Hi, so this module we're going to be talking about signal, noise, and bold physiology. So, to recap, MRI studies brain anatomy. Here we take structural images, or T1 weighted images typically, and these images have high spatial resolution and can thus be able to distinguish between different types of tissue. So in the example we see here, we see that we're able to differentiate between different tissue types. Functional magnetic resonance imaging studies brain function. Here we take functional images, or T2*-weighted images They have lower spatial resolution but higher temporal resolution. So we have multiple lower spatial resolution scans aquired rapidly. Here we can relate changes and signal to expiremental manipulations. So an fMRI experiment consists of a sequence of individual MRI images, where one can study oxygenation patterns in the brain across time. So here we see a series of brain images that have been acquired and let's say that we look at a single voxel of the brain. Again, each voxel represents a spatial location and also has an intensity associated with it. So if we extract this voxel value in each of the subsequent images, basically we get a time series of intensity values for that spatial location across time. And then we can correlate it with whatever experimental manipulation we did. The most common type of fMRI uses what's called the Blood Oxygenation Level Dependent or BOLD contrast. Now BOLD contrast allows us to measure the ratio of oxygenated to deoxygenated hemoglobin in the blood. It's important to note it doesn't measure neuronal activation directly. Instead what it does is it measures the metabolic demands, or the oxygen consumption of active neurons. So bold contrast uses the fact the hemoglobin exists in two different states, each with different magnetic properties. And these magnetic properties produce different local magnetic fields. This is a result due to Linus Pauling already in 1936. Here we know that oxyhemoglobin is diamagnetic, while deoxyhemoglobin is paramagnetic. Bold fMRI takes advantage of the difference T2* between oxygenated and deoxygenated hemoglobin. Because deoxygenated hemoglobin is paramagnetic, it works as a suppressor of the MR signal. So as the concentration of deoxygenated hemoglobin decreases, the fMRI signal tends to increase. So basically what happens is during rest, you have a normal cerebral blood flow and you have a normal T2*-weighted signal. However, when you become active, you have an increased flow of blood flow and this leads to a decreased deoxyhemoglobin level and increased cerebral blood volume. So together this leads to an increased T2*-weighted signal, which we can observe using an a properly acquired fMRI image. So the change in MR signal which is triggered by this instantaneous activity is know as the hemodynamic response function, or HRF. So as neural activation increases, so do the metabolic demands for oxygen and nutrients. And so as oxygen is extracted from the blood, the hemoglobin becomes paramagnetic, which creates these distortions in the magnetic field that cause a T2* decrease, so a faster decrease in the signal. So basically what we believe happens here is that there's an initial increase in the deoxyhemoglobin, which can sometimes lead to a decrease in the BOLD signal. This is called the "initial dip." This is followed by an overcompensation in blood flow, which dilutes the concentration of deoxyhemoglobin and tips the balance towards oxyhemoglobin. This leads to a peak in the BOLD response about 4 to 6 seconds following activation. And so after reaching its peak, the BOLD signal decreases to an amplitude below baseline level. And this post-stimulus undershoot is due to a combination of reduced blood flow and an increased blood volume. So here we see kind of an example of an empirical hemodynamic response function to brief events. So here we see first a brief dip, initial dip, which is followed by subsequent increase in the BOLD signal, which peaks after about 5 to 6 seconds after activation. There after it goes down to a below base line level, and then it returns to the normal base line after about 25 seconds or so. So what are some properties of the HRF? Well, one is the magnitude of the signal change is quite small. It's only between 0.1 to 5%, and it's very hard to see in individual images. So if you just saw a movie of the FMRI scans, you wouldn't be able to see an activation. The response is also delayed and quite slow, so extracting temporal information is tricky but it is possible. And so even short events have rather long response. So just doing something like clapping my hands, which takes place at a very short time interval leads to a long delayed response in the brain, lasting up to 30 seconds. The exact shape of the response has been shown to vary across subjects and regions, and this is something that's important that we have to take into consideration in our subsequent models. >> One import question is how well BOLD signal actually reflects neuronal activity. The good news is often, BOLD signal corresponds relatively closely with the local field potential, which is the electrical potential recorded from a group of cells. And LFP, so-called, often reflects the integrated post-synaptic activity across a group of neurons. So it's not the firing rate, it's the post-synaptic potentials. BOLD signals often localize to areas of increased neural activity, and the higher the field strength, and the closer the coil to the head, then the more true this is under more conditions. So it's called the point spread function of BOLD, how much spread you get per unit area. Just do the intrinsic imaging properties and vasculature, and this goes down as the field strength goes up. BOLD signal usually, but does not always, reflect changes in neuronal activity. So one counterexample is findings of anticipatory vasodilation in the absence of actual neural spiking. And a second one is the idea of vascular interactions or "blood steal" phenomena that may produce BOLD deactivations in the absence of actual neural firing. This is an example from Nikos Logothelis' work, who's done beautiful work recording from electrodes in cats and in monkeys, as he's doing bold imaging. So you can see here the recording electrode and then the bold response superimposed on that. And this is one of the pieces of evidence that lead us to conclude that bold response usually or often reflects pooled local field potential activity. So you can see the bold activity there in red. The neural firing in black, and really the measure that relates closely to the LFP in yellow, the integrated activity. One other point is that with Logothetis, he's shown us beautiful movies in which you can see as he varies the