Abstract

X-ray velocimetry (XV) has shown promise for investigations into various dynamic biological systems, including the motion of lungs and the flow of blood. Prior research in the field of XV has highlighted the need for both high spatial resolution to resolve features for tracking, and temporal resolution for accurate velocity measurement. In X-ray imaging systems, enhancement of spatial and temporal resolution requires a small focal spot size and high power output respectively, increasing anode power density requirements. In this paper, we present a multi-source XV regime whereby simultaneously illuminating a sample with multiple sources of small focal spot size, overall illumination can be increased whilst maintaining minimal source blurring without increasing power density requirements. Through a series of simulations, we demonstrate the capability for multi-source systems under various practical constraints, such as focal spot size and power density, to provide increased accuracy compared to single source systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (2)

H. Park, E. Yeom, and S. J. Lee, “X-ray PIV measurement of blood flow in deep vessels of a rat: An in vivo feasibility study,” Sci. Rep. 6(1), 19194 (2016).
[Crossref] [PubMed]

R. P. Murrie, D. M. Paganin, A. Fouras, and K. S. Morgan, “Phase Contrast X-Ray Velocimetry of Small Animal Lungs: Optimising Imaging Rates,” Biomed. Opt. Express 7(1), 79–92 (2016).
[Crossref] [PubMed]

2014 (1)

B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

2012 (4)

I. Ng, D. M. Paganin, and A. Fouras, “Optimisation of in-line phase contrast particl image velocimetry using a laboratory x-ray source,” J. Appl. Phys. 112, 074701 (2012).

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

S. Dubsky, S. B. Hooper, K. K. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9(74), 2213–2224 (2012).
[Crossref] [PubMed]

R. A. Jamison, K. K. Siu, S. Dubsky, J. A. Armitage, and A. Fouras, “X-ray Velocimetry within the ex vivo carotid artery,” J. Synchrotron Radiat. 19(6), 1050–1055 (2012).
[Crossref] [PubMed]

2011 (2)

R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
[Crossref] [PubMed]

S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

2009 (2)

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

2008 (1)

2002 (1)

Y. Suzuki, N. Yagi, and K. Uesugi, “X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object,” J. Synchrotron Radiat. 9(3), 160–165 (2002).
[Crossref] [PubMed]

1998 (1)

A. Fouras and J. Soria, “Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data,” Exp. Fluids 25(5-6), 409–430 (1998).
[Crossref]

1979 (1)

D. L. Davies and D. W. Bouldin, “A Cluster Separation Measure,” IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 224–227 (1979).
[Crossref] [PubMed]

Allison, B. J.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

Armitage, J. A.

R. A. Jamison, K. K. Siu, S. Dubsky, J. A. Armitage, and A. Fouras, “X-ray Velocimetry within the ex vivo carotid artery,” J. Synchrotron Radiat. 19(6), 1050–1055 (2012).
[Crossref] [PubMed]

Beckman, M.

B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

Bouldin, D. W.

D. L. Davies and D. W. Bouldin, “A Cluster Separation Measure,” IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 224–227 (1979).
[Crossref] [PubMed]

Calderon, X.

S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

Calderon-Colon, X.

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

Chang, S.

S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

Cheng, Y.

B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

Davies, D. L.

D. L. Davies and D. W. Bouldin, “A Cluster Separation Measure,” IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 224–227 (1979).
[Crossref] [PubMed]

Dubsky, S.

R. A. Jamison, K. K. Siu, S. Dubsky, J. A. Armitage, and A. Fouras, “X-ray Velocimetry within the ex vivo carotid artery,” J. Synchrotron Radiat. 19(6), 1050–1055 (2012).
[Crossref] [PubMed]

S. Dubsky, S. B. Hooper, K. K. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9(74), 2213–2224 (2012).
[Crossref] [PubMed]

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

Fouras, A.

R. P. Murrie, D. M. Paganin, A. Fouras, and K. S. Morgan, “Phase Contrast X-Ray Velocimetry of Small Animal Lungs: Optimising Imaging Rates,” Biomed. Opt. Express 7(1), 79–92 (2016).
[Crossref] [PubMed]

I. Ng, D. M. Paganin, and A. Fouras, “Optimisation of in-line phase contrast particl image velocimetry using a laboratory x-ray source,” J. Appl. Phys. 112, 074701 (2012).

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

R. A. Jamison, K. K. Siu, S. Dubsky, J. A. Armitage, and A. Fouras, “X-ray Velocimetry within the ex vivo carotid artery,” J. Synchrotron Radiat. 19(6), 1050–1055 (2012).
[Crossref] [PubMed]

S. Dubsky, S. B. Hooper, K. K. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9(74), 2213–2224 (2012).
[Crossref] [PubMed]

R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

A. Fouras and J. Soria, “Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data,” Exp. Fluids 25(5-6), 409–430 (1998).
[Crossref]

Gonzales, B.

