Ultra-slow oscillations in fMRI and resting-state connectivity: Neuronal and vascular contributions and technical confounds

Abstract

Ultra-slow, ~ 0.1 Hz variations in oxygenation level of brain blood is widely used as a fMRI-based surrogate of “resting-state” neuronal activity. The temporal correlations among these fluctuations across the brain are interpreted as “functional connections” for maps and neurological diagnostics. Ultra-slow variations in oxygenation follow a cascade. First, they closely track changes in arteriole diameter. Second, interpretable “functional connections” arise when the ultra-slow changes in amplitude of γ-band neuronal oscillations, which are shared across even far-flung but synaptically connected brain regions, entrain the ~ 0.1 Hz vasomotor oscillation in diameter of local arterioles. Significant confounds to estimates of “functional connectivity” arise from residual vasomotor activity as well as arteriole dynamics driven by self-generated movements and subcortical common modulatory inputs. Lastly, methodological limitations of fMRI can lead to spurious “functional connections”. The neuronal generator of ultra-slow variations in γ-band amplitude, including that associated with self-generated movements, remains an open issue.

INTRODUCTION

How do brains compute? The answer to this question takes on many guises. It has proven useful to differentiate brain regions on the mesoscopic scale, i.e., as an average over large number of individual neurons, and thus define connections and signaling on the same mesoscopic scale (Mitra, 2014; Zeng, 2018). As an example, the flow of sensory input in the transformation from perception to action can be described as a flow from primary sensory areas to motor areas (Ferezou et al., 2007; Li et al., 2016). Mesoscopic connectivity diagrams are readily determined based on the histological analysis of tissue subsequent to the injection and transport of anterograde and/or retrograde markers (Bohland et al., 2009; Kim et al., 2017). However, the determination of connectivity within the living animal, and the modulation of signaling along established axonal pathways as a function of brain state, requires a noninvasive procedure. A well-established, albeit incompletely understood approach is based on functional magnetic resonance imaging (fMRI), an imaging modality that infers neuronal activity from changes in localized brain blood oxygenation (Logothetis and Wandell, 2004; Shulman et al., 2002).

Here we review the use of fMRI to infer neuronal connectivity between well separated regions in the forebrain. These are correlation-based methods, and regions with strong correlations between their resting-state signals are said to be “functionally connected”. Connected graphs that are comprised of regions as vertices and strong correlations as edges are said to form “default networks” of brain activity (Greicius et al., 2003; Raichle et al., 2001; Sporns et al., 2005). Such networks have been characterized in humans (De Luca et al., 2006; De Luca et al., 2005; Majeed et al., 2011; Zhao et al., 2008), monkeys (Shmuel and Leopold, 2008; Vincent et al., 2007), and rats (Gozzi and Schwarz, 2016; Lu et al., 2012; Majeed et al., 2011; Stafford et al., 2014; Thompson et al., 2013), albeit not without controversy as to reliability (Honey et al., 2009). Our review generally avoids the discussion of signals from anesthesia animals and humans in light of the strong disruption in the interaction between neurons and blood vessels by most anesthetic agents (Gao et al., 2017; Goense and Logothetis, 2008; Pisauro et al., 2013).

FUNDAMENTALS

Both the flow and oxygenation of blood in the brain is modulated by neuronal activity. This modulation forms the basis of fMRI and intrinsic optical signal (IOS) imaging. Two coupled effects are at work. First, an increase in neuronal activity will lead to an increase in the diameter of the pial arterioles that distribute blood to the brain. This change in diameter will long outlast the stimulus (Drew et al., 2011; Uhlirova et al., 2016) (Fig. 1A). Second, an increase in neuronal activity will initially lead to a decrease in blood oxygenation in the microvessels and veins, seen most prominently in the upper layers of cortex (Buxton, 2001; Grinvald et al., 1991; Tian et al., 2010), albeit this interpretation is not universally accepted (Şencan et al., 2020; Sirotin et al., 2009; Uludağ et al., 2009). The increase in oxygen consumption is soon overcompensated by an increase in blood flow and a concomitant increase in blood oxygenation. The overcompensation reflects the active nature of neurovascular coupling (Attwell et al., 2010; Cauli and Hamel, 2010; Iadecola, 2004; Kleinfeld et al., 2011). The overcompensation can localize to one or few cortical columns (Grinvald et al., 1991), yet it may have a global component from dilation of arterioles caused by change in the activity of sympathetic input (Dacey Jr and Duling, 1984).

Figure 1. The neocortical vascular response to phasic sensory stimulation and the mechanism for fast neurovascular coupling.

(A) The canonical effect of neuronal activity on the diameter of pial vessels as measured with two-photon laser scanning microscopy (Kleinfeld et al., 1998) using a head-fixed rat. The stimulus is a 500 ms puff to the vibrissae. Adapted rom (Uhlirova et al., 2016)

(B) The canonical effect of neuronal activity on hemodynamics as measured with intrinsic optical imaging using 630 nm light (Grinvald et al., 1988) using a head-fixed mouse. The stimulus is a 4 s puff to the vibrissae. The isoflurane data refers to a breathing mixture of 1.8 % (v/v) isoflurane in oxygen. Adapted from (Knutsen et al., 2016).

(C) Rapid mechanisms for communication of neuronal activity to drive smooth muscle hyperpolarization and arteriole dilation. Neural activity (1) leads to an increase in K⁺ in the perivascular space surrounding microvessels that activates the potassium inward rectifier (2), K_IR, to generate a local hyperpolarization of the endothelial membrane (3). The hyperpolarization spreads to adjacent endothelial cells through gap junctions to activate K_IR currents in adjacent cells (4). This results in a propagating signal from microvessels to penetration arterioles and finally surface or pial vessels. The hyperpolarization spreads to adjacent smooth muscle cells (5) and deactivates voltage-dependent Ca²⁺ currents, Ca(V), to induce smooth muscle relaxation and arteriolar dilation (6). Rapid arteriole dilation is also induced by binding of nitric oxide (NO) that is released from some inhibitory neurons, as well as other brain cells, i.e., endothelial cells, astrocytes, and microglia. The increase in arteriole diameter (panel A) can lead to an increase in blood flow. Adapted from (Longden et al., 2017) and (Knot and Nelson, 1998).

The oxygenation state of blood can be detected via differences in the electronic properties of oxy- versus deoxyhemoglobin. This is reported by a greater reflection of red light by oxy- versus deoxyhemoglobin, which is routinely detected by IOS imaging (Lieke et al., 1989) (Fig. 1B). It is also reported by a change from a diamagnetic to a paramagnetic state by oxy- versus deoxyhemoglobin, respectively (Pauling and Coryell, 1936). Thus, the magnetic susceptibility of capillary and venous blood is correlated with neuronal activity. The change in arteriole diameter and blood oxygenation are coupled; the overcompensation of blood oxygenation is quenched when the pial arterioles are fully dilated using isoflurane prior to the onset of neuronal activity (Fig. 1B) (Knutsen et al., 2016).

Communication from neurons to arteriole smooth muscle.

How do neurons communicate with arterioles? There are multiple mechanisms that neurons in the brain use to control their own supply of blood (Attwell et al., 2010; Cauli and Hamel, 2010; Iadecola, 2004; Kleinfeld et al., 2011). We review two mechanisms that acts on a < 1 s time-scale. The lumen of the blood vessels is formed by endothelial cells that are connected with relatively low resistance gap junctions, such that passive signaling occurs with an ~ 2 mm electrotonic length (Segal and Duling, 1989; Welsh et al., 2018). Further, the smooth muscle cells that drive vascular tone are in strong electrical contact with the endothelial cells. In the presence of bursts of neuronal spikes, there is an outflow of K⁺ ions in the perivascular space (Caesar et al., 1999; Rasmussen et al., 2019). This can lead to regenerative, hyperpolarizing pulses that propagate along the endothelial cells from the subsurface microvessels to the penetrating arterioles (Longden et al., 2017) and then to pial arterioles (Fig. 1C). The hyperpolarization will spread to smooth muscle and dilate the pial arterioles (Filosa et al., 2006; Knot and Nelson, 1998) (insert in Fig. 1C). This sequence of activation is supported by the stimulus-driven progression in arteriole dilation from middle layers to the pia in cortex (Tian et al., 2010). While details of the conditions for passive versus active spread of signals in the pial network remain to be addressed (Harraz et al., 2018), direct electrical coupling through the endothelium provides a means for neurons to directly influence the diameter of neighboring arterioles (Fig. 1A).

