Research Papers

Computational Study of Hemodynamic Effects of Abnormal E/A Ratio on Left Ventricular Filling

[+] Author and Article Information
Xudong Zheng

Assistant Professor
Department of Mechanical Engineering,
University of Maine,
Boardman Hall 213 A,
Orono, ME 04473
e-mail: xudong.zheng@maine.edu

Qian Xue

Department of Mechanical Engineering,
University of Maine,
Orono, ME 04473

Rajat Mittal

Department of Mechanical Engineering,
Johns Hopkins University,
Baltimore, MD 21218

1Corresponding author.

Manuscript received July 2, 2013; final manuscript received March 14, 2014; accepted manuscript posted March 24, 2014; published online April 25, 2014. Assoc. Editor: Dalin Tang.

J Biomech Eng 136(6), 061005 (Apr 25, 2014) (10 pages) Paper No: BIO-13-1292; doi: 10.1115/1.4027268 History: Revised March 14, 2014; Accepted March 24, 2014; Received June 02, 2014

Three-dimensional numerical simulations are employed to investigate the hemodynamic effects of abnormal E/A ratios on left ventricular filling. The simulations are performed in a simplified geometric model of the left ventricle (LV) in conjunction with a specified endocardial motion. The model has been carefully designed to match the important geometric and flow parameters under the physiological conditions. A wide range of E/A ratios from 0 to infinity is employed with the aim to cover all the possible stages of left ventricle diastolic dysfunction (DD). The effects of abnormal E/A ratios on vortex dynamics, flow propagation velocity, energy consumption as well as flow transport and mixing are extensively discussed. Our results are able to confirm some common findings reported by the previous studies, and also uncover some interesting new features.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Wang, Z., Jalali, F., SunY., Wang, J., Parker, K., and Tyberg, J., 2005, “Assessment of LV Diastolic Suction in Dogs Using Wave-Intensity Analysis,” Am. J. Physiol. Heart Circ. Physiol., 288, pp. H1641–H1651. [CrossRef] [PubMed]
Courtois, M., Kovacs, S. J., and Ludbrook, P., 1988, “Transmitral Pressure-Flow Velocity Relation. Importance of Regional Pressure Gradients in the Left Ventricle During Diastole,” Circulation, 78, pp. 661–671. [CrossRef] [PubMed]
Bronzino, J. D., 1999, The Biomedical Engineering Handbook, 2nd ed., CRC Press, Boca, Raton, FL.
Smiseth, O. A., and Tendera, M., 2008, Diastolic Heart Failure, Springer, London.
Carcia, J. M., Smedira, N. G., Greenberg, N. L., Main, M., Firstenberg, M. S., Odabashian, J., and Thomas, J. D., 2000, “Color M-Mode Doppler Flow Propagation Velocity is a Preload Insensitive Index of LV Relaxation: Animal and Human Validation,” J. Am. Coll. Cardiol., 35, pp. 201–208. [CrossRef] [PubMed]
Leite-Moreira, A. F., Correia-Pinto, J., and Gillebert, T. C., 2001, “Diastolic Dysfunction and Hypertension,” New Engl. J. Med., 341, pp. 1401–1402.
Redfield, M., Jacobsen, S., Burnett, J., Mahoney, D., Balley, K., and Rodeheffer, R., 2003, “Burden of Systolic and Diastolic Ventricular Dysfunction in the Community: Appreciating the Scope of the Heart Failure Epidemic,” JAMA, 289(2), pp. 194–202. [CrossRef] [PubMed]
Carlhäll, C. J., and Bolger, A., 2010, “Passing Strange: Flow in the Failing Ventricle,” Circ.: Heart Failure, 3, pp. 326–331. [CrossRef]
Domenichini, F., Pederizzetti, G., and Baccani, B., 2005, “Three-Dimensional Filling Flow Into a Model Left Ventricle,” J. Fluid Mech., 539, pp. 179–198. [CrossRef]
Lemmon, J. D., and Yoganathan, A. P., 2000, “Computational Modeling of Left Heart Diastolic Function: Examination of Ventricular Dysfunction,” ASME J. Biomech. Eng., 122, pp. 297–303. [CrossRef]
