Thread 2. Flow-Structure Interactions

7919 Tu, 09:00-09:15 (P18) The Epithel iome: indiv idual-based model l ing o f emergent behaviour resulting from cellular interaction R. Smallwood 1 , M. Holcombe 1 , J. Southgate 2, S. MacNeil 3, R. Hose 4. 1Department of Computer Science, University of Sheffield, UK, 2Department of Biology, University of York, UK, 3Department of Engineering Materials, University of Sheffield, UK, 4Department of Medical Physics & Clinical Engineering, University of Sheffield, UK

The structure and function of multi-cellular organisms is an emergent property of the interaction of the individual cells in the organism, and is controlled by an instruction set (the genes) which is contained within the individual cell. The relative simplicity, and the availability of excellent in vitro biological models, makes epithelial tissue a good target for the development of predictive compu- tational models of cellular interaction. The starting point is an individual-based model of the cell, with a one-to-one mapping between individual biological cells and computational cells. Individual-based models have been widely used in ecology for about twenty years [1], but have made little impact on biology. The rationale for using an individual-based model is that the contingent nature of the interaction between the individuals can be captured in a way that is not possible using state variable models, and Iocalised interactions can be accounted for. If the number of individuals is progressively increased, the behaviour of the individual-based model will approach the state variable description of the system, which provides a mechanism for abstracting away detail in hierarchical models. We have used the models for cell signalling [3], cell growth [4], and also to study the behaviour of social insects.

References [1] Grimm V. Ecological Modelling 1999; 115: 129-148. [2] Walker DC, Southgate JS, Hill G, Holcombe M, Hose DR, Wood SM, MacNeil S,

Smallwood RH. BioSystems 2004; 76: 89-100. [3] Pogson M, Holcombe M, Smallwood R, Anderson D, Yang L, Qwarnstrom E.

2006, submitted. [4] Walker DC, Hill G, Wood SM, Smallwood RH, Southgate J. IEEE Trans Nanobio-

science 2004; 3: 153-163.

Thread 2

Flow-Structure Interactions

T2.1 Cardiovascular Mechanics FSI

T2.1.1 Heart Valves and Prostheses

6701 Tu, 11:00-11:15 (P20) Val idat ion o f fluid-structure interaction models of a mechanical heart valve and flexible heart valve N. Forsythe 1 , J.-D. MLiller 2. 1School of Mechanical and Aerospace Engineering, Queen's University, Belfast, UK, 2Department of Engineering, Queen Mary, University of London, London, UK

Fluid~Structure Interaction (FSI) plays an important role in the numerical simu- lation of many haemodynamic problems, such as the motion of a heart valves. However, particular difficulties arise in this case from the large deformation of the valves and the very strong coupling between fluid and structure. Presented in this work is a FSI simulation of a cycle of a Mechanical Heart Valve (MHV) and a flexible synthetic heart valve. In both cases the simplified models consists of a single valve leaflet and one sinus, with a pulsatile inlet flow to drive the valve motion. The study adopts a partitioned approach where the fluid and structural equations are solved separately and coupled by the communication of boundary conditions. An efficient explicit time-stepping scheme is used for the time integration of the coupled sets of equations. This is a novel approach for the FSI simulation of heart valve motion. An Arbitrary Lagrangian Eulerian (ALE) formulation is employed in the fluid solver, and a robust mesh smoothing and local remeshing approach is imple- mented to maintain the mesh quality despite the large displacement of the valve which occurs during the pulsatile cycle. For the flexible valve problem, a novel volume-spline interpolation technique is used to interpolate data between the non-matching fluid and structural meshes [1]. This approach ensures conservation of energy transferred across the fluid-structure interface. The technique was successfully applied to the simulation of a mechanical heart valve [2] and validated against experiments [3]. Here we present the extension of the method to flexible valves and its validation against an in vitro experiment [4].

References [1] Hounjet M.H.L. Evaluation of elastomechanical and aerodynamic data transfer

methods for non-planar configurations in computational aeroelastic analysis, NRL, Amsterdam, 1995.

T2.1 Cardiovascular Mechanics FSI - Heart Valves and Prostheses $437

[2] Forsythe N., MUller J.-D. Validation of a fluid-structure interaction model of a mechanical heart valve. In: Proc. II International Conference on Computational Bioengineering, Lisbon, Portugal, 2005.

