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Published online 10.1148/radiol.11110380 Radiology 2011; 259:317–320 1
From the Division of Neuroradiology, and Alzheimer Disease Imaging Research Laboratory, Department of Radiology, Duke University Medical Center, Box 3808, Durham, NC 27710-3808. Received February 18, 2011; revision requested February 20; revision received February 24; final version accepted February 25. Address correspondence to the author (e-mail:
[email protected]). Potential conflicts of interest are listed at the end of this article. See also the article by Whitlow et al in this issue. q
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Radiology: Volume 259: Number 2—May 2011
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his issue of Radiology features an article by Whitlow et al (1) in which graph theory methods are applied to neuroimaging data to extract information on how the brain is organized. Whitlow et al used resting-state functional magnetic resonance (MR) imaging to show that it is possible to accurately obtain graph theory metrics of largescale brain network connectivity in as little as 2 minutes. Graph theory is a branch of mathematics developed in the 18th century that deals with global and local characteristics of networks, systems modeled as a collection of elements, or nodes linked together by connections. The origin of graph theory is generally credited to Euler’s original publication in 1736, in which he used a graphical representation to show that it was impossible to traverse each of the city of Koningsberg’s seven bridges exactly once and return to the starting point (2). Might such a highly theoretical topic be of interest to only a handful of readers of Radiology? On the contrary, in this editorial I will discuss how the application of graph theory principles to neuroimaging data offers a powerful approach with which to characterize and quantify the large-scale structural and functional networks of the brain. Such an approach enables assessment of both the efficiency of information transfer between different brain regions and the implications of widespread damage or local damage to specific anatomic regions. Most important, however, it may yield information that is qualitatively different from that available with current anatomic or physiologic imaging techniques and therefore might have considerable diagnostic value in the future, particularly as applied to cognitive brain disorders, an area in which conventional imaging tools are limited. Since the time of Euler up to the present day, graph theory has been used as
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a powerful tool with which to model relations and process dynamics in many physical, biologic, and social systems. As recently as 1998, it was recognized that certain common properties were inherent in diverse and efficient networks in nature, such as the neural network of the Caenorhabditis elegans worm, the power grid of the western United States, and the social network of the Screen Actors Guild (3). These networks were labeled small-world networks, a term that came from the small-world phenomenon, more popularly known as six degrees of separation. Until this time, networks had been considered either highly ordered, where adjacent nodes are connected to each other in a repeating pattern, or completely random, where nodes in the network are connected randomly. Small-world networks lie somewhere on the continuum between these two extremes; they are highly connected locally, with sparse long-distance connections allowing for shortcuts. Such networks are highly efficient in transmitting information across the network because of these short cuts, while they remain robust to injury because they are sufficiently redundant. The notion that the brain can be characterized as a network consisting of discrete elements linked together by connections has been around for some time; however, application of graph theory to neuroscience is a relatively new phenomenon. The brain can be considered a network on multiple scales. At the most elementary level, there are synaptic connections between neurons; at a higher level, there are corticocortical or cortico-deep gray connections between different cell types; at a yet higher level, there are large-scale connections between brain regions in the form of white matter bundles or fascicles. These different scales are reflected in the emerging fields of connectomics and projectomics, which through imaging and 317
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Jeffrey R. Petrella, MD
REVIEWS AND COMMENTARY
Use of Graph Theory to Evaluate Brain Networks: A Clinical Tool for a Small World?1
EDITORIAL: Graph Theory to Evaluate Brain Networks
histologic techniques of varying resolution, attempt to map the multitude of neural connections in the human brain (4). Recent developments in brain imaging, such as structural and functional MR imaging, have enabled us to study large-scale human brain networks by using graph theoretical models. The large-scale organization of the brain has been an area of debate for well over 2 centuries. In the 19th century, two predominant theories had come to dominate neuroscience: functional segregation and functional integration. Functional segregation supporters maintained that different brain areas subserve different motor, perceptual, and cognitive functions. Functional integration supporters maintained that all brain regions are fundamentally the same but that they subserve different functions by virtue of their connections with other brain regions. Today, we realize that the brain is organized in a functionally specialized manner, with some areas segregated for certain specialized functions, such as vision, motor control, or language, with higher functions depending on integration of information from these regions. Recent electrophysiologic and neuroimaging