Theoretical consideration for xray phase contrast mammography by
Theoretical consideration for x-ray phase contrast mammography by Thomson Source A. Cedola IFN- CNR Rome S. Lagomarsino I. Bukreeva IFN- CNR Rome V. Petrillo C. Maroli INFN- Milano L. De Caro C. Giannini IC- CNR Bari Porto Conte , September 7 -12 , 2008
OUTLOOK Advantages of phase contrast imaging with respect to absorption imaging Experimental techniques for PC Free space propagation PC technique with Thomson Source: theoretical approach Theoretical and experimental comparison of PC mammography with standard mammography Porto Conte , September 7 -12 , 2008
OUTLOOK Advantages of phase contrast imaging with respect to absorption imaging Experimental techniques for PC Free space propagation PC technique with Thomson Source: theoretical considerations Theoretical and experimental comparison of PC mammography with standard mammography Porto Conte , September 7 -12 , 2008
Sample transmission detection Absorption coefficient mapping Porto Conte , September 7 -12 , 2008 Wave front modification Phase contrast detection
Requests for medical imaging • Request: low absorbed dose Increase energy Absorption contrast Increase energy Phase contrast decreases more slowly • Request: Improve sensibility Absorption contrast is too low for: Light materials Details with similar attenuation Porto Conte , September 7 -12 , 2008 Phase contrast Higher sensitivity Higher resolution
n=1 -d+ib Porto Conte , September 7 -12 , 2008
OUTLOOK Advantages of phase contrast imaging with respect to absorption imaging Experimental techniques for PC Free space propagation PC technique with Thomson Source: theoretical considerations Theoretical and experimental comparison of PC mammography with standard mammography Porto Conte , September 7 -12 , 2008
Porto Conte , September 7 -12 , 2008
Drift space turns phase distortions into interference fringes The technique makes use of Fresnel diffraction Porto Conte , September 7 -12 , 2008 Image loses resemblance with realspace object
OUTLOOK Advantages of phase contrast imaging with respect to absorption imaging Experimental techniques for PC Free space propagation PC technique with Thomson Source: theoretical considerations Theoretical and experimental comparison of PC mammography with standard mammography Porto Conte , September 7 -12 , 2008
Refractive index: n=1 -d+ib eik. Dz =ei(2 / ) n Dz Dz Ainc(x, y) T(x, y) Porto Conte , September 7 -12 , 2008 Ao(x, y)= Ainc(x, y) T(x, y)
In the thin-object approximation: T(x, y) =T 0(x, y) eij(x, y) Amplitude Porto Conte , September 7 -12 , 2008 Phase
R 1 R 2 D= Ainc(x, y) T(x, y) Ao(x, y) R 1 R 2 R 1+R 2 AD(x, y) AD= T P= A. F. T (FT(T)*FT(P)) P(x, y)=(i/l. D)exp(-ip(x 2+y 2)/l. D) Icoh(x, y)= │A│2 Porto Conte , September 7 -12 , 2008
SPATIAL RESOLUTION: LIMIT IMPOSED BY DETECTOR Detector resolution cannot be better than twice the pixel size rdet>2 dpix SPATIAL RESOLUTION: LIMIT IMPOSED BY SOURCE (PARTIAL COHERENCE) S R 1 R 2 Blurring due to beam size: rsource>SR 2 / R 1
• Thin–object approximation The wave equation in parabolic approximation: , where =n-1 and k=2 . transversal diffusion When the transversal diffusion term is negligible with respect to the propagation term 2 ik(∂u/∂z), the wave equation becomes Porto Conte , September 7 -12 , 2008
Limits of validity of the thin-object app. n The approximation is valid when the Fresnel parameter: >>1 a: lateral resolution b: thickness Porto Conte , September 7 -12 , 2008 In mammography: l=0. 5 Ang. a=50 mm b=15 cm f~4000
