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Peter A. Bandettini, Ph.D.!!
Section on Functional Imaging Methods!
Laboratory of Brain and Cognition!http://fim.nimh.nih.gov!
&!Functional MRI Facility!
http://fmrif.nimh.nih.gov!!
bandettini@nih.gov!
Twenty Years of Functional MRI!
(1990) Science, 250, 53-61.!angiography!
Gadolinium perfusion!
Diffusion!magnetization transfer!
metabolic imaging (NAA)!
NAA! choline!
creatine! lactate!
Five Key Factors For The !Emergence of Functional MRI!
1. Magnetic properties of red blood cells !2. Activation related hemodynamic changes!3. Spatial scale of brain activation!4. Echo Planar Imaging!5. Prevalence of MRI scanners!
Five Key Factors For The !Emergence of Functional MRI!
1. Magnetic properties of red blood cells !2. Activation related hemodynamic changes!3. Spatial scale of brain activation!4. Echo Planar Imaging!5. Prevalence of MRI scanners!
red blood cells
L. Pauling, C. D. Coryell, Proc.Natl. Acad. Sci. USA 22, 210-216, 1936.!
!
K.R. Thulborn, J. C. Waterton, et al., Biochim. Biophys. Acta. 714: 265-270, 1982.!
!
S. Ogawa, T. M. Lee, A. R. Kay, D. W. Tank, Proc. Natl. Acad. Sci. USA 87, 9868-9872, 1990.!
!
Turner, R., Lebihan, D., Moonen, C. T. W., Despres, D. & Frank, J. Magnetic Resonance in Medicine, 22, 159-166, 1991.!
oxygenated
deoxygenated
Magnetic Properties of Blood!
Blood R2 proportional to Oxygenation!R2 effect is bulk susceptibility and not dipole-dipole!
S. Ogawa, T.-M. Lee, A. S. Nayak, P. Glynn, Magn. Reson. Med, 14, 68-78 (1990) !
100% O2!
20% O2!
in vivo!
100% oxygenated blood!
0% oxygenated blood!
in vitro!
R. Turner, D. LeBihan, C.T.W. Moonen, D. Despres, J. Frank, Magn. Reson. Med, 22, 159-166 (1991) !
“BOLD contrast adds to…functional MRI methodologies that are likely to be complementary to PET imaging in the study of regional brain activity.” !
Ogawa, S., Lee, T. M., Kay, A. R. and Tank, D. W. (1990) Proceedings of the National Academy of Sciences of the United States of America, 87, 9868-9872.!
Five Key Factors For The !Emergence of Functional MRI!
1. Magnetic properties of red blood cells !2. Activation related hemodynamic changes!3. Spatial scale of brain activation!4. Echo Planar Imaging!5. Prevalence of MRI scanners!
Cerebral Tissue Activation!
Local Vasodilatation!
Increase in Cerebral Blood!Flow and Volume!
Oxygen Delivery Exceeds!Metabolic Need!
Increase in Capillary and Venous Blood Oxygenation!
Decrease in Deoxy-hemoglobin!Deoxy-hemoglobin: paramagnetic!Oxy-hemoglobin: !diamagnetic!
Decrease in susceptibility-related!intravoxel dephasing!
Increase in T2 and T2*!
Local Signal Increase in T2 and T2* - weighted sequences!
task task
Five Key Factors For The !Emergence of Functional MRI!
1. Magnetic properties of red blood cells !2. Activation related hemodynamic changes!3. Spatial scale of brain activation!4. Echo Planar Imaging!5. Prevalence of MRI scanners!
Brain Function!
visual
Language, reading, speech
motor sensory motor planning
Behavioral control, cognitive, socialization
memory auditory
1991!
http://www.thebrain.mcgill.ca!
Visual Cortex Organization!
Yacoub et al. PNAS 2008!Scalebar = 0.5 mm
Orientation Columns in Human V1 as Revealed by fMRI at 7T
Phase 0° 180°
Phase Map
Yacoub et al. PNAS 2008
Functional Neuroimaging Techniques!
Log Time (sec)!
Log
Size
(m
m)!
Non-invasive!
Invasive!
Five Key Factors For The !Emergence of Functional MRI!
