The impact of scaled boundary conditions on wall shear stress computations in atherosclerotic human coronary bifurcations.

The aim of this study was to determine if reliable patient-specific wall shear stress (WSS) can be computed when diameter-based scaling laws are used to impose the boundary conditions for computational fluid dynamics. This study focused on mildly diseased human coronary bifurcations since they are predilection sites for atherosclerosis. Eight patients scheduled for percutaneous coronary intervention were imaged with angiography. The velocity proximal and distal of a bifurcation was acquired with intravascular Doppler measurements. These measurements were used for inflow and outflow boundary conditions for the first set of WSS computations. For the second set of computations, absolute inflow and outflow ratios were derived from geometry-based scaling laws based on angiography data. Normalized WSS maps per segment were obtained by dividing the absolute WSS by the mean WSS value. Absolute and normalized WSS maps from the measured-approach and the scaled-approach were compared. A reasonable agreement was found between the measured and scaled inflows, with a median difference of 0.08 ml/s [-0.01; 0.20]. The measured and the scaled outflow ratios showed a good agreement: 1.5 percentage points [-19.0; 4.5]. Absolute WSS maps were sensitive to the inflow and outflow variations, and relatively large differences between the two approaches were observed. For normalized WSS maps, the results for the two approaches were equivalent. This study showed that normalized WSS can be obtained from angiography data alone by applying diameter-based scaling laws to define the boundary conditions. Caution should be taken when absolute WSS is assessed from computations using scaled boundary conditions.

Contrast-enhanced micro-CT imaging in murine carotid arteries: a new protocol for computing wall shear stress.

BACKGROUND: Wall shear stress (WSS) is involved in the pathophysiology of atherosclerosis. The correlation between WSS and atherosclerosis can be investigated over time using a WSS-manipulated atherosclerotic mouse model. To determine WSS in vivo, detailed 3D geometry of the vessel network is required. However, a protocol to reconstruct 3D murine vasculature using this animal model is lacking. In this project, we evaluated the adequacy of eXIA 160, a small animal contrast agent, for assessing murine vascular network on micro-CT. Also, a protocol was established for vessel geometry segmentation and WSS analysis. METHODS: A tapering cast was placed around the right common carotid artery (RCCA) of ApoE-/- mice (n = 8). Contrast-enhanced micro-CT was performed using eXIA 160. An innovative local threshold-based segmentation procedure was implemented to reconstruct 3D geometry of the RCCA. The reconstructed RCCA was compared to the vessel geometry using a global threshold-based segmentation method. Computational fluid dynamics was applied to compute the velocity field and WSS distribution along the RCCA. RESULTS: eXIA 160-enhanced micro-CT allowed clear visualization and assessment of the RCCA in all eight animals. No adverse biological effects were observed from the use of eXIA 160. Segmentation using local threshold values generated more accurate RCCA geometry than the global threshold-based approach. Mouse-specific velocity data and the RCCA geometry generated 3D WSS maps with high resolution, enabling quantitative analysis of WSS. In all animals, we observed low WSS upstream of the cast. Downstream of the cast, asymmetric WSS patterns were revealed with variation in size and location between animals. CONCLUSIONS: eXIA 160 provided good contrast to reconstruct 3D vessel geometry and determine WSS patterns in the RCCA of the atherosclerotic mouse model. We established a novel local threshold-based segmentation protocol for RCCA reconstruction and WSS computation. The observed differences between animals indicate the necessity to use mouse-specific data for WSS analysis. For our future work, our protocol makes it possible to study in vivo WSS longitudinally over a growing plaque.

Functional and anatomical measures for outflow boundary conditions in atherosclerotic coronary bifurcations.

