I. Spatial & Temporal Properties (cont.) II. Signal and Noise BIAC Graduate fMRI Course October 11, 2005.

I. Spatial & Temporal Properties (cont.)

II. Signal and NoiseBIAC Graduate fMRI CourseOctober 11, 2005

Spatial and Temporal Properties of BOLD fMRI

Why do you need to know?Spatial resolutionTrades off with coverage Influences viability of preprocessing stepsInfluences inferences about distinct ROIsTemporal resolutionTradeoffs between number of slices and TRNeeded resolution depends upon design

Spatial Resolution

What spatial resolution do we want?HemisphericLateralization studiesSelective attention studiesSystems / lobicRelation to lesion dataCentimeterIdentification of active regions MillimeterTopographic mapping (e.g., motor, vision)Sub-millimeterOcular Dominance ColumnsCortical Layers

What determines Spatial Resolution?Voxel SizeIn-plane ResolutionSlice thicknessSpatial noiseHead motionArtifactsSpatial blurringSmoothing (within subject)Coregistration (within subject)Normalization (within subject)Averaging (across subjects)Functional resolution

Why cant we just collect data from more/smaller voxels?

. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .ABFOV: 10 cm, Pixel Size: 1 cmFOV: 10cm, Pixel Size: 2 cmK Space RevisitedTo increase spatial resolution we need to sample at higher spatial frequencies.

Costs of Increased Spatial ResolutionAcquisition TimeIn-planeHigher resolution takes more time to fill K-space (resolution ~ size of K-space)#Slices/secondSample rates for 64*64 imagesEarly Duke fMRI: 2-4 sl/sGE EPI: 12 sl/sDuke Spiral: 14 sl/sDuke Inverse Spiral: 21+ sl/s

Reduced signal per voxelWhat is our dependent measure?

How large are functional voxels? 3.75mm 5.0mm 3.75mm = ~.08cm3Within a typical brain (~1300cm3), there may be about 20,000 functional voxels.

How large are anatomical voxels? .9375mm 5.0mm .9375mm = ~.004cm3Within a typical brain (~1300cm3), there may be about 300,000+ anatomical voxels.

T2* BlurringSignal decays over time needed for collection of an imageFor standard resolution images, this is not a critical issueHowever, for high-resolution (in-plane) images, the time to acquire an image may be a significant fraction of T2*Under these conditions, multi-shot imaging may be necessary.

Partial Volume EffectsA single voxel may contain multiple tissue componentsMany gray matter voxels will contain other tissue typesLarge vessels are often presentThe signal recorded from a voxel is a combination of all components

High Spatial Resolution fMRI: Ocular Dominance Columns

Early examples of ocular dominanceMenon et al., 1997Red = Left eyeBlue = Right eyePixel size 0.5mm2

Reliability of Ocular Dominance MeasurementsCheng et al., 2001Same subject participated in two sessionsRaw data at leftBoundaries of dominance columns match well across sessions

Effects of Stimulus Duration on Spatial Extent of Activity

Example: Ocular DominanceGoodyear & Menon, 2001

4sec 10sec Goodyear & Menon, 2001

Example: Visual System100ms500ms1500 ms

Temporal Resolution

What temporal resolution do we want?10,000-30,000ms: Arousal or emotional state1000-10,000ms: Decisions, recall from memory500-1000ms: Response time250ms: Reaction time10-100ms: Difference between response timesInitial visual processing10ms: Neuronal activity in one area

Basic Sampling TheoryNyquist Sampling TheoremTo be able to identify changes at frequency X, one must sample the data at (least) 2X.For example, if your task causes brain changes at 1 Hz (every second), you must take two images per second.

AliasingMismapping of high frequencies (above the Nyquist limit) to lower frequenciesResults from insufficient samplingPotential problem for long TRs and/or fast stimulus changesAlso problem when physiological variability is present

Sampling Rate in Event-related fMRI

Costs of Increased Temporal ResolutionReduced signal amplitudeShorter flip angles must be used (to allow reaching of steady state), reducing signalFewer slices acquiredUsually, throughput expressed as slices per unit time

Frequency Analysest < -1.96t < +1.96McCarthy et al., 1996

Phase AnalysesDesignLeft/right alternating flashes6.4s for eachTask frequency:1 / 12.8 = 0.078McCarthy et al., 1996

Why do we want to measure differences in timing within a brain region?Determine relative ordering of activityMake inferences about connectivityAnatomicalFunctionalRelate activity timing to other measuresStimulus presentation Reaction timeRelative amplitude

Timing Differences across RegionsMenon et al., 1998Presented left hemifield before right hemifield (0-1000ms delays)Plot of LH signal as function of RH signalfMRI vs RT (LH)fMRI vs. Stimulus

Menon et al., 1998Activation mapsRelative onset time differences

Timing of mental events measured by fMRIMiezin et al., 2000Subjects pressed button with one hand at onset of 1.5s stimulusThen, pressed another button at offset of stimulus

V1FFGHuettel et al., 2001

Table1

Table 1

Peak AmplitudeLatency to PeakMaximumNumber of Active Voxels

Age GroupTypeMeanStdDevMeanStdDevSNRMeanStdDev

YoungCC0.88%0.20%4.750.420.5253.0915.62

OldCC0.92%0.27%4.230.680.3525.8212.33

YoungFFG0.85%0.15%5.050.560.4179.0024.93

OldFFG0.83%0.20%4.550.620.3035.6015.56

YoungMax1.67%0.67%4.910.590.86--

OldMax1.61%0.95%4.890.730.47--

Figure2a

0.00044289830.0003912712

-0.00000873820.0001156617

0.0001401958-0.0002009655

-0.0000287332-0.0000758436

-0.00010272440.0001611475

0.00000667230.0001927941

0.00008758370.0000213113

0.00158998710.0018598299

0.00565683060.0062993712

0.00812137590.0085248808

0.00841284040.0077157608

0.00694245830.0060730616

0.00487329490.0045427631

0.00262682640.0027513003

0.00128309850.0016580401

0.0007117520.0006223521

0.00063349150.0003332346

0.00054918970.0009880431

0.00039337540.00077012

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Time since stimulus onset (s)

Standard Deviation at Time Point (%)

Figure2b

0.0002848524-0.0002263956

0.0001097114-0.0000135291

0.00002661550.0004930946

-0.0000106977-0.0001119483

-0.0001256293-0.0003676172

-0.00008643440.0003402062

0.00013139270.00012977

0.00101555690.0005834879

0.00395561970.0039223736

0.00703009560.0072223764

0.00812293150.0075580185

0.00721746270.0059792027

0.00516597380.0039056072

0.00332690570.0025312945

0.00163193170.0013851596

0.00083930720.0012070017

0.0006328037-0.0000230061

0.0006183110.0006840805

0.00094685310.0003029091

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Standard Deviation at Time Point (%)

