Brain Connectivity and Network Analysis in Amyotrophic Lateral Sclerosis

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease with no effective treatment or cure. ALS is characterized by the death of lower motor neurons (LMNs) in the spinal cord and upper motor neurons (UMNs) in the brain and their networks. Since the lower motor neurons are under the control of UMN and the networks, cortical degeneration may play a vital role in the pathophysiology of ALS. These changes that are not apparent on routine imaging with CT scans or MRI brain can be identified using modalities such as diffusion tensor imaging, functional MRI, arterial spin labelling (ASL), electroencephalogram (EEG), magnetoencephalogram (MEG), functional near-infrared spectroscopy (fNIRS), and positron emission tomography (PET) scan. They can help us generate a representation of brain networks and connectivity that can be visualized and parsed out to characterize and quantify the underlying pathophysiology in ALS. In addition, network analysis using graph measures provides a novel way of understanding the complex network changes occurring in the brain. These have the potential to become biomarker for the diagnosis and treatment of ALS. This article is a systematic review and overview of the various connectivity and network-based studies in ALS.


Introduction
Amyotrophic lateral sclerosis has an incidence of around 3/ 100,000. No definite etiology has been determined even though various genetic and environmental factors have been attributed [1]. ALS is mostly sporadic, but 5-10% of cases can be familial [2]. ese are associated with SOD1, C9ORF, and other gene mutations that are still being identified. Postmortem studies have shown ALS to be a degenerative disorder of the anterior horn cells in the spinal cord and the cortical neurons, primarily in the motor cortex. e death of the neuronal cell body leads to degeneration of its axons and tracts leading to progressive disability and death [3][4][5]. In addition to axonal degeneration, there is hyperexcitability of surviving neurons and their networks. Loss of inhibitory neurons, increased glutamatergic activity, and functional reorganization secondary to increased compensation may underlie these changes [5][6][7]. In addition, interhemispheric inhibition is also impaired in ALS resulting in mirror movements [8]. e pattern of disease onset and rapidity of spread are highly variable. Progression ultimately results in respiratory failure and death, despite artificial means of life support. ALS is part of a spectrum of motor neuron disorders that includes frontotemporal dementia, primary lateral sclerosis, progressive muscular atrophy, and progressive bulbar palsy.
Due to the lack of biomarkers, it is often difficult to diagnose ALS in the early stages of the disease. Misdiagnosis is very common, and patients often go through various expensive and invasive tests before the condition declares itself. Even if diagnosed early, there are too few treatment options if any and that too only in prolonging life for a few months. e lack of biomarkers poses a big hurdle in monitoring response to novel treatments in ALS research.
e role of imaging findings as potential biomarkers gains importance in this scenario. Many structural and functional imaging studies have been performed over the years to assess their utility in ALS. ere are no validated measures for clinical use yet. Newer studies using brain connectivity and network analysis look at the brain from a broader perspective as a connected network and have the potential to generate biomarkers for ALS.
is article highlights the advances in imaging and electrophysiologic techniques to diagnose, assess severity, and predict the progression of ALS based on connectivity parameters and brain network analysis.

Methods
is article is a literature review of brain connectivity and network analysis studies in ALS (Table 1). Search Terms "ALS" and "Brain Connectivity" yielded 117 articles in Medline. Sixty ALS-specific human studies measuring connectivity and network analysis in ALS were selected for this article (see Figure 1). e article also provides a primer on routine and specialized imaging in ALS, connectivity analysis, and generation and interpretation of networks using graph measures.

Clinical Imaging in ALS.
Routine imaging studies done as part of clinical workup in ALS include CT scan and MRIs. e utility of the CT scan is limited to identifying focal or global atrophy of the brain and ruling out other pathologies or space-occupying lesions. MRI sequences used for clinical purposes include T1 and T2 weighted sequences, diffusion, and FLAIR images. Rarely, hyperintensities on FLAIR sequences are seen over the motor cortex in ALS patients that at times can be symmetric [9]. While useful as an additional diagnostic finding, these imaging abnormalities are rare and do not have any intrinsic value by themselves in the diagnosis or monitoring of ALS. e high-resolution anatomical MRI images can be further analyzed using voxel-based morphometry (VBM) or surface-based analysis to compute gray matter volumes (GMV). GMV loss is seen in motor and temporal cortices in ALS and frontotemporal dementia (FTD) patients [10]. A compensatory increase in volume in the cerebellar volume has also been reported [11].