1. Magnetic properties of red blood cells !2. Activation related hemodynamic changes!3. Spatial scale of brain activation!4. Echo Planar Imaging!5. Prevalence of MRI scanners!
MRI vs. fMRI!MRI! fMRI!
one image!
many images !(e.g., every 2 sec for 5 mins)!
high resolution!(1 mm)!
…!
T2* decay!
EPI Readout Window!� 20 to 40 ms!
Single Shot Echo Planar Imaging (EPI)!
August, 1991
1991-1992"
1992-1999"
1976 P. Mansfield conceives of EPI!1989 EPI of humans emerges on a handful of scanners!
! 3 x 3 x 3-10 mm3!1989 ANMR retrofitted with GE scanners for EPI!1991 Home built head gradient coils perform EPI!1996 EPI is standard on clinical scanners!2000 Gradient performance continues to increase!2002 Parallel imaging allows for higher resolution EPI!2006 1.5 x 1.5 x 1.5 mm3 single shot EPI possible!2009 At 7T sub – mm single shot EPI for fMRI is possible!
Approximate EPI Timeline!
Five Key Factors For The !Emergence of Functional MRI!
1. Magnetic properties of red blood cells !2. Activation related hemodynamic changes!3. Spatial scale of brain activation!4. Echo Planar Imaging!5. Prevalence of MRI scanners!
“fMRI” or “functional MRI”!
Scopus: Articles or Reviews Published per Year!
EPI is sold on standard clinical scanners!
The Beginnings!
(1990) Science, 250, 53-61.
angiography
Gadolinium perfusion
Diffusion magnetization transfer
metabolic imaging (NAA)
NAA choline
creatine lactate
Resting Active
Susceptibility Contrast agent bolus injection and time series collection of T2 - weighted images
The First Functional MRI Results!
Susceptibility Contrast agent bolus injection and time series collection of T2 - weighted images
The First Functional MRI Results!
K. K. Kwong, et al, (1992) �Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation.� Proc. Natl. Acad. Sci. USA. 89, 5675-5679. S. Ogawa, et al., (1992) �Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging.� Proc. Natl. Acad. Sci. USA. 89, 5951-5955. P. A. Bandettini, et al., (1992) �Time course EPI of human brain function during task activation.���Magn. Reson. Med 25, 390-397. Blamire, A. M., et al. (1992). �Dynamic mapping of the human visual cortex by high-speed magnetic resonance imaging.� Proc. Natl. Acad. Sci. USA 89: 11069-11073. Frahm, J., et al (1992) �Dynamic MR Imaging of Human Brain Oxygenation During Rest and Photic-Stimulation.� Journal of Magnetic Resonance Imaging, 2, 501-505.
K. K. Kwong, et al, (1992) �Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation.� Proc. Natl. Acad. Sci. USA. 89, 5675-5679.
S. Ogawa, et al., (1992) �Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging.� Proc. Natl. Acad. Sci. USA. 89, 5951-5955.
P. A. Bandettini, et al., (1992) �Time course EPI of human brain function during task activation.� Magn. Reson. Med 25, 390-397.
2.5 cm !!
TR = 2 sec!TE = 50 ms!One slice!In plane 3.75 x 3.75!
1991
Blamire, A. M., et al. (1992). �Dynamic mapping of the human visual cortex by high-speed magnetic resonance imaging.� Proc. Natl. Acad. Sci. USA 89: 11069-11073.
Contrast Basics 1992…Perfusion using Arterial Spin Labeling
EPISTAR
FAIR
. . .
. . . Perfusion Time Series
�� �� �� ��
Perfusion Contrast FAIR EPISTAR TI (ms)
200
400
600
800
1000
1200
Williams, D. S., Detre, J. A., Leigh, J. S. & Koretsky, A. S. (1992) “Magnetic resonance imaging of perfusion using spin-inversion of arterial water.” Proc. Natl. Acad. Sci. USA 89, 212-216.
Edelman, R., Siewert, B. & Darby, D. (1994) “Qualitative mapping of cerebral blood flow and functional
localization with echo planar MR imaging ans signal targeting with alternating radiofrequency (EPISTAR).” Radiology 192, 1-8.
Kim, S.-G. (1995) “Quantification of relative cerebral blood flow change by flow-sensitive alternating
inversion recovery (FAIR) technique: application to functional mapping.” Magn. Reson. Med. 34, 293-301.
