Lorenzo Alessio Botti

An image-based modeling framework for patient-specific computational hemodynamics

We present a modeling framework designed for patient-specific computational hemodynamics to be performed in the context of large-scale studies. The framework takes advantage of the integration of image processing, geometric analysis and mesh generation techniques, with an accent on full automation and high-level interaction. Image segmentation is performed using implicit deformable models taking advantage of a novel approach for selective initialization of vascular branches, as well as of a strategy for the segmentation of small vessels. A robust definition of centerlines provides objective geometric criteria for the automation of surface editing and mesh generation. The framework is available as part of an open-source effort, the Vascular Modeling Toolkit, a first step towards the sharing of tools and data which will be necessary for computational hemodynamics to play a role in evidence-based medicine.

On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations

In this work we show that the flexibility of the discontinuous Galerkin (dG) discretization can be fruitfully exploited to implement numerical solution strategies based on the use of elements with very general shapes. Thanks to the freedom in defining the mesh topology, we propose a new h-adaptive technique based on agglomeration coarsening of a fine mesh. The possibility to enhance the error distribution over the computational domain is investigated on a Poisson problem with the goal of obtaining a mesh independent discretization. The main building block of our dG method consists of defining discrete polynomial spaces directly on physical frame elements. For this purpose we orthonormalize with respect to the L^2-product a set of monomials relocated in a specific element frame and we introduce an easy way to reduce the cost related to numerical integration on agglomerated meshes. To complete the dG formulation for second order problems, two extensions of the BR2 scheme to arbitrary polyhedral grids, including an estimate of the stabilization parameter ensuring the coercivity property, are here proposed.

A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure

In this work we present a pressure-correction scheme for the incompressible Navier-Stokes equations combining a discontinuous Galerkin approximation for the velocity and a standard continuous Galerkin approximation for the pressure. The main interest of pressure-correction algorithms is the reduced computational cost compared to monolithic strategies. In this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high Reynolds regimes. The proposed spatial velocity-pressure approximation is LBB stable for equal polynomial orders and it allows adaptive p-refinement for velocity and global p-refinement for pressure. The method is validated against a large set of classical two- and three-dimensional test cases covering a wide range of Reynolds numbers, in which it proves effective both in terms of accuracy and computational cost.

Very high-order accurate discontinuous Galerkin computation of transonic turbulent flows on aeronautical configurations

This chapter presents high-order DG solutions of the RANS and k-ω turbulence model equations for transonic flows around aeronautical configurations. A directional shock-capturing term, proportional to the inviscid residual, is employed to control oscillations around shocks. Implicit time integration is applied to the fully coupled RANS and k-ω equations. Several high-order DG results of 2D and 3D transonic turbulent test cases proposed within the ADIGMA project demonstrate the capability of the method.

Influence of Reference-to-Physical Frame Mappings on Approximation Properties of Discontinuous Piecewise Polynomial Spaces

In this manuscript we compare physical and reference frame discontinuous Galerkin (dG) discretizations with emphasis on the influence of reference-to-physical frame mappings on the discrete space properties. We assess the excellence of physical frame discrete spaces in terms of approximation capabilities as well as the increased flexibility compared to reference frame discretizations. As a matter of fact, whenever curved elements are considered, non-affine reference-to-physical frame mappings are able to spoil the convergence properties of reference frame discrete spaces. This poorly documented drawback does not affect basis functions defined directly in the physical frame.The convergence degradation associated to reference frame discretizations is evaluated theoretically, providing error bounds for the approximation error of the L2-orthogonal projection operator, and the findings are justified by means of numerical test cases. In particular we exemplify by means of quadrilateral elements grids challenging grid configurations characterized by non-affine mappings and demonstrate the ability to predict the convergence rates without stringent assumptions on the element shapes.

Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

Computational model for simulation of vascular adaptation following vascular access surgery in haemodialysis patients.

