Abstract

We present a time-resolved tomographic reconstruction of the velocity field associated with pulsatile blood flow through a rotationally-symmetric stenotic vessel model. The in-vitro sample was imaged using propagation-based phase contrast with monochromated X-rays from a synchrotron undulator source, and a fast shutter-synchronized detector with high-resolution used to acquire frames of the resulting dynamic speckle pattern. Having used phase retrieval to decode the phase contrast from the speckle patterns, the resulting projected-density maps were analysed using the statistical correlation methods of particle image velocimetry (PIV). This yields the probability density functions of blood-cell displacement within the vessel. The axial velocity-field component of the rotationally-symmetric flow was reconstructed using an inverse-Abel transform. A modified inverse-Abel transform was used to reconstruct the radial component. This vector tomographic phase-retrieval velocimetry was performed over the full pumping cycle, to completely characterize the velocity field of the pulsatile blood flow in both space and time.

© 2010 OSA

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2010

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

2009

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4–5), 569–577 (2009).

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

2008

A. Fouras, D. Lo Jacono, and K. Hourigan, “Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy,” Exp. Fluids 44(2), 317–329 (2008).

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

2007

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).

2005

S. J. Lee and G. B. Kim, “Synchrotron microimaging technique for measuring the velocity fields of real blood flows,” J. Appl. Phys. 97(6), 064701 (2005).

2004

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

2003

S. J. Lee and G. B. Kim, “X-ray particle image velocimetry for measuring quantitative flow information inside opaque objects,” J. Appl. Phys. 94(5), 3620 (2003).

2002

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

2001

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

2000

S. D. Shpilfoygel, R. A. Close, D. J. Valentino, and G. R. Duckwiler, “X-ray videodensitometric methods for blood flow and velocity measurement: a critical review of literature,” Med. Phys. 27(9), 2008–2023 (2000).

1996

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

1955

J. R. Womersley, “Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known,” J. Physiol. 127(3), 553–563 (1955).

Affeld, K.

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

Beiersdorfer, P.

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

Brown, G. V.

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

Chen, H.

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

Close, R. A.

S. D. Shpilfoygel, R. A. Close, D. J. Valentino, and G. R. Duckwiler, “X-ray videodensitometric methods for blood flow and velocity measurement: a critical review of literature,” Med. Phys. 27(9), 2008–2023 (2000).

Dubsky, S.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

Duckwiler, G. R.

S. D. Shpilfoygel, R. A. Close, D. J. Valentino, and G. R. Duckwiler, “X-ray videodensitometric methods for blood flow and velocity measurement: a critical review of literature,” Med. Phys. 27(9), 2008–2023 (2000).

Dusting, J.

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).

Fouras, A.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4–5), 569–577 (2009).

A. Fouras, D. Lo Jacono, and K. Hourigan, “Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy,” Exp. Fluids 44(2), 317–329 (2008).

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).

Goubergrits, L.

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

Gureyev, T. E.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

Hooper, S. B.

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

Hourigan, K.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4–5), 569–577 (2009).

A. Fouras, D. Lo Jacono, and K. Hourigan, “Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy,” Exp. Fluids 44(2), 317–329 (2008).

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).

Irvine, S. C.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

Jamison, R. A.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

Kertzscher, U.

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

Kim, G. B.

S. J. Lee and G. B. Kim, “Synchrotron microimaging technique for measuring the velocity fields of real blood flows,” J. Appl. Phys. 97(6), 064701 (2005).

S. J. Lee and G. B. Kim, “X-ray particle image velocimetry for measuring quantitative flow information inside opaque objects,” J. Appl. Phys. 94(5), 3620 (2003).

Kitchen, M. J.

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

Kohn, V.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

Lee, S. J.

S. J. Lee and G. B. Kim, “Synchrotron microimaging technique for measuring the velocity fields of real blood flows,” J. Appl. Phys. 97(6), 064701 (2005).

S. J. Lee and G. B. Kim, “X-ray particle image velocimetry for measuring quantitative flow information inside opaque objects,” J. Appl. Phys. 94(5), 3620 (2003).

Lengeler, B.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

Lewis, R.

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).

Lewis, R. A.

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

Lisse, C. M.

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

Lo Jacono, D.

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4–5), 569–577 (2009).

A. Fouras, D. Lo Jacono, and K. Hourigan, “Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy,” Exp. Fluids 44(2), 317–329 (2008).

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).

Mudie, S. T.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

Nguyen, C. V.

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4–5), 569–577 (2009).

Olson, R. E.

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

Paganin, D.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).

Paganin, D. M.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

Seeger, A.

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

Shpilfoygel, S. D.

S. D. Shpilfoygel, R. A. Close, D. J. Valentino, and G. R. Duckwiler, “X-ray videodensitometric methods for blood flow and velocity measurement: a critical review of literature,” Med. Phys. 27(9), 2008–2023 (2000).

Siu, K. K. W.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

Snigirev, A.

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

Snigireva, I.

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

Stevenson, A. W.

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

Uesugi, K.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

Valentino, D. J.

S. D. Shpilfoygel, R. A. Close, D. J. Valentino, and G. R. Duckwiler, “X-ray videodensitometric methods for blood flow and velocity measurement: a critical review of literature,” Med. Phys. 27(9), 2008–2023 (2000).

Weitkamp, T.

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

Wellnhofer, E.

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

Wilkins, S. W.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).

T. E. Gureyev, A. W. Stevenson, D. M. Paganin, T. Weitkamp, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Quantitative analysis of two-component samples using in-line hard X-ray images,” J. Synchrotron Radiat. 9(3), 148–153 (2002).

Womersley, J. R.

J. R. Womersley, “Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known,” J. Physiol. 127(3), 553–563 (1955).

Yagi, N.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).

Appl. Phys. Lett.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic X-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).

Astrophys. J.

P. Beiersdorfer, C. M. Lisse, R. E. Olson, G. V. Brown, and H. Chen, “X-ray velocimetry of solar wind ion impact on comets,” Astrophys. J. 549(1), L147–L150 (2001).

Exp. Fluids

A. Fouras, D. Lo Jacono, and K. Hourigan, “Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy,” Exp. Fluids 44(2), 317–329 (2008).

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4–5), 569–577 (2009).

A. Seeger, K. Affeld, L. Goubergrits, E. Wellnhofer, and U. Kertzscher, “X-ray-based assessment of the three-dimensional velocity of the liquid phase in a bubble column,” Exp. Fluids 31(2), 193–201 (2001).

J. Appl. Phys.

A. Fouras, M. J. Kitchen, S. Dubsky, R. A. Lewis, S. B. Hooper, and K. Hourigan, “The past, present, and future of x-ray technology for in vivo imaging of function and form,” J. Appl. Phys. 105(10), 102009 (2009).

S. J. Lee and G. B. Kim, “Synchrotron microimaging technique for measuring the velocity fields of real blood flows,” J. Appl. Phys. 97(6), 064701 (2005).

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