# Presentation: 211326

## Analysis of FMRI Data:Principles and Practice

**Robert W Cox****, PhD**
**Scientific and Statistical Computing Core**
**National Institute of Mental Health**
**Bethesda, MD**
**http://afni.nimh.nih.gov**

## Principles: Modeling

- Data analysis always takes place in the context of a mathematical model
- Model relates the properties of the system being observed to the numbers that are actually measured
- Sometimes the model is implicit in the analysis algorithm, rather than being explicitly stated
- Model also needs to take into account properties of the measurement system
- Models relating FMRI signals to neural changes are complex and tentative

## Principles: Data Quality

- FMRI data are crappy:
- Signal changes with neuronal activation are small (compared to noise), especially away from primary sensory areas
- Signal is several level of indirection away from neuronal changes of interest
- Numerous other signal fluctuations of non-neural origin have similar or greater magnitude:
- Ghosting, warping, head movement, scanner imperfections, heartbeat, breathing, long-term drifts, ...

## Conclusions from Principles

- It is better to explicitly state the mathematical model rather than implicitly rely on an algorithm
- It is a good idea to process FMRI data with more than one model, to see if results change significantly
- It is important to examine the processed data visually at each step in the analysis, to make sure that nothing bad has happened

## Practice: Pattern Matching Models

- Looking for temporal (maybe spatial) patterns of signal changes that you expect
- Based on the external stimulus and/or measured behavior
- Searching low dimensional “space” of pre-determined model to find best fit to data
- Then test fitted model parameters for statistical significance
- Draw colors on top of significant voxels

## Practice: Pattern Hunting Models

- Looking for common temporal (maybe spatial) patterns in the data
- Fuzzy clustering tries to find voxel time series that “look alike” and then creates clusters of such similar voxels
- Component analyses (PCA, ICA) try to find a small set of time series that when combined properly, explain “most” of the data in 10,000+ voxel time series
- These analyses are “exploratory” rather than for “hypothesis testing”
- Difficult to assign statistical significance

## Hemodynamic Model

- Measured MRI value in each voxel is sum of:
- Slowly drifting baseline
- Hemodynamic response that is linearly proportional to “neural activity”, delayed and blurred in time
- Non-neural physiological “noise” due to respiration and blood flow pulsations through the cardiac cycle
- White noise from random (thermal) currents in the body and the scanner
- Imaging is assumed perfect
- Or at least is fixed up in preprocessing steps

## Hemodynamic Equation

- Linear shift-invariant model for single voxel time series:
*h*(*t*) = hemodynamic response at time *t* 		after neural activity
*s*() = neural activity at time **

*time*

*data*
*=v*(*t*)

## Ways to Use This Model

- Assume *s*(*t*) is known, and then
- Assume *h*(*t*) is known except for amplitude **** correlation method
- Assume shape of *h*(*t*) is also unknown **** deconvolution method
- Assume several different classes of *s*(*t*)’s and correspondingly several different *h*(*t*)’s **** generic linear model
- Assume *h*(*t*) is known, and find *s*(*t*)
-  Wiener deconvolution
- Try to find both *h*(*t*) and *s*(*t*)
-  blind deconvolution

## Further Considerations

- How many parameters to allow in unknown *h*(*t*) depends on imaging TR, expected duration of response, and stimulus timing [event-related or blocked]
- Appropriate baseline model depends on duration of imaging run
- May also include movement parameters
- Noise models can be simple or complicated:
- Gaussian white noise
- Gaussian colored noise [correlated in time]
- Spatially correlated noise

## Software Tools

- What package to use?
- Sociological answer: the one your neighbors are using (so you can ask them for help)
- SPM: most widely used at present
*AFNI*: flexible, customizable
- and has the coolest logo
- FSL: newish package from Oxford
- Numerous other good packages out there
- Commercial products: MedX, Brain Voyager