The LifeV library: engineering mathematics beyond the proof of concept

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis. Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar

Computational methods in cardiovascular mechanics

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.Comment: 54 pages, Book Chapte

Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls

The numerical modeling of solutes absorption processes by the arterial wall is of paramount interest for the understanding of the relationships between the local features of blood flow, the nourishing of the inner arterial wall by the blood solutes, and the pathologies that can appear when this process is for some reason perturbed. In the present work, two models for the solutes dynamics are investigated. In the first model, which is essentially based on the one introduced by Rappitsch and Perktold (1996) and Rappitsch, Perktold, and Pernkopf (1997), the Navier-Stokes equations for an incompressible fluid, describing the blood velocity and pressure fields, are coupled with an advection-diffusion equation for the solute concentration. The wellposedness of this model is discussed. The second model considers also the solutes dynamics "inside" the arterial wall, described by a pure diffusion equation. Actually, this is a heterogeneous model, coupling different equations in different parts of the domain at hand. Its wellposedness is proven. Moreover, in view of the numerical study, an iterative finite element method by subdomains is proposed and its convergence properties are analyzed. Finally, several numerical results comparing the different models in situations of physiologic interest are illustrate

Low-frequency, high-power ultrasound treatment at different pressures for olive paste: Effects on olive oil yield and quality.

Abstract Ultrasound technology was employed to test its action on the extraction of olive oil at the industrial scale. Because of its mechanical effects, ultrasound waves were applied to the olive paste, between the crushing and malaxing operations. Comparative experiments were performed between traditional extraction processes and the innovative extraction process, with the addition of the ultrasound treatment. Different levels of pressure were tested on olive paste, using four different olive cultivars. Pressure level played an important role in olive oil extractability. When ultrasound was subjected to olive paste with a pressure of about 3.5 bar, there was a significant increase of extractability compared to the traditional process. On the other hand, there was no significant effect between ultrasound treatment and traditional technology on extractability when ultrasound at a pressure level of 1.7 bar was used

A domain decomposition method for advection-diffusion processes with application to blood solutes

We consider a heterogeneous model for the dynamics of a blood solute both in the vascular lumen and inside the arterial wall. In the lumen, we consider an advection-diffusion equation, where the convective field is provided by the velocity of blood, which is in turn obtained by solving the Navier-Stokes equations. Inside the arterial wall we consider a pure diffusive dynamics. Since the endothelial layer at the interface between the lumen and the wall acts as a permeable membrane, whose permeability depends on the shear rate exerted by the blood, the solute concentration is discontinuous across this membrane. A possible approach for the numerical study of this kind of problem is inspired by domain decomposition techniques. In particular, we introduce a splitting in the computation and alternate the solution of the advection diffusion equation in the lumen with that of the diffusion equation in the wall. We set up an efficient iterative method, based on a suitable reformulation of the problem in terms of a Steklov-Poincare interface equation. This formulation is a nonstandard one because of the concentration discontinuity at the lumen-wall interface and plays a key role in the proof of convergence of our method. In particular, we prove that the convergence rate performed by the proposed method is independent of the finite element space discretization and provides a criterion for the selection of an acceleration parameter. Several numerical results, referred to as biomedical applications, support our theoretical conclusions and illustrate the efficiency of this algorith

Womersley Number-Based Estimates of Blood Flow Rate in Doppler Analysis: In Vivo Validation by Means of Phase-Contrast MRI

The aim of this paper, was to present an in vivo validation of the Womersley number-based formula, by means of 2-D cine phase-contrast MRI (PCMRI)

Semi-Automatic Reconstruction of Patient-Specific Stented Coronaries based on Data Assimilation and Computer Aided Design

Purpose The interplay between geometry and hemodynamics is a significant factor in the development of cardiovascular diseases. This is particularly true for stented coronary arteries. To elucidate this factor, an accurate patient-specific analysis requires the reconstruction of the geometry following the stent deployment for a computational fluid dynamics (CFD) investigation. The image-based reconstruction is troublesome for the different possible positions of the stent struts in the lumen and the coronary wall. However, the accurate inclusion of the stent footprint in the hemodynamic analysis is critical for detecting abnormal stress conditions and flow disturbances, particularly for thick struts like in bioresorbable scaffolds. Here, we present a novel reconstruction methodology that relies on Data Assimilation and Computer Aided Design. Methods The combination of the geometrical model of the undeployed stent and image-based data assimilated by a variational approach allows the highly automated reconstruction of the skeleton of the stent. A novel approach based on computational mechanics defines the map between the intravascular frame of reference (called L-view) and the 3D geometry retrieved from angiographies. Finally, the volumetric expansion of the stent skeleton needs to be self-intersection free for the successive CFD studies; this is obtained by using implicit representations based on the definition of Nef-polyhedra. Results We assessed our approach on a vessel phantom, with less than 10% difference (properly measured) vs. a customized manual (and longer) procedure previously published, yet with a significant higher level of automation and a shorter turnaround time. Computational hemodynamics results were even closer. We tested the approach on two patient-specific cases as well. Conclusions The method presented here has a high level of automation and excellent accuracy performances, so it can be used for larger studies involving patient-specific geometries

Hi-POD solution of parametrized fluid dynamics problems: preliminary results

Numerical modeling of fluids in pipes or network of pipes (like in the circulatory system) has been recently faced with new methods that exploit the specific nature of the dynamics, so that a one dimensional axial mainstream is enriched by local secondary transverse components [4, 16, 18]. These methods - under the name of Hi-Mod approximation - construct a solution as a finite element axial discretization, completed by a spectral approximation of the transverse dynamics. It has been demonstrated that Hi-Mod reduction significantly accelerates the computations without com- promising the accuracy. In view of variational data assimilation procedures (or, more in general, control problems), it is crucial to have efficient model reduction techniques to rapidly solve, for instance, a parametrized problem for several choices of the parameters of interest. In this work, we present some preliminary results merging Hi-Mod techniques with a classical Proper Orthogonal Decomposition (POD) strategy. We name this new approach as Hi-POD model reduction. We demonstrate the efficiency and the reliability of Hi-POD on multiparameter advection-diffusion-reaction problems as well as on the incompressible Navier-Stokes equations, both in a steady and in an unsteady setting