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

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

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

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

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

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

8. Noll Non-linearity in the Hemodynamic Response TaskTask –Half visual field alternating checkerboard (8Hz) for a period of 2s –Trial –n-trials = 5 –Inter-stimulus interval = 10s –Inter-trial interval = 90s ISIITI2s

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

10. Noll Responses Differ with Position in Series Response to the 2nd stimulus is: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.This example is extreme, but not unique. Response to 2 nd stimulus Response to 1 st stimulus

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

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

13. Noll Physiologically Relevant Model Expandable compartment model (balloon) model of Buxton, et al.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)Increases in blood volume can account for some non-linear behavior (as well as the fMRI response undershoot) F in F out O2O2O2O2 capillaries venous

14. Noll Cascaded Balloon Model... V1V1V1V1 V2V2V2V2 VnVnVnVn F in F out O2O2O2O2 capillariesvenous The original model cannot predict our observed time-variant behaviorThe original model cannot predict our observed time-variant behavior –Notably, it doesn’t predict a delays for secondary stimuli New cascaded-compartment model.New cascaded-compartment model.

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

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

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

18. Noll Conclusions The hemodynamic response is quite complexThe hemodynamic response is quite complex Physiologically relevant models can predict most of this complex behaviorPhysiologically relevant models can predict most of this complex behavior There are domains in which the response behaves linearlyThere 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. Noll Conclusions It is also possible to build the non-linear model directly into the analysisIt 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 veinsParameters might tell not only where activation occurs, but might be used to discriminate between signals from distal and proximal veins

20. Noll Comments Why do some find mostly linear behavior?Why do some find mostly linear behavior? Many task designs reduce the effects of non- linearityMany 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. Noll Future Work Modifications to Buxton’s model (notably the transformation to MR signal parameters)Modifications to Buxton’s model (notably the transformation to MR signal parameters) Study of non-linearities using flow measuresStudy of non-linearities using flow measures Experimental validation of parts of modelExperimental validation of parts of model