NeuroImage 80 (2013) 475–488

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Genetics of the connectome☆

Paul M. Thompson a,⁎, Tian Ge b,c, David C. Glahn d,e, Neda Jahanshad a, Thomas E. Nichols f,g

a Imaging Genetics Center, Laboratory of NeuroImaging, Dept. of Neurology, UCLA School of Medicine, Los Angeles, CA 90095, USAb Centre for Computational Systems Biology, School of Mathematical Sciences, Fudan University, Shanghai 200433, Chinac Dept. of Computer Science, University of Warwick, Coventry CV4 7AL, UKd Olin Neuropsychiatry Research Center, Institute of Living, Hartford, CT 06106, USAe Dept. of Psychiatry, Yale University School of Medicine, New Haven, CT 06571, USAf Dept. of Statistics and Warwick Manufacturing Group, University of Warwick, Coventry CV4 7AL, UKg Functional Magnetic Resonance Imaging of the Brain (FMRIB) Centre, Nuffield Department of Clinical Neurosciences, University of Oxford, John Radcliffe Hospital, Oxford OX3 9DU, United Kingdom

☆ NeuroImage Invited Review for the Special Issue: “Medited by Stephen M. Smith.⁎ Corresponding author at: Imaging Genetics Center,

Dept. of Neurology, UCLA School of Medicine, 635 Charl225E, Los Angeles, CA 90095-7332, USA.

E-mail address: thompson@loni.ucla.edu (P.M. Thom

1053-8119/$ – see front matter © 2013 Elsevier Inc. Allhttp://dx.doi.org/10.1016/j.neuroimage.2013.05.013

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 8 May 2013Available online 21 May 2013

Connectome genetics attempts to discover how genetic factors affect brain connectivity. Here we review a vari-ety of genetic analysis methods—such as genome-wide association studies (GWAS), linkage and candidate genestudies—that have been fruitfully adapted to imaging data to implicate specific variants in the genome forbrain-related traits. Studies that emphasized the genetic influences on brain connectivity. Some of these analysesof brain integrity and connectivity using diffusionMRI, and others havemapped genetic effects on functional net-works using resting state functional MRI. Connectome-wide genome-wide scans have also been conducted, andwe review the multivariate methods required to handle the extremely high dimension of the genomic and net-work data. We also review some consortium efforts, such as ENIGMA, that offer the power to detect robustcommon genetic associations using phenotypic harmonization procedures and meta-analysis. Current work onconnectome genetics is advancing on many fronts and promises to shed light on how disease risk genes affectthe brain. It is already discovering new genetic loci and even entire genetic networks that affect brain organiza-tion and connectivity.

© 2013 Elsevier Inc. All rights reserved.

Introduction

The term “connectome” refers to the totality of neural connectionswithin a brain. It is currently not possible to assess all neuronal connec-tions in a living organism, but usingmodern neuroimaging and speciallydesigned analytic strategies, we can map the connectome at the macro-scopic scale, in living individuals. Indeed, this is the topic of the otherarticles in this Special Issue of NeuroImage. Yet, even with precise andaccurate delineation of a “macro-connectome”, the molecular factorsthat regulate the development and behavior of this system are largelyunknown. The primary goal of imaging genetics is to identify and charac-terize genes that are associatedwith brainmeasures derived from images,including connectomic maps. Once a gene is shown to definitively influ-ence an imaging trait, that trait can be anchored to a set of biological pro-cesses (such as the protein expressed by the gene, or an entire network ofinteracting genes). Such biological insights offer a window into the

apping the connectome”

Laboratory of Neuro Imaging,es E. Young Drive South, Suite

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developmental trajectories and, possibly, the adult physiological activitiesthat control individual trait differences, including those that give rise toneurological or psychiatric illness. In this context, the analysis of brainconnectivity using genetic methods, referred to here as connectomegenetics, can provide new information on biological mechanismsthat govern connectomic differences in healthy individuals and indisease.

In this reviewarticle,we summarize our current knowledge of geneticinfluences on the connectome. We first review the kinds of quantitativeandmolecular genetic approaches that canbe used for analyzing complextraits in general. Thenwe review studies that reveal genetic influenceson brain connectivity, either in terms of anatomy (diffusion-basedmeasures) or function (resting state fMRI). Finally, we discuss somemethodological challenges and innovations that arise in the geneticanalysis of the connectome, and we describe future directions.

A basic introduction to quantitative and molecular geneticsmethodology

Heritability: how do we decide if a measure is genetically influenced?

