Space: a Missing Piece of the Dynamic Puzzle

Abstract

There has been growing interest in studying the temporal reconfiguration of brain functional connectivity to understand the role of dynamic interaction (e.g. integration and segregation) among neuronal populations in cognitive functions. However, it is crucial to differentiate between various dynamic properties as nearly all existing dynamic connectivity studies are presented as spatiotemporal dynamics, even though they fall into different categories. As a result, variation in the spatial patterns of functional structures are not well characterized. Here, we present the concepts of spatially, temporally, and spatiotemporally dynamics and use this terminology to categorize existing approaches. We review current spatially dynamic connectivity work emphasizing that explicit incorporation of space into dynamic analyses can expand our understanding of brain function and disorder.

Functional Connectivity and Brain Dynamics

The fundamental question regarding functional neuroimaging is how the measurements of imaging modalities represent various integrative brain functions such as auditory processing, vision, and cognition. A significant amount of effort has been focused on understanding the interactions within and between (functional) sources and the relevance of temporal synchrony to cognitive functions through functional connectivity modeling approaches. A source is defined as a pattern of temporally synchronized neural assemblies. Each source can be described by its spatial and temporal patterns, and the potential accuracy of the estimated source is constrained at the outset by the spatial and temporal resolution of a given imaging modality [1–7]. Sources can be identified at different spatial resolutions, ranging from small focal regions to spatially distributed networks. The spatial pattern of a source characterizes the distribution of the source in space, and the amplitude of the spatial pattern at any spatial location indicates the strength of the association between the spatial location and the source. The temporal pattern of a source describes the temporal activity of the source. It is also important to note that sources are distinct from nodes (e.g. seeds) that are used to study the functional profiles of sources and the relationship among the sources that they are representing. A node is a spatial locality (spatial region) and is presumed to contain a whole or part of a source. In other words, a node is representative of a source. Thus, it is important that the voxel timecourses within the node are temporally synchronized to avoid mixing information.

To answer the fundamental question of the relationship between measurements and brain functions, various analytical approaches have been developed, with each providing a different model for functional neuroimaging measurements. Many of these modeling approaches can be explained via a generative linear model where the measurements are modeled as a linear combination of underlying the spatial patterns of sources (S) and their temporal patterns (a) at any particular point in time (i. e., x(t) = a′(t) × S). The generative linear model has been widely used in functional magnetic resonance imaging (fMRI) and has led to key new insights regarding the brain and the relationship among sources [4]. Recently, considering the rich dynamic nature of the brain, there is growing interest in the study of the temporal reconfiguration of sources. In particular, the recent findings of dynamic functional connectivity using resting-state fMRI (rsfMRI) resulted in a rapid growth in analytical approaches to model the underlying dynamic functional architecture and utilize the information obtained from these approaches for basic and clinical neuroscience applications [8, 9]. Alongside these endeavors, there is also a discussion on which portion of the temporal fluctuations of the blood oxygenation level-dependent (BOLD) signal, is meaningful and attributed to brain dynamism. Various properties such as non-stationary and dynamic modeling have been applied and evaluated for this purpose. Some studies have even questioned the presence of brain dynamism in BOLD signal, suggesting the fluctuation patterns of functional connectivity estimated from rsfMRI are mostly related to the head motion, the sample variability, and/or non-neuronal fluctuations [10–12]. However, the validity of any terminology and study depends on its hypothesis testing framework and null models [13, 14]. Recently, Matsui et. al, evaluated these controversies using simultaneous imaging of rsfMRI and neuronal calcium imaging at high signal-to-noise ratio and high temporal resolution in tightly head-restrained and lightly anesthetized mice to control for potential confounding factors such as arousal state and head motion [15]. Their results provide strong evidence of brain dynamics in BOLD signal [15]. Nonetheless, there will be constructive ongoing discussions regarding the nature of these time-varying properties of rsfMRI and their biological basis, their cognitive relevance and clinical potential, analytic approaches and methodological framework, and statistical challenges which have been extensively discussed from different perspectives in several review papers including [9, 16, 17]. We leave the above-mentioned discussion regarding the terminology and existence of meaningful time-varying properties of fMRI to other studies [14–16, 18]. Here, we use the terms “dynamic” and “time-varying” interchangeably to describe the temporal reconfiguration of properties associated with brain dynamism.

It should be noted that the focus of this work is on the dynamic properties of sources and neural temporal synchrony (commonly called dynamic functional connectivity) in fMRI, but the concepts proposed in this article can be extended to study different aspects of brain dynamism, at different spatial and temporal scales, and using other imaging modalities. Indeed, the investigation of brain dynamism via studying the dynamic properties of neural activity is just as important as studying the dynamic properties of neural synchrony. Early task-based fMRI studies demonstrated that fMRI measurements can capture activity-related brain dynamism [19, 20]. In the same area, there is a large body of work studying the rich dynamic of activity patterns at different neuronal levels, particularly by studying the traveling pattern of neuronal activity [7, 21–25]. It is important to understand how stimulus-evoked and/or spontaneous neuronal activity at the mesoscale spread across the brain and manifest as functional connectivity. It has been suggested traveling patterns of spontaneous neuronal activities relay the information between functionally connected regions and contribute to functional connectivity observed across the brain [7, 22]. The spatiotemporal dynamic activity and traveling waves and their relationship with functional connectivity can provide important insights into brain dynamism; however, such emphasis is beyond the scope of this article.

