Ann. N.Y. Acad. Sci. ISSN 0077-8923

ANNALS OF THE NEW YORK ACADEMY OF SCIENCES Issue: The Year in Cognitive Neuroscience REVIEW A network engineering perspective on probing and perturbing cognition with neurofeedback

Danielle S. Bassett1,2 and Ankit N. Khambhati1 1Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania. 2Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania

Address for correspondence: Danielle S. Bassett, Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104. [email protected]

Network science and engineering provide a flexible and generalizable tool set to describe and manipulate complex systems characterized by heterogeneous interaction patterns among component parts. While classically applied to social systems, these tools have recently proven to be particularly useful in the study of the brain. In this review, we describe the nascent use of these tools to understand human cognition, and we discuss their utility in informing the meaningful and predictable perturbation of cognition in combination with the emerging capabilities of neurofeedback. To blend these disparate strands of research, we build on emerging conceptualizations of how the brain functions (as a complex network) and how we can develop and target interventions or modulations (as a form of network control). We close with an outline of current frontiers that bridge neurofeedback, connectomics, and network control theory to better understand human cognition.

Keywords: graph theory; network neuroscience; neurofeedback; cognition; control theory

The notion that engineering principles are criti- of all BMIs, one noninvasive tool that receives cal for advancing the frontiers of modern neuro- attention for its potential to inform our under- science is not new. Indeed, the marriage of these standing of human cognition is neurofeedback.10 two disciplines is now commonly known as neuro- Experimental paradigms including neurofeedback engineering.1 The purview of this discipline is begin with the subject receiving sensory or behav- particularly large, including the use of theoret- ioral feedback that is based on the current state of ical, computational, and experimental tools to his/her brain activity—as measured by imaging or reveal fundamental principles of neural structure electrophysiology—in real time.11 The participant and function across species.2–5 It also includes then attempts to modulate that activity signal, either efforts to “engineer” the brain in reverse—creating increasing it or decreasing it, in response to prompts technological systems that perform brain-like from the experimenter. With training, many partic- computation—and forward—altering brain struc- ipants are able to learn to modulate the activity in ture and modulating brain function in a targeted specific brain regions on command. and theoretically predictable manner.6 Such engi- Historically, neurofeedback training has been neering approaches were recognized in 2013 as key developed to assist individuals in the use of tools for tackling the challenges of mapping the BMIs to overcome disabilities, injuries, or men- brain.7 In humans specifically, the discipline seeks tal illness.10,12–18 For example, if one could control to reveal the foundations of cognition. the activity of the hand motor cortex using men- A natural confluence of many of these lines of tal imagery, that signal could be used to control a inquiry lies in brain–machine interfaces (BMIs), robotic hand.4 Or, in the case of mental illness, if one which capitalize on emerging instruments for both could control a region of the brain whose function hardware and software in sensing, signal process- is altered by the illness, one might have meaningful ing, and machine learning.4,8,9 And within the class relief from undesired symptoms.19 Yet, while clinical doi: 10.1111/nyas.13338

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 1 A network engineering perspective Bassett & Khambhati applications have remained paramount in the use to these questions tell us about the distributed com- of these tools over the last decade or more, recent putations that support complex cognitive processes? evidence suggests that neurofeedback can in fact How would we choose the target region for neuro- also be used to probe the fundamental principles feedback to elicit a specific change in a large-scale, of cognition that explain how the brain relates to distributed functional network?” behavior.20,21 Answering these questions requires a paradigm The promise of neurofeedback in revealing shift in our conceptualization of how the brain func- principles of cognition builds on the fact that—in tions (as a complex network) and how we develop essence—it is a perturbative approach. Unlike the and target interventions or modulations (network lesion approaches that were ubiquitous in early control). In this review, we begin by briefly sum- studies of neuroanatomy,22 which led to the field marizing the use of neurofeedback to probe cogni- of brain mapping,23–25 neurofeedback enables the tion, and we discuss the insights that these studies investigator to modulate brain activity in a targeted have offered into higher level cognitive processes in manner by offering the participant a view into the humans. Next, we highlight both the challenges and activity of a small volume of neural tissue. As a potential inherent in acknowledging that altering tool, neurofeedback offers several advantages over the activation of a single region can have nontrivial stimulation-based perturbation techniques, such effects throughout the network. To better under- as transcranial magnetic stimulation—subjects can stand these widespread effects, we briefly describe learn to modulate activity on demand without the principles of network science and the organi- the need for external stimulation hardware, and zational structure currently known to characterize these learning effects can be sustained over several the human connectome. These data lead us into the days.26 Interestingly, such perturbative approaches question of how to perturb the human brain via neu- are in fact the bread and butter of mathematics and rofeedback to move the brain from an initial state to physics, where they are used to examine the general a predictable target state. We describe the utility of structure of the dynamic landscape surrounding network control theory in offering a mathematical a point (see, for example, Refs. 27 and 28). The framework in which to ground such questions, and major benefit of a perturbative approach is that it we offer an outline of current frontiers that bridge facilitates generalization of an observation, and by neurofeedback, connectomics, and network control extension the construction of a mechanistic theory. theory to better understand human cognition. This ability to probe both the canonical form and Neurofeedback for cognition: a primer the broader landscape of a dynamical system has proven fundamentally important in developing Like many other quintessentially complex ques- mechanistic theories in theoretical physics. tions in science, understanding how brain function In cognitive neuroscience, the potential to use a relates to cognition requires a principled empirical perturbative approach like neurofeedback becomes approach. Most current efforts implement “open- particularly interesting when viewed in light of the loop” forms of inquiry, in which an input stimulus emerging field of connectomics.29–31 Because the is used to elicit a measurable response in neuro- brain is not simply a collection of independent units physiology or behavior. At their core, open-loop but is instead a complex network of interconnected methods enable neuroscientists to map the effects elements,32,33 manipulating the activity in one area of a behavioral perturbation on the observed neu- can have nontrivial effects on other areas—even far ral dynamics and, conversely, to map the effects from the modulated source.34 Far from the mysteries of a neural perturbation on the observed behavior. of quantum mechanics, this action at a distance is a In the forward direction (perturbing stimuli), one direct consequence of the complex pattern of struc- might measure the difference in neural response tural wiring that links brain areas.35–37 Given this between different degrees of fearful stimuli. In complexity, it is natural to ask, “What distributed the reverse direction (perturbing neurophysiology), network of brain areas is affected when a participant one might lesion a neural circuit and measure the modulates the activity in a single brain region? Can change in emotional response to those same stimuli. participants learn to modulate two regions at once, Together, the two types of open-loop experiments or large groups of brain areas? What do the answers provide a forward mapping of behavior to neural