studies in which researchers used graph theoretical analysis have shown that small-world network organizational properties underlie this functionally specialized architecture (5–7). Graph theory applied to neuroimaging data can help us understand how the brain is organized. It may also help us understand the biologic underpinnings of behavioral function and dysfunction, particularly in patients with neurocognitive disorders, a population currently underserved by the radiologic community. A number of psychiatric and neurocognitive disorders can be classified as disconnection syndromes, in which there is damage to either white matter connections or association corticies bridging specialized sensorimotor regions (8–10). The emergence of particular symptoms can be theoretically related to particular types of damage to large-scale brain networks. A number of studies in which researchers have used resting-state functional MR imaging and graph theoretical approaches have shown abnormalities 318
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in intrinsic brain networks in patients with different abnormal conditions, including Alzheimer disease (AD), schizophrenia, attention deficit hyperactivity disorder, epilepsy, and traumatic brain injury (11). For example, in patients with AD, Supekar et al (12) found a significant decrease in the clustering coefficient and small-world properties in patients with AD compared with control subjects, consistent with lower regional connectivity and disruption of global organization of brain networks. These and other findings suggest that smallworld metrics may be useful imagingbased biomarkers for a number of conditions. In addition, the robustness of a network to particular types of structural damage can be tested with lesion models. For example, He and colleagues (13) examined the effect of random deletions of nodes and links versus targeted deletions of highly interconnected nodes and long-distance links in healthy subjects and those with AD. In healthy subjects, the network was resistant to both types of attack; however, in patients with AD, the network was approximately as robust to random failures but was particularly vulnerable to targeted attacks, presumably as a result of altered network organization (disrupted smallworld architecture). Various neurodegenerative disorders demonstrate deposition of abnormally folded protein, such as amyloid b 42 in patients with AD, hyperphosphorylated tau in patients with frontotemporal lobar dementia, and a synuclein in patients with dementia with Lewy bodies. The fundamental question of what drives particular patterns of protein deposition in patients with different neurodegenerative disorders may be answered by the study of large-scale human brain networks. Seeley et al (14) used high-resolution structural MR imaging and resting-state functional MR imaging to study characteristic atrophy patterns in patients with various neurodegenerative disorders and found syndrome-specific atrophy patterns that corresponded to large-scale resting-state networks in healthy subjects. These findings imply that the cause of particular patterns of protein deposition in neuro-
degenerative disease may be related to selective vulnerability in corresponding large-scale brain networks. Network analyses derived from brain imaging results may help us understand the mechanism of action of drugs that may target specific brain networks. For example, in previous clinical trials in patients with AD and those with mild cognitive impairment, researchers have used functional MR imaging to monitor the effects of cholinesterase inhibitors on the frontal lobe attention network (15,16). These and similar findings in other neurotransmitter systems suggest that measures of network organization may be sensitive markers demonstrating modification and repair of altered network configurations in those with neurodegenerative and psychiatric conditions. In addition to helping us understand the biologic underpinnings of a number of brain disorders, brain network measures may have applications in patient care, such as early diagnosis. There is evidence that network dysfunction may precede even molecular abnormalities in patients with neurodegenerative disease. Sheline et al (17) studied subjects with normal cognitive function who were at genetic risk for AD (apolipoprotein ´4 allele carriers) but who had negative evidence for cerebral amyloid deposition, presumed to be one of the earliest hallmarks of AD. Although these subjects all had negative findings on positron emission tomographic images acquired with carbon 11 Pittsburgh compound B, a radioligand that binds to fibrillar amyloid protein, they were shown to have substantial network disruption at restingstate functional MR imaging. These findings suggest that network dysfunction may represent an early manifestation of a genetic effect that can be detected with resting-state functional MR imaging and that such changes may antedate the pathologic findings of fibrillar amyloid plaque deposition. Many heritable psychiatric disorders show no structural abnormalities at computed tomography or MR imaging, yet they are likely to stem from abnormalities in the development of large-scale networks in utero or in early postnatal life. Graph theory
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Radiology: Volume 259: Number 2—May 2011
EDITORIAL: Graph Theory to Evaluate Brain Networks
