Noll Non-linearity in the Hemodynamic Response Study presented previously:Study presented previously: –An investigation of non-linear behavior of the hemodynamic.

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Non-linearity in the Hemodynamic ResponseNon-linearity in the Hemodynamic Response

• Study presented previously:Study presented previously:– An investigation of non-linear behavior of the An investigation of non-linear behavior of the

hemodynamic response in fMRIhemodynamic response in fMRI

• Examined the response to stimuli in visual Examined the response to stimuli in visual cortex with stimulus manipulations:cortex with stimulus manipulations:– Varied stimulus durationVaried stimulus duration– Varied stimulus intensity (contrast)Varied stimulus intensity (contrast)

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Non-linearity in the Hemodynamic ResponseNon-linearity in the Hemodynamic Response

• Observed non-linear behavior in terms of Observed non-linear behavior in terms of response amplitude and durationresponse amplitude and duration– responses to stimuli > 4s in duration: linearresponses to stimuli > 4s in duration: linear– responses to stimuli < 4s in duration: non-linearresponses to stimuli < 4s in duration: non-linear

• Non-linearity manifested as broadening of the Non-linearity manifested as broadening of the response with increasing durationresponse with increasing duration

• There was also an amplitude dependence, There was also an amplitude dependence, but not as strongbut not as strong

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Time-Variant Behavior of fMRI ResponseTime-Variant Behavior of fMRI Response

• Linearity (often means additivity of Linearity (often means additivity of responses)responses)

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

• We examined the responses to stimuli with We examined the responses to stimuli with manipulations of:manipulations of:– Time preceding initial stimulus in a seriesTime preceding initial stimulus in a series– Time between stimuliTime between stimuli

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Responses Differ with Position in SeriesResponses Differ with Position in Series

• Response to the 2nd Response to the 2nd stimulus is:stimulus is:– Delayed in RiseDelayed in Rise– Delayed in PeakDelayed in Peak– LowerLower– BroaderBroader

• This example is This example is extreme, but not extreme, but not unique.unique.

Response to 2Response to 2ndnd stimulus stimulus

Response to 1Response to 1stst stimulus stimulus

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Non-linearity in the Hemodynamic ResponseNon-linearity in the Hemodynamic Response

EPI DataEPI Data Activation Activation ResponseResponse

Delay in ResponseDelay in ResponseStim. 2 - Stim. 1Stim. 2 - Stim. 1

High intensity responses (probably veins)High intensity responses (probably veins)exhibit largest delaysexhibit largest delays

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Non-linearity in the Hemodynamic ResponseNon-linearity in the Hemodynamic Response

• Plot of response delays Plot of response delays (stimulus 2 - stimulus 1) (stimulus 2 - stimulus 1) vs. percentage signal vs. percentage signal changechange

• Positive correlationPositive correlation

• Larger veins usually Larger veins usually have largest responseshave largest responses– These also have longest These also have longest

delaysdelays– Implications for modeling Implications for modeling

the responsethe response

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Physiologically Relevant ModelPhysiologically Relevant Model

• Expandable compartment model (balloon) Expandable compartment model (balloon) model of Buxton, et al.model of Buxton, et al.

• Increases in blood volume can account for Increases in blood volume can account for some non-linear behavior (as well as the fMRI some non-linear behavior (as well as the fMRI response undershoot)response undershoot)

FFinin FFoutout

OO22

capillariescapillaries venousvenous

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Cascaded Balloon ModelCascaded Balloon Model

......

VV11 VV22 VVnn

FFininFFoutout

OO22

capillariescapillaries venousvenous

• The original model cannot predict our The original model cannot predict our observed time-variant behaviorobserved time-variant behavior– Notably, it doesn’t predict a delays for secondary Notably, it doesn’t predict a delays for secondary

stimulistimuli

• New cascaded-compartment model.New cascaded-compartment model.

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Responses in Different CompartmentsResponses in Different Compartments

Compartment 1Compartment 1 Compartment 5Compartment 5

No Delay or Shift in PeakNo Delay or Shift in Peak Delay and Shift in PeakDelay and Shift in Peak

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Comparison to Experimental DataComparison to Experimental Data

Delay in RiseDelay in Rise Shift in PeakShift in Peak Cross-overCross-over

Experimental DataExperimental Data Model PredictionsModel Predictions

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ConclusionsConclusions

• The hemodynamic response is quite complexThe hemodynamic response is quite complex

• Physiologically relevant models can predict Physiologically relevant models can predict most of this complex behaviormost of this complex behavior

• There are domains in which the response There are domains in which the response behaves linearly behaves linearly – This greatly eases the analysis and experimental This greatly eases the analysis and experimental

design design – The models can help establish if linear models will The models can help establish if linear models will

hold for any given experimenthold for any given experiment

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ConclusionsConclusions

• It is also possible to build the non-linear It is also possible to build the non-linear model directly into the analysismodel directly into the analysis

• Parameters might tell not only where Parameters might tell not only where activation occurs, but might be used to activation occurs, but might be used to discriminate between signals from distal veins discriminate between signals from distal veins and proximal veinsand proximal veins