Response by Oshida et al to Letter Regarding Article, "Wall Shear Stress and T1 Contrast Ratio Are Associated With Embolic Signals During Carotid Exposure in Endarterectomy".

In Response: Thank for your interest in our report. On solution strategy, each carotid artery with a stenosis was meshed using commercial software to create tetrahedral meshes with 5 layers of finer-prism meshes at the boundary. On average, the meshes comprised 570 000 nodes and 2 270 000 tetrahedral and prismatic elements in the models with stenosis. A straight inlet extension was added to the common carotid artery to obtain fully developed laminar flow. Recent studies have demonstrated that computational fluid dynamics analysis of a carotid artery with an area of stenosis can be performed by assuming laminar flow. Next, on lumen segmentation, patient-specific geometries were generated using stereolithography from preoperative timeof-flight and gadolinium-enhanced 3-dimensional magnetic resonance angiography of the cervical region. A previous study demonstrated that the degree and length of internal carotid artery (ICA) stenosis on gadolinium-enhanced 3-dimensional magnetic resonance angiography correlated significantly with those on angiography with arterial catheterization. For 3-dimensional reconstruction of the carotid arteries, the threshold magnetic resonance value of blood flow was semiautomatically extracted by a neurosurgeon blinded to other data. Small branches with diameters <1 mm from the external carotid artery were excluded from analysis as unsuitable for analysis of laminar flow. The stereolithography was remeshed to improve the quality of the constituent surface triangles. Finally, on flow rates, computational fluid dynamics analysis was performed using a high-performance computing system and a commercial solver with a finite volume method under the unsteady-state situation and governed by the Navier-Stokes and continuity equations. We applied the Semi-Implicit Method for Pressure-Linked Equation algorithm on a pressure-based solver, that is implicit, to stabilize convergence calculations of pressure and momentum. For the fluid domain, 3-dimensional unsteady incompressible laminar flow fields were obtained. Vessel walls were assumed to be rigid, and no-slip boundary conditions were applied at the walls. Blood was assumed to be an incompressible Newtonian fluid. Normalized pulsatile mass flow rate waveforms of older adults have been presented previously.5 In a previous study, traction-free boundary conditions were applied at the outlets of the ICA and external carotid artery, and the computational fluid dynamics analysis assumed traction-free boundary conditions for both the ICA and external carotid artery that were well validated by specific ultrasound data of patients. As a result, we applied traction-free boundaries for the ICA and external carotid artery. Our study enrolled only patients with ICA stenosis ≥70%. Further studies may be needed to determine whether a decrease in inlet flow into the common carotid artery or in outlet from the ICA are associated with the development of microembolic signals during exposure of the carotid arteries during carotid endarterectomy. The location at which stenosis was most severe was visually determined, and regions of interest in the most severe stenotic segment of the ICA were semiautomatically generated using AVS Express software. The maximum value for wall shear stress within regions of interest was selected in each patient because a previous study showed that a higher maximum wall shear stress in the arterial stenosis was significantly associated with intraplaque hemorrhage. The maximum value of wall shear stress was compared with all values within the regions of interest and was manually confirmed as not representing an outlier.