1. Noll Non-linearity in the Hemodynamic Response Study presented previously:Study presented previously: –An investigation of non-linear behavior of the hemodynamic response in fMRI Examined the response to stimuli in visual cortex with stimulus manipulations:Examined the response to stimuli in visual cortex with stimulus manipulations: –Varied stimulus duration –Varied stimulus intensity (contrast)

2. Noll Non-linearity in the Hemodynamic Response Observed non-linear behavior in terms of response amplitude and durationObserved non-linear behavior in terms of response amplitude and duration –responses to stimuli > 4s in duration: linear –responses to stimuli < 4s in duration: non-linear Non-linearity manifested as broadening of the response with increasing durationNon-linearity manifested as broadening of the response with increasing duration There was also an amplitude dependence, but not as strongThere was also an amplitude dependence, but not as strong

3. 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 additivity)Time-invariance (a second and necessary condition for additivity) 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

4. 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 –Broader This example is extreme, but not unique.This example is extreme, but not unique. Response to 2 nd stimulus Response to 1 st stimulus

5. 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

6. 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 responsesLarger veins usually have largest responses –These also have longest delays –Implications for modeling the response

7. 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

8. 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.

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

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

11. 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 –This greatly eases the analysis and experimental design –The models can help establish if linear models will hold for any given experiment

12. 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 veins and proximal veinsParameters might tell not only where activation occurs, but might be used to discriminate between signals from distal veins and proximal veins