Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics

When modelling the cardiovascular system, the effect of the vessel wall on the blood flow has great relevance. Arterial vessels are complex living tissues and three-dimensional specific models have been proposed to represent their behaviour. The numerical simulation of the 3D-3D Fluid-Structure Interaction (FSI) coupled problem has high computational costs in terms of required time and memory storage. Even if many possible solutions have been explored to speed up the resolution of such problem, we are far from having a 3D-3D FSI model that can be solved quickly. In 3D-3D FSI models two of the main sources of complexity are represented by the domain motion and the coupling between the fluid and the structural part. Nevertheless, in many cases, we are interested in the blood flow dynamics in compliant vessels, whereas the displacement of the domain is small and the structure dynamics is less relevant. In these situations, techniques to reduce the complexity of the problem can be used. One consists in using transpiration conditions for the fluid model as surrogate for the wall displacement, thus allowing problem's solution on a fixed domain. Another strategy consists in modelling the arterial wall as a thin membrane under specific assumptions (Figueroa et al., 2006, Nobile and Vergara, 2008) instead of using a more realistic (but more computationally intensive) 3D elastodynamic model. Using this strategy the dynamics of the vessel motion is embedded in the equation for the blood flow. Combining the transpiration conditions with the membrane model assumption, we obtain an attractive formulation, in fact, instead of solving two different models on two moving physical domains, we solve only a Navier-Stokes system in a fixed fluid domain where the structure model is integrated as a generalized Robin condition. In this paper, we present a general formulation in the boundary conditions which is independent of the time discretization scheme choice and on the stress-strain constitutive relation adopted for the vessel wall structure. Our aim is, first, to write a formulation of a reduced order model with zero order transpiration conditions for a generic time discretization scheme, then to compare a 3D-3D PSI model and a reduced FSI one in two realistic patient-specific cases: a femoropopliteal bypass and an aorta. In particular, we are interested in comparing the wall shear stresses, in fact this quantity can be used as a risk factor for some pathologies such as atherosclerosis or thrombogenesis. More in general we want to assess the accuracy and the computational convenience to use simpler formulations based on reduced order models. In particular, we show that, in the case of small displacements, using a 3D-3D PSI linear elastic model or the correspondent reduced order one yields many similar results. (c) 2013 Elsevier B.V. All rights reserved

An in silico study of the influence of vessel wall deformation on neointimal hyperplasia progression in peripheral bypass grafts

Neointimal hyperplasia (NIH) is a major obstacle to graft patency in the peripheral arteries. A complex interaction of biomechanical factors contribute to NIH development and progression, and although haemodynamic markers such as wall shear stress have been linked to the disease, these have so far been insufficient to fully capture its behaviour. Using a computational model linking computational fluid dynamics (CFD) simulations of blood flow with a biochemical model representing NIH growth mechanisms, we analyse the effect of compliance mismatch, due to the presence of surgical stitches and/or to the change in distensibility between artery and vein graft, on the haemodynamics in the lumen and, subsequently, on NIH progression. The model enabled to simulate NIH at proximal and distal anastomoses of three patient-specific end-to-side saphenous vein grafts under two compliance-mismatch configurations, and a rigid wall case for comparison, obtaining values of stenosis similar to those observed in the computed tomography (CT) scans. The maximum difference in time-averaged wall shear stress between the rigid and compliant models was 3.4 Pa, and differences in estimation of NIH progression were only observed in one patient. The impact of compliance on the haemodynamic-driven development of NIH was small in the patient-specific cases considered

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

Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics

When modelling the cardiovascular system, the effect of the vessel wall on the blood flow has great relevance. Arterial vessels are complex living tissues and three-dimensional specific models have been proposed to represent their behaviour. The numerical simulation of the 3D–3D Fluid–Structure Interaction (FSI) coupled problem has high computational costs in terms of required time and memory storage. Even if many possible solutions have been explored to speed up the resolution of such problem, we are far from having a 3D–3D FSI model that can be solved quickly. In 3D–3D FSI models two of the main sources of complexity are represented by the domain motion and the coupling between the fluid and the structural part. Nevertheless, in many cases, we are interested in the blood flow dynamics in compliant vessels, whereas the displacement of the domain is small and the structure dynamics is less relevant. In these situations, techniques to reduce the complexity of the problem can be used. One consists in using transpiration conditions for the fluid model as surrogate for the wall displacement, thus allowing problem’s solution on a fixed domain. Another strategy consists in modelling the arterial wall as a thin membrane under specific assumptions (Figueroa et al., 2006, Nobile and Vergara, 2008) instead of using a more realistic (but more computationally intensive) 3D elastodynamic model. Using this strategy the dynamics of the vessel motion is embedded in the equation for the blood flow. Combining the transpiration conditions with the membrane model assumption, we obtain an attractive formulation, in fact, instead of solving two different models on two moving physical domains, we solve only a Navier–Stokes system in a fixed fluid domain where the structure model is integrated as a generalized Robin condition. In this paper, we present a general formulation in the boundary conditions which is independent of the time discretization scheme choice and on the stress–strain constitutive relation adopted for the vessel wall structure. Our aim is, first, to write a formulation of a reduced order model with zero order transpiration conditions for a generic time discretization scheme, then to compare a 3D–3D FSI model and a reduced FSI one in two realistic patient-specific cases: a femoropopliteal bypass and an aorta. In particular, we are interested in comparing the wall shear stresses, in fact this quantity can be used as a risk factor for some pathologies such as atherosclerosis or thrombogenesis. More in general we want to assess the accuracy and the computational convenience to use simpler formulations based on reduced order models. In particular, we show that, in the case of small displacements, using a 3D–3D FSI linear elastic model or the correspondent reduced order one yields many similar results