2 Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. Bassett & Khambhati A network engineering perspective

Perturb stimulus

Perturb neurophysiology Digital acqusition system Volt per sensor Volt

Figure 1. Open-loop perturbation of brain and behavior. Neuroscience has long exercised an open-loop approach to probe the characteristics of neural systems. By perturbing behavior and measuring change in neural dynamics or—in reverse—perturbing neural dynamics and measuring change in behavior, this method is used to generate a map between neural dynamics and behavior. For example, consider the following set of experiments investigating the neural basis behind the perception of shapes: to generate a forward mapping between stimulus and neural response, one might measure the change in neural activity of specific brain regions to visual perturbations of object shape; to generate a reverse mapping between neural response and stimulus, one might measure the change in perception of shape due to perturbation of neural activity (perhaps through lesioning or neurostimulation). The forward and reverse mapping are limited in their ability to describe how neural activity and behavior change together on a dynamical continuum. Neurofeedback enables investigators to close the loop around forward and reverse mapping approaches—in real time. dynamics and a reverse mapping of neural dynamics jects can learn to regulate the activity of subcor- back to behavior. While these techniques offer par- tical areas, including the amygdala38–40 and basal ticular utility in addressing open questions in cog- ganglia,41 and extended areas of the limbic system, nitive neuroscience, they do not provide a means including the insula20,42 and parahippocampus.43 for addressing how function and behavior change Interestingly, participants can also learn to mod- concurrently, as a function of brain state. Indeed, ulate the primary sensory motor cortex (primary to address this question, one must turn to “closed- motor area,44 premotor cortex,45 and supplemen- loop” approaches (Fig. 1). tary motor area43,46)aswellashigher-orderareas, including the anterior cingulate cortex,20,42 ven- 47 Closing the loop with neurofeedback tral tegmental area, frontal and parietal cognitive 48 43,46 Neurofeedback enables closed-loop scientific control areas, anterior midcingulate cortex, 43,46 inquiry by allowing the subject to directly perturb and frontal cortex. Importantly, subjects who brain dynamics based on information about his/her learned to successfully modulate regional activity current brain state or to indirectly perturb brain demonstrated improved performance on a variety dynamics based on feedback about his/her current of cognitive tasks, including tasks eliciting cogni- 39,48 38,49 behavioral state. While both approaches enable the tive processes critical for memory, mood, 26,43–46,50 42 subject to modulate brain activity, they differentially motor imagery, and perception of pain. test distinct aspects of cognition by affording flexi- Thus, neurofeedback affords flexibility in target- bility in the design of the feedback signal,11 which ing distinct functional brain regions associated with we address further below. different facets of cognition that include sensation, To test whether a subject’s ability to directly movement, emotion, attention, and learning. modulate target brain regions improves task per- While direct modulation of a neurophysiological formance, investigators can present sensory feed- signal is a natural place to start, one might also be back that scales with the amplitude of brain activity. interested in indirectly perturbing behavioral states The use of this technique has revealed that sub- and observing concurrent changes in brain activity.

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 3 A network engineering perspective Bassett & Khambhati

