I. Spatial & Temporal Properties (cont.) II. Signal and Noise

1. I. Spatial & Temporal Properties (cont.)II. Signal and Noise BIAC Graduate fMRI Course October 11, 2005

3. Spatial and Temporal Properties of BOLD fMRI

4. Why do you need to know? • Spatial resolution • Trades off with coverage • Influences viability of preprocessing steps • Influences inferences about distinct ROIs • Temporal resolution • Tradeoffs between number of slices and TR • Needed resolution depends upon design

5. Spatial Resolution

6. What spatial resolution do we want? • Hemispheric • Lateralization studies • Selective attention studies • Systems / lobic • Relation to lesion data • Centimeter • Identification of active regions • Millimeter • Topographic mapping (e.g., motor, vision) • Sub-millimeter • Ocular Dominance Columns • Cortical Layers

7. What determines Spatial Resolution? • Voxel Size • In-plane Resolution • Slice thickness • Spatial noise • Head motion • Artifacts • Spatial blurring • Smoothing (within subject) • Coregistration (within subject) • Normalization (within subject) • Averaging (across subjects) • Functional resolution

8. Why can’t we just collect data from more/smaller voxels?

9. K – Space Revisited . . . . . . . . . . . . . . . . . . . . B A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FOV: 10cm, Pixel Size: 2 cm FOV: 10 cm, Pixel Size: 1 cm To increase spatial resolution we need to sample at higher spatial frequencies.

10. Costs of Increased Spatial Resolution • Acquisition Time • In-plane • Higher resolution takes more time to fill K-space (resolution ~ size of K-space) • #Slices/second • Sample rates for 64*64 images • Early Duke fMRI: 2-4 sl/s • GE EPI: 12 sl/s • Duke Spiral: 14 sl/s • Duke Inverse Spiral: 21+ sl/s • Reduced signal per voxel • What is our dependent measure?

11. How large are functional voxels? = ~.08cm3  5.0mm   3.75mm   3.75mm  Within a typical brain (~1300cm3), there may be about 20,000 functional voxels.

12. How large are anatomical voxels? = ~.004cm3  5.0mm   .9375mm   .9375mm  Within a typical brain (~1300cm3), there may be about 300,000+ anatomical voxels.

13. T2* Blurring • Signal decays over time needed for collection of an image • For standard resolution images, this is not a critical issue • However, for high-resolution (in-plane) images, the time to acquire an image may be a significant fraction of T2* • Under these conditions, multi-shot imaging may be necessary.

14. Partial Volume Effects • A single voxel may contain multiple tissue components • Many “gray matter” voxels will contain other tissue types • Large vessels are often present • The signal recorded from a voxel is a combination of all components

15. High Spatial Resolution fMRI: Ocular Dominance Columns

17. Early examples of ocular dominance Red = Left eye Blue = Right eye Pixel size 0.5mm2 Menon et al., 1997

18. Reliability of Ocular Dominance Measurements • Cheng et al., 2001 • Same subject participated in two sessions • Raw data at left • Boundaries of dominance columns match well across sessions

19. Effects of Stimulus Duration on Spatial Extent of Activity

20. Example: Ocular Dominance Goodyear & Menon, 2001

21. 4sec  10sec  Goodyear & Menon, 2001

22. Example: Visual System 100ms 500ms 1500 ms

23. Temporal Resolution

24. What temporal resolution do we want? • 10,000-30,000ms: Arousal or emotional state • 1000-10,000ms: Decisions, recall from memory • 500-1000ms: Response time • 250ms: Reaction time • 10-100ms: • Difference between response times • Initial visual processing • 10ms: Neuronal activity in one area

25. Basic Sampling Theory • Nyquist Sampling Theorem • To be able to identify changes at frequency X, one must sample the data at (least) 2X. • For example, if your task causes brain changes at 1 Hz (every second), you must take two images per second.

27. Aliasing • Mismapping of high frequencies (above the Nyquist limit) to lower frequencies • Results from insufficient sampling • Potential problem for long TRs and/or fast stimulus changes • Also problem when physiological variability is present

28. Sampling Rate in Event-related fMRI

29. Costs of Increased Temporal Resolution • Reduced signal amplitude • Shorter flip angles must be used (to allow reaching of steady state), reducing signal • Fewer slices acquired • Usually, throughput expressed as slices per unit time

30. Frequency Analyses t < -1.96 t < +1.96 McCarthy et al., 1996

31. Phase Analyses • Design • Left/right alternating flashes • 6.4s for each • Task frequency: • 1 / 12.8 = 0.078 McCarthy et al., 1996

32. Why do we want to measure differences in timing within a brain region? • Determine relative ordering of activity • Make inferences about connectivity • Anatomical • Functional • Relate activity timing to other measures • Stimulus presentation • Reaction time • Relative amplitude

33. Timing Differences across Regions Presented left hemifield before right hemifield (0-1000ms delays) fMRI vs RT (LH) Plot of LH signal as function of RH signal fMRI vs. Stimulus Menon et al., 1998

34. Activation maps Relative onset time differences Menon et al., 1998

35. Timing of mental events measured by fMRI • Miezin et al., 2000 • Subjects pressed button with one hand at onset of 1.5s stimulus • Then, pressed another button at offset of stimulus

36. V1 FFG Huettel et al., 2001

37. Secondary Visual Cortex (FFG) Primary Visual Cortex (V1) Subject 1 5.5s 4.0s Subject 2 Huettel et al., 2001

38. Width of fMRI response increases with duration of mental activity From Menon and Kim, 1999; after Richter et al, 1997

39. Independence of Timing and Amplitude Adapted from Miezin et al. (2000)

40. Linearity of the Hemodynamic Response

41. Linear Systems • Scaling • The ratio of inputs determines the ratio of outputs • Example: if Input1 is twice as large as Input2, Output1 will be twice as large as Output2 • Superposition • The response to a sum of inputs is equivalent to the sum of the response to individual inputs • Example: Output1+2+3 = Output1+Output2+Output3

42. Scaling (A) and Superposition (B) A B

43. Linear and Non-linear Systems A B C D

44. Possible Sources of Nonlinearity • Stimulus time course  neural activity • Activity not uniform across stimulus (for any stimulus) • Neural activity  Vascular changes • Different activity durations may lead to different blood flow or oxygen extraction • Minimum bolus size? • Minimum activity necessary to trigger? • Vascular changes  BOLD measurement • Saturation of BOLD response necessitates nonlinearity • Vascular measures combining to generate BOLD have different time courses From Buxton, 2001

45. Effects of Stimulus Duration • Short stimulus durations evoke BOLD responses • Amplitude of BOLD response often depends on duration • Stimuli < 100ms evoke measurable BOLD responses • Form of response changes with duration • Latency to peak increases with increasing duration • Onset of rise does not change with duration • Rate of rise increases with duration • Key issue: deconfounding duration of stimulus with duration of neuronal activity

46. The fMRI Linear Transform

47. Boynton et al., 1996 Varied contrast of checkerboard bars as well as their interval (B) and duration (C).

48. Boynton, et al, 1996

49. Boynton, et al, 1996

50. Differences in Nonlinearity across Brain Regions Birn, et al, 2001