1. 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

2. 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

3. 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

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

5. 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

6. n=1-d+ib
Porto Conte , September 7-12 , 2008

7. 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

8. Porto Conte , September 7-12 , 2008

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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:

15. 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

16. >>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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

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

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

25. 18 KeV Porto Conte , September 7-12 , 2008 Visibility 0.088 D= 4.5 m

26. 25 KeV Porto Conte , September 7-12 , 2008 Visibility =0.067 D= 6.5 m

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

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

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

30. 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

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

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

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

34. 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

35. Porto Conte , September 7-12 , 2008

36. See talk by RIGON

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

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

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

41. 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