Kwong, K. K. et al. (1995) “MR perfusion studies with T1-weighted echo planar imaging.”Magn. Reson.
Med. 34,878-887.
BOLD" Rest ! !Activation"
P. A. Bandettini, E. C. Wong, Magnetic resonance imaging of human brain function: principles, practicalities, and possibilities, in "Neurosurgery Clinics of North America: Functional Imaging" (M. Haglund, Ed.), p.345-371, W. B. Saunders Co., 1997.
Perfusion"
• Volume (gadolinium) • BOLD • Perfusion (ASL) • !CMRO2 • !Volume (VASO) • Neuronal Currents • Diffusion coefficient • Temperature
Functional Contrast Methodology
Interpretation Applications
Technology Coil arrays High field strength High resolution Novel functional contrast
Functional Connectivity Multi-modal integration Pattern-effect imaging Real time feedback Task design
Fluctuations Dynamics Spatial patterns
Healthy Brain Organization Clinical Pathology
J. Illes, M. P. Kirschen, J. D. E. Gabrielli, Nature Neuroscience, 6 (3)m p.205!
Motor (black)!Primary Sensory (red)!Integrative Sensory (violet)!Basic Cognition (green)!High-Order Cognition (yellow)!Emotion (blue)! 36 02 01 00 99 98 97 96 95 94 93 92 91 90 89 88 82
Methodology
Hemoglobin
Blood T2
IVIM
Baseline Volume
Interpretation
Applications
�Volume-V1
BOLD
Correlation Analysis
Linear Regression Event-related
BOLD -V1, M1, A1
TE dep
Veins
IV vs EV BOLD models
ASL
Deconvolution
Phase Mapping
V1, V2..mapping
Language Memory
Presurgical Attention
PSF of BOLD Pre-undershoot
Ocular Dominance
Mental Chronometry
Electrophys. correlation
1.5T,3T, 4T 7T
SE vs. GE
Performance prediction
Emotion
Real time fMRI
Balloon Model
Post-undershoot
Inflow
PET correlation
CO2 effect
CO2 Calibration
Drug effects
Optical Im. Correlation
Imagery
Clinical Populations
Plasticity
Complex motor
Motor learning
Venography
Face recognition
Children
Simultaneous ASL and BOLD
Surface Mapping
Linearity
Mg+
Dynamic IV volume
Bo dep.
Diff. tensor
Volume - Stroke
Z-shim
Free-behavior Designs
Extended Stim.
Local Human Head Gradient Coils
NIRS Correlation
SENSE
Baseline Susceptibility
Metab. Correlation
Fluctuations
Priming/Learning
Resolution Dep.
Tumor vasc.
Technology EPI on Clin. Syst. EPI
Quant. ASL
Multi-shot fMRI
Parametric Design
Current Imaging?
Multi-Modal Mapping
Nav. pulses
Motion Correction
MRI Spiral EPI
ASL vs. BOLD
>8 channels
Multi-variate Mapping
ICA
Fuzzy Clustering
Excite and Inhibit
03
Mirror neurons
Layer spec. latency
Latency and Width Mod
�vaso�
How fMRI Is Currently Used
Research Applications -map networks involved with specific behavior, stimulus, or performance -characterize changes over time (seconds to years) -determine correlates of behavior (response accuracy, etc…) -characterization of groups or individuals
Clinical Research
-clinical population characterization (probe task or resting state) -assessment of recovery and plasticity -attempts to characterize (classify) individuals
Clinical Applications
-presurgical mapping (CPT code in place as of Jan, 2007)
Top 10 Most Significant Developments in fMRI!
1. “Resting state” correlations!
