3D simulation of the aqueous flow in the eye

Glaucoma is one of the leading causes of blindness in the world. It results in an increase of the aqueous humour (AH) outflow pathway which leads to an increase of the intraocular pressure (IOP). Many treatments exists to reduce and stabilize the IOP such as medications, filtering surgery and Glaucoma Drainage Devices. So far computational fluid dynamics (CFD) modeling of the eye drainage system has not yet been well studied. Therefore our goals was to numerically simulate the AH outflow pattern in a model of the eye to further simulate a healthy and glaucomatous eye and various forms of glaucoma surgery. In order to do so, a 3D CDF model of the eye was created based on real geometries. Two methods were tested to this aim. The first one consisted in the injection of a CT contrast agent in an enucleated rabbit eye and visualization by a CT scan. A segmentation process was then achieved on the resulting scans to reconstruct the eye structures. The second one was based on microphotography stacks of histology of human eye whereof digital processing of the eye structure images and 3D reconstruction of a numerical model were performed. Due to resolution limitations several ocular structures could not be extracted from the segmentation process. In the second method, simulations of pressure and flow velocity distribution in healthy eye gave results comparable to physiology. Modeling the glaucomatous eye led to an increase in the IOP around 37 mmHG. We have been able to model the 3D structure of the eye based on real geometry. Flow simulations gave interesting results for the IOP and the flow velocity on a healthy eye. Mimicking glaucoma conditions led to an increase of the IOP from normal range, which went down to lower values after a filtering procedure. Further refinements in the boundary conditions for the filtering procedure shall improve the precision and efficacy of this innovative tool for modeling glaucoma surgery

3D simulation of the aqueous flow in the human eye

Reda Hasballa, Philippe Reymond, Sylvain Roy, Nikolaos Stergiopulos, Orestis Vardoulis, Adan Villamarin

Glaucoma results in an increase in the resistance of the aqueous humor outflow, which in turn leads to an increase of the intraocular pressure (IOP). Several treatments are proposed to reduce and stabilize the IOP that include medications, filtering surgery and glaucoma drainage devices (GDD). So far computational fluid dynamics (CFD) modeling of the eye drainage system has not yet been well studied. Therefore our goal was to provide a 3D CFD model of the eye based on the anatomy of a real human eye. Such a tool would serve for future evaluation of new glaucoma surgical techniques involving, for example, GOD. The model was based on stacks of microphotographs from human eye slides from which digital processing of the images of the eye structure and 3D reconstruction of the model were performed. Simulations of the distribution of pressure and flow velocity in the model of a healthy eye gave results comparable to physiology references. Mimicking glaucoma conditions led to an increase of the IOP from normal range, which went down to lower values after a filtering procedure. Further refinements in the boundary conditions for the filtering procedure shall improve the accuracy of this innovative tool for modeling glaucoma surgery. (C) 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Elsevier Sci Ltd2012

One dimensional and multiscale models for blood flow circulation

The aim of this work is to provide mathematically sound and computationally effective tools for the numerical simulation of the interaction between fluid and structures as occurring, for instance, in the simulation of the human cardiovascular system. This problem is global, in the sense that local changes can modify the solution far away. From the point of view of computing and modelling this calls for the use of multiscale methods, where simplified models are used to treat the global problem leaving to more accurate models the local description. Moreover it is characterised by the appearance of pressure waves inside the vessels. In large arteries the vessel wall dynamics can be described by a thin elastic membrane model (Navier equation) while the fluid motion can be represented by the Navier-Stokes equations for incompressible Newtonian fluids. Unfortunately, given the high levels of details furnished by this model, its computational complexity is dramatically high. Therefore reduced models have been developed. In particular, one-dimensional models, originally introduced by Euler, seem to be appropriate for the study in the time-space domain of pressure wave propagation induced by the interaction between the fluid and the vessel wall in the arterial tree. These reduced models are obtained after integrating the Navier-Stokes equations over a vessel section, supposed to be circular, and assuming an algebraic wall law to describe the relationship between pressure and wall deformation. They can be used in place of the more complex three dimensional fluid-structure models or in cooperation with them (multiscale approach). The first part of this work deals with one dimensional models. A reduced 1D model taken from literature is presented and analysed. Some extensions of the basic model, in particular with respect to vessel wall law (generalised string model) and more complex geometries (bifurcated and curved arteries), are also considered. Numerical schemes are proposed and some numerical results are presented. In the second part of this thesis we focus on a multiscale model. We consider a 55 arterial tree, described by the 1D model, coupled with lumped parameter models for heart and capillaries. In particular, specific attention has been devoted to the coupling between the left ventricle and the arterial system, whose physiopathological relevance is well known. This mathematical model gives good results in numerical tests and is able to describe the relevant features of the pressure wave propagation and reflections within the arterial system.