Nitric oxide (NO) is a well-known vasodilator that is produced by nitric oxide synthase (NOS) in neurons and can act quickly to relax smooth muscle (Fig. 6). As a caveat, the role of NO as a transient actuator of change in arteriole dilation (Ma et al., 1996), as opposed to a co-factor in effecting change (Lindauer et al., 1999), remains unsettled (Attwell et al., 2010), though optogenetic stimulation of neurons that express NO-synthase will drive an increase in blood flow (Krawchuk et al., 2019). The role of astrocytes in the control of flow is also controversial (Kleinfeld et al., 2011; Mishra et al., 2016; Nizar et al., 2013; Rosenegger et al., 2015), with arteriole dilation occurring only in the presence of relative large signaling events by astrocytes (Schulz et al., 2012).

Figure 6. The envelope of neuronal γ-band oscillations locks to and leads vasomotor oscillations in arteriole diameter.

(A) Set-up with a head-fixed awake but resting mouse for two-photon imaging of arteriole diameter along with measurement of the LFP (left panel). A thinned skull window was used to preserve vasomotion (Drew et al., 2010). Two-photon images of surface vessels and scan path to define lumen diameter (center panel). From (Mateo et al., 2017).

(B) Example data showing the LFP (top trace), the spectrogram of the LFP with a window of 2.0 s and a bandwidth of 2.5 Hz, and the time series of the integrated γ-band power and diameter for one arteriole in the field (bottom traces). From (Mateo et al., 2017).

(C) The cross correlation of the two time series used for the example of panel B, 600 s total time, show that the LFP leads the diameter change. As an average across animals, movement proceeds the vasodilation by 1.9 ± 0.2 s (82 vessels from 27 mice with 600 s of data per vessel). From (Mateo et al., 2017).

(D) New data on the recording of self-generated, i.e., spontaneous movement in a head-fixed awake but resting mouse, obtained concurrent with two-photon imaging of arteriole diameter (Winder et al., 2017) similar to that in panel A, to determine the possible contribution of such movement to the entrainment of vasomotion. Bouts of whisking were determined with videography and whole-body vertical acceleration determined with a force sensor attached to the tube supporting the mouse’s body.

(E) Correlation analysis of new data (27 vessels from 9 mice with 1700 to 12000 s of data per vessel). The time-lag of the correlation shows that movement leads the change in diameter (bottom panel) with lag times similar to that for movement proceeds the vasodilation by 1.8 ± 0.3 s for whisking and 1.5 ± 0.3 s for whole body motion.

(F) A re-analysis of the data of Mateo et al. (2017), similar to that for the new data of panels E and F, using previously unpublished simultaneous measurements of the whole body horizontal acceleration acquired during imaging (82 vessels from 27 mice). Accelerations lead to a change in arteriole diameters (left panel); the threshold detectability was ~ 0.01 g. Theses movement related changes in diameter are compared to rest events (middle panel) and dominate the largest changes in diameter (right panel).

Background on fMRI.

The blood oxygenation level dependent (BOLD) fMRI signal exploits the shift in the magnetic properties of deoxyhemoglobin versus oxyhemoglobin (Villringer and Dirnagl, 1995). In practice, these are detected by changes to the relaxation time of water protons in the brain (Ogawa et al., 1993; Stephan et al., 2004). Longer relaxation times implies greater oxygenation and a larger BOLD fMRI signal. The BOLD effect was discovered in 1990 by Seiji Ogawa using anesthetized rats (Ogawa et al., 1990). Two years later, BOLD was independently demonstrated in the awake human brain by the laboratories of James Hyde (Bandettini et al., 1992), Bruce Rosen (Kwong et al., 1992) and Kamil Ugurbil (Ogawa et al., 1992). As an example, successive eye opening and closing in humans leads to a change in the BOLD fMRI signal in the brain region that corresponds to primary visual cortex (Fox and Raichle, 2007) (Fig. 2A). In terms of impact, the use of BOLD fMRI has stormed across the disciplines of psychology and cognitive neuroscience as a means to infer changes in neuronal activity during all aspects of cognitive tasks performed by humans.

Figure 2. Functional MRI (fMRI) uses correlation in the fluctuations of signal strength to infer brain regions that are directly connected.

(A) Changes in the basic blood oxygenation level dependent (BOLD) fMRI signals generated in human visual cortex in response to changes in luminance in a full field visual input. Unaveraged BOLD signal (magenta) was obtained from a region in the primary visual cortex during a task that required subjects to open and close their eyes. The task is shown in blue, and the times are delayed to account for the hemodynamic response. The subtraction of the eyes-closed condition from the eyes-open condition identifies a BOLD signal intensity difference in the primary visual cortex (shown on the right). Note the variability as well as the average increase in signal amplitude upon stimulation. From (Fox and Raichle, 2007).

(B) Blood oxygenation level dependent fMRI signals were obtained from a coronal slice, 2.8 cm from the occipital pole (left). Three unprocessed time courses of the BOLD fMRI signal of representative voxels, numbers 1-3 and located outside of visual cortex, and their corresponding frequency spectra (right). A binocular visual stimulus, provided by a pair of flickering red LED patterns, was on during the 40 - 70 s time interval of the 110 s period and drives voxel 4; data not reproduced here. From (Mitra et al., 1997).

(C) The BOLD fMRI signals recorded from two distant regions in human cortex, the posterior cingulate / precuneus cortex (PCC) and the medial prefrontal cortex (mPFC), are highly correlated on the time scale of tens to hundreds of seconds. Correlations are calculated between a seed voxel in the PCC and all other voxels in the brain for a single subject during rest. The spatial distribution of correlation coefficients shows both positive and negative values and was thresholded at R² = 0.1 (left image). The time course for a single run is shown for the seed region (PCC) and a region (mPFC) positively correlated with this seed region. The functional connection between the PCC and the mPFC is consistent with a fiber track revealed by diffusion tensor imaging (blue trace in right image). Left and center panels from (Fox et al., 2005), right panel from (Greicius et al., 2009).

(D) Four well-matched pairs of resting-state subnetworks that show a close correspondence between the independent analyses of activated (left column) and resting-state (right columns) brain dynamics. Activation data is from the 20-component analysis of the 29,671-subject BrainMap activation database (Fox and Lancaster, 2002; Laird et al., 2005) and resting-state data is from a separate analysis of a 36-subject resting-state fMRI dataset (Smith et al., 2009). Shown are the three most informative orthogonal slices for each pair. Left columns: network from BrainMap, shown superimposed on the MNI152 standard space template image. Right columns: resting-state fMRI data, shown superimposed on the mean fMRI image from all subjects. From (Smith et al., 2009).

A complementary technique, cerebral blood volume (CBV) fMRI, infers neuronal activity from an increase in total hemoglobin in response to neuronal activity. It was first demonstrated in the human brain using subjects whose blood was doped with gadolinium, a paramagnetic ion that vastly increases the magnetic susceptibility of blood (Belliveau et al., 1991; Kwong et al., 1992). The increase in blood volume is secondary to an increase in arteriole diameter (Fig. 1B). Subsequent work has demonstrated CBV fMRI using label-free procedures (Huber et al., 2017; Lu et al., 2003).

Noise and the determination of correlated brain activity.

The physicist Lewis Branscomb famously wrote “God loves the noise as much as the signal.” (Branscomb, 1995). The noise in the fMRI signal, a part of physiological contributions such as breathing and technical noise, has dominant albeit broad spectral bands (Mitra and Bokil, 2008; Papoulis, 1962) near 0.1 Hz (Fig. 2B). The exact frequency can vary on the scale of centimeters across the human brain. Mindful of Branscomb’s prescient comment, only a few years after the advent of BOLD fMRI, additional experiments in the laboratory of James Hyde showed that the variability observed in the BOLD fMRI signal is correlated across well-separated regions in the brain. The initial observations involved subregions in motor cortex of the two hemispheres whose BOLD fMRI signals co-fluctuate in the vicinity of 0.1 Hz in the absence of a task (Biswal et al., 1995). These signals, in contrast to stimulus- and task-based fMRI, are measured in the absence of a cognitive task or any overt stimulus and are referred to as resting-state fMRI signals (Biswal et al., 2010). They are thus referred to as the resting-state BOLD fMRI. In fact, the signal between any pair of well separated regions in the brain will co-fluctuate so long as they maintain long-range, i.e., white matter, connections (Fox et al., 2005). This is illustrated for resting-state BOLD fMRI signals from the posterior cingulate cortex (PCC) and medial prefrontal cortex (mPFC) (left and center, Fig. 2C), which are connected by a white matter tract along the cingulum bundle (Greicius et al., 2009) (right, Fig. 2C). In general, resting-state fMRI signals are particularly strong between regions in opposing hemispheres with mirrored neuronal activation (Smith et al., 2009) (Fig. 2D), albeit these signals are accompanied by brain-wide activation (Schölvinck et al., 2015).

