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Nonlinear Dynamics in fMRI BOLD Response: Can Hemodynamics Adapt to Varying Stimulus Conditions?

This study explores the spatial heterogeneity and nonlinear dynamics in the fMRI BOLD response, specifically investigating the adaptability of hemodynamics to different stimulus conditions. The effects of stimulus duty cycle, "off" duration, and neuronal input on BOLD response linearity are examined. The study also explores the relationship between neuronal activity and BOLD response. The findings provide insights into the mechanisms underlying fMRI BOLD response and its interpretation.

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Nonlinear Dynamics in fMRI BOLD Response: Can Hemodynamics Adapt to Varying Stimulus Conditions?

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  1. HDR varies across regions (plumbing or neuronal?)

  2. Can FMR adaptation be at least partially due to hemodynamics?

  3. R. M. Birn, Z. Saad, P. A. Bandettini, Spatial heterogeneity of the nonlinear dynamics in the fMRI BOLD response. NeuroImage, 14: 817-826, (2001). R.M. Birn, P. A. Bandettini, The effect of stimulus duty cycle and "off" duration on BOLD response linearity. NeuroImage, 27, 70-82 (2005) A. S. Tuan, R. M. Birn, P. A. Bandettini, G. M. Boynton, Differential MEG and fMRI responses to visual stimulation onset rate (in preparation)

  4. R. M. Birn, (2001) NeuroImage, 14: 817-826. Increases: linearity Logothetis et al. (2001) Nature, 412, 150-157. R.M. Birn, et al. Neuroimage 14, 817-26, 2001 P. A. Bandettini et al, (2001) Nature Neuroscience, 4: 864-866.

  5. 8 f (SD) 6 4 0 10 20 30 40 0 10 20 30 40 2 0 1 2 3 4 5 Stimulus Duration -2 60 8 f (SD) 40 6 4 20 2 0 2 4 6 8 10 0 1 2 3 4 5 Stimulus Duration nonlinearity -2 Nonlinearity – visual task R.M. Birn, et al. Neuroimage 14, 817-26, 2001

  6. 0 10 20 30 40 0 10 20 30 40 Nonlinearity – motor task 8 f (SD) 6 4 2 0 1 2 3 4 5 Stimulus Duration 40 8 f (SD) 6 20 4 2 0 5 10 15 20 25 nonlinearity 0 1 2 3 4 5 Stimulus Duration R.M. Birn, et al. Neuroimage 14, 817-26, 2001

  7. Reproducibility Visual task Motor task Nonlinearity1 Nonlinearity1 Nonlinearity2 Nonlinearity2 Experiment 1 Experiment 2 Experiment 1 Experiment 2 R.M. Birn, et al. Neuroimage 14, 817-26, 2001

  8. 0 2 4 8 12 16 20 2000ms 1000ms Signal 500ms 250ms 0 5 10 15 time (s) 10 Amplitude (%) 5 0 0 1 2 3 4 5 Stimulus Duration (s) Estimated neuronal input Contrast Reversing Checkerboard Estimated Neuronal Activity

  9. 100 Signal 50 time (s) 0 0 1 2 3 3200ms 1600ms 800ms 400ms 200ms 100ms 50ms Measured Amplitudes 3 2 Amplitude (%) 1 0 0 1 2 3 Stimulus Duration (s) 0 2 4 6 8 10 12 14 Estimated neuronal input Static Grating Estimated Neuronal Activity time(s)

  10. Decreases: linearity R.M. Birn, P. A. Bandettini. NeuroImage,

  11. Increases: duty cycle R.M. Birn, P. A. Bandettini, The effect of stimulus duty cycle and "off" duration on BOLD response linearity. NeuroImage, 27, 70-82 (2005)

  12. Model – Neuronal effects refractory period OFF response adaptation

  13. Refractory effect ISI

  14. refractory period OFF response adaptation c d e f 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 2 2 2 2 Amplitude Amplitude Amplitude Amplitude 1 1 1 1 0 0 0 0 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 Duty Cycle Duty Cycle Duty Cycle Duty Cycle Simulation results – Neuronal effects Adaptation Adaptation + refractory Adaptation + refractory + OFF response Linear 2 1 1 1 1

  15. 11026–11031 PNAS September 26, 2000vol. 97 no. 20

  16. BOLD response amplitude and linearity to different stimulus OFF periods Amplitude Linearity 0 1.5 linear measured -2 1 Relative Amplitude (measured / linear) % Signal Change measured linear -4 0.5 -6 0 0 5 10 15 20 0 5 10 15 20 Stimulus OFF Duration (s) Stimulus OFF duration (s)

  17. 20% 20% 20% Amplitude: 50% ON Amplitude: 25% ON Amplitude: 75% ON 10% 10% 10% slope = 1.33 slope = 0.90 slope = 0.58 0 0 0 0 10% 20% 0 10% 20% 0 10% 20% Amplitude: Blocked Amplitude: Blocked Amplitude: Blocked BOLD response to different stimulus duty cycles

  18. Nonlinearity of oxygen extraction, E(f) 1.4 1.2 Linear prediction 1 E(f) / E0 Actual change Linear prediction 0.8 Actual change 0.6 0.4 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Flow Small flow decrease Small flow increase

  19. t Estimate Neuronal Input from BOLD fMRI Contrast-reversing Checkerboard estimated neuronal input measured response 20 s 1 s 2 s 0.5 s stimulus duration R.M. Birn, et al. Proc ISMRM 2002

  20. BOLD response to neuronal transients Stimulus Steady-state neurons a = initial slope BOLD Response amplitude Neurons responding to change b = final slope Stimulus Duration a Population response b

  21. CR-Checkerboard vs. Static Grating 10 Contrast-Reversing Checkerboard 5 Amplitude (%) Static Grating 0 0 1 2 3 4 5 Stimulus Duration (s)

  22. Balloon Model Parameters

  23. “on” Linearity

  24. “off” linearity

  25. Duty Cycle

  26. Neuronal effects to explain duty cycle effects

  27. measured linear time (s) Different stimulus “OFF” periods R.M. Birn, et al. Proc. ISMRM, 2001. BOLD Response Signal Stimulus timing 2 s 3 s 4 s 8 s 16 s Brief stimulus OFF periods produce smaller decreases than expected

  28. Varying “ON” and “OFF” periods R.M. Birn, et al. Proc. OHBM 2001. • Rapid event-related design with varying ISI 8% ON 25% ON 50% ON 75% ON

  29. 8% ON Measured Blocked Response 8% ON 25% ON 50% ON 25% ON Signal 50% ON 75% ON 75% ON Signal 0 10 20 30 40 0 5 15 10 time (s) time (s) Varying “ON” and “OFF” periods R.M. Birn, et al. Proc. OHBM 2001. Estimated Impulse Response Predicted Responses to 20 s stimulation

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