Consider examining how the brain dynamically Put simply, learning to self-regulate brain activity is recruits different areas to perform easy versus akin to learning any other skill.41 When given phys- difficult behavioral tasks—investigators can alter iological feedback in addition to a recommended task complexity on the fly based on the amount of modulation strategy, evidence suggests that subjects activity in the target brain region. To perform this display increased performance on related cognitive real-time decoding and mapping of brain activation tasks in comparison to the scenario in which sub- to behavior, neuroscientists have begun employing jects are only given the modulation strategy.42 machine learning tools that link general linear Nonstrategic training of neurofeedback models with multivariate pattern analysis.11,51,52 Despite the apparent utility of a cognitive modu- Briefly, a typical neurofeedback study utilizing lation strategy, it is also useful to understand to these tools would implement the following general what degree subjects can volitionally modulate brain process: train a statistical model that discriminates dynamics. Can subjects simply learn to modulate patterns of brain activation in response to different brain activity when given no pointers as to how to stimuli, present the subject with a stimulus, ask the enhance the activity of the target region? Such a subject to perform a mental operation based on the capability would be vital in modulating brain activ- stimulus, decode the altered pattern of brain activity ity or connectivity in regions for which we cannot using the statistical model, adjust the stimulus on articulate a strategy. These possibilities open up a the basis of the new brain state, and have the subject new realm of scientific investigation that could be repeat the mental operation. The ability to perturb particularly helpful in the study of neurological and behavioral state based on underlying brain dynam- psychiatric disorders with potentially discordant ics has immense utility in revealing functional mappings of functional brain areas57 or in tuning mechanisms underlying changes in behavior.53 the temporal architecture of brain activity in healthy Indeed, recent applications of this technique have individuals.58 Studies demonstrate that, even when yielded critical insights into the mechanisms of explicit instructions or strategies are not provided, attention54,55 by altering task complexity during subjects can search for an effective strategy to self- decoded states of attentional lapses.56 regulate functional brain dynamics.26,38,47,57 Such open-ended experimentation is especially powerful Learning strategies in neurofeedback training for investigating how subjects employ unique strate- Exactly how participants learn to regulate regional gies to modulate brain dynamics.38,40,57 Indeed, it is activity in response to neurofeedback remains of interest to explicitly map individual variability in incompletely understood. To date, efforts have the chosen control strategy to the subjects’ ability focused on two complementary strategies. In the to modulate target brain areas. Understanding the first, the participant is provided with cognitive tasks relationship between cognitive strategy and effective that facilitate the activation of the target region, modulation could inform experimental approaches while in the second, the participant is simply pro- to fine-tune the mapping between cognitive pro- vided with the feedback of regional activation and cesses and functional brain regions (Fig. 2). encouraged to identify his/her own strategy to mod- ulate it. The two techniques have distinct advantages Probing cognitive abilities and disabilities in the study of human cognition. Broadly, direct and indirect neurofeedback are The earliest work in this field implemented the profoundly robust in their ability to modulate brain first approach by providing subjects with instruc- dynamics. Furthermore, they provide a systematic tions to perform mental imagery by imagining the approach to query functional mechanisms of cog- perceptual experience associated with the functional nition that are often elusive in open-loop methods role of the target brain region.21,42,50 For example, of investigation. By engineering the feedback signal, to activate motor processing areas, one might pic- neurofeedback investigators can flexibly design ture oneself moving a limb, while to activate atten- novel experimental paradigms to study the role of tion processing areas, one might concentrate on the cognition in single brain areas or across multiple given task. Evidence suggests that, when given such brain areas in tandem. This practice has already instructions, subjects display improved modulation demonstrated the ability to direct neurofeedback of the target brain area within a day of training.26 to more focal targets39,40,44,59–61 or to perturb

4 Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. Bassett & Khambhati A network engineering perspective

(A) In addition to functioning as a probe for healthy human cognition, neurofeedback can also be used to identify and potentially treat cognitive disabili- ties. Particularly in populations with impaired men- 1 tal health, neurofeedback enables the clinical study of mechanisms of dysfunction in neurologic and Voxel

activation 0 psychiatric disorders, and it also has the potential to provide noninvasive therapies to minimize the Voxel classifier symptoms of such disorders.53 Indeed, soon after (B) its introduction in the late 1960s,12,13 neurofeed- back was popularized in clinical contexts. Studies ? demonstrated its therapeutic potential in managing epilepsy,14,15 treating attention-deficit/hyperactivity 16,18 1 disorder, and enhancing rehabilitation follow- ing stroke.17 Initially, these pioneering studies were

Voxel limited to electroencephalography (EEG), but with activation 0 more recent advances in other noninvasive imaging Voxel decoder techniques, the tools have been translated to real- time fMRI.68 Over the last few years, neurofeed- Figure 2. Probing cognitive state with neurofeedback. Indirect perturbation of behavioral state using neurofeedback is a pow- back with real-time fMRI has been used to study erful technique to probe the cognitive state space in individuals. schizophrenia,57,60 depression,39 obesity,61 and Suppose that one wanted to learn the neural basis underlying addiction.62,69 While direct neurofeedback is used spatial reasoning ability using a mental manipulation task. (A) to improve patients’ ability to self-regulate target The experimenter could present the subject with a circle and brain areas and reduce clinical symptoms,70 indirect a star shape, and ask the subject to observe the stimuli and mentally imagine the circle morphing into a star. Meanwhile, a neurofeedback is used to study functional dynam- statistical model could be trained to capture the voxel activation ics underlying the different cognitive strategies used pattern pertaining to the imagined shapes. (B) To probe and by healthy subjects and patients to modulate activity quantify the subject’s thought process associated with mental in dysfunctional brain regions.57,71 By using indirect manipulation, the experimenter might display the circle to the neurofeedback to map cognitive differences between subject and ask the subject to use his or her mind to manipu- late the object into a star. Using the shape-based model of voxel healthy subjects and patients, clinicians may be able activation, the experiment could decode the mentally visual- to use behaviorally driven approaches to better diag- ized shape from the voxel activation pattern—in real time—and nose individuals with disabilities and mental illness. feed the current state of the imagined shape back to the sub- ject. By tracking how subjects explore the cognitive state space while learning how to perform mental operations during a task, Advancing neurofeedback technology investigators could map how individuals use different cogni- Neurofeedback has yielded critical insights into cog- tive strategies to accomplish the task and could further map the nitive function and dysfunction and is now ripe for distinct neural drivers of these strategies. innovation as neuroscience evolves toward under- standing cognition in the broader context of brain networks.33 Indeed, the emerging view of the brain dynamics across more distributed targets.43,46,62 as a network in the mathematical sense has been In addition, the difficulty of the neurofeedback supported by a growing empirical ability to mea- training can be titrated to affect a specific change sure brain activity over a variety of spatial and tem- on both attentional circuits and regions devoted poral scales.30,32 Novel imaging technologies have to internally directed cognition.63 Particularly continued to elucidate a hierarchical organization exciting applications to cognition include the of the brain,72,73 ranging from the scale of individ- revelation of associative learning in early visual ual neurons and neuronal populations to that of areas,64 visual perceptual learning induced by specialized large-scale functional areas.74 Bridging decoded functional magnetic resonance imaging the computational units at each scale are complex (fMRI) neurofeedback,65 and the sensitivity of patterns of structural links facilitating the transmis- these learning processes to the subject’s state.66,67 sion and processing of information that support

