Abstract

This paper presents analytical approach to modeling of a full planar and volumetric acquisition system with image reconstructions originated from partial illumination x-ray phase-contrast imaging at a human scale using graphics processor units. The model is based on x-ray tracing and wave optics methods to develop a numerical framework for predicting the performance of a preclinical phase-contrast imaging system of a human-scaled phantom. In this study, experimental images of simple numerical phantoms and high resolution anthropomorphic phantoms of head and thorax based on non-uniform rational b-spline shapes (NURBS) prove the correctness of the model. Presented results can be used to simulate the performance of partial illumination x-ray phase-contrast imaging system on various preclinical applications.

© 2015 Optical Society of America

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2014 (1)

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

2013 (3)

E. Bergback Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McX-trace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A. Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40(2), 021909 (2013).
[Crossref] [PubMed]

2011 (1)

2010 (4)

P. R. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type x-ray phase contrast imaging systems,” Opt. Express 18(5), 4103–4117 (2010).
[Crossref] [PubMed]

P. R. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express 18(19), 19681–19692 (2010).
[Crossref] [PubMed]

J. Zambelli, N. Bevins, Z. Qi, and G. H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys. 37(6), 2473–2479 (2010).
[Crossref] [PubMed]

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

2008 (4)

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[Crossref] [PubMed]

S. A. Zhou and A. Brahme, “Development of phase-contrast x-ray imaging techniques and potential medical applications,” Phys. Med. 24(3), 129–148 (2008).
[Crossref] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
[Crossref] [PubMed]

I. M. Williams, K. K. Siu, R. Gan, X. He, S. A. Hart, C. B. Styles, and R. A. Lewis, “Towards the clinical application of X-ray phase contrast imaging,” Eur. J. Radiol. 68(3Suppl), S73–S77 (2008).
[Crossref] [PubMed]

2007 (2)

X. Wu and H. Liu, “Clarification of aspects in in-line phase-sensitive x-ray imaging,” Med. Phys. 34(2), 737–743 (2007).
[Crossref] [PubMed]

A. Olivo and R. Speller, “Modelling of a novel x-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol. 52(22), 6555–6573 (2007).
[Crossref] [PubMed]

2006 (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2005 (2)

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the Optimization of Experimental Parameters for X-ray In-Line Phase-Contrast Imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

2004 (2)

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49(16), 3573–3583 (2004).
[Crossref] [PubMed]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D. 37(19), 2746–2750 (2004).
[Crossref]

2003 (1)

W. Leitenberger, H. Wendrock, H. Bischoff, T. Panzner, U. Pietsch, J. Grenzer, and A. Pucher, “Double pinhole diffraction of white synchrotron radiation,” Physica B 336(1–2), 63–67 (2003).
[Crossref]

2002 (1)

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: simple theory and practical applications,” J. Phys. D. 35(13), R105–R120 (2002).
[Crossref]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[Crossref]

1998 (3)

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast X-ray medical imaging,” Phys. Med. Biol. 43(10), 2845–2852 (1998).
[Crossref] [PubMed]

M. Bhat, J. Pattison, G. Bibbo, and M. Caon, “Diagnostic x-ray spectra: a comparison of spectra generated by different computational methods with a measured spectrum,” Med. Phys. 25(1), 114–120 (1998).
[Crossref] [PubMed]

E. Acosta, X. Liovet, E. Coleoni, J. A. Riveros, and F. Salvat, “Monte Carlo simulation of x-ray emission by kilovolt electron bombardment,” J. Appl. Phys. 83(11), 6038–6049 (1998).
[Crossref]

1997 (2)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

P. Cloetens, J. P. Guigay, C. De Martino, J. Baruchel, and M. Schlenker, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22(14), 1059–1061 (1997).
[Crossref] [PubMed]

1996 (3)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X-rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[Crossref]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

1995 (2)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 352(3), 622–628 (1995).
[Crossref]

1994 (1)

A. R. Hare and G. R. Morrison, “Near-field soft X-Ray diffraction modeled by the multislice method,” J. Mod. Opt. 41(1), 31–48 (1994).
[Crossref]

1993 (1)

B. Henke, E. Gullikson, and J. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at e = 50-30,000 ev, z = 1-92,” Atom. Data Nucl. Data 54(2), 181–342 (1993).
[Crossref]

1982 (1)

L. R. M. Morin, “Molecular form factors and photon coherent scattering cross sections of water,” J. Phys. Chem. Ref. Data 11(4), 1091–1098 (1982).
[Crossref]

1981 (1)

1979 (2)

J. H. Hubbell and I. Øverbø, “Relativistic atomic form factors and photon coherent scattering cross sections,” J. Phys. Chem. Ref. Data 8(1), 69–105 (1979).
[Crossref]

M. O. Krause and J. H. Oliver, “Natural widths of atomic K and L levels, Ka X-Ray lines and several KLL auger lines,” J. Phys. Chem. Ref. Data. 8(2), 329–338 (1979).