2. SPM, FSL, AFNI, Brain Voyager processing platforms!
3. Fast even related designs with deconvolution!
4. Multi-modal integration / comparison (animal and human)!
5. Hemodynamic response models!
6. High field / high resolution results!
7. Parallel acquisition / reconstruction (SENSE/SMASH)!
8. Detailed retinotopic mapping!
9. FMRI Decoding / Multivariate / Machine Learning!
10. Robust motion correction or ICA analysis or real time fMRI or fMRI-adaptation !
Overview of fMRI
Functional Contrast: Blood volume Blood flow/perfusion Blood oxygenation
Spatial resolution:
Typical: 3 mm3 Upper: 0.5 mm3
Temporal resolution:
Minimum duration: < 16 ms Minimum onset diff: 100 ms to 2 sec
Sensitivity: tSNR = 40/1 to 120/1 fCNR = 1/1 to 6/1
Interpretability issues: Neurovascular coupling, vascular sampling, blood, physiologic noise, motion and other artifacts, etc..
task task
What fMRI Can�t Do What some would argue are shortcomings with fMRI
• Too low SNR vs subject/patient limits of compliance (about 2 hours)
• Requires motivated subjects/patients (motion sensitivity)
• Too low spatial resolution (each voxel has several million neurons)
• Any higher resolution than 3 mm3 lost with subject averaging.
• Too low temporal resolution (hemodynamics are variable and sluggish)
• Too inconsistent activation patterns
• Anatomical images for fMRI are low quality (dropout/distortion)
• Requires a task (BOLD cannot look at baseline maps).
• Too confined space and high acoustic noise (environment non-optimal).
• Too many physiologic variables influence signal.
What fMRI Can�t Do What some would argue are shortcomings with fMRI
• Too low SNR vs subject/patient limits of compliance (about 2 hours) • Higher field strength, multi-channel, temporal processing (15 min) • Requires motivated subjects/patients (motion sensitivity) • Real time fMRI, improved motion correction, navigator pulses • Too low spatial resolution (each voxel has several million neurons) • FMRI-adaptation paradigms, smallest functional unit about 0.5mm anyway • Any higher resolution than 3 mm3 lost with subject averaging. • Spatial averaging becoming a bit less common. • Too low temporal resolution (hemodynamics are variable and sluggish) • Paired pulse paradigms, timing modulation w/ latency comparison (<100 ms) • Too inconsistent activation patterns • Not typically due to low SNR. Subject differences – good problem. • Anatomical images for fMRI are low quality (dropout/distortion) • SENSE, multi-channel, and Bo correction can help. • Requires a task (BOLD cannot look at baseline maps). • Calibration methods getting much better. Baseline info is coming. • Too confined space and high acoustic noise (environment non-optimal). • Strategies around this. Vendors learning how to dampen sound. • Too many physiologic variables influence signal. • Again, calibration methods are improving
Exciting Trends!
• FMRI Decoding / Multivariate Analysis / Machine Learning!
• Resting State Fluctuations (Connectivity)!!• High Field / High Temporal & Spatial Resolution (input/output layers)!!• Longitudinal fMRI / MRI studies across time scales!
• Clinical inroads (default mode, genetic correlations, connectivity)!
• Multi-modal integration!
• Individual assessment!
• Multi-band sequences…short TR whole brain connectivity.!
1991
Parametric manipulation of brain activation demonstrated that BOLD contrast approximately followed the level of brain activation: visual system (Kwong et al., 1992), auditory system (Binder et al., 1994), and motor system (Rao et al., 1996). The use of continuous variation of visual stimuli parameters as a function of time was proven a powerful method for fMRI-based retinotopy: (Engel et al., 1994, Deyoe et al., 1994, Sereno et al., 1995). Event-related fMRI was first demonstrated (Blamire et al., 1992). Application of event-related fMRI to cognitive activation was shown (Buckner et al., 1996, McCarthy et al., 1997). Development of mixed event-related and block designs was put forward: (Donaldson et al., 2002). Paradigms were demonstrated in which the activation timing of multiple brain systems timing was orthogonal, allowing multiple conditions to be cleanly extracted from a single run (Courtney et al., 1997). High resolution maps were created: For spatial resolution: ocular dominance columns (Menon et al., 1997, Cheng et al., 2001) and cortical layer activation maps were created (Logothetis et al., 2002). Extraction of information at high spatial frequencies within regions of activation was demonstrated (Haxby et al., 2001). For temporal resolution: Timings from ms to hundreds of ms were extracted (Ogawa et al., 2000, Menon et al., 1998, Henson et al., 2002, Bellgowan et al., 2003). The development of “deconvolution” methods allowed for rapid presentation of stimuli (Dale and Buckner, 1997). Early BOLD contrast models were put forward: (Ogawa et al., 1993, Buxton and Frank, 1997). More sophisticated models were published that more fully integrated the latest data on hemodynamic and metabolic changes (Buxton et al., 2004). The development of “clustered volume” acquisition was put forth as a method to avoid scanner noise artifacts: (Edmister et al., 1999). The findings of functionally related resting state correlations: (Biswal et al., 1995) and regions that consistently show deactivation (Binder et al., 1999, Raichle et al., 2001) were described. Observation of the pre-undershoot in fMRI (Hennig et al., 1997, Menon et al., 1995, Hu et al., 1997) and correlation with optical imaging was reported (Malonek and Grinvald, 1996). Simultaneous use of fMRI and direct electrophysiological recording in non-human primate brain during visual stimulation elucidated the relationship between fMRI and BOLD contrast. (Logothetis et al., 2001). Simultaneous electrophysiological recordings in animal models revealed a correlation between negative signal changes and decreased neuronal activity (Shmuel et al., 2002). Simultaneous electrophysiological recordings in animal models provided evidence that inhibitory input could cause an increase in cerebral blood flow (Matheiesen et al., 1998). Structural equation modeling was developed in the context of fMRI time series analysis: (Buchel and Friston, 1998).
