Image-based modelling of blood flow in the human coronary arteries Ashkan Javadzadegan 1 Supervisors: Masud Behnia 1 & Leonard Kritharides 2 1 Fluid Dynamics Group, School of Mechanical Engineering, 2 Concord Repatriation Hospital I: basic and most fundamental part Susu: talk about some advanced techniques, which is essential to simulate compressible fluid such as smoke Finally, abhinav: base on our fundation and add particles into it to simulate granular materials

Contents Significance Image acquisition and geometry reconstruction Computational fluid dynamics References What can you expect from my lecture? This lecture requires no background in this field Mentally implement a simple fluid simulator Broad view about the current state-of-the-art techniques used to do fluid simulation in computer graphics community Basic understanding about how a fluid simulator work Have some basic knowledge about what’s the challenges and issues in this field Finally, of course, this lecture is very help for you to follow susu and abhniv’s lectures

Significance Coronary arteries are attached to the heart and most of the heart attacks are because of the coronary artery disease Pressure is the main force that push the fluid around. That is, The force will be pointing from a high pressure region to a low pressure region. If the pressure is equal everywhere, basically there will be no force in the fluid. Handling pressure correctly is the most important and the most involved part in a fluid simulator. We’ll re-visit it again when I talk about the pressure solve. You can just think pressure is something that keeps the fluid constant volume right now. Fluid has viscosity. Basically this property help the fluid resist deformation due to tangential forces. So you feel harder to stir fluid with high viscosity. The viscosity can change based on certain conditions. For instance, the wax will melt when it’s heated. In fact, this is exactly how people simulate the melting effect. Finally, fluids has surface tension, which tends to minimize the fluid surface area. That’s why water strider can stand on the water surface. We categorize the fluid into different types when talking about the simulation: Incompressible fluid (You’ll know why it’s called divergence free when we talk about the pressure solve): It actually doesn’t exist in real world. Every kind of fluid has at least some sort of compressibility. Here we make this assumption because in fact, the volume of some fluid such as water doesn’t change much under room temperature. Compressible fluids, on the other hand, change volume a lot. The smoke is a great example. Viscous fluid, resist deformation Inviscid fluid (sometimes called ideal fluid) has no viscosity. In real world, if that kind of fluid exist, if you stir it and come back a week later, it’s still rotating Newtonian fluids : where stress is directly proportional to rate of strain, and Non-Newtonian fluids : where stress is proportional to rate of strain, its higher powers and derivatives. In common terms, this means the fluid continues to flow, regardless of the forces acting on it. For example, water is Newtonian, because it continues to exemplify fluid properties no matter how fast it is stirred or mixed. Contrast this with a non-Newtonian fluid, in which stirring can leave a "hole" behind (that gradually fills up over time - this behaviour is seen in materials such as pudding, starch in water (oobleck), or, to a less rigorous extent, sand), or cause the fluid to become thinner, the drop in viscosity causing it to flow more (this is seen in non-drip paints, which brush on easily but become more viscous when on walls). a fluid is incompressible - that is, the density of the fluid does not change the Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces ( ) to viscous forces (μ / L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. Focus on “incompressible”, “viscous” flow Video for non-newtonian fluid

Image acquisition and geometry reconstruction 3D acquisition system

Image acquisition and geometry reconstruction Stored Slices B A B

Image acquisition and geometry reconstruction Surface reconstruction x z z x Vessel central axis y y Original contours Surface mesh fitted

Computational fluid dynamics An important task May take weeks or months One desires to perform computations for a real patient geometry  How do you determine real shapes & dimensions? Computational fluid dynamics simulation Mesh Generation Boundary Conditions Flow Solver & Post Processing Using appropriate boundary conditions in order to get realistic results Today a number of methods are available to solve the Governing Equations Some researchers write their own codes for the purpose Use of commercial codes is also wide spread –Fluent (ANSYS), Star CD, CFX etc

Computational fluid dynamics Mesh Generation Discretization of coronary artery into tetrahedrons whose size and distribution largely govern the accuracy of numerical simulation Turbulent flow: The flow appears to have chaotic behavior, usually you’ll see it spinning. Its pressure and velocity change rapidly in space and time. Laminar flow (also called streamline flow): Relatively, the laminar fluid has a smoother and much stable behavior. This cigarette smoke demonstrates the turbulent and laminar flow at the same time. Newtonian fluids: the fluid continues to flow, regardless of the force acting on it. That is, no matter how hard you stir or shake it, it still looks like fluid.

Computational fluid dynamics Boundary Conditions proximal and distal pressures are measured using three dimensional coronary angiography and are used as inlet and outlet boundery conditions for numerical studies. Proximal Proximal Pressure Turbulent flow: The flow appears to have chaotic behavior, usually you’ll see it spinning. Its pressure and velocity change rapidly in space and time. Laminar flow (also called streamline flow): Relatively, the laminar fluid has a smoother and much stable behavior. This cigarette smoke demonstrates the turbulent and laminar flow at the same time. Newtonian fluids: the fluid continues to flow, regardless of the force acting on it. That is, no matter how hard you stir or shake it, it still looks like fluid. Distal Pressure Distal

Computational fluid dynamics Flow Solver Today a number of commercial CFD codes are available to solve the governing equations, Ansys CFX is one of them. Post Processing The flow solver yields several MB or GB of data depending upon the flow The data has to be analyzed and rendered as Graphs, Charts, Tables, Vectors and contours The Flow Solvers usually have the post processors incorporated Separate processors – TECPLOT etc. are available Non-newtonian fluid, technically, this type of fluid doesn’t have constant viscosity. Its viscosity changes under certain conditions. Let see an interesting example: Finally, the fluid can change phase if you apply pressure to it or change room temperature.

References Asakura T, Karino T. Flow patterns and spatial distribution of atherosclerotic lesions in human coronary arteries. Circ Res. 1990;66(4):1045-1066. Yamagishi M, Terashima M, Awano K, Kijima M, Nakatani S, Daikoku S, Ito K, Yasumura Y, Miyatake K. Morphology of vulnerable coronary plaque: insights from follow-up of patients examined by intravascular ultrasound before an acute coronary syndrome. J Am Coll Cardiol. 2000;35(1):106-111. Yong ASC, Ng ACC, Brieger D, Lowe HC, Ng MKC, Kritharides L. Three-dimensional and two-dimensional quantitative coronary angiography, and their prediction of reduced fractional flow reserve. Eur Heart J. 2011;32(3):345-353. ANSYS, ANSYS CFX-Solver Theory Guide. 2010, Canonsburg, PA After know what the fluid is, you’ll start to know why it’s quite a challenge to simulate it. First of all, it’s a continuum material, so you can only approximate it on computer. You need to find a good way to discretize it without losing too much granularity. The fluid is a kind of material that change topology constantly. How to track the interface of it? How to handle the breaking waves? What if an air bubble is trapped in a the water? There is no easy answer. How to do fluid-object interaction in a physically correct way? You already know it is not so easy to code up a rigid body simulator. Now you’re going to add more complexity by coupling these two together. How about the collision and response? When talking about a simulation, you have to think about whether your method is stable or not. Is it accurate enough? Does it quickly converge to the solution? Performance again becomes an issue if your application has time restriction. You have only a few cycles to do all the simulations, not only fluids in one frame, how are you going to do about it? Finally, if the animator is not satisfied with the result generated by the simulator or he wants to flow to exactly follow certain patterns, what can you do?