Adrien Lefieux

Aortic hemodynamics after thoracic endovascular aortic repair, with particular attention to the bird-beak configuration.

Purpose: To quantitatively evaluate the impact of thoracic endovascular aortic repair (TEVAR) on aortic hemodynamics, focusing on the implications of a bird-beak configuration. Methods: Pre- and postoperative CTA images from a patient treated with TEVAR for post-dissecting thoracic aortic aneurysm were used to evaluate the anatomical changes induced by the stent-graft and to generate the computational network essential for computational fluid dynamics (CFD) analysis. These analyses focused on the bird-beak configuration, flow distribution into the supra-aortic branches, and narrowing of the distal descending thoracic aorta. Three different CFD analyses (A: preoperative lumen, B: postoperative lumen, and C: postoperative lumen computed without stenosis) were compared at 3 time points during the cardiac cycle (maximum acceleration of blood flow, systolic peak, and maximum deceleration of blood flow). Results: Postoperatively, disturbance of flow was reduced at the bird-beak location due to boundary conditions and change of geometry after TEVAR. Stent-graft protrusion with partial coverage of the origin of the left subclavian artery produced a disturbance of flow in this vessel. Strong velocity increase and flow disturbance were found at the aortic narrowing in the descending thoracic aorta when comparing B and C, while no effect was seen on aortic arch hemodynamics. Conclusion: CFD may help physicians to understand aortic hemodynamic changes after TEVAR, including the change in aortic arch geometry, the effects of a bird-beak configuration, the supra-aortic flow distribution, and the aortic true lumen dynamics. This study is the first step in establishing a computational framework that, when completed with patient-specific data, will allow us to study thoracic aortic pathologies and their endovascular management.

A study on unfitted 1D finite element methods

In the present paper we consider a 1D Poisson model characterized by the presence of an interface, where a transmission condition arises due to jumps of the coefficients. We aim at studying finite element methods with meshes not fitting such an interface. It is well known that when the mesh does not fit the material discontinuities the resulting scheme provides in general lower order accurate solutions. We focus on so-called embedded approaches, frequently adopted to treat fluid-structure interaction problems, with the aim of recovering higher order of approximation also in presence of non fitting meshes; we implement several methods inspired by: the Immersed Boundary method, the Fictitious Domain method, and the Extended Finite Element method. In particular, we present four formulations in a comprehensive and unified format, proposing several numerical tests and discussing their performance. Moreover, we point out issues that may be encountered in the generalization to higher dimensions and we comment on possible solutions.

Coupled Morphological–Hemodynamic Computational Analysis of Type B Aortic Dissection: A Longitudinal Study

Progressive false lumen aneurysmal degeneration in type B aortic dissection (TBAD) is a complex process with a multi-factorial etiology. Patient-specific computational fluid dynamics (CFD) simulations provide spatial and temporal hemodynamic quantities that facilitate understanding this disease progression. A longitudinal study was performed for a TBAD patient, who was diagnosed with the uncomplicated TBAD in 2006 and treated with optimal medical therapy but received surgery in 2010 due to late complication. Geometries of the aorta in 2006 and 2010 were reconstructed. With registration algorithms, we accurately quantified the evolution of the false lumen, while with CFD simulations we computed several hemodynamic indexes, including the wall shear stress (WSS), and the relative residence time (RRT). The numerical fluid model included large eddy simulation (LES) modeling for efficiently capturing the flow disturbances induced by the entry tears. In the absence of complete patient-specific data, the boundary conditions were based on a specific calibration method. Correlations between hemodynamics and the evolution field in time obtained by registration of the false lumen are discussed. Further testing of this methodology on a large cohort of patients may enable the use of CFD to predict whether patients, with originally uncomplicated TBAD, develop late complications.

On the Use of Anisotropic Triangles with Mixed Finite Elements: Application to an “Immersed” Approach for Incompressible Flow Problems

In this chapter, we discuss the use of some common mixed finite elements in the context of a locally anisotropic remeshing strategy, close in philosophy to “immersed” approaches for interface problems. A characteristic of the present method is the presence of highly flat triangles. Such a distinctive feature may imply stability issues for mixed elements with incompressible flow problems. First, we present a review of the literature dealing with interface problems and we illustrate these results with a simple 1D framework alongside of numerical tests. Second, we present the locally anisotropic remeshing approach for interface problems in 2D with a focus on the incompressible Stokes problem. We then present numerical tests to show stability issues of common mixed elements, as well as possible stable ones. We also deal with conditioning issues. Finally, we illustrate the results with two applications, including the fluid–structure interaction of a rotational rigid bar.