B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

Gureyev, T. E.

Hooper, S.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

Hooper, S. B.

S. Dubsky, S. B. Hooper, K. K. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9(74), 2213–2224 (2012).
[Crossref] [PubMed]

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

Hourigan, K.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

Jamison, R. A.

R. A. Jamison, K. K. Siu, S. Dubsky, J. A. Armitage, and A. Fouras, “X-ray Velocimetry within the ex vivo carotid artery,” J. Synchrotron Radiat. 19(6), 1050–1055 (2012).
[Crossref] [PubMed]

R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
[Crossref] [PubMed]

Kitchen, M. J.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

Lalush, D. S.

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

Lee, S. J.

H. Park, E. Yeom, and S. J. Lee, “X-ray PIV measurement of blood flow in deep vessels of a rat: An in vivo feasibility study,” Sci. Rep. 6(1), 19194 (2016).
[Crossref] [PubMed]

Lewis, R. A.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

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(102009), 1–14 (2009).

Lu, J.

B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

Miller, P. R.

Morgan, K. S.

Murrie, R. P.

Nesterets, Y. I.

Ng, I.

I. Ng, D. M. Paganin, and A. Fouras, “Optimisation of in-line phase contrast particl image velocimetry using a laboratory x-ray source,” J. Appl. Phys. 112, 074701 (2012).

Nguyen, J.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

Paganin, D. M.

R. P. Murrie, D. M. Paganin, A. Fouras, and K. S. Morgan, “Phase Contrast X-Ray Velocimetry of Small Animal Lungs: Optimising Imaging Rates,” Biomed. Opt. Express 7(1), 79–92 (2016).
[Crossref] [PubMed]

I. Ng, D. M. Paganin, and A. Fouras, “Optimisation of in-line phase contrast particl image velocimetry using a laboratory x-ray source,” J. Appl. Phys. 112, 074701 (2012).

Park, H.

H. Park, E. Yeom, and S. J. Lee, “X-ray PIV measurement of blood flow in deep vessels of a rat: An in vivo feasibility study,” Sci. Rep. 6(1), 19194 (2016).
[Crossref] [PubMed]

Peng, R.

S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

Phan, T.

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

Pogany, A.

Qian, X.

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

Rajaram, R.

X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
[Crossref] [PubMed]

Schreiber, E. C.

S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

Siu, K. K.

R. A. Jamison, K. K. Siu, S. Dubsky, J. A. Armitage, and A. Fouras, “X-ray Velocimetry within the ex vivo carotid artery,” J. Synchrotron Radiat. 19(6), 1050–1055 (2012).
[Crossref] [PubMed]

S. Dubsky, S. B. Hooper, K. K. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9(74), 2213–2224 (2012).
[Crossref] [PubMed]

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
[Crossref] [PubMed]

R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
[Crossref] [PubMed]

Soria, J.

A. Fouras and J. Soria, “Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data,” Exp. Fluids 25(5-6), 409–430 (1998).
[Crossref]

Spronk, D.

B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

Stevenson, A. W.

Suzuki, Y.

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S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

Wilkins, S. W.

Yagi, N.

Y. Suzuki, N. Yagi, and K. Uesugi, “X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object,” J. Synchrotron Radiat. 9(3), 160–165 (2002).
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X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
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Yeom, E.

H. Park, E. Yeom, and S. J. Lee, “X-ray PIV measurement of blood flow in deep vessels of a rat: An in vivo feasibility study,” Sci. Rep. 6(1), 19194 (2016).
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B. Gonzales, D. Spronk, Y. Cheng, A. W. Tucker, M. Beckman, O. Zhou, and J. Lu, “Rectangular Fixed-Gantry CT Prototype: Combining CNT X-Ray Sources and Accelerated Compressed Sensing-Based Reconstruction,” IEEE Access 2, 971–981 (2014).
[Crossref]

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X. Qian, R. Rajaram, X. Calderon-Colon, G. Yang, T. Phan, D. S. Lalush, J. Lu, and O. Zhou, “Design and characterization of a spatially distributed multibeam field emission x-ray source for stationary digital breast tomosynthesis,” Med. Phys. 36(10), 4389–4399 (2009).
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Ann. Biomed. Eng. (2)

