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CFD analysis of venous CABG based on in-vivo CT datasets in patients …

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- Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts

The results from our study indicate that considerable variations of blood flow exist in the distal perianastomotic region of venous CABG that may coincide with areas of neointimal hyperplasia. We found WSS variations in both types of anastomoses, with highest WSS values at the heel and lowest WSS values at the floor of the end-to-side anastomosis case. In contrast, high WSS in the side-to-side anastomosis configuration was only found in stenotic vessel segments but not in the close vicinity of the anastomosis. Across both types of anastomoses, elevated WSS values did coincide with vessel stenosis, being either caused by atherosclerotic wall changes or by a surgical clip.

CFD provided detailed information on instantaneous mass flow. In the case of side-to-side anastomosis, this information was important to predict the mass flow reaching the next anastomosis. In addition, the amount of blood running retrograde in the coronary artery and eventually reaching a more proximal branch can be quantitatively measured. The numerical results in our patients revealed considerable retrograde flow into the host coronary artery in both types of anastomoses, a finding that has been previously described in experimental models [38]. On the other hand stagnation zones were only found in end-to-side as compared to side-to-side anastomosis. The latter configuration showed smoother stream divisions of mass flow throughout the cardiac cycle. Finally, it was clearly demonstrated that the instantaneous blood influx through the bypasses maximizes during systole. Conversely, under physiological coronary flow conditions the maximum flux into the system occurs during diastole. This is a major difference that leads to a more balanced total instantaneous flow in the cases reported herein. Possible pathophysiological implications of this fact warrant further research.

When investigating hemodynamic features of blood flow, numerical simulation has become an important tool. This study presents realistic, patient-specific models based on CT angiography datasets of coronary and CABG anatomy. This approach circumvents the need for idealization of the main geometrical features. Most of the CFD studies that were mentioned in the introduction had to rely on some sort of geometrical regularization by introducing pre-specified parameters such as the CABG angle, the host to graft diameter ratio and the planarity or non-planarity of the entire configuration. There are merits in the latter methodology. There is the ability to parametrically study the hemodynamic effects of these strictly defined morphological parameters. Furthermore the generation of the underlying surface and volumetric grids is much easier and can lead to numerical results of greater accuracy. On the other hand, a patient specific model is much more difficult to construct and to ensure sufficient numerical accuracy. It is a closer match to reality but at the same time it is harder to parameterize the results and extract generalized conclusions.

CT angiography currently provides the most accurate representation of real anatomy. In contrast to most computational studies, our geometric models did not only include a small part of a coronary artery or CABG bypass but entailed the coronary tree and bypass grafts from their origin to the distal anastomoses. This became possible with the improvement of multi-detector row CT scanner technology with fast gantry rotation times enabling accurate and reliable depiction of coronary and bypass graft anatomy in a short imaging time [47,48]. With the advent of 64-slice CT [49] and dual-source CT [50] further improvements with regard to temporal and spatial resolution have been made allowing an even more precise depiction of anatomy that will further improve the accuracy of numerical flow simulations.

The following study limitations have to be acknowledged. Firstly, 16-detector row CT does not offer currently the best imaging for coronary arteries and CABG as compared to newer scanner technology. In addition, geometric data for CFD was obtained from a single reconstruction time-point in early to mid-diastole and vessel contours and diameters might be different at other reconstruction time-points. Secondly, the assumptions concerning inflow and outflow may not be valid under pathologic conditions and thus leading to exaggerated mass flow in the bypass grafts. The localization of the bypasses and native coronary inlets is extracted directly from the CT scans. It is expected that a realistic inflow velocity profile would not exhibit developed flow characteristics, as in Poisseuille or Womersley theories. The main discrepancy lies on the significant presence of in plane secondary flow patterns [51] due to the motion of the coronary sinuses. Typical PC-MRI resolution does not allow for the quantification of these in-plane velocity distributions. Conversely, PC-MRI or Doppler Ultrasound can be used to quantify the blood flux discharge ratios between the first few branches of the coronary and bypass configurations. It is our intention to enhance our investigation protocol with such in-vivo measurements in order to improve the imposed outflow boundary conditions.

Moreover, both the arterial and bypass walls were simplified as being stiff. Heart movement and changing pressure at the outer wall of the vessels due to the myocardium contraction were not included in the present calculations. The importance of the large scale coronary motion induced by the beating heart is hard to quantify in CABG configurations. Although the coronary arteries move considerably throughout the cardiac cycle, it has been shown that pulsatility is the main characterizing factor of WSS distributions [52]. Additionally, the bypass grafts are intentionally fixed with surgical clips and thus experience only minor displacements near the distal anastomosis sites. Their interaction is expected to affect the pressure and WSS distributions near the anastomosis. Results might differ in elastic models of coronary arterial and CABG walls that can also take into account the compliance mismatch between the host and graft sections [53,54]. Recently, Ramaswamy et al. [44] performed a fluid dynamics analysis in a diseased section of a human coronary artery by taking into account both the large scale motion as well as compliance. This was accomplished by utilizing bi-plane angiography combined with intravascular ultrasound images. Their results showed that compliance caused substantial differences in the circumferential WSS distributions. The profound change in the distal coronary lumen dimensions during systole has major consequences as far as the outflow boundary conditions are concerned, by significantly increasing the flow resistance. Additionally, the concurrent increase of arterial pressure leads to the dilatation of the proximal coronary sections. Coronary hemodynamics and the corresponding WSS distributions will now depend on the interaction between pulsatile inflow, which maximizes during diastole, and the variation of the luminal diameter, which maximizes during systole.

Finally, the assumption that blood behaves as a Newtonian liquid must be examined further. Although it is assumed that blood exhibits shear thinning behavior in vessels of smaller diameter than the coronary arteries, there is a multitude of patient dependent parameters like the hematocrit and the intake of drugs that can alter blood viscosity. Numerical simulations of non-Newtonian flow in a two dimensional end-to-side anastomosis under pulsatile flow conditions have shown only minor effects on WSS distributions [55]. However such results are bound to depend on the particulars of the constitutive equations utilized for determining blood's viscosity.

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