Jorge Tiago

Opytimal module is a Python/FEniCS framework to solve PDE-based optimization problems considering multiple controls. These problems can be defined in n-dimensional domains, for n ∈ {1, 2, 3}, and complemented with mixed boundary conditions. The controls can be distributed or boundary type and may contribute to the cost function via the H¹ norm. We show examples of the solution of control problems governed by the Poisson, Heat, and Stokes equations.

Aortic dilation is associated with congenital bicuspid aortic valve (BAV) disease, and its etiology is still not completely understood. The aim of this study is to provide further insight into aortic hemodynamics in a BAV population with different degrees of aortic dilation and regurgitation in comparison with a patient without pathology. A fluid–structure interaction (FSI) numerical approach is implemented regarding patient-specific geometries, where the aortic valves are defined by analytical orifices. Results show that, while the patient without pathology displays a typical hemodynamic behavior of flows in bends, BAV-related aortas present an accelerated flow along the outer aortic wall. Wall shear stress (WSS) overload in the outer curvature is observed, more marked in more dilated aortas. Moreover, helices in the ascending aorta are present in these patients, enhanced with greater dilation. These findings support the fact that hemodynamic factors play an important role in aortic dilation onset and development in BAV patients, caused by a prolonged exposure of the outer ascending aortic curvature to altered WSS. Besides, our results suggest that greater aortic regurgitation may be associated with abnormal WSS distributions in the ascending aorta during diastole, which can facilitate aortic root dilation.

Purpose: This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.Design/methodology/approach: The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.Findings: The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.Originality/value: The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed.

Bicuspid aortic valve (BAV) aortopathy remains of difficult clinical management due to its heterogeneity and further assessment of related aortic hemodynamics is necessary. The aim of this study was to assess systolic hemodynamic indexes and wall stresses in patients with diverse BAV phenotypes and dilated ascending aortas. The aortic geometry was reconstructed from patient-specific images while the aortic valve was generated based on patient-specific measurements. Physiologic material properties and boundary conditions were applied and fully coupled fluid-structure interaction (FSI) analysis were conducted. Our dilated aortic models were characterized by the presence of abnormal hemodynamics with elevated degrees of flow skewness and eccentricity, regardless of BAV morphotype. Retrograde flow was also present. Both features, predicted by flow angle and flow reversal ratios, were consistently higher than those reported for non-dilated aortas. Right-handed helical flow was present, as well as elevated wall shear stress (WSS) on the outer ascending aortic wall. Our results suggest that the abnormal flow associated with BAV may play a role in aortic enlargement and progress it further on already dilated aortas.