In quantitative classical genetics, all trait variance, such as a brainmeasure derived froman image, can be attributed to either genetic or en-vironmental factors or their interactions. The proportion of trait variance

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within a population that is due to genetic factors is the conceptualized asthe heritability of that trait. Broad-sense heritability reflects additive,dominant and epistatic (genetic interactions) genetic contributions to aheritability estimate and is defined as h2 = σ2

g/σ2pwhere h2 is heritabil-

ity, σ2g is trait variance due to genetic factors and σ2

p is the total pheno-typic (measured) trait variance. This definition includesmultiple sourcesof genetic variation, so broad-sense heritability is particularly importantfor selective animal breeding and for certain types of human behavioralgenetic studies (such as twin studies). In contrast, narrow-sense herita-bility reflects only the contribution of additive (allelic) genetic effectsto a heritability estimate and is defined as h2 =σ2

a/σ2p. This additive ge-

netic effect is only a portion of the total genetic effect and it refers to thedegree of the phenotypic variance predictable by the additive effect of al-lelic substitutions, such that the genetic contribution for a heterozygoticpair of alleles is halfway between that of the two homozygotic pairs. Asmolecular genetic experiments involve mapping allelic variation totrait variance, narrow-sense heritability is the focus of most modern ge-netic investigations, including imaging genetics studies.

Heritability estimates vary between 0, indicating no genetic influenceat all on trait variance, and 1, indicating complete genetic determination.A heritability estimate of h2 = 0.5 would imply that 50% of the pheno-typic variation in a particular trait is due to genetic variation, in a partic-ular population. A significant heritability estimate indicates that a trait issignificantly influenced by genetic factors, making it an appropriate tar-get for more specific molecular genetic analyses. Calculating heritabilityestimates is a valuable exercise for novel traits derived from compleximage analyses (e.g., connectome maps), as little prior research hasshown that suchmeasures are under genetic control. In efforts to discov-er genetic variants affecting brain measures, preliminary studies of heri-tability can help to prioritize the more heritable measures for geneticanalysis (Blokland et al., 2012; Glahn et al., 2012; Jahanshad et al.,2012a; Winkler et al., 2010).

Heritability is an important and compelling concept, but it is criticalto understand its limitations. Indeed, heritability estimates have beenmisused or misunderstood in several ways in imaging genomics. First,a heritability estimate describes a property of the population beingstudied, rather than effects in individual members of the population.Furthermore, heritability estimates summarize the strength of geneticinfluences on trait variation in members of a specific population andmay be population-specific, so not necessarily generalizable to othercohorts where environmental influences or ancestry may differ.Second, while a heritability estimate measures the proportion of thetrait variance explained by variations across the entire genome, it doesnot tell us anything about which specific genes contribute to it, howmany genes are involved, or the impact of any one gene on the trait.Multiple genes, each with a very small effect, can influence a highlyheritable complex trait (e.g., normal human height (Yang et al.,2010)). Discerning the impact of any single gene/locus may bedifficult. In contrast, a single gene could influence a trait with a muchlower heritability (e.g., cis-regulated transcriptional measures) and thecrucial locus may be far easier to localize. Some common hereditarydiseases, hemochromatosis for example, are strongly influenced by ahandful of genes (Jahanshad et al., 2013c), which together predictquite well whether or not someone will develop the disease. Mostbrain traits appear to be influenced by many common variants withrelatively small effects and rare variants with larger effects. The nextsection discusses approaches for searching for genetic effects onspecific traits.

Gene discovery methods

Gene discovery is a multi-stage process that requires an initial local-ization of a quantitative trait locus (QTL) harboring a genetic variant thatismechanistically related to a trait, followed bymore focused analyses toidentify a particular gene and study its biological effects. There are twomain ways to localize chromosomal regions influencing a trait: linkage

and association. Typically, association methods are used when onesearches for relatively common variants that influence an illness ortrait (e.g., common variant/common disease hypothesis). In contrast,linkage analyses are sensitive to both common and rare variation. Asthere is an increasing appreciation for the importance of rare variationin human illness, there is currently intense interest in developingmethods for localizing rare variants.

Genetic linkage analysis tests for co-segregation of phenotype andgenotype within families. Genes located in close physical proximity ona chromosome tend to be inherited together during meiosis. Linkageanalysis exploits inheritance patterns and thus, is a function of physicalconnections among genes on chromosomes. The strength of linkage istypically reported as a LOD score (log of the odds ratio), which comparesthe likelihood of obtaining a linkage between two loci by chance. A LODscore of 3.0, which has a point-wise p-value of 1 × 10−4, takes into ac-count themultiple testing in a genome-wide linkage screen and is tradi-tionally considered a significant effect. The LOD score can be used tocompute the asymptotic p-value through the chi-squared distributionwith one degree of freedom, for example in this case p = ½ ∗ P[χ2(dof = 1) > (2 ∗ log10) ∗ 3] ≈ 1 × 10−4. Advantages of linkage anal-ysis include that the power to find a QTL can be easily quantified, andthat the approach is minimally influenced by allelic heterogeneity.Disadvantages of the approach include that it requires the study of re-lated individuals and typically localizes relatively large genetic loci(e.g. 10–15 megabases). Such a large locus often harbors many genesand requires additional analytic methods to determine the gene ofinterest.