Arteriole diameter naturally oscillates near 0.1 Hz.

What are physiological attributes of blood vessels that allow them to be coupled to ongoing neuronal activity in the absence of a task (Fig. 2C,D), as opposed to be driven by strong sensory stimuli (Fig. 1)? Further, what is the origin of the ~ 0.1 Hz frequency-scale for the ultra-slow dynamics that dominate the resting-state BOLD fMRI signal (Fig. 2B)? Both of these questions are answered by recalling that arteries undergo vasomotor oscillations as part of their normal physiology (Intaglietta, 1990). These are collective oscillations of contractile tone in the smooth muscle cells that surround arterioles and lead to rhythmic changes in arteriole diameter (Aalkjær et al., 2011; Intaglietta, 1990) that are referred to as vasomotion. The rhythm thought to be generated by the interactions of active conductances in the membranes of smooth muscle and endothelial cells (Aalkjaer and Nilsson, 2005; Haddock and Hill, 2005) with the mechanical forces generated by flow (Koenigsberger et al., 2006; Stergiopulos et al., 1998). Vasomotion occurs within a broad frequency band that is centered near 0.1 Hz in humans (Noordmans et al., 2018; Obrig et al., 2000; Rayshubskiy et al., 2013), mice (Drew et al., 2011), and rats (Kleinfeld et al., 1998; Mayhew et al., 1996). Vasomotor oscillations in arteriole diameter drive oscillations in the velocity of red blood cells in the microvessels (Drew et al., 2010; Kleinfeld et al., 1998) and changes in the partial pressure of oxygen in brain tissue (Mateo et al., 2017; Mayhew et al., 1996).

As an intrinsic property, vasomotor oscillations are observed in isolated brain arterioles that are cannulated, pressurized, and maintained at physiological temperature (Osol and Halpern, 1988) (Fig. 3A). Critically, vasomotion is observed in pial arterioles in vivo (left, Fig. 3B) and is only slightly reduced in amplitude, by a factor of 0.2, when cortical activity is silenced to isolate the vessels from ongoing cortical, albeit not sympathetic, neuronal activity (Winder et al., 2017) (center and right, Fig. 3B).

Figure 3. In vitro and in vivo measurements of vasomotion, a rhythmic change in arteriole diameter with a broad band intrinsic frequency centered near 0.1 Hz.

(A) Simultaneous recording of lumen diameter (top) and temperature (bottom) in a cerebral artery that was isolated from a spontaneously hypertensive, stroke-prone rat and pressurized to 80 mmHg. Diameter oscillations appear when the artery is warmed above 35°C. From (Osol and Halpern, 1988).

(B) Example of normalized diameter measurements from a single pial arteriole with two-photon laser scanning microscopy following local artificial cerebral spinal fluid (aCSF) infusion (left) and muscimol infusion (center) infusions in a single animal. The population summary of the root-mean-square deviation in pial arteriole diameter after muscimol infusion (19 vessels from 4 animals); oscillation amplitudes were reduced following infusion of muscimol compared to aCSF. From (Winder et al., 2017).

(C) Two-photon imaging of vasomotion in cortical arterioles across both hemispheres of an awake, head-fixed mouse. A maximally projected image stack across 500 μm of the preparation was obtained with ultra-large field-of-view two-photon microscopy (Tsai et al., 2015) (top row); the dark region in the middle corresponds to a physical mask. The arbitrary-line-scan path of the beam (yellow) spans both hemispheres. The expanded images (middle row) are single planes in each hemisphere and serve to highlight the path of the line-scan through individual vessels whose diameters were concurrently monitored. Vasomotor oscillations measured simultaneously from pial arteries in the right (green) and left (red) hemispheres appear synchronous (middle panel in middle layer). The full data set of 600 s is seen to be correlated with a lag time at the peak of 0.0 ± 0.1 s (lower row left panel). The spectral coherence in the diameter from pairs of arterioles (24 traces of 540 s traces), calculated with a bandwidth of 0.04 Hz as an average over 24 measurements. From (Tsai et al., 2015).

The presence of ultra-slow natural oscillations in the diameter of brain arterioles raises three questions. First, what is the relation of the oscillation to the change in oxygenation of the neighboring tissue, i.e., the parenchymal contribution to the BOLD signal? Simultaneous measurements of the arteriole diameter and the intrinsic optical signal in awake mice show that the two are strongly coherent (Mateo et al., 2017). The peak value of oxygenation lags the peak of vasodilation by ~ 1 s. The positive coupling of blood oxygenation with a change in arteriole diameter is consistent with the changes that occur upon sensory stimulation (Fig. 1).

The second question, given the coupling of blood oxygenation to vasomotion, concerns the spatial scale of synchronous vasomotor oscillations. The results from direct measurements of vessel diameter in awake rodents indicate that vessels within a radius of ~ 2 mm tend, on average, to dilate synchronously (Mateo et al., 2017). Further, since the radius is the only dimension of blood vessels that can change, CBV fMRI provides a measure of arteriole diameter. Using this technique with anesthetized rodents, a correlation length of ~ 2 mm is also reported (He et al., 2018). Thus, despite the short-range fall-off, are changes in diameter strongly coordinated across distant but mirrored regions in the two hemispheres (Fig. 3C)? Optical imaging data from rodents shows that such transhemispheric changes are strongly correlated (Mateo et al., 2017; Tsai et al., 2015). Similar results are inferred with CBV fMRI of the primate brain (Schölvinck et al., 2010). All told, mirrored regions in the two hemispheres show synchronous oscillations in arteriole diameter (Fig. 3C) in addition to blood oxygenation (Fig. 2D).

The third question is how fast the callosal coupling between neurons in opposite hemispheres must be to support synchronous ultraslow activity. For the simplest models of weakly coupled oscillators, this means a delay of less than a quarter of a period (Sompolinsky et al., 1991; Yeung and Strogatz, 1999). This corresponds to ~ 2 s, which is two orders of magnitude longer than transhemispheric propagation delays. The arteriole vasomotion in each hemisphere is synchronous through the similarly delayed neuronal-to-vascular coupling (Fig. 1).

SOURCES OF ULTRA-SLOW ELECTRICAL SIGNALING TO COUPLE TO VASOMOTION

The theory of weakly coupled oscillators (Kuramoto, 1984) implies that vasomotor oscillations can phase-lock to rhythmic neuronal activity within the same ~ 0.1 Hz frequency band. We consider three such sources of activity (Fig. 4A). The first two involve ultra-slow variations in neuronal electrical potential. One realization is in terms of an ultra-slowly varying envelope of high-frequency electrical oscillations in the brain (Leopold et al., 2003; Nir et al., 2008; Thompson et al., 2013). A second is in terms of potential ultra-slow variations in the electrocorticogram (ECoG) or electroencephalogram (EEG) (He and Raichle, 2009). The ECoG and the EEG measure spatially extended and temporally coherent extracellular current flow in the brain (Lemon, 1984). The third potential source of ultra-slow rhythmic activity is via neuromodulator nuclei. We consider the viability of each of these signaling mechanisms as a prelude to describing the locking of vasomotor activity to ultra-slow electrical signal in the brain.

Figure 4. Ultra-slowly varying neuronal signals have multiple potential origins but are predominantly encoded by the ultra-slow modulation of the fast, γ-band oscillations.

(A) Coupled oscillator model for resting-state neurovascular coupling. The three potential coupling mechanisms for entrainment of vasomotor oscillations across separate regions of the brain: (1) the ultra-slow envelope of the γ-band oscillations shared across separate regions, as illustrated in panel B; (2) ultra-slow electrical potentials per se that are shared across separate regions; and (3) regional-specific neuromodulation of brain activity. Adapted from (Mateo et al., 2017).