Figure3a

0.00041708480.0000292284

0.00005346170.0000480911

-0.00003038480.0002598551

-0.0000522884-0.000061323

0.0000292115-0.0002466232

0.00009973320.0001268859

0.00005444750.0001305814

0.00172490850.0007995224

0.00597810090.0039389966

0.00832312830.007126236

0.00806430060.007840475

0.00650775990.0065983327

0.0047080290.0045357905

0.00268906330.0029291001

0.00147056930.0015085457

0.0006670520.0010231544

0.0004833630.0003048988

0.00076861640.0006511957

0.00058174770.0006248811

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V1

FFG


Signal Change over Pre-stimulus Baseline (%)

Figure4a

0.0001994796-0.0001845437-0.0007407340.00012584130.00060717980.00047052270.00110866110.00152619290.00050642610.00007598260.001176873

0.0000139638-0.0002154369-0.00061135870.0000380402-0.0007887129-0.00034898910.00088400530.0000885950.00042617090.00000111070.0004164914

0.0001158045-0.0000646925-0.00009213760.0000288323-0.00028124880.00038871120.0003933040.00040993160.00026446850.0002912940.0000878867

-0.00005400090.0000211540.0003846668-0.00015459470.0006909217-0.0000322832-0.00041099690.0002921286-0.000465392-0.0003704458-0.0002172225

-0.00007576740.00025897530.00031882950.00008772230.0003790401-0.0000074389-0.0008663123-0.0007906552-0.00022524740.0000780411-0.0002871556

0.00019267120.0001888035-0.0003811640.0002311330.00032718490.0004611413-0.0009925142-0.00089947370.00067208740.0002944799-0.0000209538

-0.00101036330.0006151276-0.00058508510.00017325580.00029012780.0003254693-0.00027748470.00005390090.00103682620.0003600193-0.0000183737

-0.00061169670.00285288040.00056430150.00280908470.00107199850.00092805270.00195099690.00224737720.00247467070.0013319030.0018702891

0.0013350630.00799326870.00325562570.00642716590.00386190480.00521124470.00734976270.00881664910.00629019350.00460539870.0070788595

0.00433151520.01022472450.00554740320.0086580650.00595963430.00793409650.00921919450.01150396180.00862695180.00747029920.0098592888

0.00549015340.01055818520.00612411760.00775178640.00629116840.00915586050.00862727420.00946779610.00946143170.00890332930.0107101414

0.0049271760.00767098310.0054225320.00593948180.00456401880.00875899450.00542294260.00697752320.00838071450.00846113670.0098415379

0.00449713570.00495362890.00374405670.00497812880.00300149370.00735060660.00154307110.00407267130.00616120370.00574508830.0075591593

0.00305437510.00184273370.00168085940.00240975390.00201357720.00390072530.00075177730.0021167860.0031598590.00274232880.0052223143

0.00124179090.00064665490.00036045810.00205074430.00138170820.00182857810.00037809910.00026003110.00118923030.00190774450.002869044

-0.0000381530.0004038477-0.00082848920.00173461390.0010168120.00154751330.00036257210.0012457041-0.0001187530.00075599070.001747613

-0.00082546830.0000445936-0.00121694190.0010574850.00115690880.00221428070.00073887870.0022425946-0.00051213790.00058898640.0014792266

-0.00069588140.0004574101-0.0007761250.00067631730.0007284920.0023112090.00145666760.0012865277-0.00054225740.00075990140.0003788257

-0.00046908920.0012234112-0.00067290560.00042045480.00010404150.00187257540.00123487410.0006302043-0.00011292120.0009376936-0.00084121

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Figure4b

-0.00015147550.00064152870.00026817650.0010343393-0.00103432610.00065229610.0015865408-0.00101329160.0003241185-0.00108951840.0030855951

0.00045554910.000889487-0.00048864370.0002651839-0.00138611170.0000342159-0.0006639035-0.00070650890.00059200470.00024370890.0020372965

-0.0003077647-0.0000371669-0.0000129009-0.0008029735-0.00082784350.00020882260.0009735065-0.0001316729-0.0002385023-0.0003306774-0.0007034476

0.000248298-0.00028085260.0011579478-0.0005657412-0.0004340066-0.000012568-0.0000570333-0.00052681630.00019703660.0000568312-0.0006173754

-0.0003960824-0.0005714675-0.00065640320.00110353080.0026479618-0.0002304705-0.00025256970.0013649981-0.0005505390.0000301373-0.0007164735

0.0000988069-0.0002272526-0.00037475530.00062473590.0024338405-0.0001780918-0.00020061480.0009346203-0.0010881013-0.00000221820.0000997654

0.00123243730.0010777499-0.00112203810.0000446278-0.00062902060.0003086925-0.0000878540.0015685316-0.0000690598-0.0013888401-0.0007008023

0.00198440480.00367372120.00038935390.00171883520.00372626980.00446413530.00046704630.00201778950.0004177891-0.00027161080.001870395

0.00363444860.00885957730.00251785780.00703925350.01395868550.00840029110.00364940420.00770017860.00266588550.00442055950.0064469413

0.0059005530.00906366760.00522647690.01201802440.01491846440.00778639130.00728800990.01028400390.00591810770.00737664750.0079933421

0.00777596820.00677049080.00715751120.00971181820.01123999240.00510665930.00590866580.01099684630.00610783550.00735074860.006746833

0.00501269070.00445476640.00696788190.00695832690.00871630630.00318048970.00468433570.00939045940.00515322990.00519154290.0070936477

0.00408971520.00289084860.00524611990.00778740130.00762268590.00096657440.00192037510.00644426270.00396892220.00366092690.0053725623

0.00329469940.00086877790.00180200140.00468547430.00171496380.00079197670.00320723090.00507616440.00259011370.00213029710.0041026038

0.00188021680.00034300230.00018738760.00466817020.00284296880.000404370.00140951570.00154320810.00030084990.00109072990.0035680214

0.00118486740.0003344683-0.00075793050.0023699990.00091581440.00006215380.00085108550.00041685120.000920747-0.00066802650.0012158435

0.0014521451-0.0006275106-0.0002995872-0.00068436070.00076283760.0004078611-0.00060841120.00016071540.0007065574-0.00063810090.0030334342

0.0016367446-0.0001456142-0.00022439510.00320339680.00164615260.00061458310.00046616190.00141613490.0006576338-0.0001866660.0017843419

-0.0007618846-0.0002357776-0.00044993780.00121410630.00187555130.00057268670.00019223790.00147570230.00090284810.00066278140.0030230058

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Figure4a-old

0.0001994796-0.0001845437-0.0007407340.00012584130.00060717980.00047052270.00110866110.00152619290.00050642610.00007598260.001176873

0.0000139638-0.0002154369-0.00061135870.0000380402-0.0007887129-0.00034898910.00088400530.0000885950.00042617090.00000111070.0004164914

0.0001158045-0.0000646925-0.00009213760.0000288323-0.00028124880.00038871120.0003933040.00040993160.00026446850.0002912940.0000878867

-0.00005400090.0000211540.0003846668-0.00015459470.0006909217-0.0000322832-0.00041099690.0002921286-0.000465392-0.0003704458-0.0002172225

-0.00007576740.00025897530.00031882950.00008772230.0003790401-0.0000074389-0.0008663123-0.0007906552-0.00022524740.0000780411-0.0002871556

0.00019267120.0001888035-0.0003811640.0002311330.00032718490.0004611413-0.0009925142-0.00089947370.00067208740.0002944799-0.0000209538