In the remainder of this article, unless we explicitly indicate otherwise, the term “dynamic” refers to the dynamic properties of sources. We highlight an overlooked, but important aspect of brain dynamism in fMRI studies; the explicitly spatial nature of brain dynamism. We begin with defining a unified framework that explicitly incorporates both space and time into dynamic analyses with a goal of mapping brain dynamic profiles into a full spatiotemporal dynamic space. We also provide an example model via an extension of the generative linear model (generalized generative linear model). Next, we review previous work that can be categorized as a spatially dynamic approach. We provide specific examples of how the spatially dynamic work from our group has been applied to study mental illness. Finally, we highlight potential future avenues of investigation.

Generalized Generative Linear Model.

The generative linear model is adopted to formularize brain dynamism through the dynamic properties of sources. We use the first-order probability density function (pdf) of a random process to describe the variations at a fixed point in time $f_{\mathbf{\Psi }}(\mathrm{\Psi },t_k)$ and then characterize the distribution as a function of time by assuming that it can be characterized by a given family of pdf across time via a time-varying parameter. The random process can be expanded into a vector (matrix) random process, in which the random process is a vector (matrix) random variable at each time point and can be described by a joint first-order pdf at that given time point. For instance, at time point t, the vector random process is then described by a joint first-order pdf $f_{\mathbf{\Psi }}(\mathrm{\Psi };\theta (t))$, where θ(t) are the parameters of the joint first-order pdf of random process. Thus, for simplicity, we use the terms “random variable” and “pdf” to describe a random process at a given time point and its associated joint first-order pdf. We model non-stationarity thorough a simple model, though there may be interesting dynamic and time-varying properties in data which meets the definition of stationarity. At each time point, $\mathrm{x}(t)={\mathrm{a}}^{\mathrm{\text{'}}}(t)\times \mathrm{S}(t)$, where x(t) refers to the measurements (e.g. BOLD signal), a(t) is refers to the temporal pattern (activity) of the sources (a vector random variable), and S(t) is the spatial pattern of the sources (a matrix random variable).

$$\mathbf{a}(t)=({\mathbf{a}}_{l1})~f_{\mathbf{a}}(\mathrm{a};\theta \left(t\right)),$$ (1)

where θ(t) is the parameters of the pdf describing the temporal activities of the sources. If f_a is a vector variate normal distribution:

$$\mathbf{a}~N_{L,1}(\mathrm{a};{\mu }_{\theta }(t),{\Sigma }_{\theta }(t)),$$ (2)

where ${\mu }_{\theta }(t)\in {\mathbb{R}}^{n_l\times 1}$ and ${\Sigma }_{\theta }(t)\in {\mathbb{R}}^{n_l\times n_l}$ are the mean vector and covariance matrix of the normal distribution of a at time point t.

$$\mathbf{S}(t)=({\mathbf{S}}_{lv}\left(t\right))~f_{\mathit{S}}(S;\gamma \left(t\right)),$$ (3)

where γ(t) is the parameters of pdf describing the spatial patterns of the sources. For instance, if f_S is the matrix variate normal distribution [1]:

$$\mathbf{S}~N_{L,V}\left(S;M_{\gamma }(t),{\Sigma }_{\gamma }(t)⨂{\Psi }_{\gamma }(t)\right),$$ (4)

where, $M_{\gamma }(t)\in {\mathbb{R}}^{n_l\times n_v}$ is the mean matrix of the normal distribution at time step t, ${\Sigma }_{\gamma }(t)\in {\mathbb{R}}^{n_l\times n_l}$ is describing the dependency of voxels among spatial patterns of sources at time step t, and ${\Psi }_{\gamma }(t)\in {\mathbb{R}}^{n_v\times n_v}$ is describing the dependency of spatial patterns of sources among voxels at time step t.

Figure 1.

List of notations and glossary of terms

Spatial, Temporal, and Spatiotemporal Dynamics

The terms spatial and temporal dynamics was previously introduced to describe variations in spatial and temporal properties of functional connectivity patterns over time [8]. As mentioned in the previous section, the lack of common terminology and framework results in confusion in the field and an under-appreciation of spatial dynamics (time-varying spatial patterns). Even the term “dynamic” has not always been used to describe properties of brain dynamism. For example, in [26], the term “spatial dynamic” does not convey variation over time and rather describes the distribution (histogram) of connectivity values across voxels. In this work, the authors do also look at changes in the histogram over time, which is called ‘spatiotemporal dynamics’, but we would consider what is called spatiotemporal dynamics in this work to be a measure of spatial (rather than spatiotemporal) dynamics. To illustrate our concept and terminology clearly, we use a toy example showing various types of static and dynamic patterns (Figure 1. The brain is spatially dynamic if the spatial patterns of sources or the statistical dependency among the spatial patterns of sources varies over time. This includes but is not limited to a change in the size (shrinkage and expansion) of a source, a change in the shape of a source, or translation of a source in space (Figure 1B). In other words, spatial dynamic refers to variations in the spatial distribution of a source over time. Temporally dynamic behavior, on the other hand, refers to variations in the temporal patterns of sources or the statistical dependency among the temporal patterns of sources over time (time-varying temporal patterns). Temporally dynamic behavior is commonly evaluated through variations in second-order statistics such as the correlation between sources (shown in Figure 1A as changes solid lines). If the brain holds both spatially and temporally dynamic properties, it is spatiotemporally dynamic (Figure 1C), and the brain is considered as static if it has neither spatially nor temporally dynamic properties (Figure 1D).