EPFL2004

Multiscale Computational Methodology Applied to Hydroacoustic Resonance in Cavitating Pipe Flow

Nicolas Ruchonnet

The present work is a contribution to the physical analysis and numerical simulation of the pressure surges in hydraulic machinery and connected conduit systems. Localized hydrodynamic instabilities including cavitation are prone to interact with the entire conduit through the propagation of acoustic plane waves. At resonance, the superimposition of the acoustic waves leads to the formation of large amplitudes standing waves along the entire conduit. The resulting fluctuation of velocity and pressure in the source region may have a significant role on the hydrodynamic instability. A computational methodology based on two fields is proposed to simulate this interaction in the time domain: a 1D hydroacoustic model (HA model) is selected to analyze the entire acoustic field including the source region, a 3D incompressible hydrodynamic model (HD model) is used to describe the flow in the source region. The acoustic perturbation due to the instability is precisely evaluated with the HD model and injected in the HA model through discrete sources. To describe the complete interaction between the fields, two methods are proposed: the acoustic feedback is either fully modeled (two way coupled simulation) or accounted for using interaction parameters (one way concurrent simulation). In the first method, the boundary conditions of the HD model are adjusted dynamically using the solution field of the HA model and all components of the sources are evaluated in the HD model. In the second method, the acoustics and hydrodynamics components of the sources are considered as independent. The components due to the hydrodynamic field are evaluated in the HD model with steady boundary conditions and injected in HA model through discrete sources. The components of the sources due to the acoustic fluctuations are accounted for with specific parameters of the HA model; those interaction parameters, i.e. cavity compliance and mass flow gain factor, are evaluated with the help of the HD model. A reference case study has been setup; video analysis and dynamic pressure measurement have been performed to validate the simulations. The case study consists in a straight pipe connecting two constant pressure tanks. A bluff body is placed at 3/4 of the pipe length, the resulting flow instability is characterized by the alternate shedding of vortices at a frequency proportional to the flow velocity. The hydroacoustic resonator is the pipe itself. Measurements have been performed for resonant and non-resonant conditions in cavitating and cavitation free flow regime. In cavitation free flow regime, the hydrodynamic source is identified as a pure momentum source associated with the drag force on the bluff body. The flow conditions leading to resonance can be evaluated with the two way coupled simulation. At resonance, the distribution, frequency and amplitude of pressure fluctuation predicted in the simulation is in good agreement with the measurement. For the selected case study, the acoustic feedback is very weak and has no significant effect on the momentum source. In cavitating flow regime, two hydrodynamic sources have been identified, the momentum source and the mass source. The momentum source is associated with the drag force on the bluff body, the mass source is associated with the volume fluctuation of the fl vapor phase in the wake of the bluff body. The strength of the mass source is orders of magnitude larger and the momentum source can therefore be neglected. One way concurrent simulations using dynamic update of the interaction parameters have been performed. Fair agreement is obtained between the simulations and the measurements. The amplification of the fluctuation observed experimentally below incipient cavitation is reproduced. At intermediate cavitation index, the pressure fluctuation amplitude and the spectral energy distribution is in fair agreement with the experiment. The modifications of the pipe eigenmodes and eigenfrequencies due to cavitation is satisfactorily reproduced with the cavity compliance.

EPFL2010

One dimensional and multiscale models for blood flow circulation

EPFL2004

Multiscale Computational Methodology Applied to Hydroacoustic Resonance in Cavitating Pipe Flow

Nicolas Ruchonnet

EPFL2010