Analysis of the effect of flow rate on the Doppler continuity equation for stenotic orifice area calculations: A numerical study

Circulation

Volumn 97, Issue 16, 1998, Pages 1597-1605

  DeGroff, Curt G ^a,b   Shandas, Robin ^a   Valdes Cruz, Lilliam ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Blood flow; Echocardiography; Stenosis

Indexed keywords

ARTICLE; BLOOD FLOW VELOCITY; CORONARY ARTERY BLOOD FLOW; CORONARY ARTERY OBSTRUCTION; DOPPLER FLOWMETRY; ECHOCARDIOGRAPHY; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL;

EID: 0032574652     PISSN: 00097322     EISSN: None     Source Type: Journal    
DOI: 10.1161/01.CIR.97.16.1597     Document Type: Article

References (35)

1. Snider AR, Serwer GA. Echocardiography in Pediatric Heart Disease. Baltimore, Md: Mosby Year Book; 1990:108.
2. Gorlin R, Gorlin SG. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. Am Heart J. 1951;41:1-29.
3. Kosturakis D, Allen HD, Goldberg SJ, Sahn DJ, Valdes-Cruz LM. Non-invasive quantification of stenotic semilunar valve areas by Doppler echocardiography. J Am Coll Cardiol. 1984;3:1256-1262.
4. Skjaerpe T, Hegrenaes L, Hatle L. Noninvasive estimation of valve area in patients with aortic stenosis by Doppler ultrasound and two dimensional echocardiography. Circulation. 1985;72:810-818.
5. Otto CM, Pearlman AS, Gardner CL, Enomoto DM, Togo T, Tsuboi H, Ivey TD. Experimental validation of Doppler echocardiographic measurement of volume flow through the stenotic aortic valve. Circulation. 1988;78:435-441.
6. Dumensil JG, Yoganathan AP. Theoretical and practical differences between the Gorlin formula and the continuity equation for calculating aortic and mitral valve areas. Am J Cardiol. 1991;67:1268-1272.
7. Burwash IG, Thomas DD, Sadahiro M, Pearlman AS, Verrier ED, Thomas R, Kraft CD, Otto CM. Dependence of Gorlin formula and continuity equation valve areas un transvalvular volume flow rate in valvular aortic stenosis. Circulation. 1994;89:827-835.
8. Segal J, Lerner DJ, Miller C, Mitchell RS, Alderman EA, Popp RL. When should Doppler-determined valve area be better than the Gorlin formula ? Variation in hydraulic constants in low flow states. J Am Coll Cardiol. 1987;9:1294-1305.
9. Pascoe RD, Roger VL, Pellikka PA, Seward JB, Tajik AJ. Use of dobutamine stress echocardiography in patients with aortic stenosis, reduced left ventricular ejection fraction, and low mean transvalvular gradient: preliminary experience. J Am Soc Echocardiog. 1994;7(3-II):S8. Abstract.
10. Vanoverschelde J-L, D'Hondt A-M, De Kock M. Flow-dependence of aortic stenosis severity during dobutamine infusion: comparison of the Gorlin and continuity equations with measurements of aortic valve resistance. Circulation. 1995;92(suppl I):I-464. Abstract.
11. Otto CM, Pearlman AS, Kraft CD, Miyake-Hull CY, Burwash IG, Gardner CJ. Physiologic changes with maximal exercise in asymptomatic valvular aortic stenosis assessed by Doppler echocardiography. J Am Coll Cardiol. 1992;20:1160-1167.
12. Casale PN, Palacios IF, Abrascal VM, Harrel L, Davidoff R, Weyman AE, Fifer MA. Effects of dobutamine on Gorlin and continuity equation valve areas and valve resistance in valvular aortic stenosis. Am J Cardiol. 1992;70:1175-1179.
13. Yoganathan AP, Woo YR, Sung HW, Williams FP, Franch RH, Jones MJ. In-vitro hemodynamic characteristics of tissue bioprostheses in the aortic position. J Thorac Cardiovasc Surg. 1986;92:198-209.