Research Imaging in ALS.
ere are over 100 billion neurons in the brain that are interconnected through trillions of networks. Such levels of complexity are not measurable by histology or the current level of technology. Instead, imaging techniques such as fMRI, DTI, PET scan, and fNIRS and electrophysiologic techniques such as EEG and MEG can help us generate macroscale representations of these neuronal networks. With advances in imaging techniques, machine learning techniques, and large-scale studies such as the Human Connectome Project, it may become possible for us to define these connections in finer details. Several brain connectivity studies have been done in ALS with some important and promising findings. However, results have varied and at times contradicted functional connectivity studies. Most studies in ALS have been multimodal with structural studies using high-resolution anatomical MRI and diffusion imaging for white matter tracts and functional connectivity studies using fMRI, EEG, PET, fNIRS, and MEG. e two most commonly used techniques are diffusion imaging and fMRI, which will be described further.
Connectivity studies can be based on structural or functional connectivity. Structural connectivity defines the anatomical connectivity between different regions of the brain. Typically, white matter tracts are defined using diffusion tensor imaging. Anatomical correlates can also be done using anatomical images and surface-or voxel-based techniques. Functional connectivity on the other hand establishes the electrophysiologic or metabolic functional correlates between different regions of the brain. EEG, PET scan, and time series correlates of fMRI data are used for this purpose.