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. Siu, R. A. Lewis, M. J. Wallace, S. B. Hooper, M. Wallace, and S. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40(5), 1160–1169 (2012).
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R. A. Jamison, S. Dubsky, K. K. Siu, K. Hourigan, and A. Fouras, “X-ray Velocimetry and haemodynamic forces within a stenosed femoral model at physiological flow rates,” Ann. Biomed. Eng. 39(6), 1643–1653 (2011).
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S. Wang, X. Calderon, R. Peng, E. C. Schreiber, O. Zhou, and S. Chang, “A carbon nanotube field emission multi-pixel x-ray array source for microradiotherapy application,” App. Phys. Lett. 98, 213701 (2011)

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Sci. Rep. (1)

H. Park, E. Yeom, and S. J. Lee, “X-ray PIV measurement of blood flow in deep vessels of a rat: An in vivo feasibility study,” Sci. Rep. 6(1), 19194 (2016).
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Figures (10)

Fig. 1
Fig. 1 Visualization of various source technologies. Left: A small spot size with a suitably high power density produces a sharp image. Center: As power density decreases, a source’s spot size may be increased to counteract the loss of brightness, at the cost of blurring. Right: An array source maintains the sharpness of a small spot size, whilst generating multiple images of the same object.
Fig. 2
Fig. 2 An example of the XV process. Two images at two different time points are taken, and the cross-correlation of each window is calculated. The peak of this cross-correlation determines the displacement, and hence velocity, of the feature identified in each window.
Fig. 3
Fig. 3 An example of the system simulated in this paper. Each of the variables in this system, including all source and detector properties, are digitally reproduced in order to provide simulations of the highest possible accuracy.
Fig. 4
Fig. 4 Example images of a projection of a single particle by a multi-source system (right) consisting of 9 5μm sources, and the equivalent single source system (left) consisting of a 15μm source. The resolution on these images has been enhanced by a factor of 10, in order to allow for easier visual identification of differences by the reader, such as sharpness and constructive/destructive interference. In particular, the loss of phase contrast rings as spot size increases can be clearly observed, owing to an increase in penumbral blur.
Fig. 5
Fig. 5 Contrast Ratio vs. Cluster Coefficient for an inter-source separation of 20 μm (rp/10) at two different particle seeding densities. In the higher seeding density, individual particles are indistinguishable from one another, and a speckle regime is present. This is in contrast to the lower seeding density, where individual particles can still be identified. For both data sets, the coefficient of determination, r2 > 0.95.
Fig. 6
Fig. 6 Contrast Ratio vs. SD PIV Error. Three main modes can be observed in the data presented. For small source separations, there is a strong correlation between contrast ratio (and hence cluster coefficient) and PIV Error. As this source separation increases, the range of contrast ratios decreases, relating to the inability to efficiently cluster sources. Finally, at large separations, there is a shift in regime when clustering becomes impossible, and the relationship found in smaller source separations no longer holds.
Fig. 7
Fig. 7 Source size & exposure time vs. Mean and SD PIV error for a fixed power density single source system with a base focal spot size of 5 μm. An optimum system for the given power density is identified as having a focal spot size of 7.07 μm exposing for 18 ms, with an RMS error of 0.267 px. Regions with an SD error of 2.5 px or greater, or a mean error of 1.5 px or greater, have been capped at 2.5 px and 1.5 px respectively for visibility.
Fig. 8
Fig. 8 Number of sources & exposure time vs. Mean and SD PIV error for a fixed power density multi-source system with a focal spot size of 5 μm and source separation of 20 μm. Sources are configured such as to maximize the clustering coefficient. An optimum system for the given power density is identified as having 10 sources exposing for 7 ms, with an RMS error of 0.191 px. Regions with an error of 1 px or greater have been capped at 1 px for visibility.
Fig. 9
Fig. 9 Multi-source SD error vs. increasing number of sources, and single source SD error vs. increasing spot size, for a given fixed power density. The scale for each plot has been converted into photon/s, for easier comparison. These plots, from top to bottom, represent fixed power densities of 3000 kW/mm2, 500 kW/mm2, and 125 kW/mm2, respectively. SD error has been limited to 10 px, in order to improve visibility. The legend is consistent across all plots.
Fig. 10
Fig. 10 Comparison of SD error for 125 kW/mm2, 500 kW/mm2, and 3000 kW/mm2. The percentage improvement here represents the reduction in SD error achieved by using the optimum multi-source system as opposed to the optimum single source system, and hence a negative value indicates that the optimal multi-source system results in higher error than the optimum single source system. SD error has been limited to 1 px for visibility. The legend is consistent across all plots.

Equations (3)

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d=2M r p cos( θ ), where 2θsin( 2θ )=nπ, 0n1
d s = 2M r p cos( θ ) M1
C= 1 i=1 N k i * i=1 N j=1 k i 1 d ij , where d ij = | x i x j | 2 , k i =number of sources s.t. d ij 2M r p cos(θ) M1 , and 2θsin(2θ)=nπ

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