Annals of Biomedical Engineering

, Volume 43, Issue 10, pp 2349–2360 | Cite as

Effect of the Mitral Valve’s Anterior Leaflet on Axisymmetry of Transmitral Vortex Ring

  • Ahmad Falahatpisheh
  • Niema M. Pahlevan
  • Arash Kheradvar


The shape and formation of transmitral vortex ring are shown to be associated with diastolic function of the left ventricle (LV). Transmitral vortex ring is a flow feature that is observed to be non-axisymmetric in a healthy heart and its inherent asymmetry in the LV assists in efficient ejection of the blood during systole. This study is a first step towards understanding the effects of the mitral valve’s anterior leaflet on transmitral flow. We experimentally study a single-leaflet model of the mitral valve to investigate the effect of the anterior leaflet on the axisymmetry of the generated vortex ring based on the three-dimensional data acquired using defocusing digital particle image velocimetry. Vortex rings form downstream of a D-shaped orifice in presence or absence of the anterior leaflet in various physiological stroke ratios. The results of the statistical analysis indicate that the formed vortex ring downstream of a D-shaped orifice is markedly non-axisymmetric, and presence of the anterior leaflet improves the ring’s axisymmetry. This study suggests that the improvement of axisymmetry in presence of the anterior leaflet might be due to coupled dynamic interaction between rolling-up of the shear layer at the edges of the D-shaped orifice and the borders of the anterior leaflet. This interaction can reduce the non-uniformity in vorticity generation, which results in more axisymmetric behavior compared to the D-shaped orifice without the anterior leaflet.


Mitral valve Anterior leaflet Non-axisymmetry Vortex ring 



Plateau velocity of the piston


Equivalent diameter of the D-shaped orifice


Stroke ratio


Axisymmetry index


Impulse threshold

\(\bar{I}_{ < }\)

Average of the impulses less than the impulse threshold, \(\bar{I}\)

\(\bar{I}_{ > }\)

Average of the impulses more than the impulse threshold, \(\bar{I}\)


Number of \(\theta\)-planes

\(\omega_{\theta }\)

Vorticity distribution in each \(\theta\)-plane

\(\text{Re}_{\Gamma }\)

Reynolds number of vortex ring

\(\Gamma_{\theta }\)

Circulation in each \(\theta\)-plane

\(\Gamma_{\theta }^{*}\)

Non-dimensional circulation in each \(\theta\)-plane

\(\overline{{\Gamma_{\theta } }}^{*}\)

Average of non-dimensional circulation in all \(\theta\)-planes

\(R_{\theta }\)

Radial vorticity centroid in each \(\theta\)-plane

\(R_{\theta }^{*}\)

Non-dimensional radial vorticity centroid in each \(\theta\)-plane

\(\overline{{R_{\theta } }}^{*}\)

Average of non-dimensional radial vorticity centroid in all \(\theta\)-planes

\(I_{\theta }\)

Impulse in each \(\theta\)-plane

\(I_{\theta }^{*}\)

Non-dimensional impulse in each \(\theta\)-plane

\(\overline{{I_{\theta } }}^{*}\)

Average of non-dimensional impulse in all \(\theta\)-planes



This work was supported by the American Heart Association awards 14POST20530013 and 14GRNT18800013 to Dr. Ahmad Falahatpisheh and Prof. Arash Kheradvar, respectively. The authors are also grateful to Prof. Morteza Gharib who generously allowed using his DDPIV setup at Caltech.

Supplementary material

10439_2015_1302_MOESM1_ESM.wmv (1.9 mb)
Supplementary material 1 (WMV 1944 kb)


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Copyright information

© Biomedical Engineering Society 2015

Authors and Affiliations

  • Ahmad Falahatpisheh
    • 1
    • 2
  • Niema M. Pahlevan
    • 3
    • 4
  • Arash Kheradvar
    • 1
    • 2
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of California, IrvineIrvineUSA
  2. 2.Department of Biomedical EngineeringUniversity of California, IrvineIrvineUSA
  3. 3.Department of Medical EngineeringCalifornia Institute of TechnologyPasadenaUSA
  4. 4.Huntington Medical Research InstitutePasadenaUSA

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