Diffusion
Imaging. Diffusion imaging captures the spatial diffusion of water molecules along the axonal white matter tracts in different spatial directions assuming a Gaussian distribution. Tensor-based analysis along white matter tracts can provide us fiber direction, axial, radial, and mean diffusivity as well as fractional anisotropy (FA). If the integrity of the myelin sheath is preserved, the fractional anisotropy and axial diffusivity are high, while the radial diffusivity is low. FA is reduced in conditions such as ALS where there is axonal degeneration.
Tractography, by fiber propagation, can generate a visual representation of white matter tracts that can then be further quantified. Deterministic tractography and probabilistic tractography are the two common techniques for generating the tracts. Deterministic tractography uses a set number of seed regions and parameters for propagation in a local fiber direction until a threshold is met for termination. Probabilistic tractography on the other hand takes into consideration propagation in any random direction. Both techniques have pros and cons. Newer techniques such as Q-space imaging may further improve the tracking of fiber bundles bypassing tissue edema and crossing fibers that are limitations of traditional DTI ( Figure 2) [12,13]. Preliminary studies using this technique have shown promising results in ALS that can quantify changes in white matter track volume during interval scans using a track difference paradigm [14,15].
Once tracts are identified, network models can be generated for white matter connectivity. Tract disruptions in ALS are expected in the corticospinal tracts and corpus callosum, but a variety of other non-motor tracts and networks can be affected. Tract-based spatial statistics (TBSS) studies have shown reduced fiber density and reduced mean diffusivity along several white matter tracts in ALS [16][17][18][19].
Diffusion tensor imaging studies have consistently shown reduced fractional anisotropy of the corticospinal as well as non-motor tracts for both sporadic and familial ALS [18]. Large studies have also shown a correlation between FA values of corticospinal tracts (CST) with ALS Functional Rating Scale (ALSFRS scores) [20,21]. Structural connectivity disruptions in the frontal lobe have also shown correlation with cognitive dysfunction in ALS patients [22]. Patients with a C9orf72 mutation showed widespread gray and white matter involvement at baseline and extensive loss of white matter integrity in the connectome over time. In C9orf72negative patients, there was cortical thinning of motor and frontotemporal regions and loss of white matter integrity of connections linked to the motor cortex.  Decreased spectral power in the occipital and temporal (δto β-band), lateral/ orbitofrontal (δ-to θ-band) and sensorimotor (β-band) regions of the brain in patients with ALS. Furthermore, we show increased comodulation of neural oscillations in the central and posterior (δ-, θ-, and cl-band) and frontal (δand cl-band) regions, as well as decreased synchrony in the temporal and frontal (δ-to β-band) and sensorimotor (β-band) regions.
Precentral degeneration and cerebellar compensation in amyotrophic lateral sclerosis: a multimodal MRI analysis Qiu et al., 2019 [11] 60 ALS and 60 controls sMRI, fMRI, and DTI: Gray matter volume (GMV), white matter FA, and functional connectivity (FC) Compared with healthy controls, patients with ALS showed decreased GMV in the left precentral gyrus and increased GMV in bilateral cerebellum, decreased FA in the left corticospinal tract and body of corpus callosum, and decreased FC in multiple brain regions, involving bilateral postcentral gyrus, precentral gyrus, and cerebellum anterior lobe, among others. Regional dynamics of the resting brain in amyotrophic lateral sclerosis using fractional amplitude of low-frequency fluctuations and regional homogeneity analyses Bueno et al., 2019 [88] 20 ALS and 11 controls fMRI: fractional amplitude of low-frequency fluctuations (fALFF) and regional homogeneity (ReHo) Decreased fALFF and ReHO in ALS patients compared with HC in widespread cortical regions including motor and sensory regions.  fMRI and DTRI: Voxel mirrored homotopic connectivity (VMHC) and probabilistic fiber tracking that quantifies functional connectivity between each voxel in one hemisphere and its mirrored counterpart in the opposite hemisphere Extensive reductions of VMHC associated with ALS in brain regions of the precentral and postcentral gyrus, the paracentral lobule, the superior temporal gyrus, the middle cingulate gyrus, the putamen, and the superior parietal lobules. With DTI, the analysis has also revealed reductions of interhemispheric structural connectivity through the CC subregions II, III, and V in patients with ALS. Additionally, interhemispheric functional connectivity of the bilateral precentral gyri positively correlated with fractional anisotropy values of the CC subregion III, which structurally connects the bilateral motor cortices. In ALS patients, significant regional activity alterations in the left primary motor cortex (M1), the left primary somatosensory cortex (S1) and the right supplementary motor cortex (SMA) are found. Among these regions, spectral DCM revealed a missing closed-loop circuit between the left M1 and the right SMA and lost projection from the right SMA to the left S1 in ALS.  Cross spectral density in the alpha band was higher in patients. In ALS patients, increased degree values of the network nodes were noted in the central and frontal regions in the theta band across seven of the different connectivity maps, among patients, the clustering coefficient in alpha and gamma bands was increased in all regions of the scalp and connectivity were significantly increased (p � 0.02). e nodal network showed increased assortativity in the alpha band in the patients group. e clustering coefficient in partial directed connectivity (PDC) showed significantly higher values for patients in alpha, beta, gamma, theta, and delta frequencies.

Neurology Research International
Metabolic spatial connectivity in amyotrophic lateral sclerosis as revealed by independent component analysis

Functional MRI.
Functional MRI (fMRI) measures the changes in regional blood flow during resting or task activation. It uses the blood-oxygen-level-dependent (BOLD) contrast. As regional metabolism causes a shift from oxyhemoglobin to deoxyhemoglobin, there is a change in magnetization properties of blood that can be assessed using MRI. is can be a surrogate for local metabolism and neurovascular coupling [23]. It can also determine regions connected by similar metabolism during rest or activity, helping determine the interconnectedness of various regions using a time series analysis. Connectivity maps and network architecture can be then generated similar to structural connectivity.