Parallelizing a finite element solver in computational hemodynamics: A black box approach

In the last 20 years, a new approach has emerged to investigate the physiopathology of circulation. By merging medical images with validated numerical models, it is possible to support doctors’ decision-making process. The iCardioCloud project aims at establishing a computational framework to perform a complete patient-specific numerical analysis, specially oriented to aortic diseases (like dissections or aneurysms) and to deliver a compelling synthesis. The project can be considered a pioneering example of a Computer Aided Clinical Trial: i.e., a comprehensive analysis of patients where the level of knowledge extracted by traditional measures and statistics is enhanced through the massive use of numerical modeling. From a computer engineering point of view, iCardioCloud faces multiple challenges. First, the number of problems to solve for each patient is significantly huge – this is typical of computational fluid dynamics (CFD) – and it requires parallel methods. In addition, working in a clinical environment demands efficiency as the timeline requires rapid quantitative answers (as may happen in an emergency scenario). It is therefore mandatory to employ high-end parallel systems, such as large clusters or supercomputers. Here we discuss a parallel implementation of an application within the iCardioCloud project, built with a black-box approach – i.e., by assembling and configuring existing packages and libraries and in particular LifeV, a finite element library developed to solve CFD problems. The goal of this paper is to describe the software architecture underlying LifeV and to assess its performance and the most appropriate parallel paradigm. This paper is an extension of a previous work presented at the PBio 2015 Conference. This revision extends the description of the software architecture and discusses several new serial and parallel optimizations to the application. We discuss the introduction of hybrid parallelism in order to mitigate some performance problems previously experienced.

Patient-specific CFD modelling in the thoracic aorta with PC-MRI-based boundary conditions: A least-square three-element Windkessel approach

The increasing use of computational fluid dynamics for simulating blood flow in clinics demands the identification of appropriate patient-specific boundary conditions for the customization of the mathematical models. These conditions should ideally be retrieved from measurements. However, finite resolution of devices as well as other practical/ethical reasons prevent the construction of complete data sets necessary to make the mathematical problems well posed. Available data need to be completed by modelling assumptions, whose impact on the final solution has to be carefully addressed. Focusing on aortic vascular districts and related pathologies, we present here a method for efficiently and robustly prescribing phase contrast MRI-based patient-specific data as boundary conditions at the domain of interest. In particular, for the outlets, the basic idea is to obtain pressure conditions from an appropriate elaboration of available flow rates on the basis of a 3D/0D dimensionally heterogeneous modelling. The key point is that the parameters are obtained by a constrained optimization procedure. The rationale is that pressure conditions have a reduced impact on the numerical solution compared with velocity conditions, yielding a simulation framework less exposed to noise and inconsistency of the data, as well as to the arbitrariness of the underlying modelling assumptions. Numerical results confirm the reliability of the approach in comparison with other patient-specific approaches adopted in the literature.

Computational Study of Aortic Hemodynamics: From Simplified to Patient-Specific Geometries

The investigation of aortic hemodynamics in physiological and pathological conditions by computational fluid dynamics is still one of the major topic of vascular biomechanics. In particular, thanks to the developments of new endovascular technologies such as Thoracic EndoVAscular Repair (TEVAR), a lot of attention is paid to the hemodynamics analysis of thoracic aorta. In this work, we aim at performing a sensitivity analysis of morphological aspects by comparing numerical results about three cases: (i) an idealized aortic arch with a candy cane shape; (ii) a patient-specific healthy arch; and (iii) a patient-specific dissected aorta. For the idealized aortic arch case we also compare the obtained results with respect to the theoretical and experimental literature dedicated to curved pipes.

Numerical Studies on the Stability of Mixed Finite Elements Over Anisotropic Meshes Arising from Immersed Boundary Stokes Problems

Motivated by a recently proposed local refinement strategy for immersed interface problems, in this work we aim at dealing with the behavior of mixed finite elements for the Stokes problem in (strongly) anisotropic mesh situations, leading to severely distorted elements. In fact, the majority of the theoretical results present in the finite element literature has been carried out under the assumption of well-shaped elements. In the case such a condition is not satisfied, the inf-sup constant may degenerate, thus leading to the instability of the system.