(B) A model to illustrate amplitude modulation using an ultra-slow signal to modulate a fast underlying oscillatory signal. The top trace is the product of a carrier centered at fγ = 55 Hz and a 0.1 - 0.2 Hz band-limited noise source for the ultra-slow modulate. The associated spectrum was computed with a bandwidth of 0.5 Hz (black trace) or 0.05 Hz (blue trace). The bottom trace shows the frequency components of the ultra-slow envelope after demodulation and low-pass filtering to remove signals near 2f_g. The associated spectrum was computed with a bandwidth of 0.05 Hz. From (Mateo et al., 2017).

(C) Measurements and analysis of ultra-slow variations in the power of the surface ECoG during stage 2 sleep in a human subject (left panel); from (Nir et al., 2008). The spectrogram of the ECoG shows the slow variation in power in the 40 to 90 Hz γ-band (left-of-center panel); window of 10 s, bandwidth of 1.5 Hz, and color scales the logarithm of power from black/red (low) to white/yellow (high). The time-series of the variation of integrated power in the γ-band of the ECoG shows oscillations on the 10-s time scale. The spectrum of the derivative of this time-series, a procedure that remove a power ∝ 1/f² trend from the spectrum, has statistically significant peaks at frequencies near ~ 0.1 Hz. Reanalysis from (Drew et al., 2008).

Ultra-slow electrical signaling by modulation of γ-band oscillations.

Gamma-band oscillations refer to rhythmic brain activity in a broad range of frequencies, typically 30 to 80 Hz. It can be generated in vitro by networks of solely fast-spiking inhibitory neurons (Whittington et al., 1995), consistent with theoretical predictions (Hansel et al., 1993; van Vreeswijk et al., 1994). In vivo, the details of the oscillatory waveform are shaped by the interactions between parvalbumin and pyramidal neurons (Cardin et al., 2009; Sohal et al., 2009) as well as by interactions with different classes of inhibitory neurons (White et al., 2000) and cholinergic modulation (Pinto et al., 2013).

A key feature of γ-band oscillations is that the amplitude, or equivalently the spectral power, can vary over time (Leopold et al., 2003; Liu and Duyn, 2013; Mateo et al., 2017; Nir et al., 2008; Thompson et al., 2013). In fact, an increase in power in the γ-band is a predictor of a subsequent increase in arteriole diameter and blood oxygenation (Mateo et al., 2017; Winder et al., 2017). Consistent with these physiological changes, there is a corpus of evidence that increased power in the γ-band correlates with an increase with the BOLD fMRI signal (Goense and Logothetis, 2008; Keller et al., 2013; Lachaux et al., 2007; Lima et al., 2014; Niessing et al., 2005; Nir et al., 2007; Schölvinck et al., 2010). While the power in the γ-band is the best predictor of an increase in arteriole diameter, the correlation with the spectral power extends down to lower frequencies (Goense and Logothetis, 2008; Mateo et al., 2017; Winder et al.,2017).

As a matter of principle, amplitude modulation (Black, 1953) provides a means for ultra-slow signals to be transmitted in the brain, as can occur by modulating the interspike interval in a spike train by an inhomogeneous spike rate (Okun et al., 2019). Here, the γ-rhythm oscillations serve as the underlying carrier frequency and the broad-band, ~ 0.1 Hz rhythm modulates the amplitude of the γ-rhythm oscillations (Fig. 4B). The power spectrum of the γ-rhythm oscillations is broadened by the modulation but still centered at a high frequency; there is no spectral power at the broad-band, ~ 0.1 Hz modulation (Fig. 4B). Demodulation of the signal, which involves spectral mixing and can be accomplished by the threshold properties of neurons (Ahrens et al., 2002), retrieves the ultra-slow signal (Fig. 4B). Recent data from the mouse accessory olfactory bulb implies that ultra-slow modulation can be quite strong in practice (Tsitoura et al., 2020).

Evidence for encoding of ultra-slow oscillations by the modulation of γ-rhythm oscillations comes from studies on monkey (Leopold et al., 2003) and human subjects (Nir et al., 2008). The human study involved bilateral recordings of multi-unit spike waveforms and the ECoG from the parietal and temporal lobes of both cortices in preoperative patients. A spectrogram of the ECoG acquired while a subject was in non-REM sleep shows that the power in the γ-band is slowly modulated (Fig. 4C). The spectral power of the modulation in γ-band power. i.e., the so-called second spectrum, shows peaks at frequencies near 0.1 Hz (Drew et al., 2008) (Fig. 4C). These modulations are present during both states of sleep and states of wakefulness.

Is the modulation in γ-band power correlated across hemispheres, as would be expected if these signals relate to transhemispheric correlation in the BOLD fMRI signal (Fig. 2D) and the arteriole diameter (Fig. 3C)? The spike times at spatially adjacent regions as well as at functionally linked areas of opposing hemispheres are not coincident. In contrast, there is significant coherence in the modulation of the spike rate and in the power of γ-band oscillations in the ECoG across sites in opposing hemispheres (Nir et al., 2008). During rest, there is a relatively large and positive correlation coefficient of 0.6 between ultra-slow ECoG signals from contralateral auditory areas, as compared with smaller correlation coefficients between signals from auditory and nonauditory areas. The stimulus-linked synchrony between the auditory areas in opposite hemispheres is likely mediated through callosal connections (Engel et al., 1991). The literature therefore suggest that ~ 0.1 Hz signals are transmitted as modulation of the high frequency γ-band rhythm, which is coherent across mirrored regions in the two hemispheres.

A final concern is the spatial specificity of the ultra-slow modulation that forms correlated signals across hemispheres. This was addressed using wide-field optical imaging of the dorsal surface of cortex in transgenic mice that express functional indicators of intracellular calcium (Barson et al., 2019; Ma et al., 2016; Vanni et al., 2017) or transmembrane voltage (Chan et al., 2015; Mohajerani et al., 2013). These indicators report the accumulation of spiking activity, which approximates rectification of neuronal activity above a threshold level (Fig. 4B) and thus reports the ultra-slow envelope of neuronal activity. While strong correlations occur for frequencies over the range from 0.1 Hz to 10 Hz, the amplitude of the oscillations across the dorsal surface is greatest in the 0.08 - 0.16 Hz frequency band, i.e., centered near 0.1 Hz, as opposed to bands below this frequency and up to 10 Hz (Vanni et al., 2017). Further, bilateral symmetry of the neuronal response is largely reduced in acallosal mice (Mohajerani et al., 2010), albeit this issue is not without controversy (Quigley et al., 2003; Tyszka et al., 2011).

Ultra-slow changes in the electrocorticogram report non-neuronal dynamics.

The EEG is traditionally recorded as surface potentials across the brain (Lemon, 1984). Ultra-slow variations in the ECoG or EEG, also referred to as “DC potentials”, are presumed to result from ultra-slow changes in active membrane currents (Besson et al., 1970) and are a complementary means to support ultra-slow neuronal activity to that of modulation of the high frequency γ-rhythm (Fig. 4B,C). Yet extensive experimental evidence has shown that EEG signals with spectral components below ~ 1 Hz have a non-neuronal origin. One mechanism to generate ultra-slow surface potentials is through changes in the volume of blood in the brain. The electrical potential of the blood is negative relative to that of the cerebrospinal fluid (Held et al., 1964; Sorensen and Severinghaus, 1970). Thus dilation of arterioles, which in the awake animal can take place over seconds, and dilation of veins, which can occur over tens of seconds (Drew et al., 2011; Huo et al., 2015; Pisauro et al., 2013), will generate ultra-slow changes in the EEG (Besson et al., 1970; Nita et al., 2004; Vanhataloa et al., 2003; Voipio et al., 2003) that are unrelated to neuronal activity per se.

