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 Wave front modification Absorption coefficient mapping Phase contrast detection Porto Conte , September 7-12 , 2008

Requests for medical imaging Request: low absorbed dose Increase energy Increase energy Phase contrast decreases more slowly Absorption contrast Request: Improve sensibility Absorption contrast is too low for: Phase contrast Light materials Details with similar attenuation Higher sensitivity Higher resolution Porto Conte , September 7-12 , 2008

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 Image loses resemblance with real-space object 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

Ao(x,y)= Ainc(x,y) T(x,y) Refractive index: n=1-d+ib eikDz =ei(2p/l) n Dz Dz Ainc(x,y) T(x,y) Ao(x,y)= Ainc(x,y) T(x,y) Porto Conte , September 7-12 , 2008

T(x,y) =T0(x,y) eij(x,y) Phase Amplitude In the thin-object approximation: T(x,y) =T0(x,y) eij(x,y) Phase Amplitude Porto Conte , September 7-12 , 2008

AD= TP= A.F.T (FT(T)*FT(P)) R1 R2 R1R2 R1+R2 D= Ainc(x,y) T(x,y) Ao(x,y) AD(x,y) AD= TP= A.F.T (FT(T)*FT(P)) P(x,y)=(i/lD)exp(-ip(x2+y2)/lD) Icoh(x,y)= │A│2 Porto Conte , September 7-12 , 2008

rdet>2dpix rsource>SR2 / R1 SPATIAL RESOLUTION: LIMIT IMPOSED BY DETECTOR Detector resolution cannot be better than twice the pixel size rdet>2dpix SPATIAL RESOLUTION: LIMIT IMPOSED BY SOURCE (PARTIAL COHERENCE) S R1 R2 rsource>SR2 / R1 Blurring due to beam size:

Thin–object approximation The wave equation in parabolic approximation: , transversal diffusion where =n-1 and k=2. When the transversal diffusion term is negligible with respect to the propagation term 2ik(∂u/∂z), the wave equation becomes Porto Conte , September 7-12 , 2008

>>1 Limits of validity of the thin-object app. The approximation is valid when the Fresnel parameter: >>1 In mammography: l=0.5Ang. a=50mm b=15 cm f~4000 a:lateral resolution b: thickness Porto Conte , September 7-12 , 2008

Ainc(x,y) Ainc(x,y) AD(x,y) Thomson Source: 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

x-component of the complex vector E(w) (top figure) and modulus 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=1m the radiation wave length is lr = 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 ThomsonSource: theoretical considerations Theoretical and experimental comparison of PC mammography with standard mammography Porto Conte , September 7-12 , 2008

Comparison of measured and calculated visibility First step for validation of the 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

Imax - Imin Vedge= Imax + Imin Porto Conte , September 7-12 , 2008

Imax abs- Imin abs Imax abs+ Imin abs Porto Conte , September 7-12 , 2008

18 KeV Porto Conte , September 7-12 , 2008 Visibility 0.088 D= 4.5 m

25 KeV Porto Conte , September 7-12 , 2008 Visibility =0.067 D= 6.5 m

Micro-calcifications Why micro-calcifications analyses? clusters of micro-calcifications can occur in areas of early cancer. Porto Conte , September 7-12 , 2008

Breast Sample model used for simulations 4 cm 50%adipose 50%soft m-calcification (Weddelite) Breast 4 cm Porto Conte , September 7-12 , 2008

R1=10m Ws=16m Pixel (FWHM)=30 m Input parameters compatible with Thomson Source: R1=10m Ws=16m Pixel (FWHM)=30 m

m-calcification, 1mm in 4.2 cm of breast 25 KeV D= 40 m D= 0 m D= 0.9 m D= 0.6 m D= 4.5 m D= 2 m Porto Conte , September 7-12 , 2008

m-calcification, 1mm in 4.2 cm of breast 25 KeV Porto Conte , September 7-12 , 2008

m-calcification, in 4.2 cm of breast 25 KeV D=2m Porto Conte , September 7-12 , 2008

m-calcification, in 4.2 cm of breast 25 KeV D=2m Porto Conte , September 7-12 , 2008

A brilliant ring surrounding a detail highlights it 25Kev micro-calcification of 1mm A brilliant ring surrounding a detail highlights it Porto Conte , September 7-12 , 2008

Porto Conte , September 7-12 , 2008

See talk by RIGON

Decreased absorbed dose!!!! 50 KeV Decreased absorbed dose!!!! Porto Conte , September 7-12 , 2008

m-calcification, 1mm in 4.2 cm of breast 50 KeV For absorption Porto Conte , September 7-12 , 2008

m-calcification, in 4.2 cm of breast 50 KeV D=2m 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 50Kev: Gain in absorbed dose but small contrast with respect to 25 KeV Porto Conte , September 7-12 , 2008