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Saturday, March 24, 2018

FMRI data modulators 3: Low frequency oscillations - part I

Low frequency oscillations (LFOs) may be one of the the most important sources of signal variance for resting-state fMRI. Consider this quote from a recent paper by Tong & Frederick:
"we found that the effects of pLFOs [physiological LFOs] dominated many prominent ICA components, which suggests that, contrary to the popular belief that aliased cardiac and respiration signals are the main physiological noise source in BOLD fMRI, pLFOs may be the most influential physiological signals. Understanding and measuring these pLFOs are important for denoising and accurately modeling BOLD signals."

If true, it's strange that LFOs aren't higher on many lists of problems in fMRI. They seem to be an afterthought, if thought about at all. I suspect that nomenclature may be partly responsible for much of the oversight. A lot of different processes end up in the bucket labeled "LFO." The term is used differently in different contexts, with the context most often defined by the methodology under consideration. Folks using laser Doppler flow cytometry may be referring to something quite different than fMRI folks. Or not. Which rather makes my point. In this post I shall try to sort the contents of the LFO bucket, and in at least one later post, I shall dig more deeply into "systemic LFOs." These are the LFOs having truly physiological origin; where the adjective is used according to its physiological definition:

The description I pulled up from the Google dictionary tells us the essential nature of systemic LFOs: at least some of them are likely to involve the blood gases. And I'll give you a clue to keep you interested. It's the CO component that may end up being most relevant to us.

What exactly do we mean by low frequency oscillations anyway?

"Low frequency" generally refers to fluctuations in fMRI signal that arise, apparently spontaneously, with a frequency of around 0.1 Hz. The precise range of frequencies isn't of critical importance for this post, but it's common to find a bandwidth of 0.05 - 0.15 Hz under discussion in the LFO literature. I'll just say ~ 0.1 Hz and move on. I added "apparently spontaneously" as a caveat because some of mechanisms aren't all that spontaneous, it turns out.

For the purposes of this post we're talking about variations in BOLD signal intensity in a time series with a variation of ~ 0.1 Hz. There may be other brain processes that oscillate at low frequencies, such as electrical activity, but here I am specifically concerned with processes that can leave an imprint on a BOLD-contrasted time series. Thus, neurovascular coupling resulting in LFO is relevant, whereas low frequency brain electrical activity per se is not, because the associated magnetic fields (in the nanotesla range, implied from MEG) are far too small to matter.

Is LFO the lowest modulation of interest? No. There are physiological perturbations that arise at even lower frequencies. These are often termed very low frequency oscillations (VLFOs) because, well, we scientists are an imaginative bunch. These VLFOs generally happen below about 0.05 Hz. The biological processes that fluctuate once or twice a minute may well be related to the LFOs that are the focus here, but I am going to leave them for another day.

Categorizing LFOs:  How do they originate?

There is a lot of terminology in use, much of it confusing. After reading a few dozen papers on various aspects of LFOs, I decided I needed to sort things out in my own way. Different fields may use similar terms but may mean slightly different things by them. Generally, the nomenclature changes with the methodology under consideration. An LFO identified with transcranial Doppler ultrasound in a rat brain may not be the same as an LFO observed with optical imaging on a patient's exposed cortical surface during surgery. Reconciling these differences with LFOs observed in fMRI may be quite misleading as a result.

I finally decided on the four categories of LFO you find below. They are defined in an fMRI-centric way. My goal was to identify the irreducible parts, then try to figure out how different papers use varying nomenclature to discuss the specific mechanisms involved. Hopefully, this allowed me to separate processes in a useful manner from the perspective of an fMRI experiment, since much of the literature on physiological LFOs uses non-MRI methods. To help me relate the processes to fMRI specifically, I resorted to thought experiments. I will include a few in the footnotes so you can check my categorizations. Hopefully, if I have incorrectly characterized or omitted a process, it will be more apparent this way.

1. Instrumental limitations

These do not count as true biological LFOs according to my scheme. The most common way to produce variance around ~0.1 Hz in fMRI is through aliasing. We know that if we are acquiring a volume of EPI data every 2 seconds then we are below the Nyquist sampling frequency for normal human heart rates. Some fraction of the respiratory movements might also end up aliased into our frequency band of interest. By assuming an ideal acquisition method that acquires a volume of data not less than twice per heart beat, we begin to eliminate this source of LFO from our fMRI data. (SMS-EPI may permit sufficiently rapid sampling, depending on voxel size.) Which is why I think it is important to separate fundamentally biological processes from things that are fundamentally scanner-based. I contend that sampling rate is a scanner property, and it it is only the interaction of the biology with an imperfect scanner that produces the LFO. Improvements in scanner design and/or pulse sequences will ameliorate these effects.

