# Presentation: 049883

## How Does FMRI Data Get Turned into Brain Activation Maps?

**Robert W Cox, PhD**
**SSCC ****/**** NIMH ****/**** NIH ****/**** DHHS ****/**** USA ****/**** EARTH**

- March 31, 2004

## Outline

**Prolegomenon**
**Temporal Models of Activation**
**Spatial Models of Activation**
**Spatio-Temporal Models**
**Noise Models & Statistics**
**Inter-Subject Analyses**
**FMRI Analysis Research**
**Software Tools**

** ****But hardly any equations**

## Prolegomenon

**Goal**: Find and Characterize Neural “Activations” (whatever that means)
**Shocking Revelation #1**:
-    **FMRI data are ****(mostly)**** crap**
- All other neuroimaging data are, too
-  Must know what you are doing!
**Shocking Revelation #2**:
** ****Most FMRI papers are weak on analysis   **

## Caveats

- Almost everything herein has an exception or complication
- Special types of data or stimuli may require special analysis tools
- e.g., perfusion-weighted FMRI
- Special types of questions may require special data and analyses
- e.g., relative timing of neural events

## What We Can Know

**The Data**:
-  10,000..50,000 image voxels inside brain (resolution  3 mm)
-  100..1000+ time points in each voxel (time step  2 s)
- Also know timing of stimuli delivered to subject (etc)
- Probably some hypothesis

## Sample Data: Visual Area V1

## Same Data as Last Slide

**Blowup of central time series graph:**
**about 7% signal change with a very**
**powerful neural stimulus**

- This is _**really**_ good data

## Meta-Method for Analysis

- Develop a mathematical model relating what we **know** (stimulus timing and image data) to what we **want to know** (location, amount, timing, etc of neural activity)
- Given data, use this model to solve for unknown parameters in the neural activity (e.g., when, where, how much, etc)
- Then test for statistical significance

## Why FMRI Analysis Is Hard

- Don’t know the true relation between neural “activity” and measurable MRI signal
- What is “activity”, anyway?
- What is connection between “activity” and hemodynamics and MRI signal?
- Noise in data is also poorly characterized
- Makes statistical assessment hard

## Why So Many Methods?

- Different assumptions about activity-to-MRI signal connection
- Different assumptions about noise (signal fluctuations of no interest) properties and statistics
- Different experiments and questions
**Result**: Many “reasonable” FMRI analysis methods
- Researchers _**must**_ understand the tools!!  (Models and software)

## Temporal Models:Linear Convolution

**Assumption**: FMRI (hemodynamic) response to 2 separated-in-time activations in the same voxel is the separated-in-time sum of two copies of some individual response function
- The FMRI response to a single activation is called the hemodynamic response function (**HRF**)

## Model HRF

_**Model HRF**_

## Signal = HRF  Stimulus

_**Signal = HRF **__****__** Stimulus**_

## Block Stimulus

_**Block Stimulus**_

## Fixed Shape HRF Analysis

- Assume some shape for HRF
- Signal model is **r(t)** = HRF  Stimulus = “Convolution” of HRF with neural activity timing function (e.g., stimulus)
- Model for each voxel data time series:
**         ****v(t) = a********r(t) + b + noise(t)**
- Estimate unknowns: **a**** **= amplitude, **b**=baseline, ******2 **= noise variance
- Significance of **a**** ****≠**** ****0**  activation map

## Sample Activation Map

-  Threshold on
-  significance of
-  amplitude
-  Color comes
-  from amplitude
-  Upper Image:
-  color overlay at
-  resolution of EPI
-  Lower Image:
-  color overlay
-  interpolated to
-  resolution of
-  structural image

## Variable Shape HRF Analysis

- Allow shape of HRF to be unknown, as well as amplitude (deconvolution)
-  Analysis adapts to each subject and each voxel
-  Can compare brain regions based on HRF shapes
-  e.g., early vs. late response?
-  Must estimate more parameters
-  Need more data (all else being equal)

## Multiple Stimulus Classes

- Need to calculate HRF (amplitude or amplitude+shape) separately for each class of stimulus
- Novice FMRI researcher pitfall: try to use too many stimulus classes
**Event-related FMRI**: need 25+ events per stimulus class
**Block design FMRI**: need 10+ blocks per stimulus class

