Coronary flow

Coronary vessels supply the heart with blood. Atherosclerotic changes in these vessels are described as coronary heart disease. According to the World Health Organization (WHO), coronary heart disease constitutes the main cause of death in the industrial world. The main risk factors, e.g. lipid disorders, hypertension, diabetes, cause functional impairment and damage to vascular cells. But, the risk factors don't explain the local distribution of atherosclerotic lesions. The pattern of this distribution corresponds to zones of disturbed flow with vortex formations and low-velocity flow in coronary vessels.

Based on recent research a biological paradigm of mechano-transduction of fluid forces on the vascular wall has replaced previous mechanistic concepts. A host of knowledge has been accumulated on cell signalling pathways, which are currently thought to mediate mechano-transduction of fluid forces on blood cells and the cells lining the vascular wall. These cells are called endothelial cells and play a crucial role as mechano-sensors in initiating and modulating the progress of atherosclerotic lesions. Local inflammation of the vessel wall mediates plaque growth and vascular remodelling. The Wall Shear Stress (WSS) at the vascular wall elicits a phenotype change in endothelial cells associated with humoral, metabolic, and structural changes that modulate local inflammation and adaptive remodelling. Thus WSS is the most important mechanical regulatory signal that links flow to adaptive changes of the vascular wall and atherosclerotic lesions.

Based on the hypothesis that information on local WSS pattern has prognostic value with respect to progress and risk of coronary artery disease in vivo profiling of endothelial WSS in coronary arteries is of great interest for clinically relevant studies of coronary heart disease. The WSS profiling in coronaries is the main goal of our project "Study of Flow, Geometry and Atherosclerosis in the human coronary arteries".

Project GO 1067/2 "Study of Flow, Geometry and Atherosclerosis in the human coronary arteries" is funded by DFG (German Research Foundation) in the frame of young researchers support program. The project leader is Dr.-Ing. Leonid Goubergrits. The main objective of the project is a validation of numerical simulations performed by commercial flow solver FLUENT, and an establishment of numerical model for WSS profiling in coronaries.

In order to validate numerical simulations of coronary flow Laser Doppler Anemometry (LDA) measurements are performed now in two 3.5-fold enlarged models of left coronary artery.

Both models were fabricated from transparent two components silicone rubber ELASTOSIL^® RT 601 A/B (Wacker-Chemie GmbH, Munich, Germany) by filling the box with wax cast of the respective model with liquid silicone. Figure 1 shows a photo of the silicone model of an anatomically realistic left coronary artery. After silicone hardening, the wax cast is melted out in an oven at 150°C. Wax casts were fabricated using ThermoJet technology directly from computer models by Materialise GmbH (Munich, Germany). Figure 2 shows a photo of both wax cast models.

Figure 1: Silicone model of an anatomically realistic left coronary artery

Figure 2: Wax cast models

First computer model of a left coronary was generated on the basis of literature data and represents a simplified model (circular cross-sections and constant diameters for each segment) of a left main coronary artery with diameter of 4.1 mm, and two branches: left anterior descending coronary artery with diameter of 3.2 mm and branching angle of 15° and left circumflex coronary artery with diameter of 3.1 mm and branching angle of 60°. The geometry of generated bifurcation was bended with a curvature radius of 50 mm representing a curvature of a heart surface. The geometry of the generated model is shown in figure 2 left.

Second computer model of a left coronary was generated on the basis of a post-mortem fabricated vessel cast, which is shown in figure 3. The left coronary vessel cast was done by Prof. Dr. J. Fernandez-Britto (Department of Pathology, Hospital Dr. C. J. Finlay, Havana, Cuba) using a device developed in our laboratory and described here. Then the vessel cast was digitized in 3D data processing group of GFaI using greycode-phaseshift method. Digitized data were then used for generation of a computer model.

Figure 3: Post-mortem fabricated vessel cast

LDA measurements were performed in Hermann-Föttinger-Institut of TU Berlin in cooperation with a group of Prof. Dr.-Ing. C. O. Paschereit . We used a two-component LDA system of DANTEC (Dantec FiberFlow) containing Ar-Laser (490 mW) from Ion Laser Technology. Measurement volume is 46 μm × 0.38 mm × 45 μm. First, steady flow generated by Isoflow^® centrifugal pump (St. Jude Medical Inc., USA) was investigated in both models. Velocity measurements in about 1000 points in 5 different cross-sections for each model were performed. In the model of the real coronary artery we performed also measurements under pulsatile flow conditions. Altogether in 119 points from 5 different profiles the LDA measurements were performed collecting data over 5 heart cycles. The pulsatile flow was generated using a computer controlled piston pump developed in our laboratory.

A part of our numerical studies on the development of simplest numerical model of coronary flow, which, however, is enough accurate to access clinically relevant WSS profiling, is a comprehensive methodological investigation of the impact of geometric reconstruction simplifications on wall shear stress calculations using real in vivo data. We study the impact of different methods of coronary reconstruction from standard biplane angiograms using semi-automatic procedure of vessel reconstruction developed in German Heart Institute of Berlin — Deutsches Herzzentrum Berlin (DHZB) — and our developments of further vessel volume reconstruction, which is necessary for Computational Fluid Dynamics (CFD) simulation. The biplane angiograms based reconstruction of the vessel geometry needs simplified reconstruction of vessel cross-sections.

The effect of the assumption of a circular as opposed to an elliptical cross section and the effect of reduction of the spatial resolution (distance between cross sections used in reconstruction) by a factor 0.5 on calculation of some hemodynamic parameters with CFD were investigated. Data from three 3D reconstructed right coronary arteries in control patient and patients with "dilated" versus "obstructive" coronary atherosclerosis were evaluated. Figure 4 shows a so called wire reconstruction of the coronaries used in our study. The reconstruction of endo-luminal vessel surface includes vessel tree reconstruction using software developed in DHZB and surface interpolation by using of "loft" tool in SolidWorks^® (Solidworks Corp., Concord, USA) software. Two main possible alternative methods were used for reconstruction of cross-sections for each point of vessel segments centreline with two corresponding radii. First method supposed circular cross-sections. Second method supposed elliptical cross-sections. For study described here we decided to use only the reconstruction of main coronary artery without branches. Figure 5 shows the geometries under examination. The numerical solution of Navier-Stokes equations governing the fluid motion under defined boundary conditions was done in FLUENT6 software (Fluent Inc., Lebanon, USA). Stationary laminar flow was simulated supposing rigid motionless walls. A no-slip condition at the wall was applied. The pressure was free at the outlet. Blood was assumed as a Newtonian fluid with a kinematic viscosity of 3.5·10^-6 m²/s. The mean flow rates for investigated vessels were estimated based on flow rate measurements performed in DHZB by a miniaturized ultrasound Doppler probe positioned within the coronary artery. The mean inlet velocity of 0.17 m/s for normal patients, 0.27 m/s for patients with "obstructive" coronary atherosclerosis and 0.09 m/s for patients with "dilated" coronary atherosclerosis were simulated.

Figure 4: Wire reconstruction of the coronaries used in our study

Figure 5: Geometries under examination

This work is done in cooperation with Dr. E. Wellnhofer (Cardiology Department, DHZB).