1. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 1 Medical Imaging and Pattern Recognition Lecture 7 Computed Tomography Oleh Tretiak

2. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 2 Computer Tomography: How It Works Only one plane is illuminated. Source-subject motion provides added information.

3. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 3 How it Works Original CT Scanner –Head only –One minute scanning time –Two sections –Ten minutes to compute images –Extremely successful!

4. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 4 First CT Scanner

5. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 5 Before and After CT

6. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 6 Contemporary CT

7. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 7 Fan-Beam Computer Tomography

8. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 8 Contemporary Spiral Scanner Configuration: –40 slices per rotation maximum Other options are 32 slices or 16 slices –40 mm axial distance scanned in one rotation –0.4 sec per rotation –60 kW generator

9. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 9 Example: Head Bleeding due to injury Can cause brain injury if not treated Blood between brain and dura, easy to treat

10. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 10 Example: Head FRONTAL CONTUSION WITH SUBARACHNOID HEMORRHAGE

11. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 11 Chest Study Pneumothorax (air between lung and chest) Also note the bilateral lower lobe consolidation of lungs, right being greater than left. There is a chest tube within the right hemithorax.

12. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 12 Abdomen Appendicitis (arrow) Contrast agents in stomach and in blood

13. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 13 Mathematics of Computed Tomography Model for measurements Direct problem Inverse problem Algorithm for computed tomography

14. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 14 Direct Problem Beam with intensity I 0 enters body with varying attenuation Each layer has thickness t

15. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 15 Integral Equation

16. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 16 Radon Transform f(x,y) g(t,  )

17. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 17 Inverse Radon Transform Given: X-ray transmission measurements I 1 (t,  ). Find  (x, y) Given: g(t,  ). Find f(x, y) Method: –(a) convolution –(b) backprojection

18. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 18 Example f(x, y) Lines: g(t,  ), same for all  Dots: g 1 (t,  ), after convolution

19. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 19 Backprojection One, two, and four angles of backprojection

20. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 20 More Backprojection 8, 15, and 30 angle backprojection

21. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 21 Pictures f(x, y) g(t,  Theta horizontal

22. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 22 Backprojection at 4, 16, and 100 angles

23. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 23 History 1917, Joachim Radon –Solved formal inverse problem. Interest in theory of integration and geometry 1958, Simeon Tetelbaum of KPI publishes a paper about X-ray tomography. –Publishes valid inverse problem solution.

24. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 24 More History 1963 John Cormack publishes theoretical and experimental results. –Experiment with cylindrical objects 1972 Godfrey Hounsfield develops CT scanner 1979 Hounsfield and Cormack receive Nobel prize in Medicine

25. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 25 Example of Contrast 12 bit image, full contrast range. Window for low densities

26. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 26 More Contrast Operations Window for high densities

27. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 27 3-D Images Spiral scan procedures produce sets of sectional images suitable for 3-D imaging Resectioning: Compute new section plane Projection: Compute sums along rays Rendering: Segment image and show surface.

28. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 28 Bronchoscopy PathView

29. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 29 Colonoscopy PathView

30. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 30 Medical Practice In the fall of 2003 Siemens became the first CT supplier ever to receive clearance from the FDA for a computer-aided technique of identifying nodules, that is, possible tumors, in the lung. CT is also used for the diagnosis of colon cancer: A virtual flight through the human colon can detect even the smallest polyps. If these are removed in time, an outbreak of colon cancer can very probably be prevented.

31. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 31 Comparison Left: A polyp seen with optical endoscopy. Right: View in virtual endoscopy.

32. MIPR Lecture 7 Copyright Oleh Tretiak, 2004 32 Summary Computer tomography became successful because it showed soft tissue differences that could not be seen on X-rays. Evolution of high-speed (spiral scan) machines came about through improvements in X-ray detectors This has led to 3-D imaging methods –Surgery planning –Virtual endoscopy