-0.00101036330.0006151276-0.00058508510.00017325580.00029012780.0003254693-0.00027748470.00005390090.00103682620.0003600193-0.0000183737

-0.00061169670.00285288040.00056430150.00280908470.00107199850.00092805270.00195099690.00224737720.00247467070.0013319030.0018702891

0.0013350630.00799326870.00325562570.00642716590.00386190480.00521124470.00734976270.00881664910.00629019350.00460539870.0070788595

0.00433151520.01022472450.00554740320.0086580650.00595963430.00793409650.00921919450.01150396180.00862695180.00747029920.0098592888

0.00549015340.01055818520.00612411760.00775178640.00629116840.00915586050.00862727420.00946779610.00946143170.00890332930.0107101414

0.0049271760.00767098310.0054225320.00593948180.00456401880.00875899450.00542294260.00697752320.00838071450.00846113670.0098415379

0.00449713570.00495362890.00374405670.00497812880.00300149370.00735060660.00154307110.00407267130.00616120370.00574508830.0075591593

0.00305437510.00184273370.00168085940.00240975390.00201357720.00390072530.00075177730.0021167860.0031598590.00274232880.0052223143

0.00124179090.00064665490.00036045810.00205074430.00138170820.00182857810.00037809910.00026003110.00118923030.00190774450.002869044

-0.0000381530.0004038477-0.00082848920.00173461390.0010168120.00154751330.00036257210.0012457041-0.0001187530.00075599070.001747613

-0.00082546830.0000445936-0.00121694190.0010574850.00115690880.00221428070.00073887870.0022425946-0.00051213790.00058898640.0014792266

-0.00069588140.0004574101-0.0007761250.00067631730.0007284920.0023112090.00145666760.0012865277-0.00054225740.00075990140.0003788257

-0.00046908920.0012234112-0.00067290560.00042045480.00010404150.00187257540.00123487410.0006302043-0.00011292120.0009376936-0.00084121

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Figure4b-old

-0.00015147550.00064152870.00026817650.0010343393-0.00103432610.00065229610.0015865408-0.00101329160.0003241185-0.00108951840.0030855951

0.00045554910.000889487-0.00048864370.0002651839-0.00138611170.0000342159-0.0006639035-0.00070650890.00059200470.00024370890.0020372965

-0.0003077647-0.0000371669-0.0000129009-0.0008029735-0.00082784350.00020882260.0009735065-0.0001316729-0.0002385023-0.0003306774-0.0007034476

0.000248298-0.00028085260.0011579478-0.0005657412-0.0004340066-0.000012568-0.0000570333-0.00052681630.00019703660.0000568312-0.0006173754

-0.0003960824-0.0005714675-0.00065640320.00110353080.0026479618-0.0002304705-0.00025256970.0013649981-0.0005505390.0000301373-0.0007164735

0.0000988069-0.0002272526-0.00037475530.00062473590.0024338405-0.0001780918-0.00020061480.0009346203-0.0010881013-0.00000221820.0000997654

0.00123243730.0010777499-0.00112203810.0000446278-0.00062902060.0003086925-0.0000878540.0015685316-0.0000690598-0.0013888401-0.0007008023

0.00198440480.00367372120.00038935390.00171883520.00372626980.00446413530.00046704630.00201778950.0004177891-0.00027161080.001870395

0.00363444860.00885957730.00251785780.00703925350.01395868550.00840029110.00364940420.00770017860.00266588550.00442055950.0064469413

0.0059005530.00906366760.00522647690.01201802440.01491846440.00778639130.00728800990.01028400390.00591810770.00737664750.0079933421

0.00777596820.00677049080.00715751120.00971181820.01123999240.00510665930.00590866580.01099684630.00610783550.00735074860.006746833

0.00501269070.00445476640.00696788190.00695832690.00871630630.00318048970.00468433570.00939045940.00515322990.00519154290.0070936477

0.00408971520.00289084860.00524611990.00778740130.00762268590.00096657440.00192037510.00644426270.00396892220.00366092690.0053725623

0.00329469940.00086877790.00180200140.00468547430.00171496380.00079197670.00320723090.00507616440.00259011370.00213029710.0041026038

0.00188021680.00034300230.00018738760.00466817020.00284296880.000404370.00140951570.00154320810.00030084990.00109072990.0035680214

0.00118486740.0003344683-0.00075793050.0023699990.00091581440.00006215380.00085108550.00041685120.000920747-0.00066802650.0012158435

0.0014521451-0.0006275106-0.0002995872-0.00068436070.00076283760.0004078611-0.00060841120.00016071540.0007065574-0.00063810090.0030334342

0.0016367446-0.0001456142-0.00022439510.00320339680.00164615260.00061458310.00046616190.00141613490.0006576338-0.0001866660.0017843419

-0.0007618846-0.0002357776-0.00044993780.00121410630.00187555130.00057268670.00019223790.00147570230.00090284810.00066278140.0030230058

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Figure5a

0.00065393790.0012547688

0.00048054530.0009264714

0.00022938220.0005149591

0.00036053130.0005129011

0.00041529810.0010796117

0.00054071110.0009080891

0.00056232960.0009654092

0.00105722950.001560171

0.00224266410.0034252184

0.00216230510.0029103744

0.0017790460.0020520541

0.00178759090.0019047264

0.0018010780.0022027171

0.00120616910.0014575605

0.00083273590.0014786791

0.00083899020.0008921654

0.00116112590.0011441802

0.00095393770.0010599622

0.00087654250.001106432

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Young

Old


Standard Deviation across Subjects (%)

Figure5b

0.0022471580.0017502415

0.00121823710.0007097206

0.00080881090.000578197

0.00103017050.0009935188

0.00091760250.0009231083

0.00140656330.0020043842

0.0012689050.0021015481

0.00157741090.0028595283

0.00356605910.0044156023

0.00571876740.007219473

0.0070920110.0087252572

0.00691202720.0086496891

0.00562426440.0063115815

0.00413597360.0042573268

0.0016453230.0027689695

0.00158198260.0023692567

0.00126904350.0020454565

0.00132447410.0018494567

0.00155183310.0019810754

&L&A

Young

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Figure6a

0.000992429-0.0000822825-0.00384329680.00026713950.0044071236-0.00157429850.00113509260.0031888480.00179693340.00232328230.0011811804

0.00126801920.0013287765-0.00158409450.0007448621-0.0009435134-0.00016970070.00085910590.0024503632-0.0002753160.0014186874-0.0006636468

0.00074485470.0000073692-0.0008101999-0.00124496370.0004659421-0.00012707110.0010071928-0.000603022-0.0003262159-0.00127719660.0007784078

-0.00094626390.00064913450.001825227-0.00050044410.00094093790.0005297231-0.0018730037-0.00023171590.0007788452-0.0006315609-0.0000497643

-0.00106661-0.00198528010.00056906740.0010005457-0.0004633666-0.00023295130.000006705-0.0016156254-0.00017731330.0004900701-0.0000649967

-0.001069777-0.000640658-0.0002000780.0006138614-0.0002572498-0.001548919-0.0005691324-0.00311907240.00150536660.0020048701-0.0000216656

