Experiments in Fluids

, 55:1848 | Cite as

Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields

  • Ahmad Falahatpisheh
  • Gianni Pedrizzetti
  • Arash KheradvarEmail author
Research Article


Measurement of the three-dimensional flow field inside the cardiac chambers has proven to be a challenging task. This is mainly due to the fact that generalized full-volume velocimetry techniques cannot be easily implemented to the heart chambers. In addition, the rapid pace of the events in the heart does not allow for accurate real-time flow measurements in 3D using imaging modalities such as magnetic resonance imaging, which neglects the transient variations of the flow due to averaging of the flow over multiple heartbeats. In order to overcome these current limitations, we introduce a multi-planar velocity reconstruction approach that can characterize 3D incompressible flows based on the reconstruction of 2D velocity fields. Here, two-dimensional, two-component velocity fields acquired on multiple perpendicular planes are reconstructed into a 3D velocity field through Kriging interpolation and by imposing the incompressibility constraint. Subsequently, the scattered experimental data are projected into a divergence-free vector field space using a fractional step approach. We validate the method in exemplary 3D flows, including the Hill’s spherical vortex and a numerically simulated flow downstream of a 3D orifice. During the process of validation, different signal-to-noise ratios are introduced to the flow field, and the method’s performance is assessed accordingly. The results show that as the signal-to-noise ratio decreases, the corrected velocity field significantly improves. The method is also applied to the experimental flow inside a mock model of the heart’s right ventricle. Taking advantage of the periodicity of the flow, multiple 2D velocity fields in multiple perpendicular planes at different locations of the mock model are measured while being phase-locked for the 3D reconstruction. The results suggest the metamorphosis of the original transvalvular vortex, which forms downstream of the inlet valve during the early filling phase of the right ventricular model, into a streamline single-leg vortex extending toward the outlet.


Root Mean Square Error Velocity Field Kriging Particle Image Velocimetry Right Ventricle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by a Transatlantic Career Award from Fondation Leducq to Professor Arash Kheradvar. The authors are also grateful to Professor Federico Domenichini for providing his DNS data.

Supplementary material

Supplementary material 1 (mp4 3837 KB)

Supplementary material 2 (mp4 3721 KB)


