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• W1553659639 abstract "Wall shear stress is hypothesized to be an important factor in the localization and the development of arterial disease. Wall shear stress is calculated by multiplying wall shear rate by the viscosity. Wall shear rate can be estimated by velocity gradient from the velocity profile. Velocity can be measured in vivo by Phase Contrast Magnetic Resonance Imaging. We focused on evaluating wall shear rate using pixel-by-pixel based velocity data from MR imaging. We used interpolation method to find polynomials of velocity. In this study, Lagrange's polynomial interpolation is used. The measurement equation for wall shear rate is induced from derivative of the interpolated polynomial of velocity. Since wall shear stress is determined by multiplication of the viscosity of blood and wall shear rate, it can be calculated using estimated wall shear rate value. Our method was verified using data from a flow model system of aorta. Wall shear rate and wall shear stress are reliably measured by derived equation. BACKGROUND Hemodynamic factors give information about causes of dysfunction and disease of blood vessels. In particular, wall shear stress has the strong correlation with the localization of atherosclerosis and aneurysms and is important in understanding the development of arterial disease [1]. However, in vivo wall shear stress measurement has many limitations and difficulties. Thus, noninvasive measurement methods have been studied in many ways. We suggest that a mathematical measurement method using pixel-by-pixel based velocity data and Lagrange's interpolation. METHODS First, velocity profile was needed to calculate wall shear stress. MR imaging is performed with velocity encoded phase contrast sequence. Using the in house-developed velocimetry program, velocity value can be calculated by pixel-by-pixel based. We assume that blood vessels are of the cross sectional shape of circle. The center of vessel is chosen and pixels of wall position are set in each image. Next, we estimate polynomials that satisfied given velocity value using Lagrange’s polynomial interpolation. For an arbitrary calculation point on the wall location, three reference points are selected from a targeting point to the center. Points located at the wall is set by (x0, y0) and all points can be represented by (xi, yi)=(distance from x0, velocity), i=1, 2, 3 (1) Using pixel information of four points, a third ordered polynomial P(x) is calculated. The derivative of polynomial at the wall position is wall shear rate. Finally, wall shear stress (τω) is calculated by multiplying wall shear rate (P'(0)) and the viscosity of blood (μ)." @default.
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• W1553659639 date "2011-11-01" @default.
• W1553659639 modified "2023-09-23" @default.
• W1553659639 title "Mathematical Measurement of Aortic Wall Shear Stress" @default.
• W1553659639 hasPublicationYear "2011" @default.
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