, usually available in large supercomputing centers, and requires long time to obtain results even if multi-CPU processors are used (MPI acceleration). In recent years, graphics processing units (GPUs) have emerged as a convenient platform for high performance computing, as they allow for considerable reductions of the time-to-solution. This approach is particularly appealing if the tool has to support medical decisions that require solutions within reduced times and possibly obtained by local computational resources. Accordingly, our multi-physics solver has been ported to GPU architectures using CUDA Fortran to tackle fast and accurate hemodynamics simulations of the human heart without resorting to large-scale supercomputers. This work describes the use of CUDA to accelerate the FSEI on heterogeneous clusters, where both the CPUs and GPUs are used in synergistically with minor modifications of the original source code. The resulting GPU accelerated code solves a single heartbeat within a few hours (from three to ten depending on the grid resolution) running on premises computing facility made of few GPU cards, which can be easily installed in a medical laboratory or in a hospital, thus opening towards a systematic computational fluid dynamics (CFD) aided diagnostic.
This paper presents a new method for modeling the mechanics of the aortic valve, and simulates its interaction with blood. As much as possible, the model construction is based on first principles, but such that the model is consistent with experimental observations. We require that tension in the leaflets must support a pressure, then derive a system of partial differential equations governing its mechanical equilibrium. The solution to these differential equations is referred to as the predicted loaded configuration; it includes the loaded leaflet geometry, fiber orientations and tensions needed to support the prescribed load. From this configuration, we derive a reference configuration and constitutive law. In fluid-structure interaction simulations with the immersed boundary method, the model seals reliably under physiological pressures, and opens freely over multiple cardiac cycles. Further, model closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting the unique features of this model construction, we conduct experiments on reference configurations, constitutive laws, and gross morphology. These experiments suggest the following conclusions, which are directly applicable to the design of prosthetic aortic valves. (i) The loaded geometry, tensions and tangent moduli primarily determine model function. (ii) Alterations to the reference configuration have little effect if the predicted loaded configuration is identical. (iii) The leaflets must have sufficiently nonlinear material response to function over a variety of pressures. (iv) Valve performance is highly sensitive to free edge length and leaflet height. For future use, our aortic valve modeling framework offers flexibility in patient-specific models of cardiac flow.
The analysis of quantitative hemodynamics and luminal pressure may add valuable information to aid treatment strategies and prognosis for aortic dissections. This work directly compared in vitro 4D-flow magnetic resonance imaging (MRI), catheter-based pressure measurements, and computational fluid dynamics that integrated fluid-structure interaction (CFD FSI). Experimental data was acquired with a compliant 3D-printed model of a type-B aortic dissection (TBAD) that was embedded into a physiologically tuned flow circuit. In vitro flow and pressure information were used to tune the CFD FSI Windkessel boundary conditions. Results showed very good overall agreement of complex flow patterns, true to false lumen flow splits, and pressure distribution. This work demonstrates feasibility of a tunable experimental setup that integrates a patient-specific compliant model and provides a test bed for exploring critical imaging and modeling parameters that ultimately may improve the prognosis for patients with aortic dissections.
We study fluid-structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state. The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid. The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model. We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel. For the structural problem, we employ two plate theories, namely Kirchhoff-Love theory of thin plates and Reissner-Mindlin first-order shear deformation theory. The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall. Within our perturbative (lubrication theory) approach, we determine the relationship between flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure. From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow. Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel. Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical prediction for the flow rate-pressure drop relation and the structural deformation profile of the top wall. In doing so, we also establish the limits of applicability of our perturbative theory.
Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are usually performed in an Eulerian (fixed) frame of reference with snapshots from measurements or evolution equations. The Eulerian description poses some difficulties, however, when the domain or the mesh deforms with time as, for example, in fluid-structure interactions. For such cases, we first formulate a Lagrangian modal analysis (LMA) ansatz by a posteriori transforming the Eulerian flow fields into Lagrangian flow maps through an orientation and measure-preserving domain diffeomorphism. The development is then verified for Lagrangian variants of POD and DMD using direct numerical simulations (DNS) of two canonical flow configurations at Mach 0.5, the lid-driven cavity and flow past a cylinder, representing internal and external flows, respectively, at pre- and post-bifurcation Reynolds numbers. The LMA is demonstrated for several situations encompassing unsteady flow without and with boundary and mesh deformation as well as non-uniform base flows that are steady in Eulerian but not in Lagrangian frames. We show that LMA application to steady nonuniform base flow yields insights into flow stability and post-bifurcation dynamics. LMA naturally leads to Lagrangian coherent flow structures and connections with finite-time Lyapunov exponents (FTLE). We examine the mathematical link between FTLE and LMA by considering a double-gyre flow pattern. Dynamically important flow features in the Lagrangian sense are recovered by performing LMA with forward and backward (adjoint) time procedures.
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