## Sample Variable HRF Analysis

_**Sample Variable HRF Analysis**_

-  What-vs-Where tactile stimulation
-  Red **** regions with What  Where

- What HRF

- Where HRF

## Inverse Modeling

- Instead of using stimulus timing to get HRF, could use an assumed HRF to get stimulus timing = timing of neural activity in each voxel
- Example: show a long video, see what regions are active when, then try to correlate to video contents
- e.g., amygdala activation and images of guns

## Spatial Models of Activation

- 10,000+ image voxels in brain
- Don’t really expect activation in a single voxel (usually)
- Curse of multiple comparisons:
- If have 10,000 statistical tests to perform, and 5% give false positive, would have 500 voxels “activated” by pure noise—way way too much!
- Can group voxels together somehow to manage the curse

## Spatial Grouping Methods

- Smooth data in space before analysis
- Average data across anatomically-selected regions of interest ROI (before or after analysis)
- Labor intensive (send more postdocs)
- Reject isolated small clusters of above-threshold voxels after analysis

## Spatial Smoothing of Data

-  Reduces number of comparisons
-  Reduces noise (by averaging)
-  Reduces spatial resolution
- Can make FMRI results look PET-ish
- In that case, why bother gathering high resolution MR images?
-  Smart smoothing: average only over local gray matter voxels
- Uses resolution of FMRI cleverly
- Or average over selected ROIs

## Spatial Clustering

- Analyze data, create statistical map (e.g., ***t*** statistic  in each voxel)
- Threshold map at a lowish ***t*** value, in each voxel separately
- Threshold map by rejecting clusters of voxels below a given size
- Can control false-positive rate by adjusting ***t*** threshold and cluster-size thresholds together

## Cluster-Based Detection

_**Cluster-Based Detection**_

## Clustering Fun

**Clustering ****ON**

**Clustering ****OFF**

**“****ShowThru” Volume Rendering**

## Spatio-Temporal Models:Data Driven Analyses

- Component models: PCA, ICA
- Temporal clustering
- Functional (effective, dynamic, etc.) connectivity
- Have 4D voxel data v(x,y,z,t)
-  Try to factor it into simpler pieces that make some sense

## Component Analyses

- Spatio-temporal components:
-     v(x,y,z,t)   w1(x,y,z)  u1(t)
- 			      + w2(x,y,z)  u2(t) + 
- Each ui(t) is a time series component
- Each wi(x,y,z) is a spatial map = amplitude of ui(t) in voxel at (x,y,z)
**Idea**: Explore what’s in the data
**Problem**: Can be hard to interpret

## Sample PCA

_**Sample PCA**_

-  What-vs-Where tactile stimulation
-  16th principal component (of 1040)
-  Somewhat confusing (at least to me)

## Temporal Clustering

**Idea**: Find voxel time series that are “alike” — in some sense
- e.g., highly correlated
- Average them together to make a “cluster” and iterate
**Results**: set of component time series, and classification of each voxel location (x,y,z) as belonging to one component

## Connectivity Analyses

**Idea**: look for correlated _fluctuations_ in FMRI signal amplitude between different regions during “same” state
- Usually start with a preliminary linear analysis to select regions
-                     **AND ****/**** OR**
- Usually start with some model of connectivity between regions
- e.g., region A feeds directly into region B but not into region C

## Sample Connectivity Model

**KJ Friston et al, *****NeuroImage***** 19: 1273–1302 (2003)**

- v(t)=data

- v(t)=data

- v(t)=data

- v(t)=data

- v(t)

## Noise Models & Statistics

- Subject head movement
- Biggest practical annoyance in FMRI
- Physiological noise
- Heartbeat and respiration affect signal in complex ways
- Magnetic field fluctuations
- Scanner glitches can produce gigantic (10 ) spikes in data

## Correcting Head Movement

**Best**: don’t let subjects move head!
-  Almost impossible
**Next Best**: detect movement during scan, alter MRI acquisition to compensate (prospective correction)
-  Requires special hardware and/or MRI pulse programming
**The Usual**: computationally realign (register) images after the fact (retrospective correction)

## Sample Movement Data

-  Less than 1o of head movement
-  Time between images = 5 seconds

- Motion parameters vs. time

## Physiological “Noise”

- MRI signal changes due to non-neural physiology during scan
- Can be **approximately** filtered out with external measurements
- e.g., EKG, respiratory bellows, pulse oximeter
- Somewhat harder than it sounds, and is not commonly used (yet)