1978 (1)

1977 (1)

K. Ishizuka and N. Uyeda, “A new theoretical and practical approach to the multislice method,” Acta Crystallogr. A 33(5), 740–749 (1977).
[Crossref]

1975 (1)

E. C. McCullough, “Photon attenuation in computed tomography,” Med. Phys. 2(6), 307–320 (1975).
[Crossref] [PubMed]

1971 (2)

A. H. Narten and H. A. Levy, “Liquid water: Molecular correlation functions from X-ray diffraction,” J. Chem. Phys. 55(5), 2263–2269 (1971).
[Crossref]

G. R. Grinton and J. M. Cowley, “Phase and amplitude contrast in electron micrographs of biological materials,” Optik (Stuttg.) 34, 221 (1971).

1967 (1)

J. A. Bearden, “X-Ray Wavelength,” Rev. Mod. Phys. 39(1), 78–124 (1967).
[Crossref]

1957 (1)

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. i. A new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
[Crossref]

1926 (1)

1923 (1)

H. A. Kramers, “On the theory of X-ray absorption and of the continuous X-ray spectrum,” Philos. Mag. 46(275), 836–871 (1923).
[Crossref]

Acosta, E.

E. Acosta, X. Liovet, E. Coleoni, J. A. Riveros, and F. Salvat, “Monte Carlo simulation of x-ray emission by kilovolt electron bombardment,” J. Appl. Phys. 83(11), 6038–6049 (1998).
[Crossref]

Arfelli, F.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast X-ray medical imaging,” Phys. Med. Biol. 43(10), 2845–2852 (1998).
[Crossref] [PubMed]

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T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
[Crossref] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the Optimization of Experimental Parameters for X-ray In-Line Phase-Contrast Imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Sturgeon, G.

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

Styles, C. B.

I. M. Williams, K. K. Siu, R. Gan, X. He, S. A. Hart, C. B. Styles, and R. A. Lewis, “Towards the clinical application of X-ray phase contrast imaging,” Eur. J. Radiol. 68(3Suppl), S73–S77 (2008).
[Crossref] [PubMed]

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A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

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[Crossref]

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W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
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T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
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[Crossref] [PubMed]

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D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
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J. Zambelli, N. Bevins, Z. Qi, and G. H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys. 37(6), 2473–2479 (2010).
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D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A. Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40(2), 021909 (2013).
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Figures (11)

Fig. 1
Fig. 1 Schematic illustration of the partial illumination x-ray phase-contrast imaging setup with the edge illumination concept.
Fig. 2
Fig. 2 Illustration of the partial pixel illumination condition, where a set of pre-sample slits creates an aperture and subdivides primary beam into small beamlets.
Fig. 3
Fig. 3 (a) Axial cross section of numerical sphere phantom with inserts imitating different types of tissue in water: 1-lung, 2-adipose, 3-muscles, 4-bones, 5-reference insert: dense bone, (b) 3D model of sphere phantom, and (c) numerical wire phantom with inhomogeneities.
Fig. 4
Fig. 4 Illustration of the 4D XCAT 2 anthropomorphic phantom with inhomogeneities generated throughout changes in attenuation coefficients in the volume of organs of interest recorded within binary reproduction: (a) axial scan with simulated 10 mm diameter spherical lesion (arrow), (b) 4D XCAT 2 overview of thorax and head region, and (c) sagittal cross section with 10 mm lesion (arrow).
Fig. 5
Fig. 5 Plots of simulated x-ray spectra for 80 kVp and 100 kVp tube voltage for pure tungsten target with 1.2 mm Al beam hardening filter.
Fig. 6
Fig. 6 Diffraction patterns using a coherent source (a) and partially coherent source (b) in the simulation of Leitenberger et al. experiment.
Fig. 7
Fig. 7 Simulation images of sphere and wire numerical phantoms for 40 keV photons. For all simulations the number of tracked particles was 1.5 × 109, the computational time per particle was ~0.5 × 10−6 s. Settings of pixel fraction illumination used to image both phantoms as a post-sample mask offset: 0% - (a, d); 66% - (b, e); 100% - (c, f) and percentage of attenuation image: 100% - (a, d); 60% - (b, e); 0.1% - (c, f).
Fig. 8
Fig. 8 A series of plot profiles extracted from the reconstructed maps of the wires formed as the images shown in Fig. 7(a)-7(c) corresponding to a percentage of the attenuation image: 100% - (a), 60% - (b), 0.1% - (c).
Fig. 9
Fig. 9 Images of head region of 4D XCAT 2 phantom, simulated with 60 keV x-ray source. Reconstructions in sagittal (upper row) and axial (bottom row) directions presented as phase image (a, e), attenuation (b, f), mixed phase and attenuation contrast (c, g) and dark field (d, h) corresponding to a pixel-illuminated fractions of 50% - (a, e, c, g); 100% - (b, f); 0% - (d, h). Lesion of 10 mm diameter is clearly visible (arrow) on (c) and (g) as an irregular structure in the occipital part of the brain.
Fig. 10
Fig. 10 Images of thorax region of 4D XCAT 2 phantom, simulated with 60 keV x-ray source. Reconstructions in antero–posterior (upper row) and axial (bottom row) directions presented as phase projections (a, e), attenuation (b, f), mixed phase and attenuation contrast (c, g) and dark field (d, h) corresponding to a pixel-illuminated fractions of 50% - (a, e, c, g); 100% - (b, f); 0% - (d, h).
Fig. 11
Fig. 11 Mixed phase and attenuation contrast reconstructions on sagittal cross sections of 4D XCAT 2 human scale phantom (head part) imaged at: (a) 40 keV, which served as an extreme case lower limit for hard x-ray energy, (b) 60 keV energy of conventional x-ray tube source, (c) 100 keV as a maximum hard x-ray energy. Definitely more details can be observed at (a), but by using higher x-ray energy, the dose to “body” is significantly lower and the differences between structures can still be distinguished with edge enhancement effect.

