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Accurate noninvasive quantitation of blood flow, cross-sectional lumen vessel area and wall shear stress by three-dimensional paraboloid modeling of magnetic resonance imaging velocity data

Sten Oyre, MD^* , Steffen Ringgaard, MS, Sebastian Kozerke, MS, William P. Paaske, MD, DMsc^*, Mogens Erlandsen, MS, Peter Boesiger, MS, PhD and Erik M. Pedersen, MD, PhD^*

^* Department of Cardiothoracic and Vascular Surgery T, Aarhus University Hospital, Aarhus, Denmark
MRI Research Center, Institute of Experimental Clinical Research, Skejby Sygehus, Aarhus University Hospital, Aarhus, Denmark
Department of Biostatistics, Aarhus University, Aarhus, Denmark
Institute of Biomedical Engineering and Medical Informatics, University of Zürich and Swiss Federal Institute of Technology, Zurich, Switzerland

View larger version (33K): [in a new window]   Figure 1 Three-dimensional surface plot of a 3DP. This profile is valid for Poiseuille flow in rigid tubes. u(x,y) is the velocity in the x,y-coordinate system.

View larger version (44K): [in a new window]   Figure 2 Principles of the three-dimensional paraboloid (3DP) method. a, A magnitude image is reproduced as obtained perpendicular to the longitudinal axis of the vessel. A preliminary lumen vessel edge is constructed as a perfect circle from two manually placed points. b, Pixels are identified at a distance of 0.3 to 1.3 mm (gray area) from the preliminary circle (dashed circle). Data for the 3DP fit are acquired from this ring of pixels. c, A plot of flow velocity, u, as a function of length in radial dimension, r, used for determination of wall shear rate. WSS is wall shear rate times the dynamic viscosity of the blood.

View larger version (39K): [in a new window]   Figure 3 Contour plots of velocity (m/s) profiles from peak systole for all subjects (a to g) are shown (from 0.1 m/s in steps of 0.1 m/s). A perfect paraboloid contour with fully developed profile is shown in h. Note the variation in location of centers and these blunt in vivo flow profiles.

View larger version (34K): [in a new window]   Figure 4 Peak systolic and end-diastolic velocity data from the common carotid artery of one volunteer. Blood velocity data from the cross-sectional vessel area are shown as function of their distance to the center of the vessel lumen. Open circles are the velocity data used for the 3DP fit (0.3 to 1.3 mm from vessel wall). The two-dimensional projection of the resulting 3DP is shown as solid lines. n = number of pixels.

View larger version (29K): [in a new window]   Figure 5 a, Volume blood flow; b, WSS for all subjects; c, mean values for all seven subjects.

View larger version (54K): [in a new window]   Figure 6 Lumen vessel wall position from one subject during peak systole and end-diastole determinated using the 3DP method. Note the pattern of lateral dilation in peak systole and the relatively small 95% confidence limits compared with the pixel matrix size of 0.5 x 0.5 mm2.

View larger version (21K): [in a new window]   Figure 7 Cross-sectional lumen area of CCAs during end-diastole and peak systole in all subjects (a to g).