orientation of a visual stimulus. The location of both the bold signal and the neural firing changes in concordance across the visual cortex, as it should. Let's look at some basic quality control measures for assessing signal to noise and contrast to noise. So here's some basic definitions. First, signal-to-noise ratio is in general the strength of a signal divided by an estimate of its variability. It's a basic measure of effect size. Contrast-to-noise is the difference between two signals, for example, in different tissue types, divided by an estimate of noise variability again. There are many definitions in this paper here, and many ways of calculating it. We'll distinguish between two ways of calculating both SNR and CNR, spatially and temporally. So spatial signal-to-noise and contrast-to-noise are calculated across one image, and temporal are calculated across a whole time series of images at each voxel. So we can make maps of temporal SNR. So here are some basic, scratching my chest. [LAUGH] Here's some basic single image measures that are calculated spacial statistics on a single image, so we get get one statistic value per image. So a spatial SNR is the mean intensity within a signal area of interest. We'll call that mu A, divided by a standard deviation outside the signal area, so that's mu sub N, or whoops, divided by a standard deviation outside the signal area, so we'll call that sigma sub N. So here in the bottom image, you see an example of a real fMRI image. Now we've created a mask, with the signal area inside the brain and the noise area outside the brain. So it would be the mean in brain divided by the standard deviation outside the brain. Spacial contrast-to-noise is the difference in intensity between two tissue types, divided by a measure of the variability between those measurements. So now what we've done is taken our structural brain image here, and we've segmented it into two tissue types, T1 gray matter, and T2 white matter. So the contrast-in-noise would be the mean in gray matter minus the mean in white matter, divided by the pool of standard deviation. Now we'll talk about time series measures. And time series measures are calculated at each voxel across a time series, so we make maps of them. So here is one voxel where you see the time series of signal across the voxel, across time. Time series of signal in the voxel across time, and on the right you see the marginal distribution which has two little humps, two modes there. So now temporal SNR, or functional SNR, is the mean signal across time, divided by the variability across time for that voxel. So that's mu for the voxel divided by standard deviation for the voxel. And if you use temporally detrended data, this is the same as what's called the Signal-to-Fluctuation-Noise ratio, in some projects like the fBirn Multisite Study. Now let's look at temporal CNR. This is also really signal sensitivity to an effect that I'm interested in. So it's the difference in intensity of the image at each voxel, when task is on, versus off, let's say, divided by estimate of variability. This is related to the sensitivity to task and other psychological states, that I'd like to know about at the end of the day. A final issue to consider is the issue of scaling, and this is an issue with quantifying the magnitude of BOLD responses. The absolute scaling of BOLD responses is arbitrary, and for this reason, sometimes it's said that BOLD is not quantitative. Even though there many numbers involved, the absolute magnitude of the BOLD signal varies from person to person, and voxel to voxel. And the absolute scaling depends on a number of variables. First is the field strength, also the pulse sequence, and the gain on amplifiers. Third, acquisition parameters, including the repetition time, the TE, the voxel size, and the flip angle. The tissue type, so the local concentration of water in the tissue. And it also depends on a number of choices made in analysis, and we'll talk more about those in later modules. The implications of this is that most BOLD signal responses in papers are reported in units of arbitrary strength, arbitrary units they use, or percent signal change, which is a measure of the signal minus its baseline measure, divided by the baseline. This is not a problem when comparing across conditions or tasks or even participants acquired with the same scanner, the same parameters, the same post sequence, and subjected to the same analysis procedure. But it is a problem when we want to compare across different scanners, if we want to make quantitative comparisons. A final issue to consider is nonilinearity in the BOLD response. So the BOLD response is roughly linear, and there's some departures from linearity. In particular, there's some evidence for refractory effects, or saturation which are reductions in the amplitude of the response as a function of the time since the region was last activated, essentially. There's evidence for non-linearity in the stimulus, even if you have a train of events where you have a stimulus, and then you have a stimulus 5 to 6 seconds later of the same type. There's a small 10% reduction in the bold response to the second stimulus, so that's one kind of non-linearity. There are also changes in the shape of the response, and those non-linear effects are difficult to account for in analysis. They can produce compounds in some cases in your design. Because it's difficult to account for an analysis, it's best to minimize those with appropriate experimental designs and we'll talk about that more in later modules. Here's one example of the non-linearity in the visual cortex from a study we did some years ago. And what you're seeing here are bold responses in primary visual cortex, or early visual cortex to a series of flashing checkerboard events. So the red lines are 1 or 2 flashing checkerboards, the green lines are 5 or 6, a train of 5 or 6 flashing checkerboards. The blue lines, a train of 10 or 11 flashing checkerboard events. And what you can see here is the shape of your responses without nonlinearity, the response to two events would be about twice as high as one event. But you can see here it's quite a bit last. Responses to five events, because it shifted over would be about three times as high as the response to one event. The actual responses here we can see are close to half the predicted amplitude. So this effect is a nonlinear saturation effect and it happened because we presented checkerboards one second apart. If we had presented them five or six seconds apart, the nonlinear saturation would've been much lower. That's the end of this module. Hope you've enjoyed thinking with us about a few of the considerations about bold signal and noise.