The aim of this research was finding the influence of anatomy-based and functional-based outflow boundary conditions for computational fluid dynamics (CFD) on fractional flow reserve (FFR) and wall shear stress (WSS) in mildly diseased coronary bifurcations. For 10 patient-specific bifurcations three simulations were set up with different outflow conditions, while the inflow was kept constant. First, the outflow conditions were based on the diameter of the outlets. Second, they were based on the volume estimates of the myocardium that depended on the outlets. Third, they were based on a myocardial flow measure derived from computed tomography perfusion imaging (CTP). The difference in outflow ratio between the perfusion-based and the diameter-based approach was -7 p.p. [-14 p.p.:7 p.p.] (median percentage point and interquartiles), and between the perfusion-based and volume-based this was -2 p.p. [-2 p.p.:1 p.p.]. Despite of these differences the computed FFRs matched very well. A quantitative analysis of the WSS results showed very high correlations between the methods with an r(2) ranging from 0.90 to 1.00. But despite the high correlations the diameter-based and volume-based approach generally underestimated the WSS compared to the perfusion-based approach. These differences disappeared after normalization. We demonstrated the potential of CTP for setting patient-specific boundary conditions for atherosclerotic coronary bifurcations. FFR and normalized WSS were unaffected by the variations in outflow ratios. In order to compute absolute WSS a functional measure to set the outflow ratio might be of added value in this type of vessels.

Influence of the Accuracy of Angiography-Based Reconstructions on Velocity and Wall Shear Stress Computations in Coronary Bifurcations: A Phantom Study.

INTRODUCTION: Wall shear stress (WSS) plays a key role in the onset and progression of atherosclerosis in human coronary arteries. Especially sites with low and oscillating WSS near bifurcations have a higher propensity to develop atherosclerosis. WSS computations in coronary bifurcations can be performed in angiography-based 3D reconstructions. It is essential to evaluate how reconstruction errors influence WSS computations in mildly-diseased coronary bifurcations. In mildly-diseased lesions WSS could potentially provide more insight in plaque progression. MATERIALS METHODS: Four Plexiglas phantom models of coronary bifurcations were imaged with bi-plane angiography. The lumens were segmented by two clinically experienced readers. Based on the segmentations 3D models were generated. This resulted in three models per phantom: one gold-standard from the phantom model itself, and one from each reader. Steady-state and transient simulations were performed with computational fluid dynamics to compute the WSS. A similarity index and a noninferiority test were used to compare the WSS in the phantoms and their reconstructions. The margin for this test was based on the resolution constraints of angiography. RESULTS: The reconstruction errors were similar to previously reported data; in seven out of eight reconstructions less than 0.10 mm. WSS in the regions proximal and far distal of the stenosis showed a good agreement. However, the low WSS areas directly distal of the stenosis showed some disagreement between the phantoms and the readers. This was due to small deviations in the reconstruction of the stenosis that caused differences in the resulting jet, and consequently the size and location of the low WSS area. DISCUSSION: This study showed that WSS can accurately be computed within angiography-based 3D reconstructions of coronary arteries with early stage atherosclerosis. Qualitatively, there was a good agreement between the phantoms and the readers. Quantitatively, the low WSS regions directly distal to the stenosis were sensitive to small reconstruction errors.

Fast and accurate pressure-drop prediction in straightened atherosclerotic coronary arteries.

Atherosclerotic disease progression in coronary arteries is influenced by wall shear stress. To compute patient-specific wall shear stress, computational fluid dynamics (CFD) is required. In this study we propose a method for computing the pressure-drop in regions proximal and distal to a plaque, which can serve as a boundary condition in CFD. As a first step towards exploring the proposed method we investigated ten straightened coronary arteries. First, the flow fields were calculated with CFD and velocity profiles were fitted on the results. Second, the Navier-Stokes equation was simplified and solved with the found velocity profiles to obtain a pressure-drop estimate (Δp (1)). Next, Δp (1) was compared to the pressure-drop from CFD (Δp CFD) as a validation step. Finally, the velocity profiles, and thus the pressure-drop were predicted based on geometry and flow, resulting in Δp geom. We found that Δp (1) adequately estimated Δp CFD with velocity profiles that have one free parameter ß. This ß was successfully related to geometry and flow, resulting in an excellent agreement between Δp CFD and Δp geom: 3.9 ± 4.9% difference at Re = 150. We showed that this method can quickly and accurately predict pressure-drop on the basis of geometry and flow in straightened coronary arteries that are mildly diseased.