Experiments on human subjects have shown that a shift in blood volume, driven by changes either in posture or breathing that are unlikely to induce significant neuronal effects, will drive ultra-slow changes in the EEG. In the Mueller maneuver, the subject attempts to inhale with their mouth closed and nostrils plugged. In the Valsalva maneuver, the subject attempts to exhale against a closed airway; this is a common means to equalize pressure to the sinuses. These procedures drive a change in blood volume, measured with near infrared spectroscopy (NIRS), along with relatively large amplitude EEG signals that follow the change in blood volume (Vanhataloa et al., 2003) (Fig. 5A). Tilting the head up or down (Fig. 5A), as well as compression of the jugular vein, give similar results (Vanhataloa et al., 2003). Complementary experiments that involve vasodilation support the hypothesis that slow potentials are generated by a change in volume of the blood. In particular, inhalation of carbon dioxide causes vasodilation on the time scale of minutes (Besson et al., 1970; Ngai and Winn, 1996) and leads to concurrent changes in the EEG signal in the < 1 Hz frequency range (Voipio et al., 2003).

Figure 5. Ultra-slowly varying extracellular potentials, i.e., “DC potentials”, can have a non-neuronal origin.

(A) Four changes in human body position that alter cerebral blood volume, i.e., Mueller and Vasalva maneuvers and head tilt maneuvers, drive changes in EEG potential as measured with scalp electrodes. The change in total blood volume was found from near infrared absorption of brain blood perfusion using scalp emitters and detectors (Ichikawa et al., 1999). The EEG scalp electrodes were at the 10-20 international coordinates Cz - (T3 + T4) for Mueller and Vasalva, Fz - (right mastoid) for head up and Cz - (right mastoid) for head down. From (Vanhataloa et al., 2003).

(B) Inhalation of CO₂, a vasodilator, drives a large shift in ECoG potentials with no effect on the transmembrane potential or spike rate of a simultaneously recorded neuron. Intracellular and DC ECoG recording during recurrent spike-wave seizures and hypoventilation in a cat under ketamine–xylazine anesthesia. From (Nita et al., 2004).

The gold standard in these neurovascular studies is to record slow changes in the ECoG that are induced by vasodynamics concurrent with the electrical activity of nearby neurons. Such studies were performed with cats, in which the CO₂ content of the inhalation gas could be altered to induce vasodilation (Nita et al., 2004). Consistent with a vascular, but not with a neuronal origin of ultra-slow electrical signals, simultaneous intracellular recordings from neurons (Fig. 5B) and astrocytes show that the ultra-slow ECoG signals are reflected in neither the neuronal nor astrocyte membrane potential (Nita et al., 2004). Further, extracellular measurements as a function of depth in cortex failed to find a reversal of the polarity of the ultra-slow signals with cortical depth, inconsistent with a synaptic origin of these potentials (Nita et al., 2004). In toto, the data refute the notion that ultra-slow neuronal signals are present in ultra-slow brain-wide ECoG signals, as opposed to the modulatory signal of the high frequency γ-band carrier seen in the ECoG.

Are there other neuronal origins of ultra-slow electrical activity? Intracellular neuronal currents with variation in the ~ 1 Hz range have been described (Steriade et al., 1993), but there are no reports of slower ionotropic currents with the exception of nicotinic acetylcholine receptors that contain the α7 and β2 receptor subunits. These subunits may play an important role in the generation of ultra-slow fluctuations in the spike rates of neurons in frontal cortex (Koukouli et al., 2016). Other ion channels show depolarization-induced changes in recovery times that last up to hundreds of seconds (Toib et al., 1998) and spontaneous synaptic release shows correlations over a multiplicity of long time-scales (Lowen et al., 1997). While currents that rely on reaction-diffusion kinetics and concentration dependent rates can be quite slow, they are not a priori oscillatory in nature.

Targeted neuromodulatory input to cortex.

There is evidence that slow signals from cholinergic modulatory centers provide brain-wide modulation of the γ-rhythm (Turch et al., 2018). The composite evidence also suggests that cholinergic signaling activates the M5 metabotropic pathway (Yamada et al., 2001) in penetrating arterioles (Adachi et al., 1992; Hotta et al., 2013; Sato et al., 2001; Vaucher and Hamel, 1995). Several studies have shown that projections from the basal forebrain, which contains a prominent cholinergic center, are targeted to specific brain regions (Kim et al., 2016a; Saper, 1984; Wu et al., 2014; Zaborszky et al., 2015). In particular, cholinergic targeting is specific at least down to the level of primary sensory areas (Kim et al., 2016a), consistent with the murine projectome of the basal forebrain (Li et al., 2018). Some cholinergic neurons could co-target functionally related areas (Li et al., 2018), though finer-scale organization, like retinotopy, may not be present (Huppé-Gourgues et al., 2018). The inputs to basal forebrain neurons also show a targeted input from different brain regions (Gielow and Zaborszky, 2017).

The neuromodulator noradrenaline, released by projections from the locus coeruleus, also functions to change brain-wide behavior. Chemogenetic activation of the locus coeruleus leads to an increase in the functional connectivity, as determined from the pair-wise cross-correlations among signals from different brain regions (Zerbi et al., 2019). However, unlike the case for basal forebrain input, the projections from locus coeruleus appear to be cortex-wide and diffuse, with no evidence for regional projections (Kim et al., 2016a). Of interest, noradrenaline release leads to global activation as a function of the cognitive task (Cardoso et al., 2019).

We conclude that vasomotion could in principle phase-lock to slow variations in neuromodulation. Only cholinergic modulatory input has the regional specificity that suggests feasibility, yet even for this case there is no evidence for changes in modulation on the short, 2 mm correlation length scale seen in rodents (He et al., 2018; Mateo et al., 2017). Nor is there published evidence for even broad-band oscillations at the ~ 0.1 Hz range. While we cannot dismiss neuromodulation as a candidate mechanism for locking vasomotion to neuronal activity, current evidence deems it untenable.

ULTRA-SLOW VARIATIONS IN γ-BAND POWER ENTRAINS VASOMOTION

The ability to measure electrophysiological quantities concurrent with vasodynamics is essential to decipher the biophysical basis of resting-state BOLD fMRI signals (Villringer et al., 2006). A plethora of past work has made progress with the use of mixed electrical and optical-based recording of neuronal activity concurrent with measures of blood flow, often both hemodynamics and vasodynamics, in monkeys (Goense et al., 2012; Goense and Logothetis, 2008; Logothetis et al., 2012; Logothetis et al., 2001; Schölvinck et al., 2010; Shmuel et al., 2006; Shmuel and Leopold, 2008), rat (Du et al., 2014; He et al., 2018; Schwalm et al., 2017; Thompson et al., 2014), and mouse (Anenberg et al., 2014; Lee et al., 2010; Ma et al., 2016; Mateo et al., 2017; Pan et al., 2015; Schulz et al., 2012; Vanni et al., 2017; Wang et al., 2018; Winder et al., 2017). While mice have the great advantage of genetic introduction of functional labels, this can also lead to complications when the insertion of transgenes disrupt the coding sequence of endogenous genes (Goodwin et al., 2019) or labels lead to seizure activity (Steinmetz et al., 2017).

The connection between vasomotor oscillations in pial arterioles and fluctuation in the envelope of the γ-band of the local field potential (LFP) from the superficial layers was established in mouse (Mateo et al., 2017). We first consider the temporal variation in the spectral power of the LFP in the upper layers of cortex in relation to changes in the diameter of the surface arterioles (Fig. 6A). The field potential shows epochs of enhanced activity across all frequency bands. The variations in power are greatest in γ-band and, although episodic, are broadly distributed with a periodicity near 0.1 Hz. Crucially, changes in the diameter of surface arterioles co-vary with the power in the γ-band (Fig. 6B). The timing of the fluctuations is such that the electrical activity leads that of the diameter by ~ 2 s both in this example (Fig. 6C) and as an average over all observations. These data are consistent with the hypothesis that ultra-slow fluctuations in electrical activity drive changes in arteriole diameter. While the latency between increases in neuronal activity and vasodilation is ~ 2 s, that between the increase in neural activity and the BOLD fMRI signal is slightly longer, i.e., ~ 3 s, as a result of a delay of the increased oxygenated blood reaching the veins (Mateo et al., 2017) (Fig. 1A).

To test if local neuronal activity is sufficient to entrain vasomotion, the neuronal activity in mice that expressed channelrhodopsin in layer 5b pyramidal neurons was driven by light whose intensity modulated by a 40 Hz γ-rhythm carrier frequency and a 0.1 Hz ultra-slow rhythmic envelope (Mateo et al., 2017). We observed that the envelope of the γ-band and the diameter of a nearby arteriole are phase-locked, with electrical activity leading vasodilation by the same ~ 2 s as observed under natural conditions (Fig. 6C). These data confirm that ultra-slow modulation of high-frequency neuronal activity can entrain vasomotion.