-0.0011415827-0.00090319840.0005515548-0.00080712740.001410862-0.0009622159-0.0027355703-0.00047203690.00024353740.00174034590.0002290044

-0.0005698169-0.00112641120.00124590060.00141410010.00316511340.0004339551-0.00191835260.00118933980.00095984270.00309273990.0012200009

0.00162126180.0038889650.00953649420.00528726140.00911531970.00786311520.0038707350.0101428940.00827441930.01427677220.006224896

0.00600701250.0112738480.01588207370.01173659290.01197567580.01558136380.00926119920.0176409720.01350897140.02819063510.0122170166

0.00936750690.01159053070.02129740660.01133270570.00792759240.01874785540.01255018480.01889522030.01633667290.03279133460.0120629914

0.0089441030.01033785120.01662213040.00882466190.00850402210.01964030230.00966104830.01477728940.0180200760.03110680130.0100697587

0.00683274750.01053090010.015449230.00796931310.00100742460.01230829820.00396042350.01105620740.0137347210.02167630870.0100208818

0.00528426590.0063442290.01031476690.0031638467-0.00020684980.00920932020.00181647980.00726098870.00936691360.01422297690.0053959106

0.00269615470.00302711780.00292124990.0032363120.00173925420.00416077880.00227292490.00435540950.00593573650.00728895480.0030779901

-0.00025932880.0018307952-0.00121054140.00078231270.00375501480.00099210620.00063913850.00402257350.00169893080.00265208260.0010888984

0.0001809455-0.0001339811-0.00075372910.00071646980.00126322820.00109550790.0006164280.00284729010.00077251660.00365554950.0015577768

-0.00001808850.000202709-0.0013570983-0.00046885480.00083324360.00098110180.00032241710.000715395-0.00178549680.0032301960.0007897212

-0.00098633860.00048075130.00025146570.0006230718-0.00105730950.00185887620.00056790680.001033357-0.00018436520.00461959740.000163564

&L&A

620

617

595

566

560

559

555

551

549

520

383



Figure6b

-0.0007129932-0.0002240402-0.00231038630.00073939690.00159207190.00040871040.0023612390.0012808577-0.00077325790.00151205210.0041526928

0.00025445530.00040559570.00133891970.00102147830.0002173160.00057528620.00000596450.0021341278-0.00036129410.00059501570.0012669902

-0.0001601886-0.00008412110.0002378607-0.0001186417-0.00059606910.00048478240.0009316729-0.001264384-0.0002057326-0.00022491390.000356913

-0.0003242645-0.0006663125-0.0017019519-0.00048634460.00068148010.00064802280.0008096975-0.00197241660.0010631907-0.0003919981-0.0000783068

0.00022999780.00034483790.0001251716-0.0004164921-0.000302727-0.0017080915-0.00174733490.0011026729-0.0004961640.0000218963-0.0015455964

-0.00210796230.0003250639-0.00157313960.00402656810.0026190707-0.0010028543-0.00063521140.0026915438-0.0003184150.00103467930.0022649855

0.00060212450.0008286813-0.0016910298-0.0003966832-0.00007060190.0008436548-0.00162612670.0055685007-0.0005918941-0.0019425340.001574356

0.00411088680.00051379810.00226947150.00171869980.00252703-0.00064096730.0011089590.0081126218-0.0013441488-0.00237093780.0006339794

0.00712653050.00419541920.00181992870.00769988280.00761957650.00451909820.00795169810.01825414150.00196415120.00602483850.0071341617

0.0128853840.00697017670.0082551690.01767862090.00934363950.00819447740.01676621820.03191453180.00875114580.01379958430.009338275

0.01034852440.0072295230.01163038050.0195344030.01071262680.00420416280.01347856120.03702989390.00919115550.01378265670.0111205798

0.00834932520.00571482050.01262447160.01946187890.00986187440.00436875020.01208658490.03593299240.00888451980.01150483960.0116192795

0.00687142730.0040792550.00929242870.01383921120.00487772750.00220660020.0056322490.025266780.00628135730.0084072440.0092782721

0.00385505470.00541977650.00111700890.01105026010.00331389630.00042917160.00535868680.01497027310.00660282620.00321025090.0069681602

0.00132791340.0017810970.00024262830.00640950170.00278309090.00078002630.00275416830.00860526370.00052956980.00005083940.0046630155

0.00005093970.001542112-0.00174182650.00415441380.0036922189-0.00104486710.00334931590.00482550350.00202435650.00036309280.0049777327

0.00012471710.001305868-0.00322056740.00119806440.00077326260.00031647480.00104666720.00413484110.00148387990.00089177730.0045741039

-0.00042217550.0002511234-0.0023472270.00074597810.00015299940.0000597159-0.00027542260.00484264960.00045166440.00041682270.0028401789

0.00038063020.00098837440.00075024930.00580982610.00217677590.00032513390.00038470170.00526334520.00035867650.00093968840.0011644686

&L&A

432

424

423

419

343

336

321

316

309

266

265



Figure6a-old

0.000992429-0.0000822825-0.00384329680.00026713950.0044071236-0.00157429850.00113509260.0031888480.00179693340.00232328230.0011811804

0.00126801920.0013287765-0.00158409450.0007448621-0.0009435134-0.00016970070.00085910590.0024503632-0.0002753160.0014186874-0.0006636468

0.00074485470.0000073692-0.0008101999-0.00124496370.0004659421-0.00012707110.0010071928-0.000603022-0.0003262159-0.00127719660.0007784078

-0.00094626390.00064913450.001825227-0.00050044410.00094093790.0005297231-0.0018730037-0.00023171590.0007788452-0.0006315609-0.0000497643

-0.00106661-0.00198528010.00056906740.0010005457-0.0004633666-0.00023295130.000006705-0.0016156254-0.00017731330.0004900701-0.0000649967

-0.001069777-0.000640658-0.0002000780.0006138614-0.0002572498-0.001548919-0.0005691324-0.00311907240.00150536660.0020048701-0.0000216656

-0.0011415827-0.00090319840.0005515548-0.00080712740.001410862-0.0009622159-0.0027355703-0.00047203690.00024353740.00174034590.0002290044

-0.0005698169-0.00112641120.00124590060.00141410010.00316511340.0004339551-0.00191835260.00118933980.00095984270.00309273990.0012200009

0.00162126180.0038889650.00953649420.00528726140.00911531970.00786311520.0038707350.0101428940.00827441930.01427677220.006224896

0.00600701250.0112738480.01588207370.01173659290.01197567580.01558136380.00926119920.0176409720.01350897140.02819063510.0122170166

0.00936750690.01159053070.02129740660.01133270570.00792759240.01874785540.01255018480.01889522030.01633667290.03279133460.0120629914

0.0089441030.01033785120.01662213040.00882466190.00850402210.01964030230.00966104830.01477728940.0180200760.03110680130.0100697587

0.00683274750.01053090010.015449230.00796931310.00100742460.01230829820.00396042350.01105620740.0137347210.02167630870.0100208818

0.00528426590.0063442290.01031476690.0031638467-0.00020684980.00920932020.00181647980.00726098870.00936691360.01422297690.0053959106