network measures may represent endophenotypes of such conditions, and evidence is starting to accumulate in patients with disorders such as schizophrenia, depression, and attention deficit hyperactivity disorder that suggests a possible role for graph theory network measures in early diagnosis of these conditions (18). Before we can further consider clinical applications of these techniques, we need to review issues associated with the adoption of any new technology into clinical trials and practice. There has been tremendous interest on the part of the clinical trials community, including the pharmaceutical industry, in quantitative imaging-based measurements of brain anatomy and physiology that may serve as more sensitive and specific surrogate end points for clinical trials compared with clinical measures. Such markers must be based on a known understanding of the disease process and mechanism of action of a particular drug (19). To meet this demand, the radiologic community, led by the Radiological Society of North America, considers the development of reproducible and accurate quantitative imaging markers of disease a high priority. The Radiological Society of North America has brought together stakeholders in industry, academia, and government in the Quantitative Imaging Biomarkers Alliance (QIBA), whose mission is to improve the value and practicality of quantitative biomarkers by reducing variability across devices, patients, and time (www.rsna.org/Research /QIBA/qiba_process.cfm). For a new technique to be marketable, it must be faster, cheaper, and better than what is currently available. Acquisition time is critical in a busy clinical environment. If a new biomarker does not integrate well into the clinical workflow—that is, if it takes too long or is too cumbersome—it has little chance of being adopted into clinical trials or practice. Whitlow et al (1) have shown that as little as 2 minutes of resting-state functional MR imaging is sufficient to accurately compute frequently used graph theory metrics of brain network connectivity, such as small worldness, local Radiology: Volume 259: Number 2—May 2011
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efficiency, and global efficiency. Unlike traditional functional MR imaging, restingstate functional MR imaging does not require patients to actively participate in a behavioral task while undergoing imaging. These findings suggest that clinical implementation of this technique is feasible and cost effective, even in a challenging population in which imaging time may be limited, such as young children or critically ill patients. In this context, the term better means more reproducible and/or more accurate than existing methods for a particular clinical context of use. Blood oxygen level–dependent functional MR imaging, the best candidate modality for clinical application of graph theory network measurements, is inherently nonquantitative (20) with low signal-to-noise ratios; however, Whitlow et al (1) have shown that network metrics based on resting-state blood oxygen level–dependent functional MR imaging findings can, in fact, yield stable measurements and that these measurements stabilize in a feasible time that may easily be integrated into the clinical MR imaging workflow. Whether such stability of graph theory metrics within a single session translates over multiple sessions in the same subjects remains to be determined but would be critical for the use of such metrics in a therapeutic context in clinical care or clinical trials. A substantial challenge in this regard is the lack of acquisition or analysis standards in clinical imaging. This is a particular problem with functional MR imaging for which there is a considerable number of acquisition or analysis variables that may alter quantitative imaging measures, yet insufficient knowledge of particular specifications for these variables in which we can expect acceptable quantitative measures. The study by Whitlow et al (1) helps to narrow this gap. Although resting-state functional MR imaging–based graph theory metrics of brain network connectivity may be reproducible, accuracy for a particular clinical context of use is critical in determining whether this technique will ultimately be adopted for clinical application. Such uses include early detection, assignment of prognosis, and prediction and monitoring
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of therapeutic response. Clearly, application of network metrics based on resting-state blood oxygen level–dependent imaging is in its earliest stages; however, studies have already shown utility in separating healthy control subjects from patients with a number of conditions, as previously described (11). Further work is needed to confirm and identify specific diagnostic test characteristics of various graph theory metrics in each of these conditions and for a variety of clinical contexts. In summary, if the field of radiology is to move forward into its next stage of evolution— supplementing visual interpretation of images with pertinent quantitative measurements of anatomy and function—more studies that focus on optimizing imaging-based metrics for accuracy and reproducibility are needed. This evolution will entail a shift in focus on the part of industry from creating imaging devices that make eye-catching images to creating accurate and precise image-based measurement devices. Such devices might require different specifications, such as more emphasis on signalto-noise ratio compared spatial resolution. The study by Whitlow et al (1) is an example of the technical characterization and standards ground work needed to optimize a potentially important quantitative imaging biomarker of brain network function, and it fills an important gap in the pathway to adoption of such a marker for use in clinical trials and practice. Acknowledgments: I thank P. Murali Doraiswamy, MD, for helpful comments on content; Kristin R. Trangsrud, MPH, for assistance with editing; and Forrest C. Sheldon, BS, for assistance with submission. Disclosures of Potential Conflicts of Interest: Financial activities related to the present article: none to disclose. Financial activities not related to the present article: is a consultant to Janssen Alzheimer Immunotherapy, has served as a medicolegal consultant for Elser and Wilson. Other relationships: none to disclose.
