# Geoff Boynton on fMRI

Geoff just delivered a lecture at CSHL computational vision on fMRI. He pointed out that it’s an incredibly convenient coincidence that hemoglobin and deoxyhemoglobin have sufficiently different magnetic moments that they can be picked up using MRI. I made a comment (which I thought was mind-blowing but others thought was funny; it wasn’t a joke, people!) that you couldn’t do fMRI in octopuses because they use hemocyanin instead of hemoglobin. I don’t know if deoxyhemocyanin is actually indistinguishable from hemocyanin in a scanner but it’s fun to think about how octopus-like humanoids would do brain science; come to think of it, they might be too busy enjoying having eight arms to do science.

Geoff had an influential paper in the Journal of Neuroscience (Boynton et al. 1996) that verified some of the assumptions of the linear convolutional hemodynamic response function assumption. Surprisingly, under reasonable conditions linearity seems to hold approximately. He did mention that for short stimulus durations the apparent gain of the response is higher than expected assuming a fixed HRF. It’s also the case that under very different stimuli the HRF can be different. This points out the importance of using an fMRI protocol that uses similar stimulus durations and temporal dynamics across conditions.

The efficiency associated with a given design matrix X under the assumption of iid Gaussian noise is given by $e = 1/tr((X'X)^{-1})$. Thus, it turns out that it’s better to use design matrices such that $X'X \equiv aI$. You can get a little more efficiency by using an m-sequence, which has an autocorrelation function which  is exactly a delta function. As an alternative, it’s possible to create several random sequences (using rand, say) and pick the one that has the highest theoretical efficiency (Dale 1999).

Geoff pointed out that the HRF used in their 1996 paper, a gamma pdf, is the natural HRF assuming that the signal is due to a series of leaky integrator functions. Indeed, the sum of several independent variables with exponential distributions follows a gamma distribution.

Jeremy Freeman pointed out a pretty easy way of dealing with the fact that different voxels have different HRF in a low-dimensional way. If you take your mean HRF and take its derivative, then within a certain range of a, HRF +a’HRF will give a shifted HRF (Taylor series decomposition). So Jeremy fits a single parameter a for each voxel to account for the difference in latency and apparently this gives significantly better classification accuracy. Clever.

Geoff joked that Sirotin & Das (2009), which shows anticipatory response in fMRI but not in MUA, proves that the cardiovascular system is smarter than the brain. Ahah! He has a review in Journal of Vision (2011) on the interpretation of fMRI results versus physiology.

He then talked about interesting fMRI protocols enabled by population receptive field methods (Dumoulin & Wandell, 2008). In particular, he showed some preliminary result showing that in a position illusion condition, V1 activation follows the percept rather than physical location of the stimulus. I pointed out that it’s possible to get similar receptive fields from LFPs, and it’s be interesting to compare the two.