Figure 1.

Categorization of various dynamic properties. A toy example of various types of dynamic patterns. Temporally and spatially dynamic behaviors are determined by evaluating the time-varying properties of the temporal activity and the spatial pattern of the sources. For instance, a system is temporally dynamic if the temporal coupling between the temporal activity of sources (shown in this toy example as solid lines) varies over time (A). An example of spatial dynamic can be a change in size, shape, or a translation of a source in space (B). If the brain system holds both spatially and temporally dynamic properties, it is spatiotemporally dynamic (C), and the brain is considered as static if it has no spatially and temporally dynamic properties(D). (E) Categorizing different dynamic behaviors using the proposed generalized generative linear model, (t) = a(t)′ × S(t), where a and S are spatial and temporal patterns of sources. The brain system is temporally (spatially) dynamic if the properties of a (S) varies over time. Considering a and S as random variables at any given time point, the brain system is temporally (spatially) dynamic if the parameters of interest of the probability density function (pdf) of a (S) varies over time. The corresponding equations and notations can be found in Box 1.

To take a closer look at these concepts, we can evaluate an example generative linear model which adds a time dimension to the spatial maps of sources, x(t) = a(t)′ × S(t) (Figure 1). In this formulation, spatial and temporal dynamics can be explained by variations in the properties of the spatial pattern (S) and temporal pattern (a) over time. For instance, spatially and temporally dynamic behaviors can be encoded and evaluated mathematically through θ(t) and γ(t), the parameters of the probability density functions (pdfs) of a and S, respectively (Figure 1E, and Equations 1 and 3 of Box 1). In this model, the brain’s temporally dynamic properties can be captured by estimating θ(t). For instance, its variability can be described by a covariance matrix, Σ_θ(t) (Equation 3 of Box 1). The spatially dynamic behavior is quantified by time-varying γ(t). Note that, any given analytical approach uses a specific model to evaluate the dynamic properties, thus the results of the analysis only suggest the dynamic properties of the brain system under the assumption of the model being used. In other words, the concepts of spatial, temporal, and spatiotemporal dynamics are properties of the brain and independent of a model being used to evaluate them. Note, the above generative linear model is utilized as a relatively straightforward example of the proposed framework because of its simplicity and common usage in functional connectivity analyses, rather than to capture all possible approaches, other models could and should be proposed to capture more complex spatially dynamic relationships [27–29].

Utilizing Spatially Fixed Nodes/Seeds and Dynamics

In many fMRI studies, nodes/seeds serve as proxies for spatial locations of sources. Nodes are used as an initial step for functional connectivity analyses, either to identify their corresponding sources or to measure the relationship among the sources which they represent. Thus, it is important that each node provides a good approximation of only one source. In many cases, a node is a binary mask, commonly known as a region of interest (an ROI). In seed-based analyses, nodes are commonly used as an anchor to obtain the spatial maps of sources. For instance, a posterior cingulate cortex (PCC) node can be used as a node to estimate the spatial pattern of the default mode network (DMN). In this example, we assume the PCC node is a highly temporally synchronized region providing a good representation of the DMN. In graph-theory analyses, nodes are used to identify relationships among sources. Thus, it is crucial that node A represent the same source (functional entity) across time; otherwise, the relationship of node A with node B may represent relationships between different sources across time. Considering brain dynamism, the validity of a graph-based and seed-based analyses using spatially fixed nodes is compromised if sources vary spatially over time. In the presence of spatial dynamics, the same anatomical location in space does not delineate the same source across time. Thus, fixed spatial nodes are not suitable for the study of the spatial dynamics of brain function as they assume a priori that the sources are fixed. Time-varying spatial patterns observed in spatially fixed node analyses may emerge from the spatially dynamic properties of the sources, ignoring the possibility that nodes may represent different sources over time. Only if a-priori knowledge confirming the fixed spatial node is a good representation of a source across all time points, the node can be used to study (spatial) dynamics. This assumption is especially important to consider when analytical approaches such as co-activation patterns (CAP) use fixed spatial nodes to capture different spatial patterns of sources [30], since the observed spatial variation over time are not able to be attributed to a single source. Because of this issue, in this article an approach that uses the same anatomical location as a node is not categorized as spatial dynamic. This important issue impacts the study of dynamics more generally as the use of spatially fixed nodes may result in an incorrect estimation of brain dynamism. For instance, assume the location of a source shifts over time (spatial dynamics), but this source does not exhibit temporal dynamic properties. If one uses spatially fixed nodes, then temporal coupling between these nodes will vary over time and be incorrectly attributed to temporal dynamic behavior. Table 1 provides examples of how existing analytical modeling approaches can be categorized based on our framework.

