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Vector Analysis of the Wall Shear Rate at the Human Aortoiliac Bifurcation Using Cine MR Velocity Mapping

Taeko Tsuji1, Jun-ichi Suzuki2,3, Ryoichi Shimamoto1, Tadashi Yamazaki1, Toshiaki Nakajima1, Ryozo Nagai1, Shuhei Komatsu4, Kuni Ohtomo4, Teruhiko Toyo-oka2 and Masao Omata5

1 Department of Cardiovascular Medicine, Faculty of Medicine, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 1138655, Japan.
2 Health Service Center, Faculty of Medicine, University of Tokyo, 1138655, Japan.
3 Department of Internal Medicine, Laboratory-213, Faculty of Medicine, University of Tokyo, 1138655, Japan.
4 Department of Radiology, Faculty of Medicine, University of Tokyo, 1138655, Japan.
5 Department of Gastroenterology, Faculty of Medicine, University of Tokyo, 1138655, Japan.



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  		Fig. 1A. —Diagrams of vector analysis of blood flow velocity. Angle A is intersecting angle between axis of abdominal aorta and course of common iliac artery and is less than 90° for both right and left iliac arteries. Diagram shows how to calculate blood flow velocity parallel to vessel wall (axial component of vector of blood flow velocity) (cosA x Vhead-caudal - sinA x Vright-left), which constitutes axial component of wall shear rate for right common iliac artery.

 


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  		Fig. 1B. —Diagrams of vector analysis of blood flow velocity. Angle A is intersecting angle between axis of abdominal aorta and course of common iliac artery and is less than 90° for both right and left iliac arteries. Diagram shows how to calculate axial component of vector of blood flow velocity (cosA x Vhead-caudal + sinA x Vright-left) for left common iliac artery.

 


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  		Fig. 2A. —Velocity profile curve (velocity distance relationship superimposed on MR velocity mapping). Right—left in-plane (A), head—caudal in-plane (B), and through-plane (C) MR velocity mapping is obtained cinematically with temporal resolution of 80 msec, in common imaging plane including aortoiliac bifurcation. Superimposed graph represents velocity profile for each encoded direction across common iliac artery just distal to bifurcation. Vertical line (two arrowheads) indicates anatomic position of edge of vessel wall and corresponds to site of indicator (one arrowhead) on MR velocity mapping. Horizontal and vertical axes of graph represent distance across common iliac artery from edge of vessel wall and blood flow velocity in each direction.

 


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  		Fig. 2B. —Velocity profile curve (velocity distance relationship superimposed on MR velocity mapping). Right—left in-plane (A), head—caudal in-plane (B), and through-plane (C) MR velocity mapping is obtained cinematically with temporal resolution of 80 msec, in common imaging plane including aortoiliac bifurcation. Superimposed graph represents velocity profile for each encoded direction across common iliac artery just distal to bifurcation. Vertical line (two arrowheads) indicates anatomic position of edge of vessel wall and corresponds to site of indicator (one arrowhead) on MR velocity mapping. Horizontal and vertical axes of graph represent distance across common iliac artery from edge of vessel wall and blood flow velocity in each direction.

 


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  		Fig. 2C. —Velocity profile curve (velocity distance relationship superimposed on MR velocity mapping). Right—left in-plane (A), head—caudal in-plane (B), and through-plane (C) MR velocity mapping is obtained cinematically with temporal resolution of 80 msec, incommon imaging plane including aortoiliac bifurcation. Superimposed graph represents velocity profile for each encoded direction across common iliac artery just distal to bifurcation. Vertical line (two arrowheads) indicates anatomic position of edge of vessel wall and corresponds to site of indicator (one arrowhead) on MR velocity mapping. Horizontal and vertical axes of graph represent distance across common iliac artery from edge of vessel wall and blood flow velocity in each direction.

 


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  		Fig. 3. —Diagram of three-dimensional analysis of blood flow velocity vector at vessel wall. Diagram shows how to decompose vector of blood flow velocity into three orthogonal directions including axial direction paralleling vessel axis, nonaxial direction perpendicular to axis and parallel to vessel wall, and normal direction perpendicular to vessel wall. Of three components, former two induce wall shear rate. Normal component does not contribute to wall shear stress, but to normal stress.

 


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  		Fig. 4. —Schematic graph represents time (cardiac phase)—wall shear rate curve. Oscillatory shear index is defined as follows: (oscillatory shear index) = IArecessiveI/(IAdominantI + IArecessiveI), where IAdominantI is absolute value of area with dominant flow direction under curve, and IArecessiveI is that of area with recessive flow direction.

 


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  		Fig. 5A. —Scattergrams of correlation between indexes of wall shear rate and aortoiliac angle. Scattergram represents correlation of peak wall shear rate with intersecting angle between abdominal aorta and common iliac artery. One point of 13 points represents two data. Positive correlation is shown (r = 0.577, p < 0.05).

 


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  		Fig. 5B. —Scattergrams of correlation between indexes of wall shear rate and aortoiliac angle. Scattergram shows correlation between oscillation of wall shear rate and takeoff angle. There is inverse correlation between them (r = 0.603, p < 0.05).

 

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