The possibility that variations in arteriole diameter drive electrical activity was addressed through the use of mice that express halorhodopsin in arteriole smooth muscle (Mateo et al., 2017). Illumination of an arteriole with activating laser light leads to an ~ 0.2-times dilation, similar to the value seen during vasomotion (Drew et al., 2011). Crucially, driving dilation of the smooth muscle fails to lead to a change in the LFP and a large drop in the spectral coherence between the vessel diameter and the driven envelope of the electrical activity. These data support the interpretation that vasomotion does not drive aggregate neuronal activity.

While the interaction between neuronal activity and vasomotion was unidirectional, an in vitro study has demonstrated feedback from blood vessels onto neuronal output (Kim et al., 2016b). Following pressurization of parenchymal arterioles, the vessels develop myogenic tone. A shift in the level of tone by challenging the arterioles with a change to higher pressure increases constriction, while lower pressures led to dilate. Importantly, upon an increase in pressure to induce vasoconstriction, pyramidal neurons suppressed their activity, while pressure-evoked dilation led to an increase in pyramidal neuron activity. The relation of this homeostatic feedback mechanism to neurovascular coupling remains an open issue.

‘Fidgeting’ movements are a driver of ultra-slow signals.

A potential contributor to the ultra-slow fluctuations in γ-band power are small motor movements of the face and limbs that are referred to as “fidgeting” (Drew et al., 2019; Winder et al., 2017). Studies with humans and primates have shown that blinking (Bristow et al., 2005; Guipponi et al., 2015), swallowing (Birn et al., 1999; Hamdy et al., 1999) and small head motions (Yan et al., 2013) are accompanied by bilateral activation of motor and somatosensory areas of the brain. Fidgeting appear to be independent of external sensation, but rather is a consequence of nonvolitional neuronal events. Fidgeting occurs at the rate of several events per minute, enabling these events to drive ultra-slow signals (Huo et al., 2014; Kaminer et al., 2011; Lear et al., 1965). Fidgeting can take place in absence of stimulation (Stringer et al., 2019) or accompany a learned task in mice (Musall et al., 2019; Salkoff et al., 2019), even though it is irrelevant to the task per se. For example, pressing a bar is accompanied by movements of the face and forelimbs and protraction of the vibrissae. Of relevance to blood flow, the functional form of the coupling between neuronal activity and hemodynamic signals appears the same for dilations evoked by either fidgeting, sensory stimuli, or volition (Power et al., 2012; Winder et al., 2017) (Fig. 6D,F).

Fidgeting is activated by neuronal motor circuits and presumably drives reafferent or efferent inputs to somatosensory regions in cortex. Thus, in principle, fidgeting can drive vasodilation and entrain vasomotion. We obtained new data to characterize the relation of fidgeting to the entrainment of vasomotion in alert, head-fixed, wild type mice. Following past methods (Winder et al., 2017), we recorded vibrissa movement, body movement, and concurrent changes in the diameter of pial arterioles (Fig. 6D; experimental details in the legend). Epochs of spontaneous whisking and body motion are observed, the largest of which are clearly correlated with relatively large, transient vasodilation events. As an average over mice and vessels, we observe that the movement precedes the vasodilation by ~ 2 s for both whisking and whole body motion (Fig. 6E), similar to that for the γ-band power (Fig. 6C). Thus, fidgeting is a likely contributor to the source of ultra-slow neuronal activity, albeit this shifts the question to what neuronal or environmental source drives fidgeting.

We performed a quantitative assessment of the contribution of body movement to the neuronal entrainment of vasomotion across our existing data with head-fixed mice (Mateo et al., 2017) (Fig. 6A–C). Previously unpublished accelerometer records of the motion of the body of the mouse were used to determine the contribution of fidgeting to vasomotion (Fig. 6F; experimental details in the legend). As an average over mice and vessels, body motion leads to transient dilation of the pial arterioles that rises over an interval of 2 s, the same as that for stimulus driven changes in arteriole diameter (Fig. 1A). The movement related changes in diameter encompassed 0.27 of the significantly correlated changes between vessel diameter and the γ-band LFP (center Fig. 6F). Critically, fidgeting was correlated with the largest dilations (right Fig. 6F). In toto, fidgeting is a significant contributor to the neurological events that entrain vasomotion in mice.

We suggest that fidgeting is likely to play a role in the origin of human resting-state BOLD fMRI signals as well (Drew et al., 2019). The punctate nature of fidgeting events is consistent with the punctate, albeit loosely rhythmic nature of resting-state activity in humans (Liu et al., 2018; Liu and Duyn, 2013; Petridou et al., 2013) and fidgeting behaviors often involve bilateral actions (Drew et al., 2019), consistent with the bilateral nature of spontaneous activations (Fig. 2D). Fidgeting behaviors are likely to be associated with BOLD fMRI signals in regions outside sensory and motor areas of the brain, including areas activated by cognitive tasks (Drew et al., 2019). For example, swallowing activates the insula (Martin et al., 2001) and licking (Nakano et al., 2013) and head motion (Bright and Murphy, 2015) activate multiple brain regions. It is an open issue if the sensorimotor processing that is associated with fine-scale self-motion is part of the ideation captured by resting-state BOLD fMRI. Nonetheless, experimental designs exist that can flag and censor epochs of even modest self-motion in human subjects (Power et al., 2012; Siegel et al., 2014).

Transitions among behavioral states may drive ultra-slow signals.

A seemingly high proportion of the resting-state BOLD fMRI studies in animals and humans did not closely monitor behavior or arousal. Thus, a wide variety of behavioral states may be sampled and averaged together. Head-fixed mice will sleep with their eyes open (Yüzgeç et al., 2018), so careful physiological monitoring of body motion, pupil motion, and pupil size is needed to ensure that the sleep-state vasodynamics (Fultz et al., 2019; Horovitz et al., 2009) do not contaminate resting-state measurements. Post hoc examination of human connectome data has indicated many if not most subjects fall asleep during the scanning process (Tagliazucchi and Laufs, 2014). Sleep-to-wake transitions (Horovitz et al., 2009; Liu et al., 2018) may thus drive events that account for a substantial component of functional connectivity (Liu and Duyn, 2013; Petridou et al., 2013).

MECHANISMS FOR CORRELATED BILATERAL VASODYNAMICS

The dominant feature of resting-state connectivity is the bilateral symmetry across hemispheres (Fig. 2D). The details of bilateral coactivation can be explored via the coherence between changes in arteriole diameter for vessels in mirrored regions. In fact, precise, simultaneous measurements of vessel diameter show that arterioles in mirrored regions oscillate in synchrony with near unity coherence (Mateo et al., 2017) (Fig. 3C). The coherence is severely reduced in acallosal mice (Mateo et al., 2017), consistent with the finding that bilateral neuronal signaling is similarly reduced in acallosal mice (Mohajerani et al., 2010). Yet, as noted previously, the evidence for mirrored activation in acallosal human subjects is equivocal.

Vascular geometry that enhances bilateral symmetry.

While the origin of symmetry in resting-state connectivity is typically attributed to interhemispheric projections, there are other systemic vascular contributors. Fluctuations in the inflow of blood at the level of the left and right carotids are strongly coherent at 0.01 - 0.3 Hz, i.e., the range of vasomotor frequencies in awake rats (Revel et al., 2012). Arterial blood oxygenation also fluctuates with fluctuations in respiration rate and with the respiratory cycle (Zhang et al., 2019). These lead to delayed fluctuations in the global BOLD fMRI signal throughout the brain and into the sagittal sinus (Tong et al., 2019). Unfortunately, the fluctuations from the carotid supply tend to dephase as blood travels with different transit times through the brain. Thus, fluctuations in inflow and oxygenation cannot be completely removed by regression of a brain-wide signal (Tong et al., 2015). A further complication occurs since vasomotion will change the transit times. Thus, measures of blood oxygenation can be systematically biased if they occur at locations with different transit times, as opposed to mirrored brain regions. For this reason, recent reports of small shifts in the timing of BOLD fMRI signals in humans (Mitra et al., 2015) could be the result of small changes in the perfusion times or oxygenation of blood to different regions of the brain. As a clinical matter, this effect can highlight perfusion deficits after stroke (Lv et al., 2012) and may explain how low-grade brain tumors show coherent oscillations in the BOLD fMRI with their putatively healthy contralateral brain regions (Gupta et al., 2018).