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 5 A network engineering perspective Bassett & Khambhati cognition and behavior.29 This hierarchical, multi- Network neuroscience scale network architecture of the brain brings with it At the confluence of neuroscience, engineering, and unique opportunities for the use of neurofeedback physics lies network neuroscience, a burgeoning field in understanding cognition. that offers a framework for describing brain cir- Although prior work demonstrated that neuro- cuitry at macro- and microscales.92 Drawing upon feedback is effective in modulating dynamics of fundamental tools from graph theory,93,94 network (1) individual neurons at submillimeter resolution scientists identify important features among ele- and fast time scales,75,76 (2) millimeter-scale neu- ments of a system and measure similarity between ronal populations through oscillatory rhythms,58 these elements—based on these features—to syn- and (3) macroscale functional domains at slow thesize models that describe an “ecosystem” of inter- time scales,59,68 modulating the way in which brain related parts.95,96 These models can be probed and regions functionally interact is now becoming a perturbed to understand how an individual element tractable frontier. Using statistical models to mea- or a group of elements influences the system as a sure functional connectivity and to construct an whole.97,98 This formalism can be used to study how effective feedback signal for modulation, several elements of the brain (nodes) structurally or func- studies demonstrated that subjects can directly per- tionally link (edges) to one another and support turb functional interactions between brain regions behavior and cognition in health and disease.99,100 with fMRI-77–81 and EEG-based neurofeedback.82–84 Toconstruct brain graphs,30 one can measure struc- Moreover, the feedback signal can be adapted to per- tural links between brain regions, such as those turb the dynamics of individual connections80,81 or composed of macroscale white-matter fibers or large groups of connections77–79 simultaneously. microscale synaptic connections. Alternatively, one While neurofeedback can perturb dynamics at can measure functional links between brain regions, different stages and spatial scales of functional such as those estimated by similarity in brain processing, equally important is understanding how dynamics. The pattern of edges between nodes can perturbations can have far-reaching impact on func- then be studied mathematically as a graph.30,32,33 tional dynamics in non-targeted brain areas. Several studies identify changes in functional connectivity Mathematical underpinnings of network between the neurofeedback target and other brain science regions.26,47,60,61,85–90 Other studies demonstrate Formally, a graph G consists of a set of N nodes changes in functional connectivity between pairs of V and a set of N × (N − 1) edges E.93,94 To tabu- regions completely outside of the area targeted by late the strength of edges between network nodes, neurofeedback.26,85,87–89,91 Moreover, the observed one can construct an N × N adjacency matrix A in changes in functional connectivity can be complex: which the entry at row i and column j refers to the upregulating or downregulating target brain regions weight of the edge between node i and node j.Mul- may increase functional interactions between some tilayer networks extend the notion of a static graph brain regions and may decrease functional to a higher-dimensional graph101 —where nodes or interactions between other brain regions.87 edges change with condition or time, as in the case Taken together, these findings underscore the of dynamic functional brain networks101–106 —and potential complexity of the effect of neurofeedback are represented by an N × N × T adjacency ten- on the brain. Yet, to date, little attention has been sor with N nodes and T layers.107 Using the adja- given to establishing a framework for predicting the cency matrix formulation, one can compute local, impact of neurofeedback on broader network func- mesoscale, and global statistics to quantify the topo- tion. Building such a framework is critical for the logical and topographical properties of brain graphs improvement of feedback paradigms built to iden- (Fig. 3). On the whole, these graph statistics can pro- tify neurophysiological drivers of cognition and to vide information about how neural information is treat neurological and psychiatric disorders while represented, processed, and communicated between minimizing side effects. In the following section, we brain regions. discuss the potential utility of network neuroscience Local graph measures tell us about the nature in providing just such a framework. of connections from a given node or between

6 Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. Bassett & Khambhati A network engineering perspective