Genetic association analysis tests if variants at a single location on thegenome occur more often than would be expected by chance, in onegroup relative to another (e.g., in diseased versus not diseased, or in indi-viduals with high versus low values for a measure), or with respect to aquantitative trait (e.g., height). We can extend the notion of associationto brain measures: a genetic variant is said to be associated with a brainmeasure if it helps to predict thatmeasure (howeverweakly), using stan-dard linear regression. However, genome-wide association studies(GWAS) are exclusively focused on a subset of common genetic variants,which do not represent the entirety of total genetic variation. As a result,GWAS rely on the linkage disequilibrium (statistical correlation) amongnearby genetic variants, which arises naturally and depends to some ex-tent on population ancestry. Linkage disequilibrium (LD) is thenon-random association of alleles at two or more loci—the tendency forneighboring genetic variants to be inherited together. However, LD isunpredictable, varies across the genome, and across populations. Indeed,LD need not be present at all at a particular locus in a particular popula-tion, making it challenging to estimate statistical power for genetic asso-ciation analysis, especially if the functional variant of interest is notcorrelated with anything actually genotyped. Population stratification isanother potential source of bias in association studies. If a sample collect-ed for genetic association analysis contains multiple populations that dif-fer in the trait of interest, any locus whose allele frequencies differbetween the populations could show an erroneous association (due topopulation stratification). A third major issue with genome-wide associ-ation is the need to correct for the hundreds of thousands (or even mil-lions) of separate statistical tests conducted (requiring p-valuesb5.0 × 10−8 to reject the null hypothesis of no genetic effect). Whenthe genome is searched for predictive variants, so many loci are testedthat heavy corrections must be made for the number of statistical tests.However, association analysis can be conducted on unrelated individuals,and statistical methods are fast and easy to apply making it a commonand practical approach. Statistical corrections for population stratificationand formultiple testing have been largely successful, and there arewide-ly agreed methods available to perform these corrections. Furthermore,association analyses typically provide much smaller QTL localization in-tervals (~500 kilobases) than linkage, reducing the search space for caus-al variation. It is critical to note that results fromGWAS require follow-upanalyses like those in linkage in order to identify the causal variants/gene.

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Indeed, the functionally relevant variant is likely not to be the allele iden-tified through GWAS, and may not even be on the same genes.

Recently,whole genome sequence data has become farmore cost ef-fective to acquire. Whole genome sequence data provides unique infor-mation for each of the approximately 3 billion alleles in the genome, thetotality of human genetic variation. However, to date, there are no ex-amples of investigators using whole genome sequence data to explorethe genetic underpinnings of image-derived traits. Whole genome se-quencing has been acquired for several cohorts that have been studiedextensively with neuroimaging methods (e.g. the “Genetics of BrainStructure and Function” study with over 1500 imaged individuals andover 1000 with whole genome sequence (Olvera et al., 2011) and theAlzheimer's Disease Neuroimaging Initiative, http://adni.loni.ucla.edu).

Testing candidate genes

The gene discovery methods described above involve genotypingmarkers spanning the genome and searching for loci that influence aparticular trait. In contrast, candidate gene studies involve genotypedmarkers in genes hypothetically related to a particular trait. Thus, farfewer statistical tests are typically performed and, as genes are typicallychosen a priori, it can be easier to interpret any findings. Candidate genestudies typically rely on association methods, so they are subject to thesame potential biases (e.g., LD and population stratification). Most im-aging and connectome related genetic studies have used a candidategene approach, although more recently, studies are beginning to per-form genome-wide screens of connectome data.

Biological validation of potential gene findings

Regardless of the approach used to localize or identify a gene–phenotype relationship, once such a relationship is established, itmust undergo biological validation. Such validation typically involvesin vitro tests performed on cell lines or in populations of neurons, or theutilization of model organisms. One current limitation of imaging geno-mics in general, and connectome genetics in particular, is that imaging-derived measures are not readily translated into this type of biologicalexperimentation, as there may not be comparable brain measures thatcan be studied in the wet lab.

One notable exception is a project that links neuroimaging to gene ex-pression and maps of connectivity—the Allen Brain atlas. The Allen atlas(http://www.brain-map.org) is a growing database of gene expressionpatterns in the mouse and human brains, and also provides extensive in-formation onmouse brain connectivity. In rodent studies, connectivity canbe traced using tracers injected into brain regions such as the subcorticalnuclei. TheAllen atlas also allowsusers tobrowseonlinedata fromnumer-ous types of transgenic mice—mice genetically engineered to have certaingenetic alterations. This focus on transgenic mice reveals the anatomicalconsequences of manipulating specific genes, and also relates connectionmaps to gene expression patterns compiled from multiple sources.

