1. BMI2 SS08 – Class 7 “functional MRI” Slide 1 Biomedical Imaging 2 Class 7 – Functional Magnetic Resonance Imaging (fMRI) Diffusion-Weighted Imaging (DWI) Diffusion Tensor Imaging (DTI) Blood Oxygen-Level Dependent (BOLD) fMRI 03/04/08

2. BMI2 SS08 – Class 7 “functional MRI” Slide 2 2D FT pulse sequence (spin warp) Most commonly employed pulse sequence

3. BMI2 SS08 – Class 7 “functional MRI” Slide 3 Radiation ↔ Rotating Magnetic Field I N S B0B0 Static magnetic field Sinusoidal EM field Imagine that we replace the EM field with… y x z

4. BMI2 SS08 – Class 7 “functional MRI” Slide 4 S S Radiation ↔ Rotating Magnetic Field II N S B0B0 …two more magnets, whose fields are  B 0, that rotate, in opposite directions, at the Larmor frequency N N

5. BMI2 SS08 – Class 7 “functional MRI” Slide 5 Radiation ↔ Rotating Magnetic Field III Simplified bird’s-eye view of counter-rotating magnetic field vectors t = 0 1/(8f 0 ) 1/(4f 0 ) 3/(8f 0 ) 1/(2f 0 ) 5/(8f 0 ) 3/(4f 0 ) 7/(8f 0 ) 1/f 0 So what does resulting B vs. t look like? This time-dependent field is called B 1

6. BMI2 SS08 – Class 7 “functional MRI” Slide 6 Rotating Reference Frame I y x z B0B0 (1-10 T) y x z, z’ y’ x’  Instead of a constant rotation angle , let  = 2  f 0 t =  0 t Original (laboratory) coordinate system Coordinate system rotated about z axis counter-rotating magnetic fields resultant field, sinusoidally varying in x direction x’ = ysin  + xcos  = -ysin  0 t + xcos  0 t y’ = ycos  - xsin  = ycos  0 t + xsin  0 t

7. BMI2 SS08 – Class 7 “functional MRI” Slide 7 Rotating Reference Frame II B0B0 (1-10 T) y x z, z’ y’ x’  Rotating coordinate system, observed from laboratory frame These axes are rotating in the xy plane, with frequency f 0 B0B0 z’ y’ x’ Rotating coordinate system, observed from within itself But what is the magnitude of B 0 in this reference frame? This magnetic field, rotating at 2f 0, can be ignored; its frequency is too high to induce transitions between orientational states of the protons’ magnetic moments This magnetic field, B 1, is fixed in direction and has constant magnitude: ~0.01 T

8. BMI2 SS08 – Class 7 “functional MRI” Slide 8 Spin-Spin Relaxation I What is the T 2 time constant associated with spin-spin interactions? x׳x׳ y׳y׳ z׳z׳ B0B0 M MzMz M tr If there were no spin-spin coupling, the transverse component of M, M tr, would decay to 0 at the same rate as M z returns to its original orientation What are the effects of spin-spin coupling?

9. BMI2 SS08 – Class 7 “functional MRI” Slide 9 Spin-Spin Relaxation II W hat are the effects of spin-spin coupling? Because the magnetic fields at individual 1 H nuclei are not exactly B 0, their Larmor frequencies are not exactly f 0. x׳x׳ y׳y׳ z׳z׳ B0B0 MzMz But the frequency of the rotating reference frame is exactly f 0. So in this frame M appears to separate into many magnetization vectors the precess about z׳. Some of them (f f 0 ) precess clockwise.

10. BMI2 SS08 – Class 7 “functional MRI” Slide 10 fMRI investigation of hemodynamics

11. BMI2 SS08 – Class 7 “functional MRI” Slide 11 Diffusion-Weighted Imaging (DWI)

12. BMI2 SS08 – Class 7 “functional MRI” Slide 12 Diffusion-weighted MRI (DWI) Stronger bipolar gradients → lower tissue velocities detectable Blood flow velocities: ~(0.1 – 10) cm-s -1 Water diffusion velocity: ~200 μm-s -1 Using the same basic strategy as phase-contrast MRA, can image “apparent diffusion coefficient” (ADC) Useful for diagnosing and staging conditions that significantly alter the mobility of water e.g., cerebrovascular accident (“stroke,” apoplexy)

13. BMI2 SS08 – Class 7 “functional MRI” Slide 13 Examples of Diffusion-weighted images

14. BMI2 SS08 – Class 7 “functional MRI” Slide 14 Examples of Diffusion-weighted images

15. BMI2 SS08 – Class 7 “functional MRI” Slide 15 Diffusion Tensor Imaging (DTI)

16. BMI2 SS08 – Class 7 “functional MRI” Slide 16 How Many Bipolar Gradients? 1 2 1 2 MRA

17. BMI2 SS08 – Class 7 “functional MRI” Slide 17 How Many Bipolar Gradients? DWI

18. BMI2 SS08 – Class 7 “functional MRI” Slide 18 DTI Concepts 1 M.E. Shenton et al., http://splweb.bwh.harvard.edu:8000/pages/papers/pubs/yr2002.htm