Tables (1)

Tables Icon

Table 1 Comparison between measured (Fewell 1981, Bhat 1998), calculated (IPEM report 78) and simulated (presented model) HVLs and mean spectrum energy for spectra produced using 12° target angle and different tube voltages. The percentage difference between IPEM and our model estimates is also shown.

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

I=ΦSΔΩΔλ.
w 0 = Φ(λ) N SΔΩΔλ,
sin θ 1 sin θ 2 = 1 δ 1 1 δ 2 ,
δ= n a r e λ 2 2π f 1 1 (ω)
β= n a r e λ 2 2π f 2 1 (ω)
n(ω)=1 n a r e λ 2 2π ( f 1 1 i f 2 1 ).
f 1 1 (ω)=Z 2 π P C 0 u f 2 1 (u)z u 2 ω 2 du
f 2 1 (ω)= 2ω π P C 0 f 1 1 (u)Z u 2 ω 2 du
δ= r e λ 2 2π E 2 ρ e .
μ=τ+ μ incoh + μ coh .
μ= ρ e σ tot = ρ e ( σ τ + σ incoh + σ coh ).
F at W (x)= 2 [ F H (x) ] 2 + [ F O (x) ] 2 ,
σ w s,mol = θ=0 π d σ T (θ) [ F mol W (x) ] 2 ,
σ w s,liq = θ=0 π d σ T (θ) [ F liq W (x) ] 2 ,
f(l)=exp(l( μ s + μ a )),
P( l 1 )dl= μ s f( l 1 )dl,
P( l 1 ,Ω)dldΩ= μ s f( l 1 )f( l 2 )g(Ω)dΩdl,
Q(x,y)=exp(iknΔz),
φ(x,y)=k 0 Δz δ(x,y,z)dz,
μ(x,y)=k 0 Δz β(x,y,z)dz .
Q(x,y)=exp[μ(x,y)iφ(x,y)].
P(x,y)=exp( ik x 2 + y 2 2Δz ).
P ˜ (u,v)=exp[iπλΔz( u 2 + v 2 )],
ψ N =[ ψ N1 Q N1 ]* P N1,N ,
ψ N ( x N , y N )=A ψ N1 ( x N1 , y N1 )exp{ i π λΔz [ ( x N x N1 ) 2 + ( y N y N1 ) 2 ] }d x N1 d y N1 ,
ψ N = 1 [( ψ N1 Q N1 )( P N1,N )].
I θ,d (x,y) I θ,0 (x,y)exp[ d k 2 φ θ (x,y) ],
ln[ I θ,d (x,y) ]2μ(x,y)d( 2 x 2 + 2 y 2 ) obj δ(x,y,z)dz .
f(x,y,z)2β(x,y,z)+d( 2 x 2 + 2 y 2 + 2 z 2 )δ(x,y,z),
φ θ (x,y)= 2π λ raypath δ(x',y',z')dx'dy'dz' ,
μ θ (x,y)= 4π λ raypath β(x',y',z')dx'dy'dz' ,

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