A numerical strategy tailored to model the mechanical equilibrium in vascular vessels is presented. The formulation, based on a specific arrangement of finite elements, exploits the shell-like ...structure of the vessel wall by proposing a mixed-order approximation of the displacement field. The fields across the thickness are represented by a single element with high order polynomial approximation while the in-plane components are described through low-order 2D polynomials. The formulation is versatile to accommodate any kind of hyperelastic constitutive material model undergoing large strains. A series of numerical examples is presented to validate the effectiveness of the proposed approach. These examples range from benchmark problems reported in the literature to applications in the domain of cardiovascular modeling. The proposed approach proved to be effective and efficient in simulating the mechanics of vascular vessels.
In this work, an effective numerical method specifically conceived to simulate fluid flow in networks composed by tubular domains is presented. The present contribution addresses an extension of the ...so-called Transversally Enriched Pipe Element Method (TEPEM) recently developed by the authors in the computational hemodynamics realm to embrace the case of branching domains. The TEPEM approach relies on a slab-based partition of the network of vessels complemented with basis functions devised to render high-order polynomial enrichment for transversal flow phenomena, while keeping a low-order polynomial approximation for the fields along the axial direction. The main goal of such an approach is to provide a fast numerical tool to characterize flow-related quantities in large-scale networks of vessels, which are of relevance in the hemodynamics field, such as the wall shear stress. Through several numerical examples ranging from academic to patient-specific networks, it is demonstrated that the proposed strategy yields reasonably accurate qualitative and quantitative results and substantially reduced computational cost when compared with standard 3D finite element models. Hence, we conclude that this approach can be regarded as an appealing numerical technology placed halfway over-simplistic cheap 1D and computationally demanding accurate 3D models.
Four-dimensional flow cardiac magnetic resonance (CMR) is the reference technique for analyzing blood transport in the left ventricle (LV), but similar information can be obtained from ultrasound. We ...aimed to validate ultrasound-derived transport in a head-to-head comparison against 4D flow CMR. In five patients and two healthy volunteers, we obtained 2D + t and 3D + t (4D) flow fields in the LV using transthoracic echocardiography and CMR, respectively. We compartmentalized intraventricular blood flow into four fractions of end-diastolic volume: direct flow (DF), retained inflow (RI), delayed ejection flow (DEF) and residual volume (RV). Using ultrasound we also computed the properties of LV filling waves (percentage of LV penetration and percentage of LV volume carried by E/A waves) to determine their relationships with CMR transport. Agreement between both techniques for quantifying transport fractions was good for DF and RV (R
95% confidence interval: 0.82 0.33, 0.97 and 0.85 0.41, 0.97, respectively) and moderate for RI and DEF (R
= 0.47 -0.29, 0.88 and 0.55 -0.20, 0.90, respectively). Agreement between techniques to measure kinetic energy was variable. The amount of blood carried by the E-wave correlated with DF and RV (R = 0.75 and R = 0.63, respectively). Therefore, ultrasound is a suitable method for expanding the analysis of intraventricular flow transport in the clinical setting.
In this work, a novel fluid–structure interaction algorithm for the simulation of blood flow in three-dimensional deformable vessels is addressed. The method extends the mid-fidelity strategy named ...as Transversally Enriched Pipe Element Method, extensively tested as an efficient approach to simulate the blood flow under rigid wall hypothesis, by taking into account the distensibility of the lumen boundary by means of an independent ring structural model. The Navier–Stokes equations, in Arbitrary Lagrangian–Eulerian framework, are used as the governing equations for the blood flow dynamics, the vessel wall mechanics is represented through an elastic constitutive law, and the fluid domain deformation problem is explicitly solved by exploiting the layered structure of the geometry discretization associated to the mid-fidelity model. The result is an approximation strategy able to take into account the wall deformation at nearly zero added cost when compared with a rigid wall model. An extensive numerical validation and verification of the proposed methodology is reported employing simple domains and complex patient-specific geometries to highlight the potential for real applications.
•Fluid–structure coupling is mandatory for modeling large vessels.•The TEPEM is extended for FSI by considering an independent ring structural model.•This model incorporate the fluid–structure interaction at zero added cost.•This strategy is an efficient alternative for expensive high-fidelity models.
