Patients
Two male patients, 64 and 55-years old respectively, underwent cardiac CT. Patient 1 suffered from CAD with recurrent episodes of angina pectoris and a recent myocardial infarction. Invasive coronary angiography revealed a significant stenosis of the proximal right coronary artery (RCA) and non-significant stenoses of the middle left anterior descending (LAD) and distal left circumflex artery (LCX). Subsequently, the patient underwent saphenous CABG surgery with an end-to-side anastomosis onto the distal RCA. Patient 2 suffered from dyspnoea and instable angina pectoris. Invasive coronary angiography showed serial significant stenoses of the proximal LAD and a significant stenosis of the distal LCX. Saphenous CABG surgery was performed with a sequential side-to-side anastomosis onto the middle LAD and an end-to-side anastomosis onto the distal LCX.
CT data acquisition
CT was performed 10 and 15 days after surgery, respectively, on a 16-detector row scanner (Sensation 16, Siemens Medical Solutions, Forchheim, Germany) using the following parameters: detector collimation 16 × 0.75 mm, gantry rotation time 0.37 sec, pitch 0.38, tube potential 120 kV, tube current time product 400 mAs. A bolus of 150 ml iodinated contrast material (iodixanol, Visipaque 320, 320 mg/ml, GE Healthcare, Buckinghamshire, UK) followed by 30 ml saline solution was continuously injected into a right antecubital vein via a 18-gauge catheter at a flow rate of 5 ml/sec. Bolus tracking was performed with a region of interest in the ascending aorta and image acquisition was automatically started 5 sec after signal attenuation reached a threshold of 140 HU. Synchronized to the electrocardiogram (ECG), CT data sets were retrospectively reconstructed throughout the cardiac cycle in 5% steps of the R-R interval with a slice thickness of 1 mm and an increment of 0.5 mm using a medium soft-tissue convolution kernel (B30f). The adaptive cardio volume approach was used for image reconstruction and ECG-pulsing was applied to reduce radiation exposure. The reconstruction phase providing best image quality with the lowest degree of motion artifacts was determined by two readers in consensus and was used for further post-processing. The local ethics committee approved the study protocol and written informed consent was obtained from both patients.
Geometric reconstruction
Axial CT images were digitally processed to extract geometrical contours representing the coronary arteries and the CABGs. The lumen of all coronary arteries and grafts of the two patients were semi-automatically segmented using a commercially available software package (Amira 3.1, TGS, Belgium). In regions of reduced arterial opacification, segmentation was manually complemented. The outflows (i.e., the end of the branches) and inflows (i.e., the ostia) of the vessels were separately marked to allow the imposition of boundary conditions. As a next step, an unstructured surface mesh of triangles was generated covering the segmented volume using the marching cube algorithm. Manual smoothing and low-pass spatial filtering was then applied to further reduce fine-scale surface irregularities. The final model depicted the real three dimensional (3D) geometry of the coronary arteries and bypass grafts (Figure 1). Four computational models, two for each case, were subsequently built with 750.000 – 900.000 tetrahedral cells. The finest meshes represented a spatial resolution of about 0.15 mm and the number of elements per cross-section ranged from 150 to 200 depending on the vessel diameter.
Model assumptions and boundary conditions
The flow for the simulation was considered transient, 3D, incompressible, and laminar. Corresponding to standard values from the literature, blood was assumed Newtonian with a viscosity of 0.0037 Pa· sec and a density of 1060 kg/m3. The walls were modeled as solid and stiff and a zero-velocity boundary condition was adopted at the fluid-solid interface, corresponding to a no-slip condition. In contrast to other flow simulations, we chose not to elongate the inlet part for the coronary arteries to allow for a full flow development. The instantaneous velocity at the different inlets (coronary ostia and proximal bypass anastomoses) was based on standard data [45,46] reflecting the physiologically pulsatile, biphasic blood velocity from the ascending aorta into the coronary arteries (Figure 2). We adopted a spatially uniform profile for these boundary cross-sections. The maximum inlet Re was calculated at 1230 (bypass inlet) lasting for a very short period of time. The mean Re ranged between 380 (right coronary artey inlet) and 570 (left coronary artery inlet). The duration of the cardiac cycle was normalized to 1 second for both patients. The corresponding Womersley (Wo) number was 3.5 (bypass inlet), 2.1 (right coronary inlet) and 2.45 (left coronary inlet). The stress-free boundary condition (zero normal and tangential stresses), which arises naturally from the application of the finite element method, was imposed on the velocity field at all outlets to facilitate a common comparison frame between these two highly different coronary circulations by removing the influence of their downstream impedances. In this way, the observed flow differences are mainly the result of the adopted anastomosis type.
Computational fluid dynamics
The finite element software FIDAP (Version 8.6.2, Fluent Corp., Darmstadt, Germany) was used to perform the CFD simulations by solving the Navier-Stokes equations with linear basis functions. Calculated flow variables were flow velocities and pressure following a segregated solution approach. A convergence criterion of four orders of magnitude was adopted for the residuals in velocity and pressure. The instantaneous flow field was acquired at 100 steps per cardiac cycle with a constant time step using backward Euler implicit time integration. All the results presented herein belong to the third computational cardiac cycle to allow ample time for the attenuation of the effects of the initial conditions. The sensitivity of the numerical results on the underlying grid was examined under steady flow conditions. The time averaged values of the inflow velocities, shown in Figure 2, were used for this purpose by adopting a spatially uniform profile. The resulting differences in the calculated velocity values averaged below 5% of the maximum prescribed inflow velocity. This was judged sufficient for the requirements of the present feasibility investigation. The presented CFD results for both patients came from the finest available meshes. The Fieldview software (Version 11.0, Intelligent Light, Lyndhurst, NJ) was used for visualization of flow patterns, quantification of WSS and volumetric fluxes at selected sites.
Answers to all your Biology Questions
