The linear systems model of fMRI: Strengths and Weaknesses

1. The linear systems model of fMRI: Strengths and Weaknesses Stephen Engel UCLA Dept. of Psychology

2. Talk Outline • Linear Systems • Definition • Properties • Applications in fMRI (Strengths) • Is fMRI Linear? (Weaknesses) • Implications • Current practices • Future directions

3. Linear systems • System = input -> output Stimulus or Neural activity -> fMRI responses • System is linear if shows two properties Homogeneity & Superposition

5. Useful properties of linear systems • Can add and subtract responses meaningfully • Can characterize completely using impulse response • Can use impulse response to predict output to arbitrary input via convolution • Can characterize using MTF

6. Subtracting responses

7. Characterizing linear systems

9. Predicting block response

10. Characterizing linear systems

12. Talk Outline • Linear Systems • Definition • Properties • Applications in fMRI (Strengths) • Is fMRI Linear? (Weaknesses) • Implications • Current practices • Future directions

13. Uses of linear systems in fMRI • If assume fMRI signal is generated by a linear system can: • Create model fMRI timecourses • Use GLM to estimate and test parameters • Interpret estimated parameters • Estimate temporal and spatial MTF

14. Simple GLM Example

15. Model fitting assumes homogeneity

16. Rapid designs assume superposition

17. Wagner et al. 1998, Results

18. Zarahn, ‘99; D’esposito et al.

19. D’Esposito et al.

20. More on GLM • Many other analysis types possible • ANCOVA • Simultaneous estimate of HRF • Interpretation of estimated parameters • If fMRI data are generated from linear system w/neural activity as input • Then estimated parameters will be proportional to neural activity • Allows quantitative conclusions

21. MTF • Boynton et al. (1996) estimated temporal MTF in V1 • Showed moving bars of checkerboard that drifted at various temporal frequencies • Generated periodic stimulation in retinotopic cortex • Plotted Fourier transform of MTF (which is impulse response)

23. Characterizing linear systems

25. MTF • Engel et al. (1997) estimated spatial MTF in V1 • Showed moving bars of checkerboard that varied in spatial frequency but had constant temporal frequency • Calculated cortical frequency of stimulus • Plotted MTF • Some signal at 5 mm/cyc at 1.5 T in ‘97!

27. Talk Outline • Linear Systems • Definition • Properties • Applications in fMRI (Strengths) • Is fMRI Linear? (Weaknesses) • Implications • Current practices • Future directions

28. Is fMRI really based upon a linear system? • Neural activity as input fMRI signal as output • fMRI tests of temporal superposition • Electrophysiological tests of homogeneity • fMRI test of spatial superposition

29. Tests of temporal superposition • Boynton et al. (1996) measured responses to 3, 6, 12, and 24 sec blocks of visual stimulation • Tested if r(6) = r(3)+r(3) etc. • Linearity fails mildly

31. Dale & Buckner ‘97 • Tested superposition in rapid design • Full field stimuli • Groups of 1, 2, or 3 • Closely spaced in time • Responses overlap • Q1: 2-1 = 1?

32. Dale and Buckner, Design

34. fMRI fails temporal superposition • Now many studies • Initial response is larger than later response • Looks OK w/3-5 second gap • Possible sources • Attention • Neural adaptation • Hemodynamic non-linearity

35. Test of homogeneity • Simultaneous measurements of neural activity and fMRI or optical signal • Q: As neural activity increases does fMRI response increase by same amount?

36. Logothetis et al., ‘01

38. Optical imaging studies • Measure electrophysiological response in rodents • Various components of hemodynamic response inferred from reflectance changes at different wavelengths • Devor ‘03 (whisker) and Sheth ‘04 (hindpaw)

41. Nonlinearities • Optical imaging overestimates large neural responses relative to small ones • But Logo. found opposite • fMRI overestimates brief responses relative to long ones • Amplified neural adaptation?

42. Spatial issue • W/in a local region does signal depend upon sum or average activity? • Or “is the whole garden watered for the sake of one thirsty flower?” (Grinvald)

43. Spatial Properties of HRF Thompson et al., 2003

44. Testing spatial superposition • Need to measure responses of neurons from population a, population b, and both • Where have intermingled populations that can activate separately? • LGN • Prediction twice as much fMRI response for two eye stimulation than for one eye • Should be different in V1

45. Conclusions • Linear model successful and useful but… • Hemodynamic responses possibly not proportional to neural ones • Though could be pretty close for much of range • Take care interpreting • differences in fMRI amplitude • GLM results where neural responses overlap

46. Conclusions • Temporal superposition of hemodynamic responses could still hold • Most applications of GLM may be OK w/proper interpretation and spacing to avoid neural adaptation • Run estimated fMRI amplitude through inverse of nonlinearity relating hemodynamics to neural activity (static nonlinearity)

47. Rapid designs assume superposition

48. Future Directions • Better characterization of possible non-linearities • Modeling of non-linearities • Further tests of linearity • Hemodynamic superposition • Spatial superposition