0.00269615470.00302711780.00292124990.0032363120.00173925420.00416077880.00227292490.00435540950.00593573650.00728895480.0030779901

-0.00025932880.0018307952-0.00121054140.00078231270.00375501480.00099210620.00063913850.00402257350.00169893080.00265208260.0010888984

0.0001809455-0.0001339811-0.00075372910.00071646980.00126322820.00109550790.0006164280.00284729010.00077251660.00365554950.0015577768

-0.00001808850.000202709-0.0013570983-0.00046885480.00083324360.00098110180.00032241710.000715395-0.00178549680.0032301960.0007897212

-0.00098633860.00048075130.00025146570.0006230718-0.00105730950.00185887620.00056790680.001033357-0.00018436520.00461959740.000163564

&L&A

620

617

595

566

560

559

555

551

549

520

383



Figure6b-old

-0.0007129932-0.0002240402-0.00231038630.00073939690.00159207190.00040871040.0023612390.0012808577-0.00077325790.00151205210.0041526928

0.00025445530.00040559570.00133891970.00102147830.0002173160.00057528620.00000596450.0021341278-0.00036129410.00059501570.0012669902

-0.0001601886-0.00008412110.0002378607-0.0001186417-0.00059606910.00048478240.0009316729-0.001264384-0.0002057326-0.00022491390.000356913

-0.0003242645-0.0006663125-0.0017019519-0.00048634460.00068148010.00064802280.0008096975-0.00197241660.0010631907-0.0003919981-0.0000783068

0.00022999780.00034483790.0001251716-0.0004164921-0.000302727-0.0017080915-0.00174733490.0011026729-0.0004961640.0000218963-0.0015455964

-0.00210796230.0003250639-0.00157313960.00402656810.0026190707-0.0010028543-0.00063521140.0026915438-0.0003184150.00103467930.0022649855

0.00060212450.0008286813-0.0016910298-0.0003966832-0.00007060190.0008436548-0.00162612670.0055685007-0.0005918941-0.0019425340.001574356

0.00411088680.00051379810.00226947150.00171869980.00252703-0.00064096730.0011089590.0081126218-0.0013441488-0.00237093780.0006339794

0.00712653050.00419541920.00181992870.00769988280.00761957650.00451909820.00795169810.01825414150.00196415120.00602483850.0071341617

0.0128853840.00697017670.0082551690.01767862090.00934363950.00819447740.01676621820.03191453180.00875114580.01379958430.009338275

0.01034852440.0072295230.01163038050.0195344030.01071262680.00420416280.01347856120.03702989390.00919115550.01378265670.0111205798

0.00834932520.00571482050.01262447160.01946187890.00986187440.00436875020.01208658490.03593299240.00888451980.01150483960.0116192795

0.00687142730.0040792550.00929242870.01383921120.00487772750.00220660020.0056322490.025266780.00628135730.0084072440.0092782721

0.00385505470.00541977650.00111700890.01105026010.00331389630.00042917160.00535868680.01497027310.00660282620.00321025090.0069681602

0.00132791340.0017810970.00024262830.00640950170.00278309090.00078002630.00275416830.00860526370.00052956980.00005083940.0046630155

0.00005093970.001542112-0.00174182650.00415441380.0036922189-0.00104486710.00334931590.00482550350.00202435650.00036309280.0049777327

0.00012471710.001305868-0.00322056740.00119806440.00077326260.00031647480.00104666720.00413484110.00148387990.00089177730.0045741039

-0.00042217550.0002511234-0.0023472270.00074597810.00015299940.0000597159-0.00027542260.00484264960.00045166440.00041682270.0028401789

0.00038063020.00098837440.00075024930.00580982610.00217677590.00032513390.00038470170.00526334520.00035867650.00093968840.0011644686

&L&A

432

424

423

419

343

336

321

316

309

266

265



Figure7

0.0235329810.02145548960.0277253610.0151423732

-0.0003816071-0.00743422080.0088404521-0.0015561697

0.00377222350.0054869604-0.02796186160.0048439374

0.0088427014-0.0076359742-0.0035424224-0.0020256505

-0.011403157-0.0086881308-0.0028668325-0.0089947498

-0.0243631433-0.0031841242-0.0021946948-0.0074097405

-0.02601251480.00624167850.0076843612-0.0108347354

0.08172243090.10815557370.02048613970.0428808125

0.41017190570.37093190310.22839565370.2090057758

0.76624782790.52208568460.43558327180.3525227326

0.87815801660.52280856930.46529474040.3492343556

0.81023406440.4144907270.42213073640.2790149996

0.5444332280.27525478990.31212074920.1944149423

0.32405985760.14504170940.20478507130.1272018239

0.16789818690.06045954560.11302671310.0497489259

0.08935078270.03371313270.07641718660.0311441854

0.04339495310.03621939530.02851965280.0162312292

0.01115029330.02890750860.01224559280.0304626051

0.01858230430.02303372020.04257410960.024029873

Young-Max

Young-CC

Old-Max

Old-CC


Signal-Noise Ratio

Figure8

0.45454545450.5454545455

0.90909090911.1818181818

2.36363636363.4545454545

712.3636363636

22.090909090937.6363636364

83.6363636364125.1818181818

296.1818181818372.6363636364

885.63636363641050.2727272727

20072275.6363636364

40274.272727272740079.1818181818

2391.63636363642665.8181818182

1372.45454545461409.7272727273

730.3636363636623.1818181818

392.4545454545256.4545454545

245.8181818182121.8181818182

14856.3636363636

102.181818181827.2727272727

60.272727272715.8181818182

41.54545454556.7272727273

26.90909090913.9090909091

19.90909090912.7272727273

11.45454545451.2727272727

7.72727272730.8181818182

6.36363636360.6363636364

&L&A

Young

Old

Voxel t-value (by correlation w/reference function)

Number of Voxels

Figure9

00

0.01043634730.0084533087

0.08340080970.0577202483

0.15861448490.1306300357

0.15375618530.1518953903

0.13585245160.1332716946

0.10049482680.1124025888

0.07701304540.0957601374

0.05874943770.066041474

0.04624381470.0519085986

0.0329284750.043191124

0.02860998650.03315282

0.02357174990.0210011887

0.01682411160.0191520275

0.01421502470.0143970413

0.01088618980.0110949676

0.00854700850.0091137234

0.00728744940.0056795668

0.00503823660.0056795668

0.00530814220.0046229032

0.0044084570.0048870691

0.00332883490.002641659

0.00251911830.0021133272

0.00260908680.005151235

0.00179937020.0015849954

0.00233918130.0014529124

0.00170940170.0029058249

0.00170940170.0015849954

0.00080971660.0017170783

0.00098965360.0007924977

Young

Old

Peak Amplitude (% change over baseline)