Endophenotypes

Imaging genomics, and by extension connectome genomics, has twopotential endpoints: (1) it can provide fundamental insights into basicneuroscience, particularly systems neuroscience; and (2) it can providean understanding of the genetic underpinnings of brain-related illnesses.This second endpoint rests upon the observation that the genes that in-fluence normal variation also influence pathological variation. For exam-ple, if a gene that influenced amygdala connectivity was identified, thatgene would be an outstanding candidate for illnesses associated withdisrupted amygdala connectivity (e.g.,major depression or bipolar disor-der (Anticevic et al., 2012)). In this context, the imaging trait can beconsidered an allied phenotype or endophenotype (Gottesman andGould, 2003). An endophenotype is a heritable trait that is geneticallycorrelated with an illness and hasmuch greater power to localize genetic

loci than affection status alone (Blangero, 2004; Glahn et al., 2012).Manyneuroimaging traits, including some measures of connectivity, aredisrupted in mental illness and are candidate endophenotypes forthese illnesses. For example, individuals with schizophrenia andtheir unaffected relatives have aberrant default mode connectivity(Whitfield-Gabrieli et al., 2009), raising the possibility that defaultmode connectivity could be an endophenotype for schizophrenia.

In the next few sections, we review recent genetic analyses of brainmeasures related to connectivity. As standard anatomical MRI is so widelyavailable, genetic studies of brain morphometry still far outnumber thosefocusing on connectivity. Indeed, a recent GWAS examining the effects ofcommon variants on the hippocampus used a sample of over 20,000 sub-jects (Stein et al., 2012). Currently, similar GWAS experiments involvingconnectivity traits are limited to hundreds rather than thousands of sub-jects. Yet, aswith other complex traits, our search for the genetic underpin-nings of connectivity measures may benefit from a focus on rare variationobserved in family studies, rather than common variants of small effects.

Genetic studies of diffusion-based measures of connectivity

Diffusion indices, tracts, and networks

Diffusion imaging provides a number ofmeasures that are amenableto genetic analysis. Diffusion tensor imaging (DTI) is sensitive to whitematter integrity and its connections, so it offers the potential to discovergeneral principles that affect brain organization. As noted in other pa-pers in this Special Issue, diffusion-weightedMRI and its more complexvariants such as HARDI and DSI (Zhan et al., 2011) are sensitive to thedirectional diffusion of water in the brain. By mapping the principaldirections of diffusion from one part of the brain to another, neuralpathways may be followed across the brain using tractography, and or-ganized into bundles and fiber tracts (see e.g., Jin et al., 2011, 2013). Bymapping fiber trajectories throughout the brain, it has become quitecommon to use an anatomical parcellation of the brain to group connec-tions into pathways between all pairs of regions. Properties of theseconnections, particularly their density or fiber integrity, may be storedin connectivity matrices and compared or combined across subjects.The resulting connectivity matrices then become excellent targets forstatistical analyses, and genetic analysis is no exception.

Genetic studies of structural brain connectivity, to date, fall into 3broad categories, analyzing: (1) diffusion properties of the whitematter, such as fractional anisotropy (FA) or mean diffusivity(MD); (2) 3D geometrical models of tracts or fiber paths extractedusing tractography (including tract shapes (Jin et al., 2011)); and(3) networks of brain connections, represented as connectivity matricesor graphs. The genetics of some network properties, such as networkefficiency, is also just beginning to be explored.

The first category of DTI analysis – mapping standard measures ofwhitematter integrity, such as FA orMD—may be considered as not gen-uinely mapping connectivity. Even so, disruptions or failures of connec-tivity are often inferred when these white matter measures are altered,sowe include themhere in our review. A large number of genetic studieshave focused on simple DTImeasures. Some brainmapping studies of FAhave been presented as if they are studies of connectivity, in that abnor-mal diffusion indices—in the corpus callosum, for example—are oftensigns of aberrant connectivity that are more conveniently measuredthan extracting tracts and networks. In addition, DTI indices have beenthe target of hundreds if not thousands of clinical neuroimaging studies(Thomason and Thompson, 2011), so genetic influences on these brainmeasures are important to identify.

