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The Physiological Origins of Non-Linearities in the BOLD Response

This study explores the non-linearities in the BOLD response and proposes a cascaded expandable compartment model to explain the time-variant behavior of fMRI. The model is compared to experimental data and shows promising results.

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The Physiological Origins of Non-Linearities in the BOLD Response

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  1. The Physiological Origins ofNon-Linearities in the BOLD Response Douglas C. Noll Alberto L. Vazquez Department of Biomedical Engineering University of Michigan

  2. Outline • Study of Linearity in the BOLD Response • Expandable Compartment Model(s) • Study of Time-Invariance in the BOLD Response • Cascaded Expandable Compartment Model • Comments and Future Work

  3. Fitting of EC Model to Duration Data • Single set of model parameters with different duration stimuli as input • Model parameters derived from 8 s data 2 s 4 s 8 s

  4. EC Model Shows Same Non-linearities • Comparison of 4 superimposed 2 s stimuli to response to 8 s stimulus. • Actual data and model show non-linear effects Superimposed stimuli

  5. Fitting of EC Model to Contrast Data • Single set of model parameters with different blood flow levels as input • Model parameters are from 80% contrast data 10% contrast 80% contrast

  6. EC Model Shows Same Non-linearities • Comparison of two different contrast stimuli normalized to same peak height • Actual data and model show non-linear effects 80% 10%

  7. Time-Variant Behavior of fMRI Response • Linearity (often means additivity of responses) • Time-invariance (a second and necessary condition for the convolution model) • We examined the responses to stimuli with manipulations of: • Time preceding initial stimulus in a series • Time between stimuli

  8. ISI ITI Non-linearity in the Hemodynamic Response • Task • Half visual field alternating checkerboard (8Hz) for a period of 2s • Trial • n-trials = 5 • Inter-stimulus interval = 10s • Inter-trial interval = 90s 2s

  9. Non-linearity of the Hemodynamic Response • Acquisition • General Electric 3.0 Tesla scanner • Single-shot EPI TR = 1000ms TE = 25ms FA = 60deg • Four coronal slices (3mm, skip 0mm)

  10. Responses Differ with Position in Series • Response to the 2nd stimulus is: • Delayed in Rise • Delayed in Peak • Lower in Amplitude • Broader in Time • This example is extreme, but not unique. Response to 1st stimulus Response to 2nd stimulus

  11. Non-linearity in the Hemodynamic Response Delay in ResponseStim. 2 - Stim. 1 EPI Data Activation Response High intensity responses (probably veins)exhibit largest delays

  12. Non-linearity in the Hemodynamic Response • Plot of response delays (stimulus 2 - stimulus 1) vs. percentage signal change • Positive correlation • Larger veins usually have largest responses • These also have longest delays • Implications for modeling the response

  13. Physiologically Relevant Model • Expandable compartment model (balloon) model of Buxton, et al. • Increases in blood volume can account for some non-linear behavior (as well as the fMRI response undershoot) O2 Fin Fout venous capillaries

  14. Cascaded Balloon Model capillaries venous • The original model cannot predict our observed time-variant behavior • Notably, it doesn’t predict a delays for secondary stimuli • New cascaded-compartment model. O2 Fout Fin ... Vn V2 V1

  15. Responses in Different Compartments Compartment 1 Compartment 5 Delay and Shift in Peak No Delay or Shift in Peak

  16. Comparison to Experimental Data Experimental Data Model Predictions Delay in Rise Shift in Peak Cross-over

  17. Aspects of Cascaded Model • The cascaded expandable compartment model will require one additional parameter (3 or 4 + 1). • This additional parameter might be indicative of distance in the vasculature.

  18. Conclusions • The hemodynamic response is quite complex • Physiologically relevant models can predict most of this complex behavior • There are domains in which the response behaves linearly • Linearity greatly eases the analysis and experimental design • The models can help establish if linear models will hold for any given experiment

  19. Conclusions • It is also possible to build the non-linear model directly into the analysis • Parameters might tell not only where activation occurs, but might be used to discriminate between signals from distal and proximal veins

  20. Comments • Why do some find mostly linear behavior? • Many task designs reduce the effects of non-linearity • Most block designs with block longer than 4 s • Event-related designs in the steady state • Event-related designs that do not allow for blood volume changes to return to normal (5 time constants ~ 75 s)

  21. Future Work • Modifications to Buxton’s model (notably the transformation to MR signal parameters) • Study of non-linearities using flow measures • Experimental validation of parts of model

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