Graph Theory and Brain Networks
Graph theory is a concept that is being increasingly applied to analyze complex brain networks [24]. is concept was first used by Leonard Euler in 1736 to solve the "Konigsberg Bridge" problem. Konigsberg city, which is now Kaliningrad in Russia, is set on both sides of the Pregel River. is created a mainland separated by two islands connected with seven brides. Euler was tasked to conceptualize a walkway throughout the landmasses that interconnected them in such a way that pedestrians needed to cross each bridge only once. Euler made a representation of each landmass as a node and the bridges connecting them as edges. Using early graph theory concepts, he proved that it was not possible to create such a walkway. Various network measures have since been defined to analyze and characterize network architecture. In the modern era, with the developments of transportation networks, the World Wide Web, and social networks, network-based studies became relevant again, and later, its adaptation to neuroscience as the brain is a highly complex network.
Networks consist of nodes and edges. Edges can have directions (directed or undirected) and densities (weighted or unweighted). A simple binary unweighted, undirected graph architecture and various measures are depicted in the graph shown in Figure 2. Graphs can also be depicted using an adjacency matrix that depicts the connections between nodes and edges. It can also be represented in 3D models or 2D connectograms (Figures 3-5).
Brain networks can be created if we parcellate regions of brains into nodes and their connection as edges. Nodes could be anatomical regions, sites of electrode placement, or regions of interest and the "edges" derived from white matter tracts, electrical, hemodynamic, or metabolic connections or time series correlates connecting those nodes. High-resolution structural MRI images are generally used for nodes. Brain regions can be segmented into gray and white matters and then parcelled into distinct regions using anatomical atlases. Various atlases are available that can subdivide the cortical and subcortical regions anywhere from tens to as high as thousands of nodes.
Edges are generated from structural or functional connectivity parameters. Functional connectivity is generally assessed using fMRI time-series data from one region that correlates with other regions in terms of BOLD activity. is could be resting or dynamic. Structural connections are usually derived from diffusion imaging. e diffusion images are corrected for susceptibility and eddy current distortions. White matter edges can be generated using tractography techniques as described earlier.
Once the nodes and edges are defined, networks can be generated and a variety of graph measures are then applied to understand the brain architecture and its disruptions ( Figure 4). Network-based statistical analysis can help individual or group of subjects [25]. Large-scale projects such as the Human Connectome Project can provide network databases and templates against which various disease processes could be compared and help understand the network derangement in a variety of diseases [26].    ere are some complex graph measures as shown in (Figure 4). Clustering coefficient is the fraction of triangles around a node and is equivalent to the fraction of the node's neighbors that are neighbors of each other. It is a measure of nodes clustering together. Transitivity measures the probability that the adjacent nodes of a particular node are connected and is closely related to the clustering coefficient. It is calculated as a ratio of the observed number of closed triangles and the maximum possible number of closed triangles in the graph. High transitivity and low path lengths are characteristics of a small-world network. Diameter of a graph refers to the distance towards the maximally eccentric node and radius refers to the minimum eccentricity. e efficiency of a network refers to interconnectedness in a graph network. It can be global or regional. Global efficiency is inversely related to the path length in a network. Assortativity is a measure of similar nodes to be connected. Rich club coefficients refer to well-connected nodes that connect to each other.