[3] Stijnen J.M.A. Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves, Comp. Meth. Biomech. Biomed. Eng. 2004.

[4] de Hart J. A two-dimensional fluid-structure interaction model of the aortic valve. J. Biomech. 2000.

6384 Tu, 11 : 15-11:30 (P20) A numerical f luid dynamics study of the concomitant presence of a prosthet ic aortic valve and a subaortic stenosis

C. Guivier 1 , V. Deplano 1 , P. Pibarot 2. I lRPHE UMR 6594, Equipe de Biom6canique Cardiovasculaire, Marseille, France, 2Quebec Heart Institute, Laval Hospital, Sainte Foy, Canada

Aortic stenosis (AS) affects the aortic valve which then can be replaced by a prosthetic valve. In the clinical setting, the haemodynamic severity of AS as well as the haemodynamic performance of the prosthesis can be assessed with the use of Doppler-echocardiography. In addition, hypertrophic cardiomyopathy can occur in the left ventricular outflow tract, resulting in a protusion of the interventricular septum. This abnormality creates a subaortic stenosis (SAS) that may interact with Doppler-echocardiographic assessment of the haemodynamic function of native or prosthetic valve. Fluid structure interaction (FSI) models are used to numerically investigate fluid dynamics around a moving valve [2]. Most of current FSI models are focused on the healthy situation and do not consider physiological data. With Fluent software, using an Arbitrary Lagrangian-Eulerian formulation and remeshing algorithms, we propose to model a prosthetic bileaflet aortic valve, including FSI in two bidimensional configurations, with and without SAS, and with physiological data. We study the modifications on the flow and on the leaflet behaviour caused by the presence of SAS. From these results, we show that the clinical assessment of the aortic valve haemodynamic function is not valid in such a configuration. For the first time, this study underlines the limitations of the currently used clinical indices of the aortic valve function in the presence of concomitant SAS. In a future work, our objective is to study the fluid dynamics in numerical and experimental three-dimensional models to modify current clinical indices and to improve clinical diagnosis of aortic valve function in presence of SAS.

References [1] G. Susini, et al. Diagnostic pitfalls with the combinaison of hypertrophic car-

diomyopathy and aortic valvular stenosis. J. Cardiothorac. Vasc. Anesth. 1991; 5: 66-68.

[2] K. Dumont, et al. Validation of a fluid-structure interaction model of a heart valve using the dynamic mesh method in Fluent. Comput. Meth. Biomech. and Biomed. Eng. 2004; 7: 139-146.

5851 Tu, 11:30-11:45 (P20) Simulat ing prosthet ic heart valve hemodynamics in realistic aorta anatomies L. Ge 1 , L.P. Dasi 2, H. Simon 3, F. Sotiropoulos 1 , A. Yoganathan 2. 1Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN, USA, 2 Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA, 3School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA, USA

Since the first successful implantation of a prosthetic heart valve four decades ago, over 50 different designs have been developed including both mechan- ical and bio-prosthetic valves. However, hemodynamical stresses have been implicated in thrombus initiation within the mechanical valve prostheses while regions of stress concentration on the leaflets are believed to contribute to the structural failure of bioprosthetic valves. To understand prosthetic valve hemodynamics under physiological conditions, we develop a numerical method capable of simulating flows in realistic prosthetic heart valves in anatomical ge- ometries. The method employs a newly developed hybrid numerical technique that integrates the chimera overset grid approach with a Cartesian, sharp- interface immersed boundary methodology. The capabilities of the method are demonstrated by applying it to simulate pulsatile flow in both bileaflet and tri-leaflet valves moving with prescribed leaflet kinematics. Calculations will be presented for two aorta anatomies: a simplified, single-sinus, straight, axisymmetric aorta; and a realistic, curved aorta anatomy reconstructed from MRI data. The simplified aorta geometry will be identical to that we employ in our in-vitro laboratory studies of valve prostheses. Simulations with the simple model will be carried out for validation purposes and the numerical results will be compared with PIV measurements. The calculations in the anatomically realistic configuration, on the other hand, will seek to demonstrate the potential of the method as a powerful computational tool for patient-specific optimization of prosthetic heart valves.