Traveling and standing waves in the brain

Abstract

Studying the natural wanderings of the living brain is extremely challenging. Bolt et al. describe a new framework to consider the brain’s intrinsic activity based on the geophysical concepts of standing and traveling waves.

Economists, politicians, CEOs, scientists: they all strive to understand complex dynamical systems so that they can predict—and hopefully improve—their future outcomes. They collect relevant data and morph it into actionable information using meticulously selected analytical tools. Yet, over time, conflicting views will likely emerge from the same data, either due to unaccounted-for noise or methodological discrepancies. When this happens, it is key to promptly identify and address those. This is what Bolt et al.¹ set to do in this issue of Nature Neuroscience for the field of resting-state fMRI, and more generally, for our understanding of intrinsic brain dynamics.

Scientists often study the living brain by asking people to lay still inside an MRI scanner for a few minutes while functional (e.g., BOLD², VASO³) data are being acquired. This experimental practice, commonly known as resting-state fMRI, has become ubiquitous in cognitive neuroscience due to its simple setup and low demands for participants. By the end of a single resting-state scan, researchers will have a set of timeseries recorded from thousands of small locations across the brain (voxels). Different physiological (e.g., neuronal activity, cardiac, respiration) and non-physiological (e.g., head motion, hardware instabilities) sources contribute variance to these recordings; fMRI practitioners first try to isolate neuronally-induced fluctuations from all others⁴. Next, they face the challenge of summarizing and interpreting such vast amounts of data. Some proceed by exploring average levels of inter-regional synchronicity using methods of varying complexity, ranging from pair-wise Pearson’s correlation⁵ to nonlinear dimensionality reduction⁶. Bolt et al. refer to those approaches as “zero-lag” analyses, as they are not able to account for inter-regional delays. In contrast, recent complementary modeling work that considers variable delays in inter-regional synchronicity (termed “time-lag” analyses) have provided additional exciting insights⁷. Yet, as Bolt et al. succinctly state in their abstract’s opening sentence, such methodological explosion has translated into “seemingly disparate insights into [the] large-scale organization of the human brain”. Importantly, Bolt et al. propose a solution: constructing a unifying view of methods and observations by turning our attention to the geophysical concepts of standing and traveling waves.

What are standing and Traveling waves? Traveling waves are like talking to someone using two cans connected by a string (Fig. 1A). By talking into one can, you generate a sound wave that travels through the string and reaches your interlocutor. This is possible because the string provides a means for the sound wave’s energy to be transferred across the distance from point A (your mouth) to point B (their ear). In contrast, standing waves are like jumping rope (Fig. 1B). As you get ready to jump, your friends start to move the rope up and down at a constant rate. This motion initially generates traveling waves between both; yet, because the ends of the rope are anchored, the rope almost instantly engages on a regular up-and-down movement with the maximum deflection always occurring at the rope’s mid-point. That “in-place” pattern is a standing wave. According to Bolt et al., intrinsic brain activity can be better conceptualized relying on methods that accommodate a mixture of traveling and standing waves, instead of using “zero-lag” and “time-lag” analyses which each only account for one these two interlinked components.

Figure 1.

Examples of traveling waves (A) and standing waves (B) in the real world. (C) Schematic of the proposed framework to understand resting-state intrinsic fluctuations as the combination of three spatiotemporal patterns with varying levels of standing and traveling behaviors.

This newly proposed framework turns out to be quite powerful. It allows Bolt and colleagues to explain seemingly disparate “zero-lag” and “time-lag” observations (e.g., the global signal⁸, resting-state networks, co-activation patterns⁹, quasi-periodic patterns⁷, etc.) using a limited number of spatiotemporal patterns with varying degrees of standing and traveling wave-like behaviors (Fig. 1C). Their argumentation starts with educational simulations that illustrate how discordance among “zero-lag” observations is rooted in these approaches’ inability to properly capture traveling phenomena in the brain. Next, they introduce complex principal component analysis (C-PCA), an extension of PCA for complex-domain valued data that can uncover latent dimensions of variability resulting from a mix of standing and traveling behavior. However, it is unfortunate that, in pursuit of a unifying explanation for the global signal, resting-state networks, etc., another novel method must be adopted. Yet, Bolt et al.’s results validate the use of this method.