Connectivity Studies.
Brain connectivity studies have utility in analyzing the anatomical and functional derangement in ALS [27]. ey have the potential to become biomarkers for ALS [28,29]. Longitudinal studies can define the evolution of structural and functional derangements and help us understand the underlying pathophysiology and progression of ALS [30].
Structural connectivity studies have unequivocally shown reduced fractional anisotropy along the motor and non-motor tracts [31][32][33][34]. e sites and degree of structural connectivity disruption have correlated with the rate of disease progression [35,36]. Intra-and interhemispheric connectivity is also deranged in ALS [8,20,37]. is also holds true for genetic ALS with C9ORF mutations [18,38,39]. Local connectivity and network parameters vary between different types of motor neuron disease. Primary lateral sclerosis (PLS) and progressive muscular atrophy (PMA) can have differing patterns that can be helpful in identifying the subtype [40].
In contrast to structural connectivity studies, functional connectivity studies have shown differing results with some studies showing lowered and others showing increased functional connectivity in ALS, whether it be sporadic or genetic [41][42][43]. e pattern of reduced and increased functional connectivity in various regions of the brain also differs significantly. Patients with ALS were found to have reduced short-range functional connectivity density in the primary motor cortex and increased long-range connectivity in the premotor cortex [44]. Multimodal studies using anatomical (sMRI), diffusion (DTI), and resting fMRI scans have shown that the more structurally impaired networks overlapped with more functionally impaired connections [45]. Voxel mirrored homotopic interhemispheric connectivity of structural and functional networks involving the corpus callosum has shown reduced functional connectivity [46]. Decreased functional connectivity has been reported in the premotor cortex, corpus callosum, hippocampus, and cerebellar regions [11,[47][48][49][50][51][52]. In contrast to these findings, more studies have shown increased functional connectivity in ALS patients, even in regions with reduced structural connectivity [40,[53][54][55][56][57][58]. Dynamic connectivities of default motor networks and sensorimotor networks have increased connectivity in ALS [59]. Functional MRI (fMRI) studies using motor task activation have shown increased activation clusters in ALS patients compared to controls for the same task. Higher activation was seen in the prefrontal cortex in ALS patients compared to controls [60][61][62][63]. Such hyperconnectivity has been the predominant finding in studies using EEG, fNIRS, and MEG, even though some differences were noted here as well [53,[64][65][66][67][68][69]. Such differences in results can be explained by a heterogeneous progression of functional connectivity changes in ALS occurring at different stages of disease evolution when the patients were studied [44]. Functional hyperconnectivity or hyperexcitability may be the result of an intrinsic pathophysiologic process or a compensatory response to weakened musculature. Progressive increase in functional connectivity in frontoparietal and frontostriatal networks has been shown in longitudinal studies [70]. is increase in functional connectivity has also been shown to correlate with the severity of the disease process [67,[71][72][73]. Studies interrogating specific resting-state networks of the brain have identified increased connectivity in the default mode network and reduced connectivity in sensorimotor network at the same time and both these correlated to the severity of the disease process [74,75]. While there are regions of increased and decreased regional functional connectivity in ALS, the global pattern across various studies leans towards increased functional connectivity, suggestive of the hyperexcitable cortex [59].
Despite several different studies, the functional connectivity changes in ALS remain complex and poorly defined. More longitudinal studies are needed to understand the evolution of functional connectivity disruption in ALS.