The fractional flow reserve index (FFR) is currently used as a gold standard to quantify coronary stenosis’s functional relevance. Due to its highly invasive nature, the development of noninvasive ...surrogates based on simulations has drawn much attention in recent years, emphasizing efficient strategies that enable translational research. The focus of this work is twofold. First, to assess the feasibility of using a mid-fidelity numerical strategy (transversally enriched pipe element method, TEPEM), placed between low- and high-fidelity models, for the estimation of flow-related quantities, such as FFR and wall shear stress (WSS). Low-fidelity models, as zero- or one-dimensional models, are computationally inexpensive but in detriment of poorer spatially detailed predictions. On the other hand, high-fidelity models, such as classical three-dimensional numerical approximations, can provide detailed predictions but their transition to clinical application is prohibitive due to high computational costs. As a second goal, we quantify the impact of the length of lateral branches in the blood flow through the interrogated vessel of interest to further reduce the computational burden. Both studies are addressed considering a cohort of 17 coronary geometries. A total of 20 locations were selected to estimate the FFR index for a wide range of Coronary Flow Reserve (CFR) scenarios. Numerical results suggest that the mid-fidelity TEPEM model is a reliable approach for the efficient estimation of the FFR index and WSS, with an error in the order of
1
%
and
5
%
, respectively, when compared to the high-fidelity prediction. Moreover, such mid-fidelity models require much less computational resources, in compliance with infrastructure frequently available in the clinic, by achieving a speedup between 30 and 60 times compared to a conventional finite element approach. Also, we show that shortening peripheral branches does not introduce considerable perturbations either in the flow patterns, in the wall shear stress, or the pressure drop. Comparing the different geometric models, the error in the estimation of FFR index and WSS is reduced to less than
0.1
%
and
2
%
, respectively.
Blood flow simulations in three-dimensional space pose the challenge of isolating the vascular domain of interest, which introduces artificial interfaces, both upstream and downstream, where boundary ...conditions must be prescribed. Vessel curvature, tortuosity, and blood flow pulsatility contribute to the complexity of performing these simulations. A common practice in defining boundary conditions is to prescribe Neumann-like boundary conditions over these boundaries. A typical numerical problem in such a setting is associated with the unbounded nature of the kinetic energy that enters into the system, either through antegrade upstream flow or through downstream retrograde flow. Lack of energy control in the continuum problem may become a source of numerical instability, resulting in corrupted simulations. In this work, we propose a novel approach to avoid these instabilities by considering a bulk fluid with specific properties in a small portion of the domain in the vicinity of such boundaries. More precisely, the convective term from the governing equations is nullified in these domain extensions, resulting in Stokesian regions. In contrast to the classical approach based on the inclusion of straight long extensions to allow flow development, the proposed approach involves dealing with small regions whose length is smaller than the vessel diameter, to control the kinetic energy with near zero added computational cost. This stabilization strategy is investigated within the context of the Transversally Enriched Pipe Element Method, which makes the implementation straightforward. Academic examples and patient-specific vascular geometries are employed to illustrate the performance of the proposed stabilization strategy.
•In hemodynamic simulations, incoming flows often serve as sources of instability.•We present a novel, straightforward, and computationally efficient alternative for stabilization.•No assumptions about the velocity profile nor extensive domain modifications are required.•We rigorously test the stabilization proposal's efficacy in both academic and patient-specific domains.
Motivated by its applicability to model blood flow in the cardiovascular system, in this work we propose a numerical approximation of the Navier–Stokes equations maintaining comparable accuracy with ...traditional finite element methods while performing a substantial reduction in the problem size. The method is envisaged for domains in which flow phenomena exhibits a dominant axial direction. The strategy consists of combining a finite element approximation for the description of fields (velocity components and pressure) in the primary (axial) direction, while taking a polynomial spectral approximation for the description of fields across the secondary (transversal) direction. In essence, this method can be understood as an extension of the so-called hierarchical modeling (HiMod) approach. Special attention is given to domains featuring sudden constrictions/expansions and bifurcations, for which a modified spectral approximation is considered. The capabilities and potentialities of the proposed approach to simulate fluid flow phenomena in pipe-like domains are presented through several examples.
•A simple hybrid approximation is proposed for CFD in tubular domains.•HiMod-like general purpose functions approximate the Navier–Stokes equations.•Special adaptation of space functions is proposed to deal with bifurcations.•Applications in computational hemodynamics in 2D and 3D are presented.
It has been shown experimentally that when a drop is deposited at the center of a substrate with an axial temperature gradient (hotter in the center), thermocapillarity effects makes an outward flow ...to appear so that the drop evolves towards a ring whose radius increases with time. Upon reaching a critical radius, the contact line becomes unstable, showing gentle undulations whose amplitudes grow with time. Using the lubrication approximation and adopting appropriate dimensionless variables, a parameter-free differential equation is obtained that governs this type of thermocapillary flow. Numerical solutions of this equation are presented to study the unstable stage. Experimental results are compared with those obtained from the numerical solutions.