An unstable patient table that deflects with a subject's breathing is clearly an instrumental limitation. A rock-solid patient bed eliminates mechanical deflections. Perturbation of B₀ from a subject's breathing is another instrumental limitation. There are a few potential solutions in principle. For example, we could use a field tracker that prevents modulation of the magnetic field over the head from chest motion. Or, if we had a pulse sequence other than EPI, with its low bandwidth in the phase encoding dimension, we could render respiration-induced modulations vanishingly small. (See Note 1.) The important point is that as scanner hardware and sequences are improved, we can expect to make significant advances in the amelioration of these pseudo-biological LFOs.

2. Cardiorespiratory mechanics

I apologize for the clunky term. Cardiopulmonary mechanics was another option. Not much better, huh? In this category are processes that derive from body mechanics; that is, the mechanical processes of physiology that originate outside of the brain. The two main sources are a pumping heart and a set of lungs oxygenating the blood. We seek the biological consequences in the brain that are produced by these oscillating organs. (I can't think of other body organs driving any pulsations but I await being enlightened in the comments section.) We have blood pressure waves and respiration-induced CSF pressure changes via the foramen magnum. These processes are independent of whether we are studying a person by fMRI or using any other method. See Note 2 for some thought experiments I used to derive this category.

The most important cardiorespiratory LFO I've seen in the literature is called the Mayer wave. The commonly accepted definition of a Mayer wave is an arterial blood pressure that isn't constant from heart beat to heart beat, but fluctuates about a resting mean. The fluctuations about the mean arterial BP occur with a frequency of ~ 0.1 Hz. Why the variation? It seems to be related to sympathetic nervous system activity. In lay terms, your "fight or flight" response isn't flat, but very slightly modulated.

The Mayer waves act at the speed of the arterial blood pressure wave. The effect on the BOLD signal happens as fast as the pressure wave passes through the vascular tree, which we know from a previous post can be estimated with the pulse transit time. At most it takes a few hundred milliseconds for the pressure wave to reach the toes from the aorta. We can expect differences of tens of milliseconds in arrival time across the brain, faster than the typical sampling rate of an fMRI experiment.

Can we measure it? The Mayer wave is a change in blood pressure, necessitating a good estimate of BP if we are to get a handle on it. We saw in an earlier post that measuring BP non-invasively in the scanner is non-trivial, however, so we shall have to leave isolation of Mayer waves to some future date. In the mean time, I am not unduly worried about Mayer waves as a major source of LFO because, as I shall claim below, there is likely a far more significant process afoot. 

I don't know enough about respiration-induced pulsation of CSF to estimate the importance of this mechanism at frequencies of ~ 0.1 Hz, except to say that any effects that do exist will be greatest around the brainstem, and will likely decrease the farther one gets from the foramen magnum. As with Mayer waves, I think it's safe to assume that we should worry about other mechanisms first, unless you are doing fMRI of brainstem structures, in which case you should hit the literature and keep this process top-of-mind.

3. Myogenic processes 

The third candidate LFO mechanism is vasomotion. Perturbations in the vascular tone - the tension in the smooth muscle of blood vessel walls - may vary over time. Some of the non-neural signaling mechanisms contributing to vasomotion are reviewed here. The effect is myogenic, meaning "in the muscle."

We assume that vasomotion occurs independent of the contents of the blood in the vessel. Many references also suggest that vasomotion occurs independent of nervous control. In other words, there would be some sort of local oscillatory signaling within the vessel wall that produces an idling rhythm. Additionally, however, vasomotion may be influenced by nervous system responses because the smooth muscles of the arterial walls are innervated. Indeed, this is how we get neurovascular coupling. Thus, some vasomotions might actually be responsible for the target signals in our resting state scans, as suggested very recently by Mateo et al. (See also this 1996 article from Mayhew et al.) So, for the purposes of this post, I shall consider vasomotion as a desirable property, at least for resting state fMRI, and leave the issue of any non-neural components of vasomotion for another day. As things stand, it would be nigh on impossible to separate, using current methods, the target vasomotion - that driven by neurovascular coupling - from any non-neural vasomotion that one might label as a contaminant.