Network-Based Studies in ALS.
Few studies have looked at network disruption in ALS using graph theory. ese were mostly done using structural MRI (sMRI), fMRI, and DTI. Few EEG, MEG, and fNIRS studies have also been conducted.
Analysis of graph metrics using global measures in C9ORF mutation carriers showed lower global network density than healthy controls [43]. e mean clustering coefficient has been shown to be significantly higher in ALS patients compared to controls [68]. Resting-state functional networks in ALS versus healthy controls using a voxel-level approach showed significant differences in degree centrality in some regions in ALS [71]. e nodal degree in the left superior frontal region has also correlated with the ALSFRS-r scores.
Larger studies using high-resolution T1 weighted anatomical images and structural covariance networks showed significant increases in path length, clustering coefficient, small-world index, and local efficiency in ALS patients. At the same time, there was a significant decrease in global efficiency at several network densities in ALS patients compared to controls. Modularity was higher in ALS patients for several network densities. e modularity increase indicates fragmentation of brain architecture into more tightly clustered modules with poor intermodal communication in ALS patients. Changes were also noted in regional networks and network hubs. Higher functional connectivity strength hubs were seen in ALS patients compared to healthy controls [76]. Nodal betweenness was also increased in several regions in ALS suggesting an increase in information transfer across the available nodes suggestive of an increased "traffic." Significantly different networks connecting various regions of the brain have been found in ALS patients. Such findings are important to identify heterogeneously progressing vulnerable networks in ALS. Structural network analysis of these deranged networks showed reduced local and global efficiency in ALS patients compared to controls [40,77]. Functional network studies in ALS have shown differing results like the functional connectivity studies. Verstraete et al. studied diffusion MRI-derived white matter structural connectome in patients with ALS. Subnetworks of significance were identified using network-based statistics [45,56]. ey detected impaired subnetworks within both motor cortex and distant regions, most of which were involved in motor control. In the impaired networks, they detected low network efficiency and density. A connectivity study done by the same group in ALS showed increased functional connectedness in ALS-affected structural networks [56]. A similar finding of impaired reduced structural connectivity within the prefrontal-motor-subcortical white matter network has been demonstrated using network-based statistics.
Electrophysiologic studies have also been useful in identifying the functional connectivity and network parameters in ALS patients. EEG data in ALS patients showed an increased spectral density of alpha bands. Clustering coefficients in alpha and gamma bands were increased in all regions of the scalp. Overall connectivity was increased in ALS patients with increased assortativity in the alpha band [68]. Resting-state MEG study in ALS also showed increased functional connectivity in the posterior cingulate cortex in ALS patients [53]. Functional network reorganization is perturbed in ALS, which has been shown to correlate with the disability [65,69].
We studied differences in global structural and functional connectivity patterns between eight ALS patients and eight age-matched healthy control data from online sources in a pilot connectivity in ALS (CoALS) study [54]. Global structural measures computed were density, clustering coefficient, transitivity, characteristic path length, small worldness, global efficiency, diameter, radius, assortativity, and rich club coefficients. For functional MRI global efficiency, local efficiency, betweenness centrality, average path length, clustering coefficient, and degree were compared between the groups. Structural network density was found to be significantly lower in ALS patients compared to control subjects ( Figure 5). At the same time, the global functional efficiency was found to be significantly increased in ALS patients compared to control subjects ( Figure 6). Other measures did not differ significantly. is finding is in alignment with our understanding of network architecture breakdown and hyperconnectivity in ALS. Bigger studies are underway to validate these findings and explore the network architecture further.

Conclusion
Brain connectivity and network analysis provide us with a novel and non-invasive approach to trace the progression of highly complex structural and functional derangements in ALS. Connectivity and network measures have shown correlation with disease progression and severity. While structural studies have unequivocally shown degrading connectivity and network architecture, functional studies have differed. ese differences could be related to evolutionary changes occurring in a nonuniform pattern similar to the clinical presentation of ALS. More longitudinal studies are necessary to clarify this process. e studies done so far have indicated a "traffic-jam" type pattern in the brain of ALS patients, where structural "road" networks are disrupted with an increase in functional connectedness or "traffic." is functional interconnectedness and hyperexcitability seem to increase with the disease progression [67]. Whether this hyperexcitability is a response to structural disruption, or an intrinsic pathophysiologic process remains unclear [5,81]. It can be hypothesized that a potential treatment of ALS would be the one that would either stop the structural network degradation or reduce the functional hyperconnectivity or both.
As we become more proficient in characterizing the underlying network changes with more standardized methodologies and automated analysis, we may be able to further characterize the intricate changes occurring in various stages of ALS [29,82]. Vulnerable subnetworks, which are pathways of ALS progression, need to be isolated since those could become potential targets for treatment. Changing excitability of brain tissue using techniques like brain stimulation may be helpful in ALS [83]. Multimodal brain MRI findings using DTI and fMRI have already been proposed to have biomarker value for diagnosis and stratification in ALS [84]. Adding network analysis to these techniques may provide us with additional information to clarify and quantify responses to new and emerging treatments. With further refinements in connectivity analysis and a deeper understanding of the network topology, we may finally be able to define a network fingerprint for ALS that will have great implications in the diagnosis and treatment of ALS.

Conflicts of Interest
e author declares that there are no conflicts of interest.  Figure 6: Averaged functional 2D connectogram and 3D networks of controls and patients (created using CONN Toolbox [80]). While 3D functional connection density appears similar, the pattern difference can be seen on the 2D connectograms. Analysis revealed increased interconnectedness (global efficiency) in ALS patients (not visualized in this picture).