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

In this work, we consider two kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart. For our simulations we place the stenosis in one of the tibial arteries belonging to the right lower leg (right post tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model

Numerical solving of relationship between true and false lumen in acute aortic dissection

Aorta, kao osnovni i najveći krvni sud u čoveku, neprekidno je izložena visokom pulzativnom pritisku i smičućim silama. Disekcija aorte predstavlja veoma ozbiljno i urgentno stanje, u kojem dolazi do cepanja i raslojavanja unutrašnjeg sloja aortnog zida, dok spoljnji sloj ostaje netaknut. Numeričke simulacije dinamičkog ponašanja fluida-krvi u aorti sa disekcijom mogu dosta pomoći lekarima, jer daju uvid u dalji razvoj bolesti. Osnovni metod koji je korišćen u ovom radu jeste metod konačnih elemenata (MKE). Brzine strujanja fluida, pritisaka i smičućih napona u čvorovima konačnih elemenata određuju se u karakterističnim tačkama pulzatornog strujanja krvi. U jednom delu rada, primenom komercijalnih softvera, izvršene su trodimenzionalne rekonstrukcije medicinskih snimaka, a potom, primenom softvera koji je razvijen u Istraživačko razvojnom centru za bioinženjering, sprovedeno je numeričko rešavanje odnosa pravog i lažnog lumena akutne aortne disekcije. Osnovni cilj teze je da se primenom numeričkih simulacija odrede pritisci, smičući naponi i brzine u pravom i lažnom lumenu čime se dobija jasna slika njihovog međusobnog odnosa. Virtuelnim simuliranjem efekta operacije (isecanjem uzlazne aorte i zamene tubus graftom) određuju se protoci kroz bočne opstruirane grane aorte zahvaćene disekcijom, što pokazuje kako hirurški zahvat zamene uzlazne aorte i prekidanje protoka lažnog lumena, ima uticaj na protok kroz grane aortnog luka i visceralne grane (grane abdominalne aorte). Određivanjem von Mizesovih napona u zidu lažnog lumena dobijaju se potencijalna mesta rupture aorte. Ovim putem se neinvazivnim pristupom određuje rizik od nastanka rupture aorte i daje prednost ovom metodu, umesto kriterijuma maksimalnog prečnika.Aorta, as the main and the largest blood vessel in the human body, is constantly exposed to high pulse pressure and shear forces. Aortic dissection is a very serious condition and medical emergency, which leads to tearing and delamination of the inner layer of the aortic wall, while the outer layer remains intact. Numerical simulations of the dynamic behavior of fluid-blood in the aorta dissection can be of great help to doctors, because they provide insight into further development of the disease. The main method used in this paper is the finite element method (FEM). Fluid velocity, pressure and wall shear stress in nodes of finite elements are determined by specific points of the pulsatile blood flow. One section of the paper focuses on a three-dimensional reconstruction of medical images using a commercial software and in the next section, by using the software developed in the Research and Development Centre for Bioengineering, the numerical solution of relations between true and false lumens of acute aortic dissection is performed. The main objective of the thesis is to determine pressures, wall shear stress and velocity in the true and false lumen by applying numerical simulations, which gives a clear picture of their relationship. Virtual simulation of the effects of the operation (by cutting the ascending aorta and replacing it with the stent graft) determines the flow through the obstructed side branches of aortic dissection, which shows how the surgical intervention of replacing the ascending aorta and interrupting the flow in the false lumen has an impact on the flow through the branches of the aortic arch and the visceral branches (branches of the abdominal aorta). By determining von Mises stresses in the wall of the false lumen, potential points of rupture of the aorta are obtained. In this manner, the risk of rupture of the aorta is determined by using a non-invasive approach, giving this method an advantage over the maximum diameter criterion