Heritability of structural connectivity

Some early genetic studies with DTI simply aimed to show that DTImeasures are heritable, and therefore worthy targets for more in-depthgenetic analysis. Using a twin design, Chiang and colleagues (Chiang et

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al., 2009) assessed white matter integrity using DTI at a high magneticfield (4 T) in 92 identical and fraternal twins. By fitting structuralequation models to a variety of DTI-derived indices, they wereable to show that white matter integrity (FA) was under strong ge-netic control and was highly heritable in bilateral frontal (a2 = 0.55,p = 0.04, left; a2 = 0.74, p = 0.006, right), bilateral parietal (a2 =0.85, p b 0.001, left; a2 = 0.84, p b 0.001, right) and left occipital(a2 = 0.76, p = 0.003) lobes. These measures of white matter integritywere also correlated with full-scale IQ (FIQ) and performance IQ (PIQ) inthe cingulum, optic radiations, superior fronto-occipital fasciculus, internalcapsule, callosal isthmus, and the corona radiata (p = 0.04 for FIQ andp = 0.01 for PIQ, corrected for multiple comparisons). They also used amodeling approach called a “cross-twin cross-trait”design, to demonstrate“genetic correlations” between DTI and IQ measures, in the sense that theDTImeasure in one twin is correlatedwith the IQof the other twin and thiscorrelation is significantly higher in monozygotic twins than dizygotictwins. This type of design can reveal pleiotropy—overlapping genetic influ-ences on IQ and DTI measures, or common underlying genes that affectthem both. In other words, if some genetic variants could be found thatare associated with DTI measures, they may also be good candidates foraffecting cognition. Ultimately, this is the premise of the endophenotypeapproach, whereby genetic analysis of images is intended to eventuallyshed light on the genetics of cognition, or risk for disease.

The heritability of DTI measures was confirmed in a much larger,family based study. Kochunov and colleagues (Kochunov et al., 2010)performed heritability, genetic correlation and quantitative linkageanalyses for DTI measures derived from the whole-brain and from 10major cerebral white-matter tracts. The sample included 467 healthyindividuals from large extended pedigrees (182 males/285 females;average age 47.9 ± 13.5 years; age range: 19–85 years) from the“Genetics of Brain Structure and Function” study. Average measure-ments for fractional anisotropy (FA), radial and axial diffusivitiesserved as quantitative traits. Significant heritability was observed forFA (h2 = 0.52 ± 0.11; p = 10−7) and radial diffusivity (h2 = 0.37 ±0.14; p = 0.001), while axial diffusivity was not significantly heritable(h2 = 0.09 ± 0.12; p = 0.20). Genetic correlation analysis indicatedthat the FA and radial diffusivity shared 46% of the genetic variance.Tract-wise analysis revealed a regionally diverse pattern of genetic control,which was unrelated to ontogenic factors, such as tract-wise age-of-peakFA values and rates of age-related change in FA. Linkage analysis indicatedlinkages for whole-brain average FA (LOD = 2.36) at the markerD15S816 on chromosome 15q25, and for radial diffusivity (LOD = 2.24)near the marker D3S1754 on the chromosome 3q27. These sites havebeen reported to have significant co-inheritance with two psychiatric dis-orders (major depression and obsessive-compulsive disorders) in whichpatients show characteristic alterations in cerebral white matter. Thesefindings suggest that the microstructure of cerebral white matter isunder a strong genetic control and further studies in healthy individuals,as well as patients with brain related illnesses, are imperative to identifythe genes that may influence white matter connectivity.

Ranking the heritability of DTI measures

Among various imaging measures, metrics from DTI have beenshown to be especially promising phenotypes for genetic analyses(Blokland et al., 2012). The search for specific genes or SNPs that affectDTI measures can clearly be empowered by pooling large amounts ofDTI data, from cohorts worldwide where genetic data is available. TheENIGMA Consortium DTI Working Group is leading one such effort asthey have created a common DTI template from 4 large cohorts of sub-jects, and subdivided it into regions of interest for assessing geneticinfluences on the diffusion imaging indices (Jahanshad et al., 2013a;Kochunov et al., 2012). Both voxel-wise tract-based spatial statistics(TBSS; Smith et al., 2006) and regional averagemeasureswere evaluated.By ranking the ROI measures in order of their heritability, brain regionscould be prioritized in order of their promise for future genetic analysis.

Measures from some regions, such as the cortico-spinal tract, showedpoor (i.e., low) heritability, and it was challenging to measure them con-sistently across a cohort. Most regional measures were highly heritable(with aroundhalf of the observed variance attributable to genetic factors)across two different cohorts—cohorts of different ethnicities scannedusing different scanners and protocols on different continents. Asmentioned previously, a highly heritable trait does not necessarily meanthat a GWAS will produce significant results. Even so, this large-scale ge-netic analysis of DTI lends confidence to the notion that the DTImeasuresshowconsistent and reliable heritabilitymeasures across populations andimaging sequences. Meta-analytic GWAS may therefore be feasible forDTI, without being seriously limited by differences among cohorts andscanning protocols. A meta-analytic approach is extremely importantas some single site GWAS of DTI measures have already been conducted(Lopez et al., 2013; Sprooten et al., 2012), yet while results are extremelypromising, these studies were not able to find statistically significant var-iants associated with the DTI measures.