Table 1.

A (non-comprehensive) categorization of some existing analytical approaches based on the type of estimated sources.

Analytical approaches	Node = Source*	Multiple spatial patterns	Spatiotemporal dynamic		References (example)
			Spatially dynamic	Temporally dynamic
Seed-based analysis (SBA)	No	No	No	No	[31]
Independent component analysis (ICA)	Yes	Yes	No	No	[32],[33]
Co-activation pattern analysis (CAP)‡	No	Yes	No	No	[30]
Dynamic functional connectivity (dFC) w/ fixed nodes/seeds	No	No	No	Yes	[34],[35],[36]
Dynamic functional network connectivity analysis (dFNC)	Yes	Yes	No	Yes	[37],[38]
Dynamic coupling map analysis (dCM) †	Yes	Yes	Yes	No	[39]
Windowed ICA/vector analysis (SW-ICA/IVA) ††	Yes	Yes	Yes	No	[40],[41]
Constrained SW-IVA	Yes	Yes	Yes	Yes	[42]
Dynamic hierarchy analysis (dHA)	Yes	Yes	Yes	Yes	[43]

^*one of the advantages of having the node equal to the source is the source is inherently adaptive, e.g. to changes across subjects.

^‡Typical CAP analysis is not a spatially dynamic approach, but extensions of CAP, such as the whole-brain CAP approach [44], can be considered to be spatially dynamic.

^{†, ††}Here we highlight the approaches as previously used, but many of these can be adapted to capture other properties if desired, e.g. SW-ICA/IVA can be used to capture temporally dynamic properties.

Identifying Spatially Dynamic Patterns

In this section, we review previous fMRI work that can be categorized within our proposed spatially dynamic framework. We categorize the existing work into three major categories: amplitude-based, hierarchical, and time-resolved analyses. These include studies that identify spatial variation that can be considered as the spatial variation of sources, even if this was not an explicitly highlighted concept in the original work. In addition, we provide specific examples of how the spatially dynamic work from our group has been applied to study mental illness. A spatially dynamic analysis allows us to capture typically overlooked information about the functional architecture of the brain and provides additional insight into spatial dynamic properties associated with schizophrenia (SZ). One of the promises of a spatially dynamic framework is its potential to better characterize patterns of brain functional organization at the single-subject level. This is required for goals such as identifying biomarkers, single subject prediction of brain disorders, and identification of heterogeneous changes due to neurological and psychiatric disease. While structural studies have demonstrated clear clinical utility by describing brain structure within a single individual, functional studies are typically based on static group tendencies, which ignore both inter- and intra-subject variability, causing individualized information (subject-specific features) to be obscured and diluted [39, 43, 45, 46].

Spatial Dynamics via an Amplitude-based Models

An amplitude-based framework suggests brief or momentarily sparse neuronal events yield neural-related information captured by the BOLD signal and associated distinct spatial patterns. Thus, BOLD-based time series can be used to identify the time points related to neural events (e.g., time points exceeding a threshold) and their associated spatial maps. This concept is very similar to the idea of microstate in EEG studies [47] and related to co-activation patterns observed in traveling waves of spontaneous neuronal activity [7, 22]. Evaluating the average spatial pattern of time points associated with each identified event finds that many voxels co-activate together, resulting in a voxel-wise CAPs [48]. The most widely used CAP model assumes a single CAP is active at each time point [48]. The whole-brain CAP approach can be considered to model the spatial dynamic of a single source system with constant temporal pattern over time, thus each CAP represents one spatial pattern of the source. Such a view provides a limited amount of information of brain dynamism and is oversimplified because whole-brain CAPs/large-scale networks are clearly different functional entities (sources responsible for different sets of functions). Other variations of CAP approach go further than this, for example, selecting the time points with strong links to BOLD signal in the posterior cingulate cortex (PCC) and clustering them based on spatial similarity generates spatial patterns highlighting variations around the static spatial pattern of the DMN [30]. These findings indicate that the amplitude-based framework, which involves extracting the moment-to-moment dominant spatial co-activation and/or connectivity patterns, can potentially capture spatially dynamic properties. However, this requires assuring seeds to represent the same sources across time (see “Utilizing Spatially Fixed Nodes/Seeds and Dynamics”) by using spatially adaptive seeds. For instance, one can use functional seeds while allowing seeds to reconfigure over time. One additional benefit of allowing seeds to vary spatially is that it addresses the inter-subject variability which is another major problem of using spatially fixed nodes in functional studies. Importantly, these models assume binary temporal CAPs, as such they provide very limited information about temporal dynamic properties. Analytical approaches that provide better estimation of temporal patterns are needed to improve upon this category. Considering the complexity of the brain, it is important to consider that brain sources may coexist and allow the sources’ temporal patterns to overlap. For instance, Zoller et al., used innovation-driven co-activation pattern (iCAP) approach, a derivation of CAP which relies on significant transient activity, to estimate the spatial patterns of sources and then utilized a spatiotemporal regression to estimate the temporal patterns of sources while allowing the temporal overlap of their temporal activity [49]. Another potential solution is to use a modified version of the whole-brain CAP approach that allows better capturing different spatial patterns associated with each brain source. One example is to use hierarchical clustering instead of k-means clustering to identify the spatial patterns of the brain sources.