(A) (B) Hubness Clustering coefficient

Node (brain region) Edge (connection) (C) (D) Modularity Core−periphery

Figure 3. Multiscaletopologyinbrainnetworks.Brainnetworks haveuniqueorganizingprinciples atlocal,meso-,andglobalscales that provide information about how neural information is represented, processed, and communicated between brain regions. Brain networks are modeled as a collection of nodes—representing regions of interest with presumably coherent functional responsibilities —and edges—structural connections or functional interactions between brain regions. (A) Node centrality describes the importance of individual nodes in terms of their connectivity relative to other nodes in the network. Nodes with more connections or stronger edges tend to be hubs (red), while nodes with fewer connections tend to be isolated (blue). (B) Clustering coefficient, a measure of connectivity between the neighbors of a node, is another local measure of network topology. Unlike network topologies with strong hubness qualities, as in (A), networks with strong clustering coefficient demonstrate a high density of triangles that is believed to facilitate local information processing. (C) Modularity is a mesoscale topological property that captures communities of nodes that are tightly connected to one another and weakly connected to nodes in other communities. Modular organization underlies a rich functional specialization within individual communities. Here, nodes of different communities are colored red, blue, or pink. (D) Networks with core–periphery structure exhibit a set of tightly connected nodes (core; red) sparsely connected to a set of isolated nodes (periphery; blue). This organization is in stark contrast to the modular organization in (C). The core–periphery architecture is a characteristic of networks that integrate information from isolated regions in a central area. Adapted with permission from Ref. 127. neighbors of that node. One simple, yet impor- (Fig. 3C). This modular architecture is thought tant, local statistic of a node is centrality—how to support the brain’s segregation into function- influential a node is in the context of the broader ally specialized units.33,115,116 Brain graphs can also network.95 Centrality can take many forms, such exhibit core–periphery structure, in which a densely as degree, the number of edges connected to the interconnected group of core nodes is connected node (Fig. 3A), or betweenness, the number of short- to a sparsely interconnected group of peripheral est paths between any two nodes that must cross nodes117,118 (Fig. 3D). The core–periphery network the node in question. Degree centrality has been structure has been studied for its role in explain- particularly useful in identifying hubs of neural ing domain-general versus domain-specific process- processing that interact with many different brain ing of brain areas,119 in which specialized neural regions.97,108,109 A second local statistic that is often processing in peripheral regions is integrated by used to describe brain graphs is the clustering coef- a strongly connected core to support higher-order ficient —the fraction of a node’s neighbors that are cognition in learning104,120 and language.106 also connected to one another110 (Fig. 3B). The Finally, global statistics provide a summary of clustering coefficient describes topological organi- network topology. For brain networks, the charac- zation thought to underlie local processing of neural teristic path length —average shortest path between information.111,112 all node pairs95—is thought to measure how eas- At the mesoscale, one can quantify the tendency ily neural information can be transferred between of brain regions to form communities —tightly con- brain regions. Brains with shorter path lengths are nected groups of nodes that have more connections thought to transfer information more efficiently to one another than to other groups of nodes113,114 than brain networks with longer path lengths,121

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 7 A network engineering perspective Bassett & Khambhati thereby leading to greater intelligence.122 A similar, new skills,131,132 and moreover that the strength of dynamical measure of information transfer that has structural connections between task-relevant brain been of recent interest is synchronizability —the ease regions predicts individual differences in the rate at with which dynamics at each node can synchronize which those skills are learned.133 The relevance of based on the arrangement of edges.123 Synchroniz- structural connectivity for cognition extends to clin- ability has also been studied in the context of graph ical cohorts. For example, patients with anatomical robustness and vulnerability to random and tar- disruptions caused by traumatic brain injury exhibit geted attacks to nodes.124 In brain networks, syn- structural network changes—such as a lengthen- chronizability is thought to be maintained between ing of the shortest path length—that are associated a critical boundary of order and disorder.125 with decreased performance on tasks that required It is important to remember that each statistic is switching and inhibition of cognitive resources.134 sensitive to network phenomena of a specific scale, While structural brain networks reveal important and a comprehensive, multiscale quantification of correlates of cognitive ability, a more nuanced dis- brain network topology requires integration of the section of cognitive processing also requires the use output of these measures.120 For instance, local of functional imaging methods. Functional brain information processing at hub nodes might be pro- networks provide a glimpse into network processes jected broadly to mesoscale modules for function- (as opposed to structures) that support cognitive specific processing that might require globally short function. One recent study highlighted the impor- path lengths to ultimately integrate and bind the tance of functional network topology for cognition information of each module.100 This framework can by tracking longitudinal changes in the behavior of be used to query how different elements across mul- patients with traumatic brain injury; patients with tiple scales of network architecture contribute to the lesions in brain regions that connected to several processes underlying human cognition.126 functional modules exhibited more widespread cog- nitive deficits compared with patients with lesions in Cognitive network neuroscience network hubs.135 Patients with traumatic injury also Graph theoretic approaches for understanding cog- exhibit distributed increases in connectivity during nition have become increasingly popular over the the Stroop task—which requires switching of cog- past decade, largely due to their utility in describ- nitive resources—that is associated with reduced ing the interregional relationships between neural performance on the task.136 In healthy individu- processing units elicited by cognitively demanding als, differences in global connectivity from specific tasks.105 Application of graph theory to noninvasive cognitive control areas predict fluid intelligence.137 brain imaging in humans has yielded critical insight Beyond the performance of a single task, evidence into mechanisms of intelligence, linguistic process- suggests that functional brain networks also recon- ing, attention, decision making, learning, memory, figure as individuals traverse different cognitive and cognitive control.100,126 Pragmatically, it is use- states125 and that the flexibility of this reconfig- ful to separate these insights into those produced by uration can be used to predict learning in future structural brain networks35,128 and those produced training sessions.36 by functional brain networks.97,125 Together, these studies underscore the role of net- First, structural brain networks constructed from work topology and network dynamics as fundamen- diffusion-weighted imaging of white-matter fiber tal mechanisms of cognition. Such insights lay the pathways35,36 describe the fundamental scaffolding groundwork for exploring how neurofeedback can upon which functional brain networks operate.115 be used to perturb network properties and thereby Because of their potential role in constraining more effectively probe drivers of cognition. functional brain dynamics,129,130 structural brain networks are thought to play important roles in Linking neurofeedback to network shaping our basic cognitive abilities—such as pro- neuroscience cessing speed, working memory, motor skills, and In the preceeding sections, we explored state-of-the- task switching.126 For example, longitudinal struc- art capabilities in neurofeedback to perturb brain tural imaging has revealed localized changes in net- dynamics, and we introduced a robust framework in work microarchitecture associated with learning network neuroscience for studying the interactions

