, Volume 52, Issue 3, pp 555–561 | Cite as

A framework for synthetic validation of 3D echocardiographic particle image velocimetry

  • Ahmad Falahatpisheh
  • Arash Kheradvar
Advances in Biomechanics: from foundations to applications


Particle image velocimetry (PIV) has been significantly advanced since its conception in early 1990s. With the advancement of imaging modalities, applications of 2D PIV have far expanded into biology and medicine. One example is echocardiographic particle image velocimetry that is used for in vivo mapping of the flow inside the heart chambers with opaque boundaries. Velocimetry methods can help better understanding the biomechanical problems. The current trend is to develop three-dimensional velocimetry techniques that take advantage of modern medical imaging tools. This study provides a novel framework for validation of velocimetry methods that are inherently three dimensional such as but not limited to those acquired by 3D echocardiography machines. This framework creates 3D synthetic fields based on a known 3D velocity field \({\mathbf{V}}\) and a given 3D brightness field \({\mathbf{B}}\). The method begins with computing the inverse flow \({\mathbf{V}}^{\varvec{*}} \) based on the velocity field \({\mathbf{V}}\). Then the transformation of \({\mathbf{B}}\), imposed by \({\mathbf{V}}\), is calculated using the computed inverse flow according to \({\mathbf{B}}^{\varvec{*}} \left( {\mathbf{x}} \right) = {\mathbf{B}}\left( {{\mathbf{x}} + {\mathbf{V}}^{\varvec{*}} \left( {\mathbf{x}} \right)} \right)\), where x is the coordinates of voxels in \({\mathbf{B}}^{\varvec{*}} \), with a 3D weighted average interpolation, which provides high accuracy, low memory requirement, and low computational time. To check the validity of the framework, we generate pairs of 3D brightness fields by employing Hill’s spherical vortex velocity field. \({\mathbf{B}}\) and the generated \({\mathbf{B}}^{\varvec{*}} \) are then processed by our in-house 3D particle image velocimetry software to obtain the interrelated velocity field. The results indicates that the computed and imposed velocity fields are in agreement.


Particle image velocimetry Hill’s spherical vortex Echocardiography Brightness field Echo-PIV 



This study has been partially supported by an American Heart Association grant (14GRNT18800013) to Prof. Kheradvar, and a postdoctoral fellowship (14POST20530013) from the American Heart Association awarded to Dr. Falahatpisheh.


  1. 1.
    Westerweel J, Elsinga GE, Adrian RJ (2013) Particle image velocimetry for complex and turbulent flows. Annu Rev Fluid Mech 45(1):409–436ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Pereira F, Gharib M (2002) Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows. Meas Sci Technol 13:683–694ADSCrossRefGoogle Scholar
  3. 3.
    Barnhart DH, Adrian RJ, Papen GC (1994) Phase-conjugate holographic system for high-resolution particle-image velocimetry. Appl Opt 33(30):7159–7170ADSCrossRefGoogle Scholar
  4. 4.
    Falahatpisheh A, Pedrizzetti G, Kheradvar A (2014) Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields. Exp Fluids 55(11):1–15CrossRefGoogle Scholar
  5. 5.
    Elsinga GE et al (2006) Tomographic particle image velocimetry. Exp Fluids 41(6):933–947CrossRefGoogle Scholar
  6. 6.
    Okamoto K et al (2000) Evaluation of the 3D-PIV standard images (PIV-STD project). J Vis 3(2):115–123CrossRefGoogle Scholar
  7. 7.
    Stanislas M et al (2008) Main results of the third international PIV challenge. Exp Fluids 45(1):27–71MathSciNetCrossRefGoogle Scholar
  8. 8.
    Falahatpisheh A, Kheradvar A (2012) High-speed particle image velocimetry to assess cardiac fluid dynamics in vitro: From performance to validation. Eur J Mech B Fluids 35:2–8CrossRefGoogle Scholar
  9. 9.
    Kheradvar A, Falahatpisheh A (2012) The effects of dynamic saddle annulus and leaflet length on transmitral flow pattern and leaflet stress of a bileaflet bioprosthetic mitral valve. J Heart Valve Dis 21(2):225Google Scholar
  10. 10.
    Groves EM et al (2014) The effects of positioning of transcatheter aortic valves on fluid dynamics of the aortic root. ASAIO J 60(5):545–552CrossRefGoogle Scholar
  11. 11.
    Sengupta PP et al (2012) Emerging trends in CV flow visualization. JACC Cardiovasc Imaging 5(3):305–316CrossRefGoogle Scholar
  12. 12.
    Falahatpisheh A, Kheradvar A (2015) A measure of axisymmetry for vortex rings. Eur J Mech B/Fluids 49, Part A(0):264–271CrossRefGoogle Scholar
  13. 13.
    Falahatpisheh A, Pahlevan N, Kheradvar A (2015) Effect of the mitral valve’s anterior leaflet on axisymmetry of transmitral vortex ring. Ann Biomed Eng 43(10):2349–2360CrossRefGoogle Scholar
  14. 14.
    Sánchez J, Salgado A, Monzón N (2015) Computing inverse optical flow. Pattern Recogn Lett 52:32–39CrossRefGoogle Scholar
  15. 15.
    Norbury J (1973) A family of steady vortex rings. J Fluid Mech 57(03):417–431ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    Falahatpisheh A, Kheradvar A (2014) Volumetric echocardiographic particle image velocimetry (V-Echo-PIV). Circulation 130(Suppl 2):A14952Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Biomedical Engineering, Edwards Lifesciences Center for Advanced Cardiovascular EngineeringUniversity of California, IrvineIrvineUSA

Personalised recommendations