Searching for anatomic connectivity genes

Kochunov et al. (2011) combined cortical thickness and tract-basedDTI measures to search for genes influencing anatomic connectivity. Thethickness of the brain's cortical graymatter and the fractional anisotropyof the cerebral white matter are positively correlated andmay bemodu-lated by common biologicalmechanisms.Whole-brain and regional graymatter thickness and FA valuesweremeasured fromhigh-resolution an-atomical and diffusion tensorMR images collected from 712 participantsof the “Genetics of Brain Structure and Function” study (438 females,age range: 47.9 ± 13.2 years). Significant genetic correlation was ob-served among gray matter thickness and FA values, suggesting that thesame genetic factors influenced these traits. Linkage analysis implicateda region of chromosome 15q22–23, with the strongest LOD of 4.51 ob-served for a bivariate linkage between superior parietal thickness andFA values in the corpus callosum. These data strongly suggest that agene in this area influences anatomic connectivity.

Candidate genes

Several studies have attempted to find associations between singlenucleotide polymorphisms (SNPs) and DTI-derived measures, such asFA. To some degree, FA may reflect axonal packing, coherence andeven the extent of myelination, so there is a host of candidate biologicalpathways and genes already implicated in axonal guidance and neuralmigration that may also affect DTI measures. As such, it seems logicalto testwhether SNPs in these candidate genesmight affectwhitematterintegrity on DTI.

One class of studies of FA has focused on brain growth factors, orneurotrophins, which influence brain growth and the guidance andmi-gration of axons during development. Many commonly carried variantsin growth factor genes have been implicated in neuropsychiatric disor-ders, albeit not entirely consistently. Among them, the brain-derivedneurotrophic factor (BDNF) gene is critically involved in learning andmemory—it modulates hippocampal neurogenesis, synaptic transmis-sion, and activity-induced long-term potentiation and depression(Poo, 2001). In a landmark study, Egan et al. (2003) showed that a com-mon variant in the BDNF gene, amethionine (Met) for valine (Val) substi-tution at codon 66 in the 5′-proregion of the BDNF protein (Val66Met;dbSNP number rs6265), led to poorer episodicmemory and hippocampalactivation in a cohort of 641 cognitively intact adults aged 25–45.

Chiang et al. (2011) genotyped 455 healthy adult twins and theirnon-twin siblings and scanned them with high angular resolutiondiffusion imaging, and found that the BDNF Val66Met polymorphismappears to affectwhitemattermicrostructure. By applying genetic asso-ciation analysis at every 3D point in the brain images, they found thatthe Val-BDNF genetic variant was associated with lower white matterintegrity in the splenium of the corpus callosum, left optic radiation,

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inferior fronto-occipital fasciculus, and superior corona radiata. Recent-ly, plasma levels of BDNF have also been associated with differences inbrain microstructure (Dalby et al., 2013).

Braskie et al. (2012) also found associations between white matterintegrity (FA) and common variants in the NTRK1 gene (also known asTRKA), which encodes a high affinity receptor for NGF, a neurotrophininvolved in nervous system development and myelination.

Jahanshad et al. (2012a) used a twin study design to show thatwhite matter integrity (measured by FA) is genetically correlatedto serum transferrin levels in the blood; searching all variants intwo genes known to associate with transferrin, they found that FAalso relates to whether a person carries the H63D polymorphism inthe HFE gene. This gene, involved in iron metabolism, is one of themain genetic contributors to the most common hereditary disorder inthe world—hemochromatosis. This disorder affects up to 1% of the popu-lation in some countries (e.g., Ireland). As iron is an essential componentin neural development and has also been linked to neurodegeneration,the authors first determined the association between an iron measureproxy, transferrin, and brain volumetric measures in healthy adults;finding significant associations, they then determined whether genesassociated with iron regulation correlated with healthy brain structuralvariations. This general inductive approach uses genetic effects on bio-markers (iron) as a way to discover genetic effects on the brain.

Combining SNPs in DTI

As the effects on the brain of any one SNP are likely to be small, somestudies have boosted the predictive power by using a set of SNPs, alongwith regressionmethods that favor sparsity or efficiency in the resultingpredictive model (Kohannim et al., 2012b). Kohannim et al. (2012c)investigated the aggregate effects of commonly carried variants in 6well-studied candidate genes, on white matter structure in 395 healthyadult twins and siblings (aged 20–30 years). When combined usingmixed-effects linear regression, a joint model based on five candidateSNPs (COMT,NTRK1, ErbB4, CLU, andHFE) explained ~6% of the variancein the average FA of the corpus callosum. Clearly, such a predictivemodel requires replication, but the known function of these genes sug-gests a number of mechanisms whereby these pathways might affectwhite matter integrity.