Bilaterally-synchronized modulatory inputs can drive bilateral oscillations.

There are direct, cholinergic cross-hemispheric connections between the basal forebrain in the two hemispheres (Carnes et al., 1990; Semba et al., 1988). These connections should not be affected in acallosal animals, thus preserving common input to mirrored, transhemispheric cortical regions.

Activation of the rostral ventral lateral medulla (RVLM), a brainstem nucleus that sits on the ventral surface of the brain below the breathing center (Golanov et al., 1994) leads to an increase in cortical blood flow. This nucleus receives input from neighboring breathing centers (Dempsey et al., 2017) and will increase blood flow in response to a decrease in atmospheric pO₂ (Golanov and Reis, 1996). The RVLM contains primarily noradrenergic neurons (Abbott et al., 2012). The limited anatomical studies published to date have not identified direct nor complete indirect projections from RVLM to the cortex (Card et al., 2006). Nonetheless, in one likely pathway, the RVLM projects to the medullary cerebral vasodilator area in brainstem, then projects to the subthalamic cerebral vasodilator area in the diencephalon, which incorporates zona incerta and the Fields of Forel, and finally projects to deep layers of cortex (Golanov et al., 2001; Ilcha and Golanov, 2004). The specifics of the drive to cortical blood vessels is an open issue.

TECHNICAL SOURCES OF ULTRA-SLOW NOISE CONTRIBUTIONS IN fMRI

As a means to reduce voluntary motion of the head, contemporary rodent resting-state fMRI studies have been primarily performed on anesthetized head-fixed but free-breathing animals (Biswal and Kannurpatti, 2009; Williams et al., 2010; Zhao et al., 2008). However, cardiac- and respiratory-based artifacts in rodent resting-state BOLD and CBV fMRI remain to be carefully identified and removed from the data. These difficulties stand in contrast to the significant efforts made for the human BOLD fMRI studies (Birn et al., 2006; Dagli et al., 1999; Glover and Li, 2000; Hu et al., 1995; Shmueli et al., 2007; Wise et al., 2004). The adoption of signal processing methods developed for human studies (Caballero-Gaudes and Reynolds, 2017; Murphy et al., 2013) will be crucial to reduce the interference of cardiorespiratory artifacts with the spatiotemporal patterns of the resting-state fMRI signals in animals (Abreu et al., 2017; Biswal et al., 1996; Bright and Murphy, 2017; Feinberg and Setsompop, 2013; Kiviniemi et al., 2005).

Respiration-induced “B₀ offset” motion.

Magnetic resonance image acquisition relies on Larmor frequency-based spatial encoding through the sequence-specific magnetic field gradients across a subject. The homogeneity of the constant magnetic field, designated B₀, determines the quality of magnetic resonance images (Durand et al., 2001). However, the subject inside the magnetic resonance scanner can continually disturb the homogeneity of the B₀ field by movement of their body (Biswal et al., 1996; Frank et al., 2001; Lowe et al., 1998; Van de Moortele et al., 2002). This includes fidgeting (Fig. 6D) as well as breathing and other physiological motions. In practice, breathing leads to an expanding and contracting B₀ field near the brain (Fig. 7A). Thus, artifacts in BOLD MRI can originate from parts of the body that are far away from the field of view in the brain (Fig. 7B).

Figure 7. The aliasing effect of the respiratory-induced magnetic field (B₀) distortion.

(A) Schematic drawing of the B₀ field on free-breathing rats with different extents of chest movements and associated magnetic field lines. The distorted B₀ field is caused by the large chest movement during the respiratory cycles (red lines). Amber circles are pick-up coils. From (Pais-Roldan et al., 2018).

(B) The coronal sections from a three-dimensional echo-planar imaging sequence acquired at 1.2 s repetition time (TR), from 0 to 7.2 s, from a spontaneously breathing anesthetized rat. These data show the effect of the B₀-related motion artifacts at ~ 0.16 Hz as the function of time. From (Pais-Roldan et al., 2018).

(C) The respiratory trace (black, chest movement) and the down-sampled time course (red line) for a 1/TR sampling rate with TR = 1.2 s, upper panel). The power spectral density shows the aliased signal, peaked (f_res − 1/TR), i.e., 0.16 Hz, of which the f_res is around 1.0 ± 0.1 Hz. The fMRI time course and spectral density of a voxel in the brain (middle panel) or in a phantom (bottom panel) over the animal’s head shows the oscillatory signal with a bandwidth of 0.16 ± 0.1 Hz, which is dominated by the respiration-induced B₀ artifacts. The brain and phantom voxels are defined by the two arrows in panel D. From (Pais-Roldan et al., 2018).

(D) Map of the power at the artifact frequency, 0.16 ± 0.1 Hz shows the voxel-wise spatial correlation to the B₀-related artifacts. The high-power scales indicate the strong B₀-related artifacts. From (Pais-Roldan et al., 2018).

Methods to compensate for the time-dependent B₀ field distortions are known (Raj et al., 2000; van Gelderen et al., 2007). Yet, in contrast to studies on human subjects, the higher magnetic fields used for animal BOLD and CBV fMRI studies will exaggerate the effects of physiological contributions to an inhomogeneous B₀ field. In addition, both arteriole CO₂ (Wise et al., 2004) and respiratory volume changes (Birn et al., 2006) can cause variations in the resting-state BOLD fMRI signals that lead to falsely interpreted signals.

Aliasing of physiological rhythms.

Rats have an approximately 5 - 7 Hz cardiac frequency and approximately 1 - 2 Hz respiration rates under anesthesia. The conventional echo-planar imaging protocol with rodents involves a 1 - 2 s period of repetition (TR) or equivalently a sampling rate, denoted f_s, of f_s = 1/TR = 0.5 - 1.0 Hz. The low rate of sampling compared to physiological processes that distort the fMRI signal will cause aliasing of both cardiac and respiratory contributions down to frequencies that may also be erroneously associated with resting-state dynamics. This is well described for human resting-state fMRI studies (Biswal et al., 1996; Dagli et al., 1999; De Luca et al., 2006; Frank et al., 2001; Lowe et al., 1998) and is seen in rat as well (Pais-Roldan et al., 2018). For example, when the sampling rate is f_s = 0.8 Hz and the spontaneous breathing rate of an anesthetized rat is f_B = 1.0 ± 0.1 Hz, the signal is aliased to f_B - f_s = 0.2 ± 0.1 Hz. This is illustrated by measuring breathing at f_s >> f_B and observing the aliased rate that is seen when the data is down-sampled to f_s = 0.8 Hz (Fig. 7C). Aliasing is observed in the fMRI signal of both brain and a phantom above the head of the animal when the sampling rate is f_s = 0.8 Hz (Fig. 7C). This illustrates the combined effect of distortion of the B₀ field and aliasing to form a false image of a resting-sate signal (Fig. 7D).

Fast fMRI methods clearly will avoid aliasing of both the cardiac and respiratory contributions to the fMRI signals from rodents (Williams et al., 2010; Yu et al., 2014). A similar fast sampling strategy has been well implemented to remove the physiological noise for fMRI measurements from human brains (Agrawal et al., 2020). However, it is much more difficult to avoid the higher frequency cardiac-specific aliasing artifacts, especially for awake rodent fMRI (Desai et al., 2011; Ferenczi et al., 2016; Liang et al., 2015). Further, cardiac and respiratory cycles can fluctuate individually and in a coupled manner at frequencies close to the ~ 0.1 Hz frequency range for ultra-slow signals. These fluctuations can serve as additional, confounding sources for resting-state BOLD fMRI studies (Shmueli et al., 2007).