Percentage of All Active Voxels

Figure10

00

0.00008438110

00

00.0001838911

00

00

00

00

0.00033752430.0003677823

0.00016876210

0.00016876210.0001838911

0.00143447810.0016550202

0.00869124970.00809121

0.0273394650.0220669364

0.02556746270.0312614932

0.0442156780.041743288

0.09914775120.0994851048

0.09560374650.0882677455

0.0702050460.0678558293

0.09678508140.0888194189

0.12657159730.1289076866

0.07535229090.0796248621

0.05130368750.0470761309

0.06303265550.0617874218

0.07138638090.076866495

0.03628385790.036410445

0.02025145560.0237219566

0.0286051810.0257447591

0.02278288750.0264803236

0.00869124970.0095623391

0.00506286390.006803972

0.00658172310.0079073189

0.00590667450.0084589923

0.00151885920.0018389114

0.0012657160.0009194557

0.00143447810.0023905848

0.00236266980.001287238

&L&A

Young

Old

Peak latency (seconds)

Percentage of all Active Voxels

Figure11a

-7-0.0002009164

-60.0001439892

0.0004428983-0.0002183595

-0.0000087382-0.0000897524

0.00014019580.0001641227

-0.00002873320.0001122967

-0.00010272440.0001754665

0.00000667230.0001686958

0.0000875837-0.0004816259

0.0015899871-0.0001652516

0.00565683060.0021797345

0.00812137590.0044904474

0.00841284040.0054854581

0.00694245830.0053570765

0.00487329490.0036547452

0.00262682640.0018026685

0.00128309850.0002716521

0.000711752-0.0001398711

0.0006334915-0.0001571379

0.000549189712

0.000393375413

&L&A

Single

2s IPI



Figure11b

-7-0.0003030359

-60.000196098

0.00039127120.000225093

0.0001156617-0.000109256

-0.0002009655-0.000311935

-0.0000758436-0.000597045

0.0001611475-0.0001402768

0.0001927941-0.0007841734

0.0000213113-0.0007999693

0.0018598299-0.000647459

0.00629937120.0028040002

0.00852488080.0053890375

0.00771576080.0057673728

0.00607306160.0051718972

0.00454276310.0033003835

0.00275130030.0019429611

0.00165804010.0007020322

0.0006223521-0.0005194374

0.0003332346-0.0002371062

0.000988043112

0.0007701213

&L&A

Single

2s IPI



Figure12

0.000225093-0.0001619564-0.0002881930.0000452622

-0.000109256-0.00015136810.0002510415-0.0000598826

-0.0003119350.00018836670.00029011450.0000048629

-0.0005970450.0002748113-0.0004275740.0004305983

-0.00014027680.0002702881-0.00032928210.0001550151

-0.00078417340.000267405-0.0002801354-0.0002653871

-0.0007999693-0.000328272-0.0007208404-0.0006900423

-0.0006474590.0000187039-0.0010369778-0.0012925429

0.00280400020.00238664360.00083480830.000290537

0.00538903750.00460747950.00320385250.0024027116

0.00576737280.00566520470.00450568440.0038493889

0.00517189720.00541147260.00367539790.0037378512

0.00330038350.00356425850.00239613080.0023280408

0.00194296110.0017003240.00022732930.001012067

0.00070203220.00005312330.00067474810.0001190449

-0.0005194374-0.0002466141-0.0005457737-0.0001887908

-0.0002371062-0.00013179330.0000479335-0.0008240839

&L&A

CC-Old

CC-Young

FFG-Old

FFG-Young



FigRandA

0.00049554030.00044296490.0002109965-0.0008865490.0007737929-0.00157426110.00106032480.00199978170.00080591790.00296142530.0025559076

0.00089870560.0010298221-0.00057211770.0002980405-0.0001977735-0.00016973820.0006543038-0.00060823480.0009005854-0.00060935260.0025633819

-0.00061225530.0006372417-0.00057860490.0009976334-0.0019129409-0.0001270194-0.00033797530.0007220985-0.00040001740.0004734707-0.000313619

-0.0003631069-0.00081419010.0010509818-0.00081396840.00077120240.0005296807-0.00059700540.0002835173-0.0009194786-0.0010881128-0.0010670762

0.0000766565-0.00085287380.0000997408-0.00048170550.001339512-0.00023292310.0002806769-0.00039738090.00041891060.0012239947-0.0011826867

0.00072181490.0006332149-0.0007317031-0.0004956857-0.0001291865-0.0015489222-0.00207775190.0022084789-0.0005984965-0.0012714828-0.0012140305

0.00026023340.0013482697-0.0006554784-0.0001810146-0.000631623-0.0009622289-0.00358675170.00057924560.0017664437-0.00170357770.0010423628

0.00080521630.0054842596-0.00033847010.00166052820.0000192130.00043401010.00100613180.00403359570.0038695690.00038695770.0021518134

0.0009735440.01038131540.00190177920.00366936750.00394174560.00786318420.00615969930.00786195130.00897233720.00807368650.0055591276

0.00205752740.01180535180.00384891490.00261456090.00477194390.01558131930.00527495360.01122749410.00695244940.01457944210.0076257702

0.00269858020.00893252410.00299476570.00351768230.00623694160.01874787120.00461392130.01084498840.00657673770.01357243530.0086373317

0.00187043140.00597090880.00033036110.00232610260.00523034160.01964025570.00177360150.00686147370.00557721530.01247879780.0080384237

0.00117588910.0028417519-0.00031208880.00126686890.00491923310.01230837650.001122190.00470612060.00304916190.00679044920.0059169294

0.0004020510.0012087179-0.00047556640.00220831940.001480880.00920939510.00053507930.00421539690.00050712350.00158309420.0026061782

0.00029730070.001149306-0.0008256595-0.00062791520.00027209660.00416077930.00016206130.00318168-0.0002997021-0.00108446890.0019278257

0.0004630478-0.0003141402-0.0013124163-0.00316776930.00212184740.0009921159-0.00132185140.00213794050.00083012260.0013835030.000341949

0.00000850440.0001118428-0.0013919928-0.0010405643-0.00057660540.0010955831-0.00134827810.00265010490.00032357070.0008429142-0.0012829869

0.00035524770.0003508105-0.0010701191-0.00028260410.00135246450.0009810707-0.00233605130.001091410.00114814640.0027552516-0.0008751556

-0.00010997020.0001505266-0.0017485730.00022079990.00060022840.0018588366-0.0007689615-0.00020872890.00092546250.0052193446-0.0024518702

&L&A

620

617

595

566

560

559

555

551

549

520

383



FigRandB

-0.00282624670.0014226639-0.0020313417-0.00093224430.00059173650.0020617730.0002492203-0.00238575370.00016813470.00056440750.0009116671

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-0.0010245315-0.00076798580.0002352722-0.0008874509-0.0001995793-0.00187935920.0009103879-0.00158188150.00032564720.000518067-0.0011023268

0.0010071445-0.0001766342-0.000537142-0.00044886110.0003691470.0002337779-0.0008796718-0.00021898980.0033707332-0.0005630697-0.0002246867

0.00099595290.00026370810.00192372310.00297635150.0007138252-0.0004902941-0.00101897560.0019774061-0.0000234156-0.0008011938-0.0003066308

-0.0004336414-0.00149715370.00083074850.00267777820.0025272146-0.0002571253-0.0011366484-0.0031579147-0.0001952475-0.00099757920.0002010192

-0.0004590890.00112450170.00152603930.00055735910.00198503570.0012504022-0.00001047560.0001556538-0.00275124640.0001039987-0.0016658478

