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Modeling coronary blood flow using a non newtonian fluid model : fractional flow reserve estimation

Abstract : In this thesis, we explore the possibility of virtual coronary stenosis assessment, through the simulation of Fractional Flow Reserve (FFR) measurement, that is an indispensable but binding tool during diagnosis. First, we use a 2D non Newtonian flow model, and later a weakly coupled FSI model to make a preliminary study of the main features of flow over a stenotic coronary arterial portion. We then introduce a methodology to estimate the virtual FFR in analogy with the clinical device. The FFR device was considered non-physical (integrated to the flow domain) at a first place. We led different experiments to enumerate the factors affecting the virtual FFR and computed its profiles with respect to different lesion’s parameters. Second, we consider two realistic geometries: a 2D left coronary tree obtained from the segmentation of an angiography image and a 3D bifurcation tree. We define generalized flow models inside the two geometries and consider the arterial wall to be rigid. The presence of several outlets in these new geometries led us to define a new type of boundary conditions. For the inlet, we propose a bi-sinusoidal function approaching the velocity profile recorded inside a left coronary tree. For the outlets, we implement a 2 elementWindkessel model. We led a comparative study between Navier Stokes and the flow model considered and between free outlets boundary conditions and Windkessel model in 2D and define the flow inside the 3D bifurcation tree. We also compute the virtual FFR of two artificial lesions added to the coronary tree and demonstrate that angiography alone is not enough to evaluate the severity of stenosis. Third, we investigate - through 2D and 3D modelling - one possible reason of pressure drift during FFR measurement, that is the arbitrary position and configuration of the FFR device, considered during this study extrinsic to the flow domain. We consider the same non Newtonian flow models as previously. In 2D, the FFR device is assimilated to a disk with a variable position incorporated inside the left coronary tree. While the 3D domain corresponds to a diseased arterial portion to which we introduce a deformed 3D tube (wire+sensor) with a given length and coefficient of bending. The bending effect of the tube is obtained thanks to an elastic problem based on Hooke’s law. Using a Gaussian process, we model the FFR depending on these variables - and two additional stenosis variables later - we perform a set of samples corresponding to the design space considered. The 2D data indicates a good accuracy for FFR prediction while the 4D data emphasis the fact that mi- crocatheters with important diameters overestimate lesion’s severity. The results obtained demonstrate that drift occurring because of the variable device configuration may lead to stenosis misclassification. All resolution algorithms and simulation tools were implemented under FreeFem++ software. The need of more space memory for 3D simulations led us to adopt a parallel resolution strategy using FreeFem++ MPI and MUMPS solver.
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Contributor : Keltoum Chahour <>
Submitted on : Friday, January 17, 2020 - 10:40:25 AM
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Keltoum Chahour. Modeling coronary blood flow using a non newtonian fluid model : fractional flow reserve estimation. Mathematics [math]. Université Nice Sophia Antipolis, 2019. English. ⟨tel-02430901⟩

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