8 Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. Bassett & Khambhati A network engineering perspective between brain dynamics and the structural net- cognition. Simultaneously, advancements in neuro- works from which these dynamics originate. Here, feedback can be used to investigate network drivers we begin to address how the thoughtful integration of cognition: by designing the appropriate feedback of neurofeedback and network neuroscience could signal, neurofeedback can be engineered to modu- enhance the study of cognition. late not only brain regions but also specific brain In principle, network neuroscience can be used networks. This capability opens new doors to test to identify target brain regions for neurofeedback. the ability of subjects to modulate specific network Evidence suggests that neurofeedback is differen- properties: Could a subject be trained to modulate tially effective in distinct brain areas.138 While ini- the flexibility of a functional module, the participa- tial interpretations suggested that this differential tion of a brain region in multiple modules, or even effectiveness is due to the inherent differences in the characteristic path length of the global network? the types of cognitive processes that brain regions Our ability to modify the feedback signal to accom- perform, a second possible explanation is that brain modate network statistics could have substantial areas are differentially sensitive to neurofeedback impact on our understanding of how perturbation based on their connectivity profile. It is intuitively of network structure affects cognitive ability. Such plausible, for example, that regions of the brain that a capability would also inform the design of novel are densely functionally connected with one another intervention strategies for patients with neurologi- (such as the default mode) will be easier to control cal disorders or psychiatric disease characterized by as a collective—owing to the breadth of potential disrupted patterns of functional connectivity. control mechanisms139 and cognitive strategies— than regions of the brain that are sparsely function- Caveats and future directions ally connected (such as the frontal pole). It will be While the prospect of linking neurofeedback and interesting in the future to determine whether the network neuroscience is promising, it is also impor- connectivity profile of a region, or the complexity tant to adopt a measured approach in which we of the information it processes, is a better predictor acknowledge the pitfalls and limitations inherent of its response to neurofeedback. in the techniques. First, a note on interpretability: Beyond informing our understanding of the network statistics quantify graph properties from impact of neurofeedback on specific brain areas, the theoretical perspective of statistical mechanics network neuroscience can also be used to predict and information processing, and thus they require the impact of targeted neurofeedback on other a conceptual leap if connected to neurophysiologic brain regions. For example, structural connectivity phenomena.145,146 For instance, the relationship or resting-state functional connectivity could between connectivity derived from functional pinpoint network hubs, such as cognitive con- imaging and the amount that two brain regions are trol areas,140–142 that interact with many other in fact communicating147 remains undetermined. brain areas and serve as a potential target for Or consider the shortest path between areas in modulating distributed brain dynamics with a brain graph: Does the brain utilize shortest neurofeedback. Such a capability could be used to paths?130 Or does it preferentially utilize longer study self-regulating brain dynamics143 in cognitive paths or walks?37,133 Although novel technologies control regions and their effective control of other are needed to help bridge these areas of scientific brain areas as humans switch between distinct understanding, we remain optimistic that network tasks.142 A similar approach might be employed to neuroscience will provide a dynamical systems-level investigate whether modulating brain regions that characterization and understanding of behavioral integrate functionally distinct network modules142 and cognitive processes. could help subjects better learn tasks that require A second crucial caveat relates to the importance cooperative or competitive interactions between of distinguishing between correlation and causa- separate cognitive domains140—such as visuomotor tion. A substantial body of work now demonstrates interactions in novel skill acquisition.144 thatnetworkmeasurescanbegoodpredictorsof More generally, our ability to connect network cognitive ability based on their degree of correlation topology to cognition offers a critical opportunity to performance metrics. However, these predictions to model and predict the effects of neurofeedback on do not equate to causation. In fact, explicitly

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 9 A network engineering perspective Bassett & Khambhati identifying causation will require a coupling tions. Nevertheless, it will be important in the future between neurofeedback and network-based to understand the degree of targeting possible in any approaches to the study of cognition: by mod- given neurofeedback training paradigm, as well as in ulating network topology with neurofeedback any given subject, when considering informing such and evaluating the concurrent change in task experiments with predictions from network science. performance, we can begin to understand causal Perhaps most importantly, the possibility of effects of network architecture on cognition. revealing causal relationships between network A third and very fundamental consideration architecture and cognition with neurofeedback also relates to the question of whether neurofeedback supports the potential to build computational mod- can be truly targeted to a single region or whether it els or theories of brain network function from only ever activates a distributed network. In truth, first principles.148,149 Setting aside characterization knowing the degree to which a specific neurofeed- and description, and even setting aside correla- back paradigm targets a single region versus many tive approaches to link brain network function to regions remains challenging, and this uncertainty is observable behavioral variables, models and theo- an important consideration for studies seeking to ries provide mechanistic understanding150 and the combine network approaches and neurofeedback ability to generalize inferences to unseen scenarios. training. For example, prior work demonstrates What might such a model or theory look like? In the ability of subjects to regulate brain activity in the following section, we discuss the potential util- spatially confined brain regions.59 Specifically, they ity of network control theory in providing just such show that, with training, activation was significantly amodel. increased within a predefined target area (somato- Network control theory: a tool to predict motor cortex) relative to the rest of the brain, an impact of modulation observation that suggests that spatial specificity may be achieved with neurofeedback. More recent work Network control theory is a mathematical model- confirmed the hypothesis that functional connectiv- ing framework that addresses the question of how ity from the target brain region (ventral tegmental energetic input to a node in a network affects area) to adjoining brain regions is directly caused by the dynamics of the networked system.151,152 Stem- volitional activation of the target and not mediated ming from early work in the 1970s on structural by practice with or without false neurofeedback.47 controllability,153 the theory is built on two pillars: a Thus, they reason that changes in network con- model of the system’s dynamics and an estimate of nectivity are due to the successful perturbation of the system’s network structure.154 In contrast, graph the target and not associated with the task. This theory stands on only one of these pillars (the net- observation, however, still leaves open the ques- work structure) and is devoid of the other (a model tion of whether increased functional connectivity of system dynamics). These differences in the nature occurred in successful perturbations during train- of the two theories directly affect how they can be ing or as a result of posttest perturbation. Other used:142,155 graph theory provides descriptive statis- work has developed techniques to study the differ- tics of a network’s organization, while network con- ential effects of perturbation during training and trol theory provides a prediction of how the change perturbation after training (transfer) on functional in energy at a node will alter the system’s dynamics. connectivity.89 Comparing functional connections While graph theory offers tools for characterization, stemming from the neurofeedback target, they network control theory posits a mechanism for sys- found more distributed changes during training tem function. and specific changes during transfer. These studies Traditionally, network control theory stems from present evidence that (1) neurofeedback can activate theolderfieldofsimplycontrol theory,which spatially confined brain regions, (2) target activation has been used to inform the control of robotic, and the resulting increase in functional connectivity technological, and mechanical systems. The simple can be directly related to successful neurofeedback, difference between control theory and network con- and (3) methodological innovations are capable of trol theory is that network control theory deals with teasing apart changes in functional connectivity due the application of control theory to systems charac- to training perturbations versus transfer perturba- terized by complex interconnection patterns.151,152