0.00071602960.00491384070.00215063370.00104356040.0023190657-0.00008648670.0005683705-0.0025983752-0.00433388360.0008353873-0.0021312842

0.00435290160.0064386490.00236154250.00376097780.0068733980.00389941150.00312021310.00638198110.00065170520.00053551160.0016176591

0.00617939820.00793707130.00392853720.00518561580.00989527610.007818110.00467406210.0052687940.00667720550.0015571440.0045845637

0.00663892010.00767026790.00355459380.00745153940.00817859490.00353712180.00322948060.00815452020.00387132260.00521686990.0034070826

0.00299791790.00523646070.00213673050.00510136860.0029793950.00358056810.00362773860.00571985660.00549809150.00391473260.0017065871

0.00259395430.00441829070.00285431880.0019152520.00376604320.00285842480.00098887760.00289478040.00481205510.00001195970.0046578168

0.0013624780.00176152150.00217489870.00352469990.00367823260.00032330990.00051793940.00327011710.00200065580.00058581190.0017941183

-0.00058459480.0020854608-0.00102362250.00415566410.00393174540.00000781630.00096786460.0017911240.00195312030.00055531060.0011859005

-0.0010202680.0053837151-0.00251021480.00432490010.00181612440.00111468310.0005199171-0.0033967023-0.0006258835-0.00002496290.0004575601

0.00108828370.0028967299-0.00180508690.00193705540.0026123996-0.00006070310.0016310099-0.00617845710.00057435740.00000254180.0006762329

0.00011754520.0020584659-0.0009278741-0.00198429610.00358050330.00125588380.00248067650.00128305040.0008995938-0.00011111560.0016522681

-0.00300251450.00194449850.0005981980.00305036440.00103924920.00095916960.001843612-0.0001962893-0.00340876150.00040976070.0010712098

&L&A

432

424

423

419

343

336

321

316

309

266

265



FigRandSTD

0.00135319640.001615476

0.00096485410.0017120156

0.00081932930.0009094502

0.00078795760.0011806088

0.0007826330.0012864433

0.00122139720.0016997953

0.00152667990.0014035038

0.00190284670.0025652825

0.00301961110.0022573873

0.00475440180.0022634625

0.00495732840.0020958903

0.0055922460.0013725315

0.00355523380.001511953

0.00266872380.0011919033

0.00169470770.0016618148

0.001617810.0026204284

0.0012583460.0025298188

0.00139624080.0015857161

0.00201159780.0019784767

&L&A

Young

Old



Subject 14.0s5.5sSubject 2Huettel et al., 2001

Width of fMRI response increases with duration of mental activityFrom Menon and Kim, 1999; after Richter et al, 1997

Independence of Timing and AmplitudeAdapted from Miezin et al. (2000)

Linearity of the Hemodynamic Response

Linear SystemsScalingThe ratio of inputs determines the ratio of outputsExample: if Input1 is twice as large as Input2, Output1 will be twice as large as Output2

SuperpositionThe response to a sum of inputs is equivalent to the sum of the response to individual inputsExample: Output1+2+3 = Output1+Output2+Output3

Scaling (A) and Superposition (B)BA

Chart1

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0

-0.03

-0.3

0.6

1.65

2.76

3

2.82

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5123

60.941.882.82

70.81.62.4

80.61.21.8

90.40.81.2

100.220.440.66

110.10.20.3

12000

13-0.05-0.1-0.15

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21000

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ImpulseExtendedeventsust1/2 event

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00051110.5

0.5-0.0560.940.940.940.47

1-0.1-0.170.80.80.820.4

1.5-0.0780.60.60.80.3

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2.50.1100.220.220.80.11

30.25110.10.10.80.05

3.50.412000.80

40.613-0.05-0.050.8-0.025

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7.50.7520-0.05-0.05-0.1-0.025

80.652100-0.10

8.50.552200-0.050

90.47

9.50.4

100.2

10.50.10

110-0.05

11.5-0.05-0.1

12-0.1-0.2

12.5-0.2-0.2

13-0.2-0.15

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14.5-0.050

1500

15.500

1600

16.500

1700

17.500

1800

18.50

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19.5

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Chart2

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1.84

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30.551.11.65

40.921.842.76

5123

60.941.882.82

70.81.62.4

80.61.21.8

90.40.81.2

100.220.440.66

110.10.20.3

12000

13-0.05-0.1-0.15

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15-0.1-0.2-0.3

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21000

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-10030.550.550.550.275

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00051110.5

0.5-0.0560.940.940.940.47

1-0.1-0.170.80.80.820.4

1.5-0.0780.60.60.80.3

2-0.0290.40.40.80.2

2.50.1100.220.220.80.11

30.25110.10.10.80.05

3.50.412000.80

40.613-0.05-0.050.8-0.025

4.50.814-0.08-0.080.75-0.04

50.9415-0.1-0.10.6-0.05

5.51116-0.1-0.10.43-0.05

6117-0.1-0.10.25-0.05

6.50.9418-0.1-0.10.12-0.05

70.8519-0.08-0.08-0.08-0.04

7.50.7520-0.05-0.05-0.1-0.025

80.652100-0.10

8.50.552200-0.050

90.47

9.50.4

100.2

10.50.10

110-0.05

11.5-0.05-0.1

12-0.1-0.2

12.5-0.2-0.2

13-0.2-0.15

13.5-0.15-0.1

14-0.1-0.05

14.5-0.050

1500

15.500

1600

16.500

1700

17.500

1800

18.50

19

19.5

20

Chart3

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0

0

0

0

-0.01

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0.55

0.92

1

0.94

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20.20.40.6

30.551.11.65

40.921.842.76

5123

60.941.882.82

70.81.62.4

80.61.21.8

90.40.81.2

100.220.440.66

110.10.20.3

12000

13-0.05-0.1-0.15

14-0.08-0.16-0.24

15-0.1-0.2-0.3

16-0.1-0.2-0.3

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21000

22000

Sheet2

Sheet1


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00051110.5

0.5-0.0560.940.940.940.47

1-0.1-0.170.80.80.820.4

1.5-0.0780.60.60.80.3

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2.50.1100.220.220.80.11

30.25110.10.10.80.05

3.50.412000.80

40.613-0.05-0.050.8-0.025

4.50.814-0.08-0.080.75-0.04

50.9415-0.1-0.10.6-0.05

5.51116-0.1-0.10.43-0.05

6117-0.1-0.10.25-0.05

6.50.9418-0.1-0.10.12-0.05

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7.50.7520-0.05-0.05-0.1-0.025

80.652100-0.10

8.50.552200-0.050

90.47

9.50.4

100.2

10.50.10

110-0.05

11.5-0.05-0.1

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1500

15.500

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17.500

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Chart2

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20.200.2

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100.220.20.42

110.10.550.65

1200.920.92

13-0.0510.95

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16-0.10.60.5

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210-0.05-0.05

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30000

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Sheet1


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-10030.550.550.550.275

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00051110.5

0.5-0.0560.940.940.940.47

1-0.1-0.170.80.80.820.4

1.5-0.0780.60.60.80.3

2-0.0290.40.40.80.2

2.50.1100.220.220.80.11

30.25110.10.10.80.05

3.50.412000.80

40.613-0.05-0.050.8-0.025

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7.50.7520-0.05-0.05-0.1-0.025