Ainc(x, y) Thomson Source: AD(x, y) Ainc(x, y) Introduction of amplitude and phase distribution of the source in the calculation to study the coherence at the sample level Porto Conte , September 7 -12 , 2008
Calculation of radiation in the X-rays frequency range in a linear Thomson back–scattering See poster V. Petrillo and C. Maroli The calculation is based on the usual Liénard-Wiechert formulas Longitudinal (top) and transverse (bottom) views of the electron beam used in the present calculations Preliminary results Porto Conte , September 7 -12 , 2008
Phase of the x-component of the complex vector E(w) (top figure) and modulus of E(w) calculated on the object plane at r=1 m the radiation wave length is r = 0. 8 angstrom Preliminary results Porto Conte , September 7 -12 , 2008
Preliminary results Modulus of the E(w) vector (top figure) and phase of (bottom) vs x and y on the object plane. Coherent length about 3 -5 microns Work in progrss……………………… Porto Conte , September 7 -12 , 2008
OUTLOOK Advantages of phase contrast imaging with respect to absorption imaging Experimental techniques for PC Free space propagation PC technique with Thomson. Source: theoretical considerations Theoretical and experimental comparison of PC mammography with standard mammography Porto Conte , September 7 -12 , 2008
First step for validation of theoretical approach : fitting of experimental data by Fresnel propagator Nylon fiber in paraffin medium Experimental data by Pagot et al. Phys. Med. Biol. 50 (2005) 709– 724 Comparison of measured and calculated visibility Porto Conte , September 7 -12 , 2008
Vedge= Imax - Imin Porto Conte , September 7 -12 , 2008 Imax + Imin
Imax abs- Imin abs Imax abs+ Imin abs Porto Conte , September 7 -12 , 2008
18 Ke. V D= 6. 5 0. 6 0. 9 4. 5 0. 008 mm Visibility =0. 12 0. 016 0. 02 0. 088 0. 00 Porto Conte , September 7 -12 , 2008
25 Ke. V D= 4. 5 m D= 6. 5 0. 6 0. 9 0. 008 mm Visibility 0. 049 Visibility 0. 0067 0. 024 =0. 067 0. 00 Porto Conte , September 7 -12 , 2008
Micro-calcifications Why micro-calcifications analyses? clusters of micro-calcifications can occur in areas of early cancer. Porto Conte , September 7 -12 , 2008
Sample model used for simulations Breast: 50%adipose 50%soft m-calcification (Weddelite) Breast Porto Conte , September 7 -12 , 2008 4 cm
Input parameters compatible with Thomson Source: R 1=10 m Ws=16 m Pixel (FWHM)=30 m
25 Ke. V m-calcification, 1 mm in 4. 2 cm of breast D= mm D= D= 0. 9 2 D= 0. 6 D= D= 40 04. 5 m mm Porto Conte , September 7 -12 , 2008
25 Ke. V m-calcification, 1 mm in 4. 2 cm of breast Porto Conte , September 7 -12 , 2008
25 Ke. V m-calcification, in 4. 2 cm of breast Porto Conte , September 7 -12 , 2008 D=2 m
25 Ke. V m-calcification, in 4. 2 cm of breast Porto Conte , September 7 -12 , 2008 D=2 m
25 Kev micro-calcification of 1 mm A brilliant ring surrounding a detail highlights it Porto Conte , September 7 -12 , 2008
Porto Conte , September 7 -12 , 2008
See talk by RIGON
50 Ke. V Decreased absorbed dose!!!! Porto Conte , September 7 -12 , 2008
50 Ke. V m-calcification, 1 mm in 4. 2 cm of breast For absorption Porto Conte , September 7 -12 , 2008
50 Ke. V m-calcification, in 4. 2 cm of breast D=2 m Porto Conte , September 7 -12 , 2008
CONCLUSIONS Phase contrast for medical imaging Theoretical approach for free space propagation with Thomson source Results for phase contrast mammography: Clear advantages for small details (m-calcification, early stage tumor) Highlighting ring which increases visibility 50 Kev: Gain in absorbed dose but small contrast with respect to 25 Ke. V Porto Conte , September 7 -12 , 2008
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