4. Blood-borne agents

A fourth category of LFOs was suggested relatively recently. Mayer waves and vasomotion were observed long before fMRI came about. But it was the advent of resting state fMRI that seems to have precipitated the interest in this category. Blood constituents are not stationary. Instead, the concentration of blood gases - oxygen and carbon dioxide in particular - vary based on your rate and depth of breathing, your stress level, and so on. Anything traveling in the blood that either directly or indirectly mediates BOLD signal changes is therefore of concern, and is included in this category.

The spatial-temporal propagation of LFOs through the brain, arising from blood-borne agents, is naturally at the speed of the bulk blood flow. Whereas Meyer waves propagate through the brain with the velocity of the blood pressure wave, agents carried in the blood tend to move much more slowly. We usually use a mass displacement unit for cerebral blood flow (CBF), typically milliliters of blood per fixed mass of tissue per minute.  But that's not very intuitive for this discussion. Instead, consider the average time taken for blood to transit the brain, from an internal carotid artery to a jugular vein. In normal people this journey takes 7-10 seconds. This is the timescale of relevance to LFOs produced by blood-borne agents.

The most important vasodilative agent carried in the blood is carbon dioxide. It is so important that I am dedicating the entire next post - part II - to it. I hadn't expected to be digging into CO effects until later in this series, since I had anticipated that all the main LFO effects would be vascular, with no direct overlap to respiratory effects. Live and learn. It's a timely reminder of just how complex and interwoven are these physiologic confounds.

Summing up the categories

Okay, to summarize, we have instrumental limitations, which could be eliminated in principle, then three categories of LFO arising out of a subject's physiology. The latter three categories can be expected to occur regardless of the particular MRI scanner you use. These physiological mechanisms arise spontaneously; there is no need to evoke them. Thus, it means they are likely ubiquitous in both resting and task fMRI experiments. 

The pulsatile effects of cardiorespiratory mechanics don't seem to be amenable to independent measurement at the present time. We can possibly infer them from the fMRI data, but then we are forced to deal with the consequences of aliasing and any other instrumental limitations that produce signal variance derived from cardiac or lung motion, manifest via different pathways.

We also don't seem to have a way to separate in principle any non-neural vasomotion from that which may be driven by neurovascular coupling. Multi-modal, invasive measurements in animals, such as performed by Mateo et al., may be the only way to discriminate these processes.

That leaves blood-borne agents. Changes in oxygen tension may be important since, for a fixed metabolic rate of oxygen consumption, any process that alters the supply of oxygen in arterial blood necessarily produces a concomitant change in deoxyhemoglobin in venous blood. I am still investigating the potential importance of oxygen tension, but based on several converging lines of evidence, it appears that fluctuations in arterial CO are the far bigger concern.

Coming up in Part II: Systemic LFOs arising from changes in arterial CO (we think).



1. If you don't like my field tracker ideal, try this out instead. Imagine we have an fMRI scanner that operates at a main magnetic field of 100 microtesla (μT). A 3 ppm field shift at 3 T equates to nearly 400 Hz; a staggeringly vast frequency shift that would cause horrendous distortions and translations in EPI. But a 3 ppm shift at B₀ = 100 μT corresponds to a frequency of just over 0.01 Hz, against a typical linedwidth of ~20 Hz. The magnetic susceptibility due to chest movement vanishes at this low field. Thus, an ultralow field MRI scanner is robust against the modulation of B₀ from chest movements. The corollary? High field, whole body scanners exhibit enhanced sensitivity to chest movement. (3 ppm at 7 T is a frequency of almost 1 kHz. Ouch.)

2. Imagine we stopped the subject's heart and chest motions and instead replaced the biological functions of heart and lungs with a machine that scrubbed CO₂ and oxygenated the blood before recirculating it through the arteries. It does this in smooth, continuous fashion, without pulsations of any kind. If the machine delivers oxygenated blood to the brain at the same effective rate as the brain needs, all should be okay and the brain should continue to behave normally. But what would happen to the cardiorespiratory mechanical effects? If the machine is ideal, if it doesn't pulse at all, and there are no moving parts to produce any sort of pressure wave through the body, we would have successfully eliminated two sources of LFO.

An alternative way to think about LFOs arising from cardio-respiratory mechanics is to note that the pulsations are independent of the substances being manipulated. Pretending for a moment that the biology wouldn't mind, the mechanical effects across the brain would be the same if the heart was pumping olive oil instead of blood and the lungs were inspiring and expiring pure helium instead of 20% oxygen. The respiratory and cardiac mechanical processes would continue unabated, as would any LFOs produced in our fMRI data, because they arise from the pulsations inherent in the plumbing.

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