First, they observed that intrinsic hemodynamic fluctuations in resting-state fMRI are dominated by a wave of global, non-uniformly distributed, negative activity that peaks in somato-motor, visual, superior parietal, and superior temporal cortex. This negative wave slowly progresses towards regions of the fronto-parietal network and default mode network (DMN) before switching into a wave of positive activity with similar spatial properties. Noticeably, the temporal dynamics of this pattern match those of the global signal. Two additional patterns—a standing oscillation between DMN and somato-motor-visual regions; and a traveling one perched over a larger portion of cortex—account for the task-positive/task-negative networks¹⁰, the first functional connectivity gradient¹¹ and much of the functional connectome.

Second, the authors found that these three newly uncovered patterns are primarily of a standing nature. As such, “zero-lag” tools can readily access snapshots of their spatial structure. Bolt et al. confirm this empirically and provide clear examples using standard PCA, temporal independent component analysis (TICA¹²), Hidden Markov models (HMM¹³) and co-activity patterns (CAPs⁹) among several others. Finally, Bolt et al. demonstrated that the remnant non-standing aspects of these three spatiotemporal patterns can explain observations previously made with “time-lag” models. In this regard, they exemplify how both short-term (~ 2 seconds) and long-term (~ 20 seconds) latency profiles previously derived with mathematically distinct approaches (i.e., propagation analysis and quasi-periodic pattern analysis) can be accounted for by using a single framework. In summary, the strongest (i.e., those accounting for up to 33% of variance) and most-often discussed aspects (e.g., global signal, resting-state networks, quasi-periodic patterns, etc.) of intrinsic resting-state fMRI fluctuations can be succinctly summarized using only three spatiotemporal patterns generated via a single analytical tool, namely C-PCA.

Now, how do these empirical observations broaden our understanding of intrinsic fluctuations during rest and of the inner workings of the human brain? The answer is unclear. On the one hand, unification of observations under the umbrella of a single analytical tool is a real asset for the field as it constructs solid bridges across otherwise isolated pieces of work, and it has the potential to set the foundation towards a common vocabulary for the description of these phenomena. Moreover, conceptualizing fMRI as a mixture of standing and traveling waves seems to be a powerful way to jointly model the many divergent phenomena (e.g., systemic vascular waves, fluctuations in arousal, localized neuronal activity, etc.) that contribute variance to the resting-state. On the other hand, here we sit with a new set of observations for which we lack definitive insights about their etiology (neuronal or vascular) or the functions they subserve. Because of this knowledge gap, it is unclear whether these dominant spatiotemporal patterns hold the key to a better understanding of the brain’s intrinsic activity or if is it that those insights await hidden underneath (i.e., in the additional 67% of variance they do not account for).

So, what’s next? As Bolt et al. state near the end of their paper: “the consistency of analytical approaches… suggest that these three spatiotemporal patterns are robust phenomena in need of explanation”. I believe that to reach those explanations, fMRI researchers can no longer afford the privilege of experimental simplicity. Resting-state scans should be annotated with additional data targeting the most likely explanatory sources. These should not be limited to concurrent recordings of cardiac and respiratory function (a common, yet not ubiquitous practice), but also include data sources that can track fluctuations in vigilance (EEG, eye tracking), stress levels (skin conductance), targets of visual attention (eye tracking), body motion (electromyography) and even some aspects of the content and form of subjects’ mental life inside the MRI bore¹⁴. With their intriguing work, Bolt et al. have clearly captured a large portion of variance in resting-state fMRI data, and therefore have provided a focal point for future investigations of the underlying mechanisms for these three spatiotemporal patterns. Now that we know where the waves are, let’s go surf them—we may reach the other side of the obstructive reef and discover the true beauty of the ocean underneath.