14. Dumensil JG, Honos GN, Lemieux M, Beauchemin J. Validation and applications of mitral prosthetic valvular areas calculated by Doppler echocardiography. Am J Cardiol. 1990;65:1443-1448.
15. Fox RW, McDonald AT. Introduction to Fluid Mechanics. 4th ed. New York, NY: John Wiley & Sons; 1992:98-354.
16. Shandas R, Kwon J, Kringlen M, Jones M, Valdes-Cruz LM. Hysteresis behavior of stenotic aortic bioprosthesis as a function of flow rate: in-vitro studies. J Am Coll Cardiol. 1996;27(suppl A):233A. Abstract.
17. Lemler MS, Shaffer EM, Valdes-Cruz LM, Wiggins JW, Cape EG. Insights into catheter/Doppler discrepancies: a clinical study of congenital aortic stenosis. Circulation. 1996;941 (suppl I):I-415. Abstract.
18. Cape EG, Jones M, Yamada I, VanAuker MD, Valdes-Cruz LM. Turbulent/viscous interactions control Doppler/catheter pressure discrepancies in aortic stenosis: the role of the Reynolds number. Circulation. 1996; 94:2975-2981.
19. CFD Research Theory Manual. Version 1.0. Huntsville, Ala: CFD Research; 1993:9.12-9.13.
20. Wilcox DC. Turbulence Modeling for CFD. La Canada, Calif: DCW Industries; 1993.
21. Versteeg HK, Malalasekera W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. New York, NY: John Wiley & Sons; 1995.
22. Patankar SV, Spalding DB. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transfer. 1972;15:1787-1806.
23. Van Doormal JP, Raithby GD. Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numerical Heat Transfer. 1984;7: 147-163.
24. Yang HQ, Habchi SD, Przekwas AJ. A general strong conservation formulation of Navier-Stokes equations in non-orthogonal curvilinear coordinates. AIAA J. 1994;32:936-941.
25. Makhijani VB, Yang HQ, Singhal AK, Hwang NC. An experimental-numerical analysis of MHV cavitation: effects of leaflet squeezing and rebound. J Heart Valve Dis. 1994;3(suppl I):35-48.
26. Makhijani VB, Siegel JM, Hwang NC. Numerical analysis of squeeze-flow in tilting disc mechanical heart valves. J Heart Valve Dis. 1996;5:97-103.
27. Makhijani VB, Yang HQ, Dionne PJ, Thubrikar MJ. Three-dimensional coupled fluid-structure simulation of pericardial bioprosthetic aortic valve function. ASAIO J. 1997;43:M387-M392.
28. Sukumar R, Athavale MM, Makhijani VB, Przekwas AJ. Application of computational fluid dynamics techniques to blood pumps. Artif Organs. 1996;20:529-533.
29. Bergman HL, Siegel JM, Oshinski JN, Pettigrew RI, Ku DN. Computational simulation of magnetic resonance angiograms in stenotic vessels: effect of stenosis severity. Adv Bioeng. 1996;33:295-296.
30. Voelker W, Reul H, Nienhaus G, Stelzer T, Schmitz B, Steegers A, Karsch KR. Comparison of valvular resistance, stroke work loss, and Gorlin valve area for quantification of aortic stenosis: an in-vitro study in a pulsatile aortic flow model. Circulation. 1995;91:1196-1204.
31. Gorlin R. Calculations of cardiac valve stenosis: restoring an old concept for advanced applications. J Am Coll Cardiol. 1987;10:920-922.
32. Cannon SR, Richards KL, Crawford M. Hydraulic estimation of stenotic orifice area: a correction of the Gorlin formula. Circulation. 1985;71: 1170-1178.
33. Caro CG, Pedley TJ, Schroter RC, Seed WA. The Mechanics of the Circulation. New York, NY: Oxford University Press; 1978:55-63.
34. Shandas R, Kwon J, Valdes-Cruz LM. In-vitro studies of velocity profiles within the proximal jet using digital particle image velocimetry: implications for clinical Doppler method. Circulation. 1996;94(suppl I):I-492. Abstract.
35. Landahl MT, Mollo-Christensen E. Turbulence and Random Processes in Fluid Mechanics. New York, NY: Cambridge University Press; 1992.