X-ray diagnostics and Computed tomography

1. X-ray diagnostics and Computed tomography

2. 15th century head examination

6. I0 I Projection Imaging with X Rays X-Ray Source Patient Detector

7. Chest X-Ray This frontal chest radiograph demonstrates a dense (radio-opaque) left lung field consistent with a hemothorax in a patient with a gunshot wound to the chest.

8. Data Acquisition System (DAS) Pre-Collimator Post-Collimator Scattering Source Detector Filter Patient

9. Exponential Attenuation of X-ray Ni No m Ni: input intensity of X-ray No: output intensity of X-ray m: linear X-ray attenuation x Ni No    x Attenuatedmore X-rays

10. Ray-Sum of X-ray Attenuation Ni No k x Ray-sum Line integral

11. First Generation One detector Translation-rotation Parallel-beam

12. Second Generation Multiple detectors Translation-rotation Small fan-beam

13. Third Generation Multiple detectors Translation-rotation Large fan-beam

14. Fourth Generation Detector ring Source-rotation Large fan-beam

15. A Little Bit History Nobel prizesRoentgen (1901): Discovery of X-rays Hounsfield & Cormack (1979): Computed tomography

16. Chest X-Ray This frontal chest radiograph demonstrates a dense (radio-opaque)left lung field consistent with a hemothorax in a patient with agunshot wound to the chest. COMPUTED TOMPGRAPHY, CT This CT image demonstrates the large bullae characteristic of patients with Chronic Obstructive Pulmonary Disease (COPD) representing lung destruction

17. CT DETECTORS

18. CT DETECTORS

19. CT DETECTORS

20. (From Siemens) (From Picker) Third & Fourth Generations

21. E-Beam CT Scanner • Speed: 50, 100 ms • Thickness: 1.5, 3, 6, 10 mm • ECG trigger cardiac images (From Imatron)

24. Spiral/Helical/Volumetric CT • Continuous & • Simultaneous • Source rotation • Patient translation • Data acquisition

25. Dual-slice Single-slice Quad-slice 1992 1989 1998 A rapid development

26. I0 I Projection Imaging with X Rays X-Ray Source Patient Detector

29. Image Analysis • Visualization & analysis • 3D, 4D • Networked, PC-based • Image fusion • Computer aided diagnosis • Image-based surgery

30. FUTURE • MONOENERGETIC RADIATION • DUAL ENERGY AROUND THE K-EDGE • ENERGY SENSITIVE PIXELDETECTORS

31. IMAGE RECONSTRUCTION

36. Projection & Sinogram Sinogram:All projections Projection:All ray-sums in a direction  y P(t) t p  x f(x,y) t X-rays Sinogram

37. SINOGRAM CONSTRUCTION

38. Computed Tomography y Computed tomography (CT):Image reconstruction fromprojections t P(t) f(x,y) P(t)  x f(x,y) X-rays

39. Reconstruction Idea =4 2=3 3=2 4=1

40. 6 4 Error 0 0 4 3 3 2 Guess 1 0 0 2 1 3 2 Guess 0 2 4 3 Update a guessbased ondata differences Guess 2 -2 Error 2 1 Algebraic Reconstruction Technique(ART)

41. Fourier Transformation f(x,y) F(u,v) Fourier Transform Image Space Fourier Space

42. y P(t) t F[P(t)]   x f(x,y) X-rays Fourier Slice Theorem v u F(u,v)

43. y v F-1[F(u,v)] x u f(x,y) F(u,v) P(t) From Projections to Image

44. P(t) P’(t) f(x,y) f(x,y) 1) Convolve projections with a filter 2) Backproject filtered projections Filtered Backprojection

45. Example: Projection Projection Projection Sinogram Ideal Image

46. Example: Backprojection Projection

47. Example: Backprojection Sinogram Backprojected Image

48. Example: Filtering Sinogram Filtered Sinogram

49. Example: Filtered Backprojection Filtered Sinogram Reconstructed Image

50. Some examples