  1. Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluids 39(2):159–169CrossRefGoogle Scholar
  2. Afanasyev Y, Demirov E (2005) A variational filtration and interpolation technique for PIV employing fluid dynamical constraints. Exp Fluids 39(5):828–835CrossRefGoogle Scholar
  3. Asakawa D, Pappas G, Blemker S, Drace JE, Delp S et al (2003) Cine phase-contrast magnetic resonance imaging as a tool for quantification of skeletal muscle motion. In: Seminars in musculoskeletal radiology, THIEME, vol 7, pp 287–296Google Scholar
  4. Barnhart DH, Adrian RJ, Papen GC (1994) Phase-conjugate holographic system for high-resolution particle-image velocimetry. Appl Opt 33(30):7159–7170CrossRefGoogle Scholar
  5. Cimino S, Pedrizzetti G, Tonti G, Canali E, Petronilli V, De Luca L, Iacoboni C, Agati L (2012) In vivo analysis of intraventricular fluid dynamics in healthy hearts. Eur J Mech B Fluids 35:40–46Google Scholar
  6. Cressie N (1992) Statistics for spatial data. Terra Nova 4(5):613–617CrossRefGoogle Scholar
  7. Domenichini F (2011) Three-dimensional impulsive vortex formation from slender orifices. J Fluid Mech 666:506–520CrossRefzbMATHGoogle Scholar
  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. Fredriksson AG, Zajac J, Eriksson J, Dyverfeldt P, Bolger AF, Ebbers T, Carlhäll CJ (2011) 4-D blood flow in the human right ventricle. Am J Physiol Heart Circ Physiol 301(6):H2344–H2350CrossRefGoogle Scholar
  10. Gunes H, Rist U (2007) Spatial resolution enhancement/smoothing of stereo-particle-image-velocimetry data using proper-orthogonal-decomposition-based and Kriging interpolation methods. Phys Fluids 19(064):101Google Scholar
  11. Gunes H, Rist U (2008) On the use of kriging for enhanced data reconstruction in a separated transitional flat-plate boundary layer. Phys Fluids 20(104):109Google Scholar
  12. Harlander U, Wright GB, Egbers C (2012) Reconstruction of the 3D flow field in a differentially heated rotating annulus by synchronized particle image velocimetry and infrared thermography measurements. In: 16th International symposium on applied laser techniques to fluid mechanics, Lisbon, PortugalGoogle Scholar
  13. Hill MJM (1894) On a spherical vortex. Proc R Soc Lond 55(331–335):219–224CrossRefGoogle Scholar
  14. Hong GR, Pedrizzetti G, Tonti G, Li P, Wei Z, Kim JK, Baweja A, Liu S, Chung N, Houle H et al (2008) Characterization and quantification of vortex flow in the human left ventricle by contrast echocardiography using vector particle image velocimetry. JACC Cardiovasc Imaging 1(6):705–717CrossRefGoogle Scholar
  15. Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285(69):69–94CrossRefzbMATHMathSciNetGoogle Scholar
  16. Kheradvar A, Gharib M (2009) On mitral valve dynamics and its connection to early diastolic flow. Ann Biomed Eng 37(1):1–13CrossRefGoogle Scholar
  17. Kheradvar A, Houle H, Pedrizzetti G, Tonti G, Belcik T, Ashraf M, Lindner JR, Gharib M, Sahn D (2010) Echocardiographic particle image velocimetry: a novel technique for quantification of left ventricular blood vorticity pattern. J Am Soc Echocardiogr 23(1):86–94CrossRefGoogle Scholar
  18. Kim H, Hertzberg J, Shandas R (2004) Development and validation of echo PIV. Exp Fluids 36(3):455–462CrossRefGoogle Scholar
  19. Kim J, Moin P (1985) Application of a fractional-step method to incompressible Navier–Stokes equations. J Comput Phys 59(2):308–323CrossRefzbMATHMathSciNetGoogle Scholar
  20. Leonard A (1985) Computing three-dimensional incompressible flows with vortex elements. Annu Rev Fluid Mech 17(1):523–559CrossRefGoogle Scholar
  21. Liburdy JA, Young EF (1992) Processing of three-dimensional particle tracking velocimetry data. Opt Lasers Eng 17(3):209–227CrossRefGoogle Scholar
  22. Mangual J, Domenichini F, Pedrizzetti G (2012) Three dimensional numerical assessment of the right ventricular flow using 4D echocardiography boundary data. Eur J Mech B Fluids 35:25–30CrossRefGoogle Scholar
  23. Mullin JA, Dahm WJ (2005) Dual-plane stereo particle image velocimetry (DSPIV) for measuring velocity gradient fields at intermediate and small scales of turbulent flows. Exp Fluids 38(2):185–196CrossRefGoogle Scholar
  24. Mullin JA, Dahm WJ (2006) Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. I. Accuracy assessments. Phys Fluids 18(035):101Google Scholar
  25. Norbury J (1973) A family of steady vortex rings. J Fluid Mech 57(3):417–431CrossRefzbMATHGoogle Scholar
  26. Novikov E (1983) Generalized dynamics of three-dimensional vortical singularities (vortons). Zh Eksp Teor Fiz 84:981Google Scholar
  27. Núñez MA, Flores C, Juárez H (2006) A study of hydrodynamic mass-consistent models. J Comput Methods Sci Eng 6(5):365–385zbMATHGoogle Scholar
  28. Núñez MA, Flores C, Juárez H (2007) Interpolation of hydrodynamic velocity data with the continuity equation. J Comput Methods Sci Eng 7(1):21–42zbMATHMathSciNetGoogle Scholar
  29. Pereira F, Gharib M (2002) Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows. Meas Sci Technol 13(5):683CrossRefGoogle Scholar
  30. Poelma C, Mari J, Foin N, Tang MX, Krams R, Caro C, Weinberg P, Westerweel J (2011) 3D flow reconstruction using ultrasound piv. Exp fluids 50(4):777–785CrossRefGoogle Scholar
  31. Ratto C, Festa R, Romeo C, Frumento O, Galluzzi M (1994) Mass-consistent models for wind fields over complex terrain: the state of the art. Environ Softw 9(4):247–268CrossRefGoogle Scholar
  32. Sengupta PP, Pedrizzetti G, Kilner PJ, Kheradvar A, Ebbers T, Tonti G, Fraser AG, Narula J (2012) Emerging trends in CV flow visualization. JACC Cardiovasc Imaging 5(3):305–316CrossRefGoogle Scholar
  33. Stamatopoulos C, Mathioulakis D, Papaharilaou Y, Katsamouris A (2011) Experimental unsteady flow study in a patient-specific abdominal aortic aneurysm model. Exp fluids 50(6):1695–1709CrossRefGoogle Scholar
  34. Su LK, Dahm WJ (1996) Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. I. Assessment of errors. Phys Fluids 8:1869–1882Google Scholar
  35. Sung J, Yoo J (2001) Three-dimensional phase averaging of time-resolved piv measurement data. Meas Sci Technol 12(6):655CrossRefGoogle Scholar
  36. Vedula P, Adrian R (2005) Optimal solenoidal interpolation of turbulent vector fields: application to PTV and super-resolution PIV. Exp Fluids 39(2):213–221CrossRefGoogle Scholar
  37. Westerdale J, Belohlavek M, McMahon EM, Jiamsripong P, Heys JJ, Milano M (2011) Flow velocity vector fields by ultrasound particle imaging velocimetry in vitro comparison with optical flow velocimetry. J Ultrasound Med 30(2):187–195Google Scholar
  38. Willert C, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10(4):181–193CrossRefGoogle Scholar
  39. Zhang F, Lanning C, Mazzaro L, Barker AJ, Gates PE, Strain WD, Fulford J, Gosling OE, Shore AC, Bellenger NG et al (2011) In vitro and preliminary in vivo validation of echo particle image velocimetry in carotid vascular imaging. Ultrasound Med Biol 37(3):450–464CrossRefGoogle Scholar
  40. Zhong J (1995) Vector-valued multidimensional signal processing and analysis in the context of fluid flows. PhD thesis, University of Illinois, ChicagoGoogle Scholar
  41. Zhong JL, Weng JY, Huang TS (1991) Vector field interpolation in fluid flow. In: Digital Signal. Processing '91, Int'l. Conf. on DSP, Florence, ItalyGoogle Scholar
  42. Ziskin I, Adrian R, Prestridge K (2011) Volume segmentation tomographic particle image velocimetry. In: Proceedings of 9th international symposium on particle image velocimetry. Kobe University, Kobe, Japan, pp 21–23Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ahmad Falahatpisheh
    • 1
    • 2
    • 4
  • Gianni Pedrizzetti
    • 3
  • Arash Kheradvar
    • 1
    • 2
    • 4
    Email author
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of California, IrvineIrvineUSA
  2. 2.Department of Biomedical EngineeringUniversity of California, IrvineIrvineUSA
  3. 3.Department of Engineering and ArchitectureUniversity of TriesteTriesteItaly
  4. 4.The Edwards Lifesciences Center for Advances Cardiovascular Technologies, Henry Samueli School of EngineeringUniversity of California, IrvineIrvineUSA

Personalised recommendations