Capturing Spatial Dynamics via a Hierarchical Models

Another very interesting direction is to use the hierarchical models of brain function to encode spatiotemporally dynamic properties both within and between different hierarchical levels. Within these models, we construct the brain function as a hierarchical structure based on functional homogeneity. In these models, different levels of the hierarchy represent different estimations of the sources. The lower levels have higher spatial granularity and functional homogeneity (i.e., higher temporal synchrony_), and they are suggested to be involved in lower functional complexity. Thus, the elements of the lowest level of a hierarchical model, called functional units (FUs), are the most minute estimation of sources in the model. For instance, in a columnar model, the macrocolumn is defined as the elementary unit of cognitive operations [50]. For imaging modalities, the spatial granularity of functional hierarchies is limited by the spatial resolution of data, which means the spatial dynamic resolution is also hindered by spatial resolution of imaging modalities. For fMRI (and many other imaging modalities), functional hierarchies can only be reconstructed at a macro-scale, and each FU is defined as a pattern of regions with highly similar functional activity over time given the associated imaging modality. Defining FUs to be individual voxels may be attractive for fMRI studies, but this solution is limited by several factors such as the computational load, signal-to-noise ratio, and inter-subject variabilities, which motivates finding a superior solution. This solution should be computationally economic, robust to noise, and preserve neural-related spatial, temporal, and individual variabilities. One good candidate is high-order ICA, which parcellates the brain into fine, overlapping, and personalized FUs. Other mathematical methods can be equally suitable.

In a recent study [43], a functional hierarchical model was used to capture spatially dynamic patterns of functional domains (FDs) (Figure 2(A)). Each FD is comprised of a set of spatially distinct and functionally linked (temporally covarying) FUs, which are closely associated to large-scale brain networks. The findings from [43] showed the advantages of the functional hierarchical model to capture spatial dynamic patterns of FDs. FDs evolve spatially over time, and the spatial patterns of each FD can be summarized as a set of distinct, recurring, highly replicable spatial patterns called spatial domain states [43]. The spatial pattern of each FD evolves with a broad spectrum of how closely associated regions are to the FD, from strong association to complete dissociation over time. Figure 2(B) shows examples from [43] in which hot and cold colors represent positive and negative associations and gray represents complete dissociation of the regions with FDs at different states [43]. Interestingly, different FDs show different levels of spatial variation over time [43], which was similar with the findings of a previous multi-task fMRI study which investigated variations in functional connectivity among predefined anatomical regions across different tasks [51]. For instance, the frontoparietal and attention domains show the greatest level of changes in the spatial maps over time, and the subcortical domain exhibit the lowest spatial variation over time (Figure 2(B)). Hierarchical spatiotemporally dynamic models may provide new insights into brain disorders, particularly because these models are well-suited to examine the alterations in the brain’s capacity to integrate information. The findings of [43] suggest that patients with SZ show transient reductions in the spatial patterns of several FDs (e.g., the subcortical, attention, and language domains), and the dynamic state-level interaction between FDs are altered [43]. Overall, the findings of [43] suggest the incorporation of spatial dynamics within functional hierarchical models can yield a better understanding of both macro-scale functional hierarchy and brain dynamism, which emphasizes a direction ripe for further improvements and investigation in this area. This category benefits significantly from a better estimation of FUs, meaning future work should allow FUs to vary spatially over time, which is a major limitation of [43].

Figure 2.

A dynamic hierarchy model. (A) A toy example of the hierarchical model used in [43] to evaluate spatially dynamic properties of functional domains (FDs). An FD is a formation of functionally linked (temporally covarying) functional units (FUs), and each FU is defined as a pattern of regions with highly similar functional activity (high functional homogeneity). FUs form the lowest level of a hierarchy model, and their estimations are limited by the spatial and temporal resolution of the data. For fMRI and many other imaging modalities, FUs and functional hierarchies can only be reconstructed at macro-scale levels. The findings showed that FDs evolve spatially over time, and the spatial patterns of each FD can be summarized into a set of recurring, highly replicable spatial patterns called spatial domain states. The states of the default mode domain have been illustrated. (B) depicts examples of the spatial variation(s) of functional domains over time. The spatial variation of FDs over time include a broad spectrum of changes in regions’ membership to FDs from strong association to a given FD to complete dissociation. Iraji et. al. [43] explicate the spatial dynamics of FDs by evaluating the changes in anatomical regions’ membership to FDs at different states. The chart represents the regions associated with the frontoparietal and subcortical domains at different spatial domain states, reported in [43]. Hot and cold colors represent positive and negative associations, and gray represents complete dissociation of the regions at the states. t-value indicates the strength of the regions’ association to FDs. “Variability index” was defined as the standard deviation of a region’s association to an FD to evaluate the level of spatial variability for each FD [43]. The total number associated regions and the mean and standard error of variability index are listed above each chart indicating the level of spatial variation in each FD. Iraji et. al. [43] reported that different FDs have different levels of spatial dynamics, where the frontoparietal and subcortical domains have the highest and lowest changes in the spatial maps over time. Figure modified and reprinted with permission from [43].