Shenkel, T., Malve, M., Reik, M., Markl, M., Jung, B., and Oertel, H., 2009, “MRI-Based CFD Analysis and Application to Healthy Heart,” Ann. Biomed. Eng., 37, pp. 503–515. [CrossRef] [PubMed]
Kheradvar, A., Assadi, R., Falahatpisheh, A., and Sengupta, P., 2011, “Assessment of Transmitral Vortex Formation in Patients With Diastolic Dysfunction,” J. Am. Soc. Echocardiogr., 25, pp. 220–227. [CrossRef] [PubMed]
Ishizu, T., Seo, Y., Ishimitsu, T., Obara, K., Moriyama, N., Kawano, S., Watanabe, S., and Yamaguchi, I., 2006, “The Wake of a Large Vortex is Associated With Intraventricular Filling Delay in Impaired Left Ventricles With a Pseudonormalized Transmitral Flow Pattern,” Echocardiography, 23, pp. 368–375. [CrossRef]
Baccani, B., Domenichini, F., and Pedrizzetti, G., 2002, “Vortex Dynamics in a Model Left Ventricle During Filling,” Eur. J. Mech., B, 21, pp. 527–543. [CrossRef]
Domenichini, F., Querzoli, G., Genedese, A., and Pedrizzetti, G., 2007, “Combined Experimental and Numerical Analysis of the Flow Structure into the Left Ventricle,” J. Biomech., 40, pp. 1988–1994. [CrossRef] [PubMed]
Hong, G., Pedrizzetti, G., Tonti, G., Li, P., Wei, Z., Kim, J., Baweja, A., Liu, S.,Chung, N., Houle, H., Narula, J., and Vannan, M., 2008, “Characterization and Quantification of Vortex Flow in the Human Left Ventricle by Contrast Echocardiography Using Vector Particle Image Velocimetry,” JACC Cardiovasc. Imaging, 1, pp. 705–717. [CrossRef] [PubMed]
Kheradar, A., Houle, H., Pedrizzetti, G., Tonti, G., Belcik, T., Ashraf, M., LindnerJ., Gharib, M., and Sahn, D., 2010, “Echocardiographic Particle Image Velocimetry: A Novel Technique for Quantificatioin of LV Blood Vorticity Pattern,” J. Am. Soc. Echocardiogr., 23, pp. 86–94. [CrossRef] [PubMed]
Gharib, M., Rambod, E., and Shariff, K., 1998, “A universal Time-Scale of Vortex Formation Time,” ASME J. Fluid Mech., 360, pp. 121–141. [CrossRef]
Gharib, M., Rambod, E., Kheradvar, A., Sahn, D. J., and Dabiri, J. O., 2006, “Optimal Vortex Formation as an Index of Cardiac Health,” Proc. Natl. Acad. Sci., 103(16), pp. 6305–6308. [CrossRef]
Kheradvar, A., Assadi, R., Falahatpisheh, A., and Sengupta, P. P., 2012, “Assessment of Transmitral Vortex Formation in Patients with Diastolic Dysfunction,” J. Am. Soc. Echocardiogr., 25(5), pp. 220–227. [CrossRef]
Kilner, P., Yang, G., Wilkes, A., Mohiaddin, R., Firmin, D., and Yacoub, M., 2000, “Asymmetric Redirection of Flow Through the Heart,” Nature, 404, pp. 759–761. [CrossRef] [PubMed]
Pedrizzetti, G., and Domenichini, F., 2005, “Nature Optimizes the Swirling Flow in the Human Left Ventricle,” Phys. Rev. Lett., 95, p. 108101. [CrossRef] [PubMed]
Mangual, J., Krainer, E., De Luca, A., Toncelli, L., Shah, A., Solomon, S., Galanti, G., Domenichini, F., and Pedrizzetti, G., 2013, “Comparative Numerical Study on LV Fluid Dynamics After Dilated Cardiomyopathy,” J. Biomech., 46, pp. 1611–1617. [CrossRef] [PubMed]
Shorland, A. P., Black, R. A., Jarvis, J. C., Henry, S., Iudicello, F., and Collins, M. W., 1996, “Formation and Travel of Vortices in Model Ventricles: Application to the Design of Skeletal Muscle Ventricles,” J. Biomech., 4, pp. 503–511. [CrossRef]
Kheradvar, A., Milano, M., and Gharib, M., 2007, “Correlation Between Vortex Ring Formation and Mitral Annulus Dynamics During Ventricular Rapid Filling,” ASAIO J., 53, pp. 8–16. [CrossRef] [PubMed]
Mandinov, L., Eberli, F. R., Seiler, C., and Hess, O. M., 2000, “Review: Distolic Heart Failure,” Cardiovasc. Res., 45, pp. 813–825. [CrossRef] [PubMed]
Pierrakos, O., and Vlachos, P., 2006, “The Effect of Vortex Formation on LV Filling and Mitral Valve Efficiency,” ASME J. Biomech. Eng., 128, pp. 527–539. [CrossRef]
