Abstract
A new method for quantitative reconstruction of a three dimensional (3D) velocity field from ultrasound color doppler mapping (USCDM) images is used here to calculate the shear stress distribution on the endothelial layer of an artery. Measurements of a few spatially unrestricted USCDM transverse cross sectional images of the artery, and of several echo-ultrasound B-mode images of the same area, are required for reconstructing the geometry of the vessel’s endothelial surface. The calculation is based on assuming a physical model of flow, and solving the Continuity and the Navier-Stokes equations numerically for a steady flow of an incompressible Newtonian fluid at constant temperature within a non-flexible tube. The correct choice of the penalty parameter in the finite element method (FEM) algorithm provides proper convergence of the reconstruction. The endothelial shear stress is calculated from the gradient of the velocity field at each point of the vessel’s inner surface.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nerem RM, Levesque MJ. Fluid mechanics in atherosclerosis. In: Handbook of Bioengineering (Skalak R, Chien S, editors), McGraw Hill: NY, 1987, pp. 21.1 21.22.
Fox MD, Gardiner M. Three-dimensional doppler velocimetry of flow jets. IEEE Trans Biomed Eng 1988;35:834–841.
Schrank E, Phillips DJ, Morits WE, Strandness DE Jr. A triangulation method for the quantitative measurement of arterial blood velocity magnitude and directions in humams. Ultrasound in Med Biol 1990;16(5):499–509.
Recchia FA, Senzaki H, Saeki A, Byrne BJ, Kass DA. Pulse pressure-related changes in coronary flow in vivo are modulated by nitric oxide and adenosine. Circ Res 1996;79:849–856.
Bernstein RD, Ochoa FY, Xu X, Forfia P, Shen W, Thompson CI, Hintze TH. Function and production of nitric oxide in the coronary circulation of the conscious dog during exercise. Circ Res 1996;79:840–848.
Gudi SRP, Clark CG, Frangos JA. Fluid flow rapidly activates g proteins in human endothelial cells. Circ Res 1996;79:834–839.
Nadaud S, Philippe M, Arnal JF, Michel JB, Soubrier F. Sustained increase in aortic endothelial nitric oxide synthase expression in vivo in a model of chronic high blood flow. Circ Res 1996;79:857–863.
Vonderleyen HE, Gibbons GH, Morishita R, Lewis NP, Zhang L, Nakajima M, Kaneda Y, Cooke JP, Dzau VJ. Gene therapy inhibiting neointimal vascular lesion: in vivo transfer of endothelial cell nitric oxide synthase gene. Proc Natl Acad Sci USA 1995;92:1137–1141.
Zarins CK, Zatina MA, Giddens DR, Ku DN, Glagov S. Shear stress regulation of artery lumen diameter in experimental atherogenesis. J Vasc Surg 1987;5(3):413–420.
Van Dijk P: Direct cardiac NMR imaging of heart wall and blood flow velocity. J Comput Assist Tomogr 1984;8:429–436.
Bryant DJ, Payne JA, Firmin DN, Longmore DB. Measurement of flow with NMR imaging using a gradient pulse and phase difference technique. J Comput Assist Tomogr 1984;8:588–593.
Mohiaddin RH, Amanuma MA, Kilner PJ, Pennel DJ, Manzara C, Longmore DB. MR phase-shift velocity mapping of mitral and pulmonary venous flow. J Comput Assist Tomogr 1991;15:237–243.
Wang T, Wu X, Chung N, Ritman EL. Myocardial blood flow estimated by synchronous, multislice, high-speed computed tomography. IEEE Trans Med Imaging 1989;8:70–77.
Bailliart O, Bonnin P, Capderou A, Savin E, Kedra AW, Martineaud JP. Simultaneous ultrasonic measurement of carotic blood-flow and intracerebral hemodynamics in man. Arch Int de Physiol de Biochem et de Biophysic 1993;101(2):149–154.
Van Rossum A, Sprenger ICH, Peels FC, et al. In vivo validation of quantitative flow imaging in arteries and veins using magnetic resonance phase shift techniques. Society of Magnetic Resonance in Medicine, Berkly CA, 9th Annual Sci Meeting, Amsterdam, 1989; 205.
Kilner PJ, Firmin DN, Rees RSO, et al. Magnetic resonance jet velocity mapping for assessment of valve and great vessel stenosis. Radiology 1991; 178: 229–235.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Adam, D.R., Burstein, P. (1997). Vascular Imaging by Ultrasound: 3D Reconstruction of Flow Velocity Fields for Endothelial Shear Stress Calculation. In: Sideman, S., Beyar, R. (eds) Analytical and Quantitative Cardiology. Advances in Experimental Medicine and Biology, vol 430. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5959-7_15
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5959-7_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7731-3
Online ISBN: 978-1-4615-5959-7
eBook Packages: Springer Book Archive