An important number of surgical procedures for creation of vascular access (VA) in haemodialysis patients still results in non-adequate increase in blood flow (non-maturation). The rise in blood flow in arteriovenous shunts depends on vascular remodelling. Computational tools to predict the outcome of VA surgery would be important in this clinical context. The aim of our investigation was then to develop a 0D/1D computational model of arm vasculature able to simulate vessel wall remodelling and related changes in blood flow. We assumed that blood vessel remodelling is driven by peak wall shear stress. The model was calibrated with previously reported values of radial artery diameter and blood flow after end-to-end distal fistula creation. Good agreement was obtained between predicted changes in VA flow and in arterial diameter after surgery and corresponding measured values. The use of this computational model may allow accurate vascular surgery planning and ameliorate VA surgery outcomes.

Time Integration in the Discontinuous Galerkin Code MIGALE - Unsteady Problems

This chapter presents recent developments of a high-order Discontinuous Galerkin (DG) method to deal with unsteady simulation of turbulent flows by using high-order implicit time integration schemes. The approaches considered during the IDIHOM project were the Implicit Large Eddy Simulation (ILES), where no explicit subgrid-scale (SGS) model is included and the DG discretization itself acts like a SGS model, and two hybrid approaches between Reynolds-averaged Navier- Stokes (RANS) and Large Eddy Simulation (LES) models, namely the Spalart-Allmaras Detached Eddy Simulation (SA-DES) and the eXtra- Large Eddy Simulation (X-LES). Accurate time integration is based on high-order linearly implicit Rosenbrock-type Runge-Kutta schemes, implemented in the DG code MIGALE up to sixth-order accuracy. Several high-order DG results of both incompressible and compressible 3D turbulent test cases proposed within the IDIHOM project demonstrate the capability of the method.

pyNS: an open-source framework for 0D haemodynamic modelling.

A number of computational approaches have been proposed for the simulation of haemodynamics and vascular wall dynamics in complex vascular networks. Among them, 0D pulse wave propagation methods allow to efficiently model flow and pressure distributions and wall displacements throughout vascular networks at low computational costs. Although several techniques are documented in literature, the availability of open-source computational tools is still limited. We here present python Network Solver, a modular solver framework for 0D problems released under a BSD license as part of the archToolkit (http://archtk.github.com). As an application, we describe patient-specific models of the systemic circulation and detailed upper extremity for use in the prediction of maturation after surgical creation of vascular access for haemodialysis.

Effect of ACE inhibition on glomerular permselectivity and tubular albumin concentration in the renal ablation model

Despite the central role of tubular plasma proteins that characterize progressive kidney diseases, protein concentrations along the nephron in pathological conditions have not been quantified so far. We combined experimental techniques and theoretical analysis to estimate glomerular and tubular levels of albumin in the experimental model of 5/6 nephrectomy (Nx) in the rat, with or without angiotensin-converting enzyme (ACE) inhibition. We measured glomerular permselectivity by clearance of fluorescent Ficoll and albumin and used theoretical analysis to estimate tubular albumin. As expected, 5/6 Nx induced an elevation of the fractional clearance of the largest Ficoll molecules (radii >56 Å, P < 0.05), increasing the importance of the shunt pathway of the glomerular membrane and the albumin excretion rate (119 ± 41 vs. 0.6 ± 0.2 mg/24 h, P < 0.01). ACE inhibition normalized glomerular permselectivity and urinary albumin (0.5 ± 0.3 mg/24 h). Theoretical analysis indicates that with 5/6 Nx, an increased albumin filtration overcomes proximal tubule reabsorption, with a massive increase in average albumin concentration along the tubule, reaching the highest value of >2,500 μg/ml at the end of the collecting duct. ACE inhibition improved glomerular permselectivity, limiting albumin filtration under proximal tubule reabsorption capacity, with low albumin concentration along the entire nephron, averaging <13 μg/ml at the end of the collecting duct. These results reinforce our understanding of the mechanisms of renal disease progression and the effects of angiotensin II antagonism. They also suggest that evaluation of tubular protein concentration levels could help to identify patients at risk of kidney disease progression and to improve clinical management.