An improvement in estimation of FUs can also be implemented by increasing the spatial granularity of FUs, for instance by using ultra-high independent components analysis [52]. Another important improvement is to capture both spatial and temporal dynamics across several levels of the functional hierarchical models (a multi-level, spatiotemporally dynamic, functional hierarchy). Allowing transitory associations between the elements of different levels of the hierarchy over time would also achieve more realistic, data-based approximations of spatial fluidity and spatiotemporal dynamic properties. One possible implementation of this would be to allow FUs to change their membership to FDs over time. Finally, merging blind-source and network/graph theoretical modeling would considerably improve our perception of spatiotemporal dynamics of functional brain hierarchies.

Spatial Dynamics and a Time-Resolved Analysis

In one of the first published works, Kiviniemi et al. used sliding-window approach with a relatively long window length (108 seconds) and ran separate ICA (i.e., windowed ICA) subsets of data over time [40]. Although the large window length can filter out high-frequency variations, the result showed variations in the spatial pattern of the DMN over time (Figure 3(A)). Interestingly, the spatial similarity of successive the DMN patterns presented a power spectral 1/f frequency distribution. Next, Ma et al. [41] suggested using independent vector analysis (IVA) instead to capture the spatial variation of underlying sources. IVA maximizes independence among underlying matched sources across the datasets, while also considering the dependency of each source across datasets [53–55]. By considering data from each time window as a separate dataset for IVA, Ma et al. [41] were able to capture the spatial dependency of each source across time windows and subjects (Figure 3(B)). Compared to the windowed ICA [40], the windowed IVA [41] overcomes the need for source matching across time windows and allows tracking of their spatial variation over time. Moreover, using the full dataset improves the ability of the windowed IVA [41] to estimate the sources from short records of data and alleviates the issue with low SNR in the windowed ICA [40]. Comparison between healthy controls and patients with SZ suggests that certain spatially dynamic properties might be sensitive to brain conditions [41]. For instance, the results indicate that patients with SZ compared to healthy controls showed overall higher spatial variation particularly in the source distributed in the temporal lobe. Although IVA is attractive for jointly capturing spatial and temporal variations, its performance becomes increasingly limited as the number of datasets grows due to the curse of dimensionality. Bhinge et al. proposed an adaptively constrained IVA approach that alleviates this issue by limiting the size of the solution space while still capturing spatiotemporal variations in large datasets [42]. This provided an improvement for capturing time-varying spatial patterns using IVA in large datasets studies but imposes constraints that could result in underestimating the spatial dynamic properties that exist in the data.

Figure 3.

(A) An example of single-window independent component analysis (windowed ICA) for a given individual. (Top) The default mode network (DMN) calculated by applying ICA on single windows at different time points. (Bottom) Mean and standard deviation (SD) of z-score maps for the same subject. The finding suggests that the spatial map of the DMN fluctuates markedly over time. Figure modified and reprinted with permission from [40]. (B) The schematic of windowed independent vector analysis (IVA) to estimate the time-varying spatial patterns and time courses over time. The data of each individual are partitioned into L time windows and treated as one input dataset for IVA. The spatial maps of a given source component vector (SCV) are related over the time windows and across individuals but can be distinct from the spatial maps of all other components (Both within each subject and across subjects). Figure modified and reprinted with permission from [41].

In the same category (spatial dynamics and a time-resolved analysis), we recently proposed an approach sensitive to spatial variation across time windows to the maximum extent without any constraint in the spatial variability [39]. The approach does not require source matching across datasets and is also computationally inexpensive, which makes it suitable for large datasets analysis. The general steps of the proposed approach include: 1) estimating the temporal patterns of sources (a) from BOLD signals (x) and 2) calculating their spatial patterns (S) at any given time window using a and x. Various mathematical methods can be used in the two steps of this approach to estimate temporal and spatial patterns of sources. For example, [39] focused on estimating spatial dynamics of large-scale networks as sources of interest. In [39], low-order spatial ICA was used to obtain the temporal pattern of large-scale networks, and the spatial patterns of networks at each time window were calculated using temporal correlation. While different choices of methods are available for each step, one should choose methods based on their goals and hypotheses and considering the assumptions and limitations of methods. For instance, spatial ICA estimates temporal patterns of sources, while considering averaged (static) spatial patterns for sources. This can average out some of the spatial variation that exists in the data. Other potential methods are principal component analysis (PCA) [56], probabilistic functional mode decomposition [57], and temporal ICA [58, 59]. For the second step, [39] used temporal correlation to fully capture the association of a given voxel to each individual brain network without regard to its contribution to other networks. An alternative method can be using multivariate analyses, such as multiple linear regression, to estimate the contribution of each voxel to a given source while controlling for the contribution of other sources. However, such an approach may regress away true associations and requires a larger time window compared to Pearson correlation to achieve stability (small standard error). Computationally inexpensive approaches that combine two steps to simultaneously estimate temporal activities and spatial maps of sources without imposing any constraint on spatial or temporal patterns of sources can be one intriguing area of future research.

