Cartography and ChronometryWhy do you need to know?Spatial ResolutionWhat spatial resolution do we want?What determines Spatial Resolution?K – Space RevisitedHow large are functional voxels?How large are anatomical voxels?Costs of Increased Spatial ResolutionEffects of Stimulus Duration on Spatial Extent of ActivityExample: Ocular DominancePowerPoint PresentationExample: Visual SystemT2* BlurringTemporal ResolutionWhat temporal resolution do we want?Basic Sampling TheorySlide 18AliasingFrequency AnalysesPhase AnalysesWhy do we want to measure differences in timing within a brain region?Timing Differences across RegionsSlide 24Slide 25Slide 26Linearity of the Hemodynamic ResponseLinear SystemsPossible Sources of NonlinearityEffects of Stimulus DurationBoynton et al., 1996Slide 32Slide 33Differences in Nonlinearity across Brain RegionsSMA vs. M1Caveat: Stimulus Duration ≠ Neuronal Activity DurationSlide 37Slide 38Refractory PeriodsDale & Buckner, 1997Slide 41Methods and AnalysisHemodynamic Responses to Closely Spaced StimuliRefractory Effects in the fMRI Hemodynamic ResponseRefractory Effects across Visual RegionsSlide 46Figure 2Refractory Effect SummaryUsing refractory effects to study cognition: fMRI Adaptation StudiesNeuronal AdaptationSlide 51Overall SummaryCartography and ChronometryfMRI Graduate CourseOctober 9, 2002Why do you need to know?•Spatial resolution–Tradeoffs between coverage and spatial resolution–Influences viability of preprocessing steps•Temporal resolution–Tradeoffs between number of slices and TR–Needed resolution depends upon design•Non-linearity of the hemodynamic response–Limits experimental designs–Affects subsequent analyses–Reduces powerSpatial ResolutionWhat spatial resolution do we want?•Hemispheric–Lateralization studies–Selective attention studies•Systems / lobic–Relation to lesion data•Centimeter–Identification of active regions •Millimeter–Topographic mapping (e.g., motor, vision)•Sub-millimeter–Ocular Dominance Columns–Cortical LayersWhat determines Spatial Resolution?•Voxel Size–In-plane Resolution–Slice thickness•Spatial noise–Head motion–Artifacts•Spatial blurring–Smoothing (within subject)–Coregistration (within subject)–Normalization (within subject)–Averaging (across subjects). . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .AABBFOV: 10 cm, Pixel Size: 1 cmFOV: 10 cm, Pixel Size: 1 cmFOV: 10cm, Pixel Size: 2 cmFOV: 10cm, Pixel Size: 2 cmK – Space RevisitedTo increase spatial resolution we need to sample at higher spatial frequencies.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.Costs of Increased Spatial Resolution•Acquisition Time–In-plane•Higher resolution takes more time to fill K-space (resolution ~ size of K-space)–#Slices/second–Sample rates for 64*64 images•Early Duke fMRI: 2-4 sl/s•GE EPI: 12 sl/s•Duke Spiral (1.5T): 14 sl/s•Duke Inverse Spiral (4.0T): 21 sl/s•Reduced signal per voxel–What is our dependent measure?Effects of Stimulus Duration on Spatial Extent of ActivityExample: Ocular DominanceGoodyear & Menon, 20014sec 10sec Goodyear & Menon, 2001Example: Visual System100ms500ms1500 msT2* Blurring•Signal decays over time needed for collection of an image•For standard resolution images, this is not a critical issue•However, 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.Temporal ResolutionWhat temporal resolution do we want?•10,000ms: Change in arousal or emotional state•1000ms: Decisions, recall from memory•500-1000ms: Response time•250ms: Reaction time•10-100ms: –Difference between response times–Initial visual processing•10ms: Neuronal activity in one areaBasic Sampling Theory•Nyquist Sampling Theorem–To be able to identify changes at frequency X, one must sample the data at 2X.–For example, if your task causes brain changes at 1 Hz (every second), you must take two images per second.Aliasing•Mismapping of high frequencies (above the Nyquist limit) to lower frequencies–Results from insufficient sampling–Potential problem for designs with long TRs and fast stimulus changesFrequency Analysest < -1.96 t < +1.96McCarthy et al., 1996Phase Analyses•Design–Left/right alternating flashes–6.4s for each•Task frequency:–1 / 12.8 = 0.078McCarthy et al., 1996Why do we want to measure differences in timing within a brain region?•Determine relative ordering of activity•Make inferences about connectivity–Anatomical–Functional•Relate activity timing to other measures–Stimulus presentation –Reaction time–Relative amplitudeTiming 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. StimulusMenon et al., 1998Activation mapsRelative onset time differencesV1FFGHuettel et al., 2001Subject 14.0s5.5sSubject 2Primary Visual Cortex (V1)Secondary Visual Cortex (FFG)Huettel et al., 2001Linearity of the Hemodynamic ResponseLinear Systems•Scaling–The ratio of inputs determines the ratio of outputs–Example: if Input1 is twice as large as Input2, Output1 will be twice as large as Output2•Superposition–The response to a sum of inputs is equivalent to the sum of the response to individual inputs–Example: Output1+2+3 = Output1+Output2+Output3Possible Sources of Nonlinearity•Stimulus time course  neural activity–Activity not uniform across stimulus (for any stimulus)•Neural activity  Vascular changes–Different activity durations may lead to different blood flow or oxygen extraction•Minimum bolus size?•Minimum activity necessary to