Section: New Results

Numerical methods for biological flows

Participants : Ludovic Boilevin-Kayl, Miguel Ángel Fernández Varela, Jean-Frédéric Gerbeau, Florian Joly, Alexandre This, Marc Thiriet, Irene Vignon Clementel.

Cirrhosis is the common end-stage of chronic liver disease, with architectural distortion increasing the intrahepatic vascular resistance, leading to portal hypertension and systemic circulatory disorders. In [13] we investigate the impact of the changing vascular resistances on the hepatic and global circulation hemodynamics during cirrhogenesis. Morphological quantification of vascular trees from corosion casts of rats developing the disease provide the input for a lumped parameter model of the liver that was coupled to a model of the entire circulation of the rat. The simulations explain how vascular changes due to cirrhosis severely disrupt both hepatic and global hemodynamics.

Image-based models derived from CT angiography are being used clinically to simulate blood flow in the coronary arteries of individual patients to aid in the diagnosis of disease and planning treatments. However, image resolution limits vessel segmentation to larger epicardial arteries. In [20], we propose an algorithm for the generation of a patient-specific cardiac vascular network from epicardial vessels down to arterioles. We extend a tree generation method based on satisfaction of functional principles, to account for competing vascular trees, with flow-related and geometrical constraints adapting the simultaneous tree growths to patient priors.

Growth and remodeling of the embryo pharyngeal arch artery (PAA) network into the extracardiac great vessels is poorly understood but a major source of clinically serious malformations. In [21] we develop a methodological pipeline from high-resolution nano-computed tomography imaging and live-imaging flow measurements to multiscale pulsatile computational models. We identify local morphological variation along the PAAs and their association with specific hemodynamic changes in embryos of different stages, advancing our understanding of morphogenesis.

In [22] we evaluate atrioventricular valve regurgitation (AVVR) in babies born with an already very challenging heart condition, i.e., with single ventricle physiology. Although the second surgery that single ventricle patients undergo is thought to decrease AVVR, there is much controversy in the clinical literature about AVVR treatment. The effect of AVVR on Stage 1 haemodynamics and resulting acute changes from conversion to Stage 2 circulation in single ventricle patients are analyzed through lumped parameter models. Several degrees of AVVR severity are analyzed, for two types of valve regurgitation: incomplete leaflet closure and valve prolapse.

The medical imaging community is eager to define quantitative biophysical parameters. As part of a book addressing this question, in [26], we give a short overview of the mathematical modeling of blood flow at different resolutions, from the large vessel scale (three-dimensional, one-dimensional, and zero-dimensional modeling) to microcirculation and tissue perfusion.

In order to reduce the complexity of heart hemodynamics simulations, uncoupling approaches are often considered for the modeling of the immersed valves as an alternative to complex fluid-structure interaction (FSI) models. A possible shortcoming of these simplified approaches is the difficulty to correctly capture the pressure dynamics during the isovolumetric phases. In [35], we propose an enhanced resistive immersed surfaces (RIS) model of cardiac valves which overcomes this issue. The benefits of the model are investigated and tested in blood flow simulations of the left heart.