Focusing on a spatially fluid chronnectome, [39] shows that brain networks evolve spatial over time, and their moment-to-moment spatial reconfiguration explains the broad spectrum of inconsistencies in previous spatially static studies [39]. For instance, different spatial patterns for the DMN that have been observed within the spatially static literature were identified as different spatial states of the DMN, suggesting only overall patterns of the DMN during data acquisition are identified in a static analysis (Figure 4(A)) [39]. Spatially dynamic analysis also suggests that brain networks are heavily enmeshed with each other, transiently merging and separating, highlighting the brain’s dynamic segregation and integration [39]. The transient role of the cerebellum in various networks is another interesting finding [39]. The findings of [39] further show the additional information that spatially dynamic analyses can provide on brain disorders by evaluating a large multi-site dataset of healthy controls and patients with SZ [39]. The spatially dynamic analysis identifies robust and nuanced alterations of the SZ brain that were not detected using previous analytical approaches [39]. In general, the results in [39] indicate that clinically relevant alterations in the spatially dynamic properties are significantly more pronounced than those in static functional connectivity (e.g. Figure 4(B)), suggesting the higher sensitivity of spatially dynamic analyses to detect brain alterations associated with brain disorders. Furthermore, Iraji et. al. [39] introduced examples of spatial dynamic measures (metrics) to capture the information of brain function that can be only obtained by incorporating space in dynamic analysis [39]. For instance, the “spatiotemporal transition matrix” captures and summarizes the voxel level information of the spatially dynamics of each brain network and reveals very distinct patterns between two groups across various brain networks (e.g. Figure 4(C)). Spatiotemporal uniformity is another unique feature which can only be measured by incorporating space in dynamic analyses [39]. Spatiotemporal uniformity was significantly different in patients with SZ across various networks and reveals significant associations with cognitive domain scores highlighting the potential cognitive relevance of the proposed spatial dynamic measures (Figure 4(D)). Overall the findings of [39] strengthens the earlier findings in [41] and [43] suggesting spatial dynamics can unveil typically overlooked features of the dynamic brain which are likely to be affected by the pathophysiological aspects of schizophrenia.

Figure 4.

Findings of a spatially fluid chronnectome study [37]. (A) The spatial states of the default mode network (DMN), each representing a different spatial pattern for the DMN. Results also reveals different anti-correlation patterns for the DMN. Hot and cold colors represent positive and negative associations to the DMN, respectively. Sensorimotor areas are anti-correlated with the DMN during State 2, and the salience network is anti-correlated with the DMN during State 4. Importantly, States 1 and 3 do not exhibit an anti-correlative relationship with the DMN. (B) Examples of voxel-wise statistical comparisons between healthy subjects and patients with schizophrenia (SZ). Hot and cold colors represent higher and lower associations of regions to the networks in patients with SZ relative to healthy subjects, respectively. For the subcortical network, the same patterns of alterations were observed in both spatial static and spatial dynamics. However, the areas of alterations were larger in spatial dynamics analysis suggesting higher sensitivity to detect abnormalities brain functional connectivity. Moreover, while the static analysis did not reveal any significant differences in the somatomotor network, spatial dynamic analysis detects statistically significant differences in the somatomotor network among patients with SZ. (C) Examples of spatiotemporal transition matrices and statistical analysis for the somatomotor network. The spatiotemporal transition matrix for each network (source) summarizes its voxel level spatial dynamic information [39]. The spatial pattern of a given source at each time window is calculated as the dynamic coupling map (dCM). The values of the dCMs are discretized into ten bins, and for each voxel, the number of transitions between bins is noted. The value in each array of the matrix indicates the percentage of the transition compared to the total number of transitions using warm colors. For instance, if the number of transitions were uniform, the value of each array would be 1% because there are 100 arrays in the transition matrix. (Right) t-statistics for group comparisons by diagnosis. Blue (cold) and red (hot) colors represent lower and higher transition values in patients with SZ compared to healthy subjects, respectively. (D) Energy index was calculated to evaluate spatiotemporal uniformity, with greater spatiotemporal uniformity towards the center of the chart. The energy index was measured for the spatiotemporal transition matrix and compared between healthy subjects and patients with SZ. Blue and red colors represent healthy subjects and patients with SZ, respectively. Green asterisks indicate the statistically significant differences between the two groups. Attention (ATN), default mode (DMN), cerebellar (CER), auditory (AUD), secondary visual (VisSec), primary visual (VisPri), subcortical (SUB), salience (SN), right and left frontoparietal (RPFN and LPFN), language (LANG), somatomotor (MTR) Networks. Figure modified and reprinted with permission from [37].