How most fMRI studies are performed
MRI parameters: 1.5T - 3T, 64 x 64 matrix, 3mm x 3mm x 5mm voxel size, whole brain, TR = 2 sec. Paradigm: Block design or event-related, single or multiple conditions. Analysis: Motion correct, multi-regression, spatial smoothing and spatial normalization, standard classical statistical tests, multi-subject averaging. Hypothesis: A region or network of regions show modulation with a task. This modulation is unique to the task and/or population.
How fMRI might be be performed MRI parameters: 3T - 11.7T, 256 x 256 matrix, 0.5 x 0.5 x 0.5 voxel size, whole brain TR = 1sec or select slab TR = 100 ms. Paradigm: Natural, continuous, fMRI-adaptation, or no stimuli/task. Simultaneous multi-modal, or multiple contrast measurements. Analysis: Motion correct, dynamic Bo-field correction, no spatial or temporal smoothing, machine learning algorithms, pattern classification, resting state connectivity assessment, hemodynamic parameter assessment - calibration, correlation with behavior. Hypothesis: Similar to previous but using the high resolution patterns, fluctuations, dynamics, and contrast mechanisms that we are still figuring out how to interpret and extract.
What fMRI Might Do
Clinical Research Complementarity -usage of clinical research findings for more effective diagnoses, prediction, characterization, and/or intervention
Clinical treatment and assessment of therapy -better understanding of the specific pathology mechanism -drug effect assessment -assessment of therapy progress, biofeedback -epileptic foci mapping -neurovascular physiology assessment
Non clinical uses
-lie detection -prediction of behavior tendencies -brain/computer interface
Neuronal Activation
Hemodynamics ? ? ?
Measured Signal
Noise
?
Interpretation Issues
Scale bar = 0.5 mm
Orientation Columns in Human V1 as Revealed by fMRI at 7T
Phase 0° 180°
Phase Map
Yacoub, Ugurbil & Harel
Real time fMRI feedback from Anterior Cingulate Cortex to reduce chronic pain
Control over brain activation and pain learned by using real-time functional MRI, R. C. deCharms, et al. PNAS, 102; 18626-18631 (2005)
SC NL KB
JL HG EE
CC BK BB
Individual activations from the left hemisphere of the 9 subjects
group Individual Differences in Brain Activations During Episodic Retrieval
Miller et al., 2002
Courtesy, Mike Miler, UC Santa Barbara and Jack Van Horn, fMRI Data Center, Dartmouth University
group Individual Differences in Brain Activations During Episodic Retrieval
Miller et al., 2002
KB NL SC
HG JL
BB BK CC
EE
Individual activations from the right hemisphere of the 9 subjects
Courtesy, Mike Miler, UC Santa Barbara and Jack Van Horn, fMRI Data Center, Dartmouth University
Group Analysis of Episodic Retrieval
Subject SC
Subject SC 6 months later
These individual patterns of activations are stable over time
Courtesy, Mike Miler, UC Santa Barbara and Jack Van Horn, fMRI Data Center, Dartmouth University
Finger Movement
Left Right
Finger Movement
Toe Movement
Left Right Left Right
Tactile Stimulation Finger Movement Tapping vs Pure Somatosensory
Simple Left Complex Left
Simple Right Complex Right Imagined
Complex Right
Imagined Complex Left
Reading
Listening to Spoken Words
≈ 5 to 30 ms"Pruessmann, et al. !