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These patterns significantly affect the control strate- Average control node gies that a system can perform or respond to and Modal control node further affect the energy required for certain con- trol goals. In the realm of neuroscience, network control theory therefore differs from neural control engineering more generally156 in its explicit treat-

ment of brain network architecture. cost Energy

A few relevant concepts and tools Inabrain,questionsofcontrolcanbeseparated Dynamical network states into two types: (1) how does the brain control its own dynamics and (2) how can brain dynam- Figure 4. Brain network controllers drive transitions between dynamical states. To accomplish behavioral and cognitive goals, ics be controlled via external intervention. When brain networks internally navigate a complex space of dynam- applied to the former question, network control ical states. Stable brain states may lie in basins of local mini- theory can offer insights into cognitive control,157 mum energy—requiring the brain to expend metabolic energy decision making, and other forms of executive to move over high-energy peaks when transitioning from the function.142,158 When applied to the latter, network current state to the next state. Within the space of possible dynamical states, there are easily accessible states and harder-to- control theory can inform the use of neural modu- reach states; in some cases, the accessible states are healthy, while 34,159 lation via neurofeedback or brain stimulation, in other cases they may contribute to dysfunction, and similarly the development of cognitive tasks for explicit tun- for the harder-to-reach states. Two commonly observed control ing of brain dynamics, and the understanding of strategies in complex systems are average control and modal how sensory stimuli impact those dynamics. control. In average control, highly central nodes navigate the brain toward easy-to-reach states. In contrast, modal control To address both types of questions regarding nodes tend to be isolated brain regions that navigate the brain internal and external control, one needs to begin toward hard-to-reach states that may require additional energy by writing down the two pillars of the theory: a expenditure.142 Adapted with permission from Ref. 127. model of the system’s dynamics and an estimate of the system’s network structure. A simple first assessment of whether there are particular control step is to use a discrete-time, time-invariant, noise- strategies that are possible for the brain and whether free model of system dynamics129,160 and a struc- the system is controllable with a larger number of tural network estimated from diffusion imaging input sites. tractography in humans,35 representing the white- In the engineering literature, common control matter pathways crisscrossing cortical and subcorti- strategies include (1) average controllability, which cal areas. Of course, these choices are accompanied describes the ease with which the system can be by model assumptions and caveats associated with moved to nearby states on the energy landscape; (2) the empirical data, both of which need to be modal controllability, which describes the ease with acknowledged. (See next section for an explicit treat- which the system can be moved to distant states on ment of these topics.) Nevertheless, they remain a the energy landscape; and (3) boundary controlla- useful starting point for the application of the theory bility, which describes the ease with which mod- to human neuroscience. ules in the network can be coupled or decoupled.152 Within this framework, network control theory In applications to human diffusion imaging data, offers a few important concepts and tools. The first these concepts have proven useful in offering struc- important concept is that of controllability,which tural explanations for the areas that affect cogni- indicates whether a system can be moved from a tive control142,158 and the impact of stimulation to specified initial state to a specified final state with the target brain region.34 An even finer account finite energy and in finite time.151 In initial applica- of the brain’s dynamics can be obtained by study- tions of these algorithms to noninvasive structural ing the exact transitions from one brain state to neuroimaging data in humans, evidence suggests another, with assumptions on the need to mini- that the human brain is practically impossible to mize energy of transitions and minimize the dis- control from energy injected into a single brain tance that the brain traverses through state space to region.142 This result motivates a more nuanced affect the transition155 (Fig. 4). Applications of these

