The interrelationships between pathological processes and emerging clinical phenotypes in Alzheimer's disease (AD) are important yet complicated to study, because the brain is a complex network where local disruptions can have widespread effects. Recently, properties in brain networks obtained with neuroimaging techniques have been studied in AD with tools from graph theory. However, the interpretation of graph alterations remains unclear, because the definition of connectivity depends on the imaging modality used. Here we examined which graph properties have been consistently reported to be disturbed in AD studies, using a heuristically defined “graph space” to investigate which theoretical models can best explain graph alterations in AD. Findings from structural and functional graphs point to a loss of highly connected areas in AD. However, studies showed considerable variability in reported group differences of most graph properties. This suggests that brain graphs might not be isometric, which complicates the interpretation of graph measurements. We highlight confounding factors such as differences in graph construction methods and provide recommendations for future research.
Alzheimer's disease (AD) is a progressive, disabling neurodegenerative disorder that accounts for approximately 50%–80% of all dementia cases. AD is histopathologically defined by the presence of amyloid-β plaques and tau-related neurofibrillary tangles. These plaques and tangles have been associated with local synaptic disruptions, suggesting that AD is a dysconnectivity disease (Arendt, 2009; Blennow et al., 1996; Delbeuck et al., 2003; Takahashi et al., 2010). At later stages of the disease, cortical atrophy progresses in an orderly fashion from subcortical structures such as the hippocampus into associative cortical areas and finally primary sensory areas (Braak and Braak, 1991; Jack et al., 2010). These observations suggest that specific cortical areas are vulnerable for AD pathology, which may determine how the disease propagates along specific paths in a network. If AD is indeed a dysconnectivity disease then this can only be captured with a network approach, because the structural elements of the brain form an intricate network at different spatial scales (ranging from neurons to anatomical regions) from which functional dynamics emerge. Local disruptions in such complex networks can have unpredictable and widespread effects (see e.g., Gratton et al., 2012).
Graph theory provides tools to concisely quantify the properties of complex networks that describe interrelationships (represented by edges) between objects (represented by nodes; see Section 2 for an explanation of graph theoretical concepts). It has been proposed that a detailed understanding of structural connectivity between cortical areas (i.e., the ‘human connectome’) will provide a mechanistic understanding of the dynamic function that can emerge (Sporns et al., 2005). Graph theory offers at least 2 important advantages in comparison with other network approaches. First, it provides for each node quantitative measurements that incorporate connectivity information from the complete network, reflecting the integrated nature of local brain activity. For example, hubs can be defined as nodes that make information processing in a graph more efficient and increase a network's robustness to random failure (Albert et al., 2000; see section 2). However, such nodes are also bottlenecks, because the loss of a hub is likely to fragment a network into disconnected parts. Interestingly, hubs have been associated with epidemic transfer, and might therefore be important to study how a disease propagates in a network (Paster-Satorras and Vespignani, 2001).
A second advantage of graph theory is that it provides a general language that enables direct comparison of graphs that describe different types of data (e.g., functional connectivity vs. anatomical connectivity). For these reasons, graph theory seems to be a promising framework to disentangle how various pathological processes in AD, such as spatial patterns of cortical atrophy and functional disruptions, are associated with each other and why the disease propagates along specific routes.
Up to now graph theory has been mainly used to describe brain graphs that were obtained with anatomical, morphological, and functional neuroimaging techniques, because a detailed a description of the human connectome is difficult to obtain (for reviews see Bassett and Bullmore, 2006; Bullmore and Bassett, 2011; Bullmore and Sporns, 2009, 2012, 2013; Stam and Reijneveld, 2007). It has been argued that if graphs constructed from different imaging modalities reflect true brain connectivity, they should have corresponding network topologies. Yet, it is still an open question whether connectivity as defined across neuroimaging modalities measure the same underlying construct (although associations across modalities have been reported: Gong et al., 2012; Honey et al., 2007, 2009).
Recently, brain networks in AD have been investigated by applying the theoretical framework of graph theory to neuroimaging data (Çiftçi, 2011; de Haan et al., 2009, 2012b, 2012c; He et al., 2008; Li et al., 2012; Lo et al., 2010; Sanz-Arigita et al., 2010; Stam et al., 2009; Supekar et al., 2008; Tijms et al., 2013; Yao et al., 2010; Zhao et al., 2012. For AD-specific reviews see: He et al., 2009; Xie and He, 2012; and for neurodegenerative diseases in general, see: Greicius and Kimmel, 2012). Importantly, these studies have reported altered local and global graph properties in AD, supporting the clinical relevance of brain graphs. However, the interpretation of ‘disturbance’ might be ambiguous, because the definition for connectivity depends on the imaging modality used.
It could be hypothesized that if brain graphs are robust across neuroimaging modalities and of an isometric nature, then group differences in graph measurements between AD and control subjects should converge across studies. Here we investigate this question by reviewing graph studies in AD and we will introduce a heuristically defined graph space to investigate which theoretical models best explain converging network alterations.