Concluding Remarks and Future Perspectives

Neuroimaging research, fMRI studies in particular, has been shifting rapidly toward studying brain dynamism from the perspective of the temporal reconfiguration of brain functional connectivity. We suggest the incorporation of spatial dynamics into brain functional analyses is a promising avenue for understanding the mechanisms and clinical implications of brain dynamism. However, this broad, but still emerging area is still in the very early stages and will make a greater contribution as a continued focus yields improved methods and replicable findings (see Outstanding Questions). One important differentiating factor in spatially dynamic analyses is the extent to which the analytical tools use spatial information and properties. Dynamic approaches can directly utilize the spatial properties, such as distance or direction, when identifying dynamic patterns, or they can evaluate the spatially dynamic behaviors using spatial statistics. Some examples include studying spatial properties and patterns like spatial diffusivity, spatial fluidity, spatial interactions, spatial dependency, and spatial expansion and contraction of the source over time. Among all spatial dynamic properties, temporal variations in spatial coupling and voxel coupling are probably the most straightforward properties that will benefit from investigations. Spatial coupling is defined as similarity between two spatial patterns, and voxel coupling describes the similarity of the contributions of two voxels to sources. If we model the spatial patterns of sources by a matrix variate normal distribution (see Box 1), spatial and voxel couplings are captured as Σ_γ(t) and Ψ_γ(t) matrices. Σ_γ is an n_l × n_l matrix in which element (i,j) indicates the similarity between the spatial patterns of source i and source j (the dependency of voxels between two sources), also known as spatial coupling. Ψ_γ is n_v × n_v matrix in which element (i,j) indicates the similarity between source contributions to voxel i and voxel j (the dependency of spatial patterns of sources between voxels), called voxel coupling.

Outstanding Questions.

• Are the existing dynamic models and mathematical tools sufficient to capture the complexity of brain function changes in both space and time? What new approaches are needed?

• What are the neuronal origins and the neurophysiological bases of spatiotemporally dynamics? Can evidence be found from other imaging modalities?

• How does the brain dynamically reconfigure itself at different spatial and temporal scales? Will evaluating spatial and temporal dynamic properties within and between different levels of brain functional hierarchy provide answers?

• Can spatially dynamic properties characterize individualized information, such as fingerprinting, and provide improved characterization of heterogeneity between individuals? Are there any diseases or disorders that are linked to specific to aspects of the spatial chronnectome, and are there any spatial dynamic properties which can be used to improve diagnostic accuracy or personalized treatments?

Another interesting direction of spatially-focused research is the inclusion of spatially varying nodes in graph-based and connectomic analyses. Graph-based approaches can characterize the brain connectivity profile using a wide range of graph measures and mathematical tools such as measuring interconnected local communities and the global efficiency of communication to assess functional integration and segregation. However, the validity of graph-based models depends on the extent to which nodes and edges represent the true underlying sources [60]. Particularly, the correct identification of nodes is very crucial because the validity of fMRI studies requires comparing functionally homologous regions with themselves [61]. In other words, the findings of graph-based models are not valid if nodes do not represent the same sources (see “Utilizing Spatially Fixed Nodes/Seeds and Dynamics” for more details). Incorporating spatially varying nodes also enable us to leverage the advanced mathematical tools and concepts from network science and graph theory to study the spatially dynamic properties of the brain. While the proposed framework is used to categorize different dynamic behaviors of temporal synchrony, the same concepts can be extended to study rich brain dynamics from the perspective of neural activity. For instance, it would be interesting to differentiate between several spatiotemporal dynamic patterns may exist in the activity propagating patterns[7, 21–24]. Dynamic models of the brain that focus on spatial properties, such as propagating waves, that are defined over a spatial continuum also offer new insights into mechanisms of the brain’s adaptivity and functional organization[25, 62, 63].

In addition, while time-varying functional studies primarily focus on changes in joint first-order pdfs, higher-order pdfs can potentially provide more information about brain dynamism. As the neighborhood time points are not totally independent (e.g., given slow hemodynamic response in fMRI), a model which takes the dependency between measurements into consideration can provide additional information about brain dynamism. While ICA has been used often in previous studies to evaluate spatial dynamic properties, future work would benefit significantly from application of other analytical approaches including neuronal field model, graph analysis, time-frequency analysis, and deep learning approaches. One should be aware of different assumptions and limitations of each technique. Another recent approach to study spatially dynamic behavior is multi-fractal analysis [64]. And finally, evaluating the links between spatially dynamic measures and multimodal data (e.g., structural MRI) is another promising and understudied area [65]. One interesting direction is structurally-informed dynamic modeling approaches that leverage the structural connectivity profile in dynamic modeling to study brain dynamics [29, 62].

Highlights.

• One of the most fundamental question of neuroimaging studies is how the measurements of imaging modalities represent (model) underlying neural activity and integrative brain function.

• Recently, there is a growing interest in modeling whole brain dynamic connectivity (i.e. the chronnectome). However most efforts are limited to variations in temporal activity of networks and/or regions and changes in temporal coupling between them. There is a need for more realistic brain models that include spatial and temporal properties of brain dynamism.

• We introduce a framework to explicitly incorporate space into dynamic analyses. Preliminary results provide strong evidence that spatially dynamic analyses reveal missed information about brain functional architecture and unveils new patterns of alterations in patients with schizophrenia, suggesting a promising avenue to reveal patient-specific dynamic signatures for this and other brain disorders.