## Fluctuations:

**Fluctuations**:
- 16 images/sec
-    **0.22 Hz**
-        **1.08 Hz**

## Temporal (‘Serial’) Correlation

- Most statistical tests assume separate data samples are independent
- Physiological noise is inherently correlated in time
-  Statistical thresholds (*p-*values) and power are affected

## Adapting to Correlated Noise

- Can adjust degrees-of-freedom in statistical parameters to approximate  for correlation
- Can do this with attempts to band-pass filter out physiological noise
- Can “prewhiten” data  time series to approximately remove correlation
- In both methods, must estimate various correlation parameters

## Avoiding Some Assumptions

- All statistical methods require assumptions about noise
- Gaussianity, independence, ...
- Can use modern statistical resampling methods to reduce the number of assumptions
**Very** computationally intensive
- Substituting number crunching for mathematical theory

## Spatially Structured Noise

- Physiological noise is also **spatially** correlated
- But in spotty ways (e.g., among major blood vessels) that are hard to allow for
- This issue is usually ignored since it is very hard to model
- Exception: “spiral” imaging methods

## Inter-Subject Analyses

- Cortical folding patterns are (at least) as unique as fingerprints
- Inter-subject comparisons requires some way to bring brain regions into alignment
- Solutions: Brain Warping and ROIs

## ROIs

- Manually draw anatomically defined brain regions on 3D structural MRIs
- Can be tediously boring
- Use ROIs to select data from each subject
- Combine averages from ROIs as desired
- e.g., ANOVA on signal levels

## Easy Brain Warping

- Align brain volume so that inter-hemispheric fissure is vertical (z), and Anterior-Posterior Commissure line is horizontal (y)
- Stretch/shrink brain to fit **Talairach**-Tournoux Atlas dimensions
- Use (x,y,z) coordinates based at AC=(0,0,0)
**Accuracy**: Not so hot (5-15 mm)

## Hard Brain Warping (3D)

- Nonlinearly distort (warp, morph) brain volume images in 3D to match sulcus-to-sulcus, gyrus-to-gyrus
**Very** computationally intensive
- Accuracy: hard to gauge, since method is not widely used
- Software for this is not easily available

## Hard Brain Warping (2D)

**Idea**: Warp brain only along cortical sheet (curved 2D surface) rather than in general 3D way
**Hope**: 2D is a little easier than 3D and may be more anatomically meaningful
- Not widely used at present
- More on this next week!

## Preview of Surface Stuff

- Gray-White
- matter
- boundary

## Individual “Brainotyping”?

- Most FMRI work to date has been on finding group differences
- e.g., patients vs. normals, old vs. young
- Is it possible to classify an individual using FMRI brain mapping?
- e.g., into disease sub-types?
**No one knows how to do this**, but it would be cool and useful

## FMRI Analysis Research

- Lots of “reasonable” analyses
- Too many good ideas to list here!
- Methodology for comparing them
- Closer integration of analysis to neural-level hypotheses
- Cognitive models; signaling networks
- Understand physiology better!
- “Brainotyping”: methods for grouping and discriminating among brain maps

## Software Tools

- Several widely used packages
- In order of popularity;  authors
-  **SPM** - Wellcome Institute/London
-  John Ashburner
-  **AFNI** - NIMH IRP/Bethesda
-  Robert Cox
-  **FSL**   - FMRIB/Oxford
-  Steve Smith
-  Homegrown and/or pastiche

## Most Common Analysis (SPM)

- Smooth data spatially (4-8 mm radius)
- Retrospective 3D image registration
- Bandpass filter data in time
- Fixed shape hemodynamic model
- Adjust statistics for spatial and temporal smoothing
- Report Talairach-ish coordinates of activation peaks

## Finally ... Thanks

- The list of people I should thank is not quite endless ...

**MM Klosek.  JS Hyde.  JR Binder.  EA DeYoe.  SM Rao. **
**EA Stein.  A Jesmanowicz.  MS Beauchamp.  BD Ward. **
**KM Donahue.  PA Bandettini.  AS Bloom.  T Ross.**
**M Huerta.  ZS Saad.  K Ropella.  B Knutson.  J Bobholz.**
**G Chen.  RM Birn.  J Ratke.  PSF Bellgowan.  J Frost.  **
**K Bove-Bettis.  R Doucette.  RC Reynolds.  PP Christidis. **
**LR Frank.  R Desimone.  L Ungerleider.  KR Hammett. **
**A Clark.  DS Cohen.  DA Jacobson.  EC Wong.**
**   ****Et alii ...**