Computational methods in cardiovascular mechanics

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.Comment: 54 pages, Book Chapte

Sequential Structural and Fluid Dynamics Analysis of Balloon-Expandable Coronary Stents.

As in-stent restenosis following coronary stent deployment has been strongly linked with stent-induced arterial injury and altered vessel hemodynamics, the sequential numerical analysis of the mechanical and hemodynamic impact of stent deployment within a coronary artery is likely to provide an excellent indication of coronary stent performance. Despite this observation, very few numerical studies have considered both the mechanical and hemodynamic impact of stent deployment. In light of this observation, the aim of this research is to develop a robust numerical methodology for investigating the performance of balloon-expandable coronary stents in terms of their mechanical and hemodynamic impact within a coronary artery. The proposed methodology is divided into two stages. In the first stage, a numerical model of the stent is generated and a computational structural analysis is carried out to simulate its deployment within a coronary artery. In the second stage, the results of the structural analysis are used to generate a realistic model of the stented coronary lumen and a computational fluid dynamics analysis is carried out to simulate pulsatile blood flow within a coronary artery. Following the completion of the analyses, the mechanical impact of the stent is evaluated in terms of the stress distribution predicted within the artery whilst the hemodynamic impact of the stent is evaluated in terms of the wall shear stress distribution predicted upon the luminal surface of the artery. In order to demonstrate its application, the proposed numerical methodology was applied to six generic stents. Comparing the predicted performance of the generic stents revealed that strut thickness is likely to have a significant influence upon both the mechanical and hemodynamic impact of coronary stent deployment. Additionally, comparing the predicted performance of three of the investigated stents to the clinical performance of three comparable commercial stents, as reported in two large-scale clinical trials, revealed that that the proposed numerical methodology successfully identified the stents that resulted in higher rates of angiographic in-stent restenosis, late lumen loss and target-vessel revascularisation at short-term follow-up. In light of the conflicting requirements of coronary stent design, the proposed numerical methodology should prove useful in the design and optimisation of future coronary stents

Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System

<p>Abstract</p> <p>Background</p> <p>Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.</p> <p>Method and Results</p> <p>The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository <url>http://models.cellml.org/</url>. They are freely available to the research and education communities.</p> <p>Conclusion</p> <p>Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.</p

Numerical modelling of the Oldroyd-B fluid

The purpose of this thesis is to develop a 3D finite element model of the Oldroyd-B fluid for use in a complex geometry. The model is developed in deal.ii, which is a C++ finite element library. In addition to the standard finite element approach for the momentum equation, the discontinuous Galerkin method is used for the constitutive relation of the fluid model, with the extra stress as the unknown variable. The model developed is verified by using the symmetric “flow over a cylinder” benchmark problem. The effect of using piecewise-constant discontinuous and bilinear discontinuous elements for the extra stress field is investigated. The the results of the scheme are compared to those found in literature. The model is implemented in the solution of a complex problem of blood flow in an arteriovenous fistula, using geometry acquired from MRI data. A resistance boundary condition is used for the outlets. The flow profiles obtained from using both the Newtonian and Oldroyd-B fluids are validated against velocity encoded MRI and also compared to Fluid-Structure Interaction results for Newtonian fluids, from the literature. The effect of using a viscoelastic fluid on the flow profile and wall shear stresses are investigated. The results from this work show that using a viscoelastic fluid, rather than a Newtonian fluid, provides additional details regarding the wall shear stress in the arteriovenous fistula