19. BMI2 SS08 – Class 7 “functional MRI” Slide 19 DTI Concepts 2 Isotropic diffusion limit: For anisotropic diffusion:

20. BMI2 SS08 – Class 7 “functional MRI” Slide 20 Indices of Diffusion Anisotropy Relative anisotropy (RA): Fractional anisotropy: Volume ratio (VR):

21. BMI2 SS08 – Class 7 “functional MRI” Slide 21 Comparison of Anatomical, DWI, DTI D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

22. BMI2 SS08 – Class 7 “functional MRI” Slide 22 Comparison of Anisotropy Indices D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

23. BMI2 SS08 – Class 7 “functional MRI” Slide 23 How Many Bipolar Gradients? DTI D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

24. BMI2 SS08 – Class 7 “functional MRI” Slide 24 Diffusion Tensor Mapping D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

25. BMI2 SS08 – Class 7 “functional MRI” Slide 25 Diffusion Tensor Mapping D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

26. BMI2 SS08 – Class 7 “functional MRI” Slide 26 Magnetic Susceptibility-based Imaging

27. BMI2 SS08 – Class 7 “functional MRI” Slide 27 Magnetic interaction of Hb  Image local field inhomogeneities (T2* weighted)

28. BMI2 SS08 – Class 7 “functional MRI” Slide 28 Magnetic Susceptibility Effects I

29. BMI2 SS08 – Class 7 “functional MRI” Slide 29 Magnetic Susceptibility Effects II

30. BMI2 SS08 – Class 7 “functional MRI” Slide 30 Reminder: Neuro-vascular coupling intensity

31. BMI2 SS08 – Class 7 “functional MRI” Slide 31 Blood vessels Capillaries

32. BMI2 SS08 – Class 7 “functional MRI” Slide 32 Hemoglobin-Oxygen Interaction

33. BMI2 SS08 – Class 7 “functional MRI” Slide 33 Hemoglobin-Oxygen Interaction

34. BMI2 SS08 – Class 7 “functional MRI” Slide 34 Hemoglobin-Oxygen Interaction

35. BMI2 SS08 – Class 7 “functional MRI” Slide 35 Effect of Oxygen Binding Deoxyhemoglobin: “puckered” heme; paramagnetic Oxyhemoglobin: planar heme; diamagnetic

36. BMI2 SS08 – Class 7 “functional MRI” Slide 36 T2* weighted images restactivation

37. BMI2 SS08 – Class 7 “functional MRI” Slide 37 Subtraction

38. BMI2 SS08 – Class 7 “functional MRI” Slide 38 Average for multiple stimulations Spatial mean over 426 non- activated voxels Spatial mean over 426 activated voxels

39. BMI2 SS08 – Class 7 “functional MRI” Slide 39 Example for visual stimulation

40. BMI2 SS08 – Class 7 “functional MRI” Slide 40 fMRI study

41. BMI2 SS08 – Class 7 “functional MRI” Slide 41 Analysis

42. BMI2 SS08 – Class 7 “functional MRI” Slide 42 Another paradigm

43. BMI2 SS08 – Class 7 “functional MRI” Slide 43 Data considered  Time series analysis

44. BMI2 SS08 – Class 7 “functional MRI” Slide 44 Exploring individual voxel time series … not efficient or quantitative

45. BMI2 SS08 – Class 7 “functional MRI” Slide 45 Predicted Model

46. BMI2 SS08 – Class 7 “functional MRI” Slide 46 Statistical Parametric Mapping (SPM) http://www.fil.ion.ucl.ac.uk/spm/ K. J. Friston, UCL, UK

47. BMI2 SS08 – Class 7 “functional MRI” Slide 47 SPM preprocessing Movement correction: Sensitivity: Large error variance may prevent us from finding activations Specificity: Task correlated motion may appear as activation Normalization: Deals with individual morphological differences

48. BMI2 SS08 – Class 7 “functional MRI” Slide 48 SPM preprocessing Smoothing (): Convolution with Gaussian kernel Reduced effects of noise

49. BMI2 SS08 – Class 7 “functional MRI” Slide 49 General Linear Model GLM

50. BMI2 SS08 – Class 7 “functional MRI” Slide 50 GLM matrices

51. BMI2 SS08 – Class 7 “functional MRI” Slide 51 GLM matrices

52. BMI2 SS08 – Class 7 “functional MRI” Slide 52 GLM matrices

53. BMI2 SS08 – Class 7 “functional MRI” Slide 53 Correlation maps