3T single-shot SENSE EPI using 16 channels: 1.25x1.25x2mm
Menon, R. S., S. Ogawa, et al. (1997). J Neurophysiol 77(5): 2780-7.
R. D. Frostig et. al, PNAS 87: 6082-6086, (1990).
Ocular Dominance Column Mapping
Optical Imaging
Cheng, et al. (2001) Neuron,32:359-374
0.47 x 0.47 in plane resolution
0.54 x 0.54 in plane resolution
Cheng, et al. (2001) Neuron,32:359-374
Technology
Yacoub et al. PNAS 2008
Scalebar = 0.5 mm
Orientation Columns in Human V1 as Revealed by fMRI at 7T
Phase 0° 180°
Phase Map
Yacoub et al. PNAS 2008
Visual Activation Paradigm: 1 , 2, & 3 Trials""
20 sec"0 sec"
0 sec"2 sec" 20 sec"
0 sec"2 sec" 20 sec"4 sec"
-"1"
0"
1"
2"
3"
4"
5"
0" 1" 2" 3" 4" 5" 6" 7" 8" 9"1"0"1"1"1"2"1"3"1"4"1"5"1"6"1"7"1"8"1"9"T"I"M"E" "("S"E"C")"
O N E - T R I A L
T W O - T R I A L
T H R E E - T R I A L
-"1"
0"
1"
2"
3"
4"
5"
0" 1" 2" 3" 4" 5" 6" 7" 8" 9"1"0"1"1"1"2"1"3"1"4"1"5"1"6"1"7"1"8"1"9"T"I"M"E" "("S"E"C")"
RAW DATA" ESTIMATED RESPONSES"
Rest: seed voxel in motor cortex
Activation: correlation with reference function
B. Biswal et al., MRM, 34:537 (1995)
Resting State Correlations
94!
Resting state networks identified with ICA
M. DeLuca, C.F. Beckmann, N. De Stefano, P.M. Matthews, S.M. Smith, fMRI resting state networks define distinct modes of long-distance interactions in the human brain. NeuroImage, 29, 1359-1367
Goldman, et al (2002), Neuroreport
BOLD correlated with 10 Hz power during “Rest”
Positive
Negative
10 Hz power
Fluctuations Patterns
1991
Ventral temporal category representations
Object categories are associated with distributed representations in ventral temporal cortex
Haxby et al. 2001
Pattern-recognition analysis of fMRI activity patterns
• Haxby et al. (2001) • Cox & Savoy (2003) • Carlson et al. (2003) • Kamitani & Tong (2005) • Haynes & Rees (2005) • Kriegeskorte et al (2006)
S.A. Engel, et al. Investigative Ophthalmology & Visual Science 35 (1994) 1977-1977.
PSF FWHM = 3.5mm
Logothetis et al. (2001) “Neurophysiological investigation of the basis of the fMRI signal” Nature, 412, 150-157
16 channel parallel receiver coil!
GE birdcage GE 8 channel coil Nova 8 channel coil
8 channel parallel receiver coil
J. Bodurka, et al, Magnetic Resonance in Medicine 51 (2004) 165-171.
≈ 5 to 30 ms"Pruessmann, et al. !
3T single-shot SENSE EPI using 16 channels: 1.25x1.25x2mm
Menon, R. S., S. Ogawa, et al. (1997). J Neurophysiol 77(5): 2780-7.
R. D. Frostig et. al, PNAS 87: 6082-6086, (1990).
Ocular Dominance Column Mapping
Optical Imaging
Cheng, et al. (2001) Neuron,32:359-374
0.47 x 0.47 in plane resolution
0.54 x 0.54 in plane resolution
Cheng, et al. (2001) Neuron,32:359-374
Technology
Yacoub et al. PNAS 2008 Scalebar = 0.5 mm
Orientation Columns in Human V1 as Revealed by fMRI at 7T
Phase 0° 180°
Phase Map
Yacoub et al. PNAS 2008
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