80.652100-0.10

8.50.552200-0.050

90.47

9.50.4

100.2

10.50.10

110-0.05

11.5-0.05-0.1

12-0.1-0.2

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1500

15.500

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16.500

1700

17.500

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18.50

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19.5

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Chart1

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20.200.2

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100.220.20.42

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1200.920.92

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Sheet1


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00051110.5

0.5-0.0560.940.940.940.47

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30.25110.10.10.80.05

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40.613-0.05-0.050.8-0.025

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7.50.7520-0.05-0.05-0.1-0.025

80.652100-0.10

8.50.552200-0.050

90.47

9.50.4

100.2

10.50.10

110-0.05

11.5-0.05-0.1

12-0.1-0.2

12.5-0.2-0.2

13-0.2-0.15

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14.5-0.050

1500

15.500

1600

16.500

1700

17.500

1800

18.50

19

19.5

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Chart3

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Possible Sources of NonlinearityStimulus time course neural activityActivity not uniform across stimulus (for any stimulus)

Neural activity Vascular changesDifferent activity durations may lead to different blood flow or oxygen extractionMinimum bolus size?Minimum activity necessary to trigger?

Vascular changes BOLD measurementSaturation of BOLD response necessitates nonlinearityVascular measures combining to generate BOLD have different time coursesFrom Buxton, 2001

Effects of Stimulus DurationShort stimulus durations evoke BOLD responsesAmplitude of BOLD response often depends on durationStimuli < 100ms evoke measurable BOLD responses

Form of response changes with durationLatency to peak increases with increasing durationOnset of rise does not change with duration Rate of rise increases with duration

Key issue: deconfounding duration of stimulus with duration of neuronal activity

The fMRI Linear Transform

Boynton et al., 1996Varied contrast of checkerboard bars as well as their interval (B) and duration (C).

Boynton, et al, 1996

Differences in Nonlinearity across Brain RegionsBirn, et al, 2001

SMA vs. M1Birn, et al, 2001

Caveat: Stimulus Duration Neuronal Activity Duration

Refractory PeriodsDefinition: a change in the responsiveness to an event based upon the presence or absence of a similar preceding eventNeuronal refractory periodVascular refractory period

Dale & Buckner, 1997Responses to consecutive presentations of a stimulus add in a roughly linear fashionSubtle departures from linearity are evident

Huettel & McCarthy, 2000500 ms duration

Methods and Analysis16 male subjects (mean age: 27y) GE 1.5T scanner CAMRDGradient-echo EPI TR : 1 secTE : 50 msecResolution: 3.125 * 3.125 * 7 mmAnalysisVoxel-based analysesWaveforms derived from active voxels within anatomical ROIHuettel & McCarthy, 2000

Hemodynamic Responses to Closely Spaced StimuliHuettel & McCarthy, 2000

Refractory Effects in the fMRI Hemodynamic ResponseHuettel & McCarthy, 2000Time since onset of second stimulus (sec)Signal Change over Baseline(%)

Refractory Effects across Visual RegionsHDRs to 1st and 2nd stimuli in a pair (calcarine cortex)Relative amplitude of 2nd stimulus in pair across regions

Figure 2LRMean HDRsTime since stimulus onset (sec)Signal Change over baseline (%)

Refractory Effect SummaryDurationHDR evoked by a long-duration stimulus is less than predicted by convolution of short-duration stimuliPresent for durations < ~6sInterstimulus interval HDR evoked by a stimulus is reduced by a preceding similar stimulusPresent for intervals < ~6sDifferences across brain regionsSome regions show considerable departures from linearityMay result from differences in processingSource of non-linearity not well understoodNeuronal effects comprise at least part of the overall effectVascular differences may also contribute

Using refractory effects to study cognition: fMRI Adaptation Studies

Neuronal AdaptationSeveral neuronal populations vs. homogeneous populationAdaptationIf neurons are insensitive to the feature being varied, then their activity will adapt.Viewpoint SensitiveViewpoint InvariantGrill-Spector & Malach, 2001

Lateral OccipitalPosterior Fusiform

Is the refractory effect attribute specific?Boynton et al., 2003

Lateral Temporal-OccipitalPeri-CalcarineABCDLongShortHuettel, Obembe, Song, Woldorff, in preparation

Overall SummarySpatial resolutionAdvantages (of increasing)Smaller voxels allow distinction among areasDisadvantagesRequire more slices, thus longer TRReduces signal per voxelTemporal resolutionAdvantages (of increasing)Improves sampling of hemodynamic responseDisadvantagesReduces # of slices per TRMay not be necessary for some designsNon-linearity of hemodynamic responseAdvantages (of phenomenon for design)May be used to study adaptationDisadvantagesReduces power of short interval designsMust be accounted for in analyses

fmri-fig-08-01-0.jpg fmri-fig-08-06-0.jpg We also investigated the latency of the hemodynamic response across brain regions.We found, in both elderly and young adults, that the hemodynamic response in primary visual cortex anticipates that in fusiform cortex by about 300 ms. This result has since been replicated using face stimuli. These figures demonstrate this effect on an individual voxel level. The overlaid color maps are not traditional significance maps; they are maps of latency to hemodynamic peak, with earliest responses in blue and latest responses in yellow. As can be seen, on the left image, activation in the fusiform gyri generally has a much later peak than that in calcarine cortex, shown at right.Our basic design was derived from electrophysiological studies of refractory periods. We presented either a single short duration visual checkerboard, or a pair of checkerboards separated by an intra-pair interval of either 1, 2, 4, or 6 seconds. A long inter-trial interval ensured that the hemodynamic response returned to baseline before the onset of the next trial. Our hypothesis was that the second stimulus in the pair would have relatively little effect upon the composite waveform at short intervals, like 1 or 2 seconds, but would have a large effect at long intervals. That is, the hemodynamic response would be relatively linearly additive at long-intervals, but non-linear at short intervals.The study was conducted at 1.5T in the center for advanced magnetic resonance development at Duke. We took two echo-planar slices chosen to bracket the calcarine sulcus in each subject, and sampled those slices with repetition time of 1 sec. In each subject we identified a functional ROI consisting of contiguous active voxels in calcarine cortex. These graphs show the time courses of fMRI activation in calcarine cortex. The yellow line that is repeated in each graph shows the response to a single stimulus. The colored lines show the response to pairs of stimuli. Readily apparent is the contribution of the second stimulus above that of the single stimulus condition. To determine how large of a hemodynamic response was evoked by the second stimulus, we took the residual area between the two curves (the additive effect of the second stimulus), and we time-locked that difference to the onset of the second stimulus.The independent contribution of the second stimulus is shown on this plot.The yellow line shows the response to a single stimulus.Readily apparent are the significant refractory effects. At 1 second intervals, the response to the second stimulus is attenuated in amplitude by about 45% and is increased in latency by about a second. Both amplitude and latency values recover to near single-stimulus values by about six seconds.

I. Spatial & Temporal Properties (cont.) II. Signal and Noise BIAC Graduate fMRI Course October 11, 2005.

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