Genetics of brain networks

Only a handful of papers have studied genetic effects on brain net-works computed fromDTI. Several studies usewhole-brain tractographyto compile a network of connections between all pairs of regions in thebrain, resulting in an N × N matrix, or “connectome” for each person inthe study. These N × N matrices may be treated as 2D images, and ana-lyzed statistically across subjects, using voxel-wisemethods, or anymul-tivariate method used to analyze images (we note of course that thereis not necessarily smoothness in an matrix of connectivity as adjacentmatrix elements may not index adjacent tracts, so the data in the matrixis not a discrete representation of an underlying spatially continuousfunction. Adjacent elements in the connectivity matrix do not alwayscorrespond to neighboring regions of the brain, but there is a covariancestructure that can still be estimated and exploited).

Similar to DTI, candidate gene studies on these N × N networks andtopological network measures (see Methodological issues section) arealso growing in popularity. Dennis et al. (2011) examined a knownautism risk gene, CNTNAP2; carriers of a common variant in this genehad shown altered brain connectivity on functional MRI (Scott-VanZeeland et al., 2010). Dennis et al. (2011) found that subjects homozy-gous for the risk allele (CC) had lower characteristic path length, greatersmall-worldness and global efficiency in anatomical network analyses,and greater eccentricity (maximum path length) in most nodes of theanatomical network. These results were not reducible to differences inmore commonly studied traits such as fiber density or FA. This was

one of the first studies to link graph theorymeasures of brain connectiv-ity to a common genetic variant.

In another study, Jahanshad et al. (2013b)fitted a structural equationmodel to every element of the anatomical connectivity matrices fromtwins, to find connections with significant heritability. After discardingconnections with low heritability and those not found reliably acrossthe cohort, they performed a GWAS on each of the remaining connec-tions. A commonly carried variant in one gene, SPON1, survived the ex-tremely stringent correction for multiple comparisons, involved insearching across both the genome and the network. This kind of studywill no doubt become more popular, as more population studies of theconnectome are published.

These connectome-widemethods are in a sense, an extension of thevoxel-wise genome-wide association methods (known as “vGWAS”)that are now are under rapid development. Early work on vGWAS(Stein et al., 2010a) showed that it is computationally feasible to searchthe entire image and genome in a large cohort of subjects, but sufferedfrom lack of power, due to the heavy correction for multiple testing.Later works using dimension reduction or sparsemodeling has allowedmore efficient and muchmore highly powered searches of the genomeand the image (Chi et al., 2013; Ge et al., 2012; Hibar et al., 2011;Vounou et al., 2010). See the Methodological issues section below formore detail on these methods.

The genetic analysis of brain networks may involve evaluating topo-logical summary measures of network properties to describe networkorganization—for example, integration, interconnectedness, or segrega-tion of nodal measures rather than strictly examining nodes or edges ofthe network. As in other connectomics studies, summaries of networktopology—such as efficiency, small-worldness, and clustering – may alsobe computed and analyzed. The Brain Connectivity Toolbox (Rubinovand Sporns, 2010), for example, is one of many toolkits now usedto derive a range of summary measures of local and global networkproperties in connectivity studies. See Methodological issues sectionfor more details.

Clearly, there is an enormous potential for “fishing”—screening mea-sures until some show promising associations. To address this in a princi-pled way, Duarte-Carvajalino et al. (2012) suggested a hierarchicalhypothesis testing approach, specialized for analyzing networkmeasures.They advocate efficient hypothesis testing while not unduly inflating thefalse positive rate with the vast numbers of possible tests. Such methodsare important, as connectomics is still in its infancy, and it is not alwaysclear in advancewhich networkmeasureswill be themost promising tar-gets of analysis. As in all areas of genetics, studies are sorely needed thatgauge the reproducibility of genetic associations. This is especially thecase inneuroimaging. Small samples are the rule, partly because of the ex-pensive of collecting images relative to other types of phenotypic data(e.g., clinical diagnosis). Only a handful of studies have examined howconnectomic measures, such as network properties, depend on the algo-rithms used to compute them (e.g. Bassett et al., 2011; Zhan et al., 2013a).

Genetic studies of functional connectivity using resting state fMRI

As discussed in several articles in this Special Issue, intrinsic brainactivity, assessed while an organism is at rest, provides a sensitivemeasure of default mode connectivity (Fox and Raichle, 2007). Itcan also assess connectivity in networks that support informationprocessing (Smith et al., 2009). In this section, we examine evidencethat resting state networks are, to some extent, under genetic controland provide some clues about the genes that may influence functionalconnectivity. Task based functional MRI measures have been used asquantitative phenotypes for GWAS (Ousdal et al., 2012; Potkin et al.,2009b). To date, however, no gene discovery experiments (e.g., linkageor GWAS) have been reported using resting state functional MRI or PETderived traits. Thus, our review focuses on evidence for heritability ofthese traits, and a selection of candidate gene studies.