Zhong, L., Su, Y., Gobeawan, L., Sola, S., Tan, R., Navia, J., Ghista, D., Chua, T., Guccione, J., and Kassab, G., 2011, Impact of Surgical Ventricular Restoration on Ventricular Shape, Wall Stress, and Function in Heart Failure Patients,” Am. J. Physiol. Heart Circ. Physiol., 300, pp. 1653–1660. [CrossRef]
Le, T., and Sotiropoulos, F., 2012, “On the Three-Dimensional Vortical Structure of Early Diastolic Flow in a Patient-Specific Left Ventricle,” Eur. J. Mech. B, 35, pp. 20–24. [CrossRef]
Nakanura, M., Wada, S., Mikami, T., Kitabatake, A., and Karino, T., 2003, “Computational Study on the Evolution of an Intraventricular Vortical Flow During Early Diastole for the Interpretation of Color M-Mode Doppler Echocardiograms,” Biomech. Model. Mechanobiol., 2, pp. 59–72. [CrossRef] [PubMed]
Georgiadis, M., and Pasipoularides, A., 1992, “Computational Fluid Dynamics of LV Ejection,” Ann. Biomed. Eng., 20, pp. 81–97. [CrossRef] [PubMed]
Domenichini, F., and Pedrizzetti, G., 2011, “Intraventricular Vortex Flow Changes in the Infracted Left Ventricle: Numerical Results in a Idealized 3D Shape,” Comput. Methods Biomech. Biomed. Eng., 14(1), pp. 95–101. [CrossRef]
Talor, T., Okino, H., and Yamaguchi, T., 1994, “Three Dimensional Analysis of LV Ejection Using Computational Fluid Dynamics,” ASME J. Biomech. Eng., 116, pp. 127–130. [CrossRef]
Watanabe, H., Sugiura, S., Kafuku, H., and Hisada, T., 2004, “Multiphysics Simulation of Left Ventricle Filling Dynamics Using Fluid-Structure Interaction Finite Element Method,” Biophys. J., 87, pp. 2074–2085. [CrossRef] [PubMed]
Nichols, W., O'Rourke, M., and Vlachopoulos, C., 2011, McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, 6th ed., CRC Press, Boca Raton, FL.
Mittal, R., Dong, H., Bozkuittas, M., Najiar, F. M., Vargas, A., and Loebbecke, A., 2008, “A Versatile Sharp Interface Immersed Boundary Method for Incompressible Flows With Complex Boundaries,” J. Comput. Phys., 227(10), pp. 4825–4852. [CrossRef] [PubMed]
Arts, W. C., Hunter, A., Douglas, M. M., Muijtjens, and R. S.Reneman, 1992, “Description of the Deformation of the LV by a Kinematic Model,” J. Biomech., 25, pp. 1119–1127. [CrossRef] [PubMed]
Yoganathan, A., He, Z., and Jones, S. C., 2004, “Fluid Mechanics of Heart Valves,” Annu. Rev. Biomed. Eng., 6, pp. 331–362. [CrossRef] [PubMed]
Eriksson, J., Carlhall, C., Dyverfeldt, P., Engvall, J., Bolger, A., and Ebbers, T., 2010, “Semi-Automatic Quantification of 4d LV Blood Flow,” J. Cardiovasc. Magn. Reson., 12, p. 9. [CrossRef] [PubMed]
Markl, M., Kilner, P., Ebbers, T., 2011, “Comprehensive 4d Velocity Mapping of the Heart and Great Vessels by Cardiovascular Magnetic Resonance,” J. Cardiovasc. Magn. Reson., 13, p. 7. [CrossRef] [PubMed]
Pasipoularides, A., 2009, Heart's Vortex: Intracardiac Blood Flow Phenomena, PMPH-USA, Shelton, CT.
Charonko, J., Kumar, R., Stewart, K., Little, W., and Vlachos, P., 2013, “Vortices Formed on the Mitral Valve Tips Aid Normal LV Filling,” Ann. Biomed. Eng., 41(5) pp. 1049–1061. [CrossRef] [PubMed]
Olcay, A. B., and Krueger, P. S., 2008, “Measurement of Ambient Fluid Entrainment During Laminar Vortex Ring Formation,” Exp. Fluids, 44, pp. 235–247. [CrossRef]
Töger, J., Kanski, M., Carlsson, M., Kovacs, S. J., Soderlind, G., Arhenden, H., and Heiberg, E., 2012, “Vortex Ring Formation in the Left Ventricle of the Heart: Analysis by 4D Flow MRI and Lagrangian Coherent Structure,” Ann. Biomed. Eng., 40, 2652–2662. [CrossRef] [PubMed]
Hendabadi, S., Bermejo, J., Benito, Y., Yotti, R., Fernandez-Aviles, F., Alamo, J. C., and Shadden, S., 2013, “Topology of Blood Transport in the Human Left Ventricle by Novel Processing of Doppler Echocardiography,” Ann. Biomed. Eng., 41, pp. 2603–2616. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 7

