fMRI Experimental Design at the U of S

Current protocol for functional imaging studies at the University of Saskatchewan are the results of a collaborative effort of many different researchers. The current protocols are part of the ever present goal of increasing the accuracy and precision of neuroimaging analysis. Like most things in life, this is a continually evolving process and new strategies and improvements are continually employed.

The arguments and reasons outlined below pertain specifically to the evaluation of functional datasets using deconvolution analysis. If unfamiliar with 3dDeconvolve please peruse the 3dDeconvolve introduction (in the AFNI documentation) so the following will make more sense. The 3dDeconvolve is an alternative program to the BoldFOLD for evaluating statistically significant areas of activation

CURRENT EXPERIMENT DESIGN

Before proposing changes to the current design, let us briefly consider what is now being done. The current standard is to use a block design. This means that there are periods in which a specific task is being performed by the participant followed by periods of rest. These blocks are repeated usually anywhere from 4-10 times to make a complete dataset. In general, current experiments only deal with one specific stimulus. If a researcher wishes to test two stimuli he/she usually performs two different runs using the block format. This has been successful for many experiments and will continue to be successful in the future but there are a few arguments to alter protocol for future experiments.

WHY CHANGE?

Well, there are a few reasons that given researcher may wish to alter the block design. Stimuli that occur at the same intervals have a greater chance of being correlated with natural process (e.g. respiration or pulse). By randomizing stimulus presentation it makes it less likely that this untoward occurrence will be a problem. Also when stimuli occur at the same frequency it is possible for the participant to anticipate the next block. This could taint the results with so called "anticipatory" effects. A random design discourages this sort of effect from occurring.

Let's also look at what randomization can do for an experiment statistically.

The following are givens:

The peak HRF occurs 4-6 seconds post stimulus presentation.

The TR of our MRI for EPI is approximately 1.6 seconds but varies from experiment to experiment but we will assume 1600ms TR for now.

The HRF lasts on average 10-12 seconds before returning to baseline.

EXAMPLE 1a (a predictable block design)

In order to cover the full hrf we should lag for 7 TRs ( 7 X 1.6= 11.2s about the time of the hrf) We cannot lag for more than 7 TRs because if we do it will be impossible for the program to know whether an activation is from the final part of the previous hrf or the beginning of the hrf that corresponds to the current stimulus. A muliticollinearity problem...cannot invert the X matrix...OK then.

So let's examine the experimental design of a block design containing 4 blocks of 8 stimulus and 8 rest scans. That will give us a total of 64 volumes. In order to examine this set-up we need to write a 1D file containing the stimulation file listed above. This file contains 1 column with 64 rows with ones where the stimulation will be and 0s for the rest phase. Look at the file Example1a.1D

We now run the program using the following code

3dDeconvolve \

-nodata \

-nlast 63 \

-polort 0 \

-num_stimts 1 \

-stim_file 1 Example1a.1D \

-stim_maxlag 1 7

This prints out the following information (I removed the inverse X matrix..call me if you want to see it)

Program: 3dDeconvolve

Author: B. Douglas Ward

Initial Release: 02 Sept 1998

Latest Revision: 06 July 2001

Stimulus: Stim #1

h[ 0] norm. std. dev. = 0.5179

h[ 1] norm. std. dev. = 0.5345

h[ 2] norm. std. dev. = 0.5345

h[ 3] norm. std. dev. = 0.5345

h[ 4] norm. std. dev. = 0.5345

h[ 5] norm. std. dev. = 0.5345

h[ 6] norm. std. dev. = 0.5345

h[ 7] norm. std. dev. = 0.5179

OK we see then the norm. std. dev. for any given lag is approximately 0.53.

Example 1b (randomized block design)

OK so in example 1a we had a predictable block design. Now, suppose we would like to stick with the same total length of 64 and keep half of the volumes as activations and half as control. The differences in this example are that one, we will now use 8 blocks of 4TR instead of 4 block of 8 for the stimulus. Two, the rest conditions will occur randomly. We are able to shorten the length of the stimulus because 3dDeconvolve is able to pick up the hrf with any length of stimulus. This gives us a little more flexibility in terms of being to randomize our design. Note also that we would be unable to analyze the data if we did not randomize for this 4TR stimulus. If the stim file was 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 … then we would run into the problem of multicollinearity if we tried to analyze hrf for a lag of 7 TR. This is because at any point in would be impossible for the program to tell whether a given signal was due to the prvious or current hrf. Make sense? So I suggest not setting up an experiment in this fashion.

Please view the file RSFgen.doc for information on how to set up this randomized experiment.

I typed this at the command line

RSFgen -nt 64 -num_stimts 1 -seed 14536 -prefix Example1b -nreps 1 8 -nblock 1 4

This generates a file Example1b.1D that contains the following single column of numbers

0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

Notice the beautiful unpredictability of the design…wowee woohoo yip yip yippee.

So now we will run this design through the nodata option of 3dDeconvolve

akasha% 3dDeconvolve \

-nodata \

-nlast 63 \

-polort 0 \

-num_stimts 1 \

-stim_file 1 Example1b.1D \

-stim_maxlag 1 7

Program: 3dDeconvolve

Author: B. Douglas Ward

Initial Release: 02 Sept 1998

Latest Revision: 06 July 2001

Stimulus: Stim #1

h[ 0] norm. std. dev. = 0.3743

h[ 1] norm. std. dev. = 0.4350

h[ 2] norm. std. dev. = 0.4356

h[ 3] norm. std. dev. = 0.4194

h[ 4] norm. std. dev. = 0.4351

h[ 5] norm. std. dev. = 0.4465

h[ 6] norm. std. dev. = 0.4339

h[ 7] norm. std. dev. = 0.3655

So the average norm. std. dev. With this experimental design is slightly less than 0.42

Compared with the norm. std. Dev from the example1a of 0.53.

Great you says to yourself but exactly what does that mean. OK so I’ll be the first to admit that I am no statistician but from what I gather this is a good thing eh? Here’s why.

Please forgive this will be a real hackjob but was enough to convince me so just think like me and you will be OK…fMRI wise not in society though.

Basically, this normalized standard deviation is the square root of the measurement error variance. Now this variance is unknown so we estimate it with the MSE (sample error variance). So a large smaller norm. std. Dev mean a smaller MSE which is really good if what we want is to find the most accurate solution to our problem.

Taken a step further (and likely more of a hack job) the statistical power of an experiment is the fraction of experiments that would lead to a statistically significant response.

Power is inversely related to MSE. So by reducing the MSE (norm. std. Dev.) in Example1b we have increased the Power of our experiment and all this before taking even one scan.

For a more detailed explanation again see the 3dDeconvolve manual.

Now, we can further reduce the norm. std. Dev. If we reduce the activations to 2TR etc., you can run RSFgen and just change the –seed number and then run the resulting 1D file through 3dDeconvolve and pick the experimental result that minimizes the MSE.

Other possible approaches to increase statistical power could involve maximizing the magnitude of effect. 3dDeconvolve has the ability to run general linear tests to compare the magnitude of response at multiple time points as well as comparing the area under the curve. As there is no perfect protocol to elicit desired responses. I foresee the possibility of an experimenter running an experiment with 3 or 4 very similar stimuli. If all of these variations on the stimuli activate nearly identical regions it would then be possible for an experimenter to choose the variation that elicits the maximal change in intensity. Perhaps, the changes will be too small to be statistically significant but for multi subject experiments a day of scanning with this goal in mind may prove useful in the long run if it results in a noticeable increase in statistical power.

Just my thoughts. They may all be muddled and confused but so is fMRI and anything is worth a shot.