References 1. Whitlow CT, Casanova R, Maldjian JA. Effect of resting-state functional MR imaging duration on stability of graph theory metrics of brain network connectivity. Radiology 2011;259(2):516–524.
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2. Euler L. Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 1736; 8:128–140. 3. Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature 1998; 393(6684):440–442. 4. Kasthuri N, Lichtman JW. The rise of the ‘projectome’. Nat Methods 2007;4(4):307–308. 5. Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. Scale-free brain functional networks. Phys Rev Lett 2005;94(1):018102. 6. Salvador R, Suckling J, Coleman MR, Pickard JD, Menon D, Bullmore E. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb Cortex 2005;15(9):1332–1342. 7. Stam CJ. Functional connectivity patterns of human magnetoencephalographic recordings: a ‘small-world’ network? Neurosci Lett 2004; 355(1-2):25–28. 8. Geschwind N. Disconnexion syndromes in animals and man. I. Brain 1965;88(2): 237–294.
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9. Geschwind N. Disconnexion syndromes in animals and man. II. Brain 1965;88(3):585–644. 10. Catani M, Ffytche DH. The rises and falls of disconnection syndromes. Brain 2005;128(pt 10): 2224–2239. 11. Wang J, Zuo X, He Y. Graph-based network analysis of resting-state functional MRI. Front Syst Neurosci 2010;4:16. 12. Supekar K, Menon V, Rubin D, Musen M, Greicius MD. Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease. PLOS Comput Biol 2008;4(6): e1000100. 13. He Y, Chen Z, Evans A. Structural insights into aberrant topological patterns of largescale cortical networks in Alzheimer’s disease. J Neurosci 2008;28(18):4756–4766. 14. Seeley WW, Crawford RK, Zhou J, Miller BL, Greicius MD. Neurodegenerative diseases target large-scale human brain networks. Neuron 2009;62(1):42–52. 15. Petrella JR, Prince SE, Krishnan S, Husn H, Kelley L, Doraiswamy PM. Effects of donepezil on cortical activation in mild cognitive impairment: a pilot double-blind placebo-
controlled trial using functional MR imaging. AJNR Am J Neuroradiol 2009;30(2): 411–416. 16. Saykin AJ, Wishart HA, Rabin LA, et al. Cholinergic enhancement of frontal lobe activity in mild cognitive impairment. Brain 2004;127(pt 7):1574–1583. 17. Sheline YI, Morris JC, Snyder AZ, et al. APOE4 allele disrupts resting state fMRI connectivity in the absence of amyloid plaques or decreased CSF Ab42. J Neurosci 2010; 30(50):17035–17040. 18. Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 2009;10(3):186–198. 19. Katz R. Biomarkers and surrogate markers: an FDA perspective. NeuroRx 2004;1(2): 189–195. 20. Ances BM, Leontiev O, Perthen JE, Liang C, Lansing AE, Buxton RB. Regional differences in the coupling of cerebral blood flow and oxygen metabolism changes in response to activation: implications for BOLD-fMRI. Neuroimage 2008;39(4):1510–1521.
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