(a) The instantaneous time rate of the changes of five energetics components of the normal case (E/A = 1.88) during the diastole. The volume flow rate is superimposed at the bottom. (b) The total energy of five components during the diastole versus E/A ratio.

Grahic Jump Location
Fig. 8

(a) The time variation of the volume-averaged pressure inside the LV for the normal filling case; (b) the magnitude of the peak averaged pressure during the acceleration and deceleration for both E wave and A wave versus the amplitude of inflow acceleration

Grahic Jump Location
Fig. 2

The time evolution of the vortical structure during the diastole phase for the normal filling case (E/A = 1.88). The vortical structure is visualized by using the eigenvalue of velocity gradient. (a) t = 0.06T, (b) t = 0.156T, (c) t = 0.22T, (d) t = 0.272T, (e) t = 0.316T, (f) t = 0.448T, (g) t = 0.488T, and (h) t = 0.648T. T is the time for one cardiac cycle. T = 1 s.

Grahic Jump Location
Fig. 3

The velocity vectors and 3D swirl strength at the midaxial plane at three time instants. (a) t = 0.272T, (b) t = 0.316T, and (c) t = 0.648T.

Grahic Jump Location
Fig. 6

(a) A spatiotemporal contour of the flow velocity along the long axis for the normal filling. (b) The variations of the flow propagation speeds with vortex formation number for the E wave and A wave.

Grahic Jump Location
Fig. 1

(a) The geometric model of the left ventricle and (b) the time history of the ventricular volume flow rate for various cases

Grahic Jump Location
Fig. 9

The contour of the volume content of the atrial blood inside the LV at five instants during one cycle. (a) t = 0.152TE, (b) t = 0.316T, (c) t = 0.488T, (d) t = 0.568T, and (e) t = 0.648T. The first row is from the normal case (E/A = 1.88) and the second raw is from the diseased case (E/A = 0.129).

Grahic Jump Location
Fig. 4

The time evolution of the vortical structure during the diastole phase for the case with E/A = 0.129. The vortical structure is visualized by using the eigenvalue of velocity gradient. (a) t = 0.156T, (b) t = 0.568T, (c) t = 0.604T, (d) t = 0.64T, and (e) t = 0.668T.

Grahic Jump Location
Fig. 5

The flow propagation speed versus the vortex formation time for each E wave and A wave of all the cases. Grey region represents the “strong” filling waves associated with complex vortical structures.

Grahic Jump Location
Fig. 10

The variations of the standard deviation of the volume content of the atrial blood from the EF (std) and the volume percentage of the stagnation region inside the LV (stag) with the varying E/A ratio




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In