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 11 A network engineering perspective Bassett & Khambhati algorithms to human diffusion imaging data have By analyzing the functional network topology of offered an explanation for the anatomical structure focal and distributed (clinically known as secondar- of the brain’s default mode network155 and a predic- ily generalized) seizures, recent work demonstrates tion of which regions in the network are most likely that desynchronizing and synchronizing brain to assist in a given state transition.155,161 regions antagonistically regulate the ability for seizures to synchronize network dynamics.143 Thus, Limitations, caveats, and extensions control strategies like push–pull control may be of network control theory relevant for homeostatic regulation of (nonlinear) Because network control theory is fundamentally synchronization dynamics in the human brain. a modeling endeavor, it is important to consider Beyond nonlinear extensions, other interesting model assumptions, model validation, and model questions to consider include the possibility that extension. First, it is important to acknowledge some regions of the state space are inaccessible that the model can only be as accurate as the data or pathological,154 that the brain may be under- used to construct it, and thus one must deal with actuated in certain states,170 and that control can the inherent limitations associated with construct- be implemented by distributed as well as focal ing the anatomical network from diffusion imag- strategies.159 Moreover, although structural control- ing data.162–164 Second, when considering a linear lability theory153 is inherently built on knowledge model of system dynamics,153 the assumption is that about the structural connections in a network, it will brain network dynamics are linear. In the brain, be interesting in the future to extend these models these linear models have preliminary support in to statistically estimate the set of either structural empirically measurable dynamics,129,160 but fur- or extrasynaptic171 connections that are being uti- ther work is needed to delineate the breadth of lized at a particular moment in time and how that their applicability. Moreover, it is important to note set might change as humans perform a cognitively that, if using this linear approach to model non- effortful task. linear dynamics (e.g., those observed in EEG and MEG data), the assumption of linearity neverthe- Putting it all together: neurofeedback, less remains true over short time horizons and in network neuroscience, and control the vicinity of the operating point.165 If one wishes to expand beyond short time What does network control theory add to the con- horizons and states surrounding the operating versation between neurofeedback and network neu- point, then one must consider nonlinear models roscience? Far from being a third wheel, network of brain dynamics.166 Which nonlinear models control theory in fact offers the theoretical frame- might be relevant while remaining theoretically work in which to predict how the activation of a tractable? This is an open question, but one region (or connection or subgraph) by neurofeed- particularly useful approach might be to use system back will affect brain network dynamics, moving identification to extract the appropriate nonlinear the brain into a new mental state and thereby alter- model from real data.167 Better understanding of ing intrinsic cognitive processes. Thus, in essence, control strategies for appropriate nonlinear models network control theory offers a theoretical back- of brain dynamics could be particularly important bone on which to begin formulating ideas about in understanding large-scale circuit function sup- the mechanisms of cognition and begin developing porting cognition. For example, synchronization theoretically grounded interventions to target their dynamics are thought to play a critical role in facil- modulation. itating the transfer of information between brain To be a bit more concrete, one could use network regions at the mesoscale,168 but principles of the control theory to simulate the impact of a change brain’s endogenous regulation of synchronization in energy at one (or several) regions (or connec- remain far from understood. One hypothesis from tions) on the subsequent brain network dynam- theoretical physics is that these networks employ ics. Using this approach, one could identify the a push–pull control strategy in which antagonistic constellation of regions and connections that— desynchronizing and synchronizing nodes regulate when brought to a specific pattern of activation— the transfer of information through the network.169 would have a predictable effect on brain state

12 Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. Bassett & Khambhati A network engineering perspective

(A)

Average controller

(B)

Modal controller

(C)

Boundary controller

Figure 5. Self-regulating brain network controllers for cognition. Neurofeedback could be used to teach individuals how to modulate brain activity in important control points that drive changes in dynamical brain state—an experimental tool that would offer tremendous opportunities for studying “cognition dynamics,” or the ability to perform specific tasks based on the current brain state. Furthermore, this approach might be used to train individuals with specific cognitive deficits to better manage their ability to perform certain types of tasks. (A) Suppose that individuals could be trained to upregulate the brain’s average controller (red node) to assist in navigating different brain states associated with a specific task, such as opening up and reading a book. (B) If the subject has difficulty with switching between tasks—such as reading and doing math—he/she might be trained to upregulate his/her brain’s modal controller (blue node) to switch more efficiently. (C) If the subject has difficulty with comprehension or reading aloud, he/she might be trained to upregulate his/her brain boundary controllers between functional modules associated with language and speech.

(Fig. 5). Then, one could use neurofeedback to pro- anistic understanding of human cognition, seems at duce that pattern of activation, validate the pre- this point to be well worth the effort. dicted subsequent effect on brain state dynamics, and observe the associated change in cognitive func- Acknowledgments tion. In essence, this approach enables a closed loop We thank Andrew C. Murphy for helpful feedback between theory and experiment, providing a frame- on an earlier version of this manuscript. D.S.B. and work in which to develop more general theories A.N.K. would like to acknowledge support from of brain function, explain existing empirical data, the John D. and Catherine T. MacArthur Foun- suggest new directions for empirical research, and dation, the Alfred P. Sloan Foundation, the Army inform experimental hypotheses. Research Laboratory and the Army Research Office Indeed, the confluence of these three disparate through Contract Numbers W911NF-10-2-0022 disciplines—network control theory, neurofeed- and W911NF-14-1-0679, the National Institute of back, and network neuroscience—offers much Health (2-R01-DC-009209-11, 1R01HD086888-01, promise in advancing our understanding of human R01-MH107235, R01-MH107703, R01MH109520, cognition. Both neurofeedback and network neuro- 1R01NS099348, and R21-M MH-106799), the science are well-developed fields at this point, and Office of Naval Research, and the National Sci- they are ripe for integration. Network control theory ence Foundation (BCS-1441502, CAREER PHY- is the newest field of the three, and its integration will 1554488, BCS-1631550, and CNS-1626008). The require careful development, characterization, and content is solely the responsibility of the authors validation to reach its full promise. Nevertheless, the and does not necessarily represent the official views potential payoff in terms of obtaining a basic, mech- of any of the funding agencies.

Ann. N.Y. Acad. Sci. xxxx (2017) 1–18 C 2017 New York Academy of Sciences. 13 A network engineering perspective Bassett & Khambhati

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