CONCLUSIONS

Motivated by a desire to understand the biophysical basis of resting-state fMRI (Fig. 2), we have reviewed data on the relation of spontaneous changes in blood flow and blood oxygenation in the brain to changes in the underlying neuronal activity (Fig. 8A). Ultra-slow vasomotor oscillations occur in the smooth muscle cells that encircle brain arterioles and lead to rhythmic changes in the diameter of arterioles within a frequency band near 0.1 Hz (Fig. 3). Further, collective neuronal dynamics in the forebrain lead to the generation of high frequency γ-band oscillations whose amplitude is modulated at the ultra-slow rate of ~ 0.1 Hz. (Fig. 6B). These ultra-slow neuronal oscillations will entrain the arteriole oscillations to link brain vasodynamics with nonvolitional neuronal activity (Figs. 6A–C). The entrainment is statistically significant (Fig. 6), even though the vasculature also responds to common, cortex-wide inputs and homeostatic physiological inputs. The entrainment of vasomotion by neuronal spiking provides a means for arterioles in regions of the brain that are separated yet connected through callosal projections to have synchronous vasomotor activity (Fig. 3C). Within the technological framework of fMRI, vasomotor activity can be measured through changes in arteriole volume, i.e., CBV fMRI, or changes in blood oxygenation secondary to changes in diameter, i.e., BOLD fMRI. The flow diagram of Figure 8A formalizes this description.

Figure 8. Coupled oscillator model for resting-state neurovascular coupling.

(A) Interactions for one region. Variations in γ-band electrical power lead to partial entrainment of the vasomotor oscillations in the smooth muscle of cortical surface and penetrating arterioles. Increases in γ-band electrical power dilate the arterioles and lead to an increase in the supply of fresh blood, as measured by CBV fMRI. The increase in diameter subsequently leads to an increase in blood oxygenation and a positive change in the BOLD fMRI signal. Coupling can be via callosal projections or via common input.

(B) Circuit of the pial arteriole network in terms of coupled smooth muscle oscillators. Each oscillator represents the activity of all muscles in one arteriole. The oscillators communicate with one another via the hexagonal lattice of electrically-joined endothelial cells that form the lumen (Fig. 6). Oscillators in a given region of the brain may also receive electrical input from underlying neuronal oscillators. This input can dominate and lead to a parcellation of the frequency of vasomotor oscillations, as observed by fMRI (Fig. 2B). Vasomotion is synchronous within a given region of the brain yet can occur with different frequencies in different regions; e.g., labeled blue and red for regions 1 and 2, respectively, and labeled green for an intermediate region without neuronal drive.

Significance of the ultra-slow coupling.

Functional MRI allows one to ‘decode’ the neural activity in the brain to the extent that neural activity is represented by BOLD signals (Kay et al., 2008). A key issue is how well hemodynamic signals report neural activity. In Supplemental Table 1 we list the correlation coefficient R², the so-called “variance explained”, between neural activity and either the BOLD or CBV fMRI or equivalent optical signal; Supplemental Text Box 1 relates R² to the spectral coherence, C(f). In all of these studies there was a highly significant correlation between the hemodynamic response and neural activity. This means that resting-state BOLD fMRI signal or equivalent are, to varying extents, driven by neural activity. Yet the value of R² is universally less than 0.5 and typically around 0.1 (Schölvinck et al., 2010; Shmuel and Leopold, 2008). This means that only 0.1 to 0.5 of the hemodynamic signal is related to neural activity. A value of R² = 0.5 between γ-band neuronal activity and the simultaneously recorded BOLD fMRI signal occurs for visual stimulus-evoked activity in the un-anesthetized primate (Goense and Logothetis, 2008). Given the strong drive of visual stimuli, this suggest that the value R² = 0.5 seen in rest-state measurement is likely to be is an upper bound. If we further consider that fidgeting occurs ~ 0.3 of the time, as an upper bound we expect that at the most 0.5 x 0.7 ~ 0.4 of the resting-state BOLD fMRI signal is related to internally driven brain dynamics. Thus resting-state BOLD fMRI, as currently practiced, provides unique capabilities to infer connectivity in the human brain, yet is a technique with an inherently low signal-to-noise ratio.

The role of vasomotion.

What is the normal, physiological purpose served by the ultra-slow vasomotor oscillations of brain arterioles? Recent work points to the necessity of vasomotion for the clearance of large solutes (van Veluw et al., 2020), principally through the paravascular space between the smooth muscle and endothelial cells (Cserr and Ostrach, 1974; Rennels et al., 1985). These solutes include β-amyloid (Iliff et al., 2012). To the extent that vasomotion is entrained by the envelope of the γ-band power (Mateo et al., 2017) (Fig. 6), it is of interest whether increases in γ-power in the brain through sensory stimulation also increases the clearance of β-amyloid (Iaccarino et al.). The ability of vasomotion to drive solutes must depend on a mechanism to set the direction of flow, such as peristaltic motion (Aldea et al., 2019) or yet-to-be discovered valves in the paravascular space (Mathiisen et al., 2010).

Next steps.

The nature of the local neuronal circuitry that generates ultra-slow signals and modulates the γ-rhythm remains an open issue. In particular, the exact frequency of ultra-slow signals varies across the brain with millimeters to centimeters of coherence (Mitra et al., 1997; Vanni et al., 2017) (Fig. 2B). Such spatially restricted modulation could be accomplished by even small changes in the activation of currents in individual cells that contribute to generate the γ-rhythm (Kopell and LeMasson, 1994). In this way, the ultra-slow signals are purely modulatory (Fig. 4) and the ECoG will not contain ultra-slow signals (Fig. 5).

Recent work describes a fast mechanism to transform subsurface microvasculature signaling into changes in arteriole diameter (Longden et al., 2017) (Fig. 1C). Yet the nature of electrical signaling across the lattice of pial surface vasculature remains to be solved (Hillman, 2014). At a phenomenological level, the pial arteriole oscillators form two sets of interactions (Fig. 8B). On the one hand, each arteriole is directly connected with four neighboring oscillators (Blinder et al., 2010) via gap junctions between endothelial cells (Fig. 1C); this connectivity acts to frequency lock vasomotion across all vessels across the surface (Sakaguchi et al., 1988; Strogatz and Mirolla, 1988). On the other hand, underlying neurons can drive the local pial vessels at different frequencies; this should break the coherence of vessels across the cortical mantle so that the vessels parcellate into regions with different vasomotor center frequencies (Fig. 8B). BOLD fMRI data from humans supports such a parcellation on the scale of tens of millimeters (Fig. 1B). In fact, such parcellation has been used to segment different regions in cortex (Fox et al., 2005; Glasser et al., 2016). Animal models, together with large-field, high precision optical imaging (Sofroniew et al., 2016; Tsai et al., 2015), should allow us to assess the phenomenology and the biophysics for this parcellation.

A more accurate and high resolution measure of functional connectivity may be obtained through measurements of CBV rather than BOLD fMRI (He et al., 2018). When the spatial resolution of fMRI can distinguish individual vessels that penetrate the cortex of the rat brain (Moon et al., 2013; Poplawsky et al., 2019; Yu et al., 2012), the BOLD fMRI signal is located mainly at venule voxels while the CBV fMRI signal is detected primarily at arteriole voxels (He et al., 2018; Yu et al., 2016). Thus the single-vessel fMRI method will enable detection of the spatial correlation patterns of the resting-state signal with vascular specificity, as seen optically in restricted regions (Mateo et al., 2017) (Fig. 3C). From a technical perspective, the spatial localization of single-vessel fMRI decouples the resting-state signal from respiration-induced B₀-related motion artifacts (Fig. 7). The ability to resolve individual penetrating vessels with CBV fMRI provides a critical platform to explore the ultra-slow oscillatory patterns of vasodynamics across the brain. This is particularly important for understanding how pair-wise interactions among different brain regions may lead to the great multitude of “default networks” of rodent (Chan et al., 2015; Ma et al., 2016; Mohajerani et al., 2013; Mohajerani et al., 2010) and human (Greicius et al., 2003; Raichle et al., 2001; Sporns et al., 2005) brain activity.

Finally, as a practical matter, experimenters should monitor behavior and arousal state as much as possible to differentiate between activity generated during spontaneous movements, sleep, and activity generated during true “rest” (Drew et al., 2019). Monitoring of behavioral state has become de rigueur in systems neuroscience experiments using awake rodents and primates (Egnor and Branson, 2016; Whishaw and IQ Whishaw, 2014), makes use of standard equipment for studies with rodents (Kurnikova et al., 2017; Mathis et al., 2018; Reimer et al., 2014), and should be adopted by the human fMRI community as well. Thus, it may be possible to use behavioral event markers to segregate resting-state epochs with fidgeting from those without these movements and presumably increase the sensitivity to purely intrinsically driven brain-wide changes in BOLD or CBV fMRI signals.