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Heritability of functional connectivity

Functional connectivity has been assessedwith EEG (Smit et al., 2008)as well as resting state fMRI. Our focus in this review is on the latter.Assessing functional connectivity in resting state functionalMRI data typ-ically involves placing seed regions in the brain (often followed by graphtheory to analyze temporal correlations with signals in the seed regions)or using multivariate decomposition methods (typically ICA). Whilethese analytic approaches have very different underlying assumptionsand interpretive utility, it is assumed that the functional connectivitymeasures index the same neurophysiological processes. However, thisassumption has not been directly biologically validated. At one level, her-itability estimates provide an external biological validator for imagingmeasures. To date, heritability estimates generated using either ICA(Glahn et al., 2010) or graph theory (Fornito et al., 2011; van denHeuvel et al., 2012), indices of functional connectivity have been striking-ly similar, suggesting that the analytic approach to define resting stateconnectivitymay index similar biological processes.Heritabilitymeasuresvary between 0.42 and 0.60. So while functional connectivity is heritable,it is probably less influenced by genetic factors than anatomical connec-tivity measures (see above). Or, it may be that resting state measuresare simply noisier or less reproducible than DTImeasures of connectivity.

Glahn et al. (2010) were the first to publish heritability estimates formeasures of defaultmode connectivity. They used an ICA approach in 333individuals from 29 randomly selected large extended pedigrees. Herita-bility for default mode connectivity was estimated to be 0.424 ± 0.17(p = 0.0046).While an index of anatomic variability (graymatter densi-ty) within this brain network was also heritable (h2 = 0.327 ± 0.17,p = 0.020), the genetic correlation between functional connectivity andanatomic variance was non-significant (ρg = 0.077 ± 0.38, p = 0.836),suggesting that different genes may influence structure and functionwithin the default mode, or that there is a lack of power to detect geneticoverlap at this point.

By balancing different graph theory based parameters to maximize“communication efficiency”while minimizing “connection cost”, Fornitoet al. (2011) developed optimized cost-efficiency network from restingstate functional MRI data in 58 healthy twins (16 monozygotic pairsand13 dizygotic pairs).While therewas little evidence for genetic controlof BOLD signal fluctuations in the 0.02–0.04 Hz, 0.04–0.09 Hz, or 0.18–0.35 Hz ranges, the heritability estimate for network connectivity in the0.09–0.18 Hz range was h2 = 0.60 (95% confidence interval 0.17–0.83),suggesting substantial heritability. De-composing this global network ef-fect in the 0.09–0.18 Hz range indicated that genetic influences were notdistributedhomogeneously throughout the cortex, and regional heritabil-ity estimates ranged from b0.10 to 0.81 (0.51 median).

A third recent manuscript found evidence for resting state connectiv-ity in normally developing children (age = 12). Using 21 monozygoticand 22 dizygotic healthy twin-pairs, van den Heuvel et al. (2011) foundsignificant heritability (h2 = 0.42, p b 0.05, CI = 0.05–0.73) for a globalnetwork measure, lambda (the normalized characteristic path length)derived fromresting state connectivity graphs,while gamma, thenormal-ized mean clustering coefficient, of the network was not. The authorstherefore suggest that even in childhood, the global efficiency of commu-nication in the network is heritable.

Candidate genes

There have been numerous candidate gene studies of resting statefunctional connectivity. However, most include only a single polymor-phism in relatively small samples and have not been replicated byother groups.Where possiblewe focus here on candidate genes studiedin at least two separate samples or with relatively large samples, usingresting state functional MRI.

The apolipoprotein E (APOE) gene is the most well-verified sus-ceptibility gene for the most common form of (sporadic late-onset)Alzheimer's disease (Coon et al., 2007; Farrer et al., 1997). The odds

ratio for individuals homozygous for the ε4 risk allele is 14.9, while theε2 allele is moderately protective (OR = 0.6) (Farrer et al., 1997). In anearly study, Filippini et al. (2009b) reported increased default mode con-nectivity, particularly in hippocampal and surrounding regions, in 18healthy ε4 carriers (ages 20–35 years) relative to 18 demographicallymatched non-carriers. This finding was replicated in a larger sample(N = 95) of healthy individuals between 50 and 80 years of age(Westlye et al., 2011). Recently, Trachtenberg et al. (2012) extendedthese results by examining 77 healthy participants aged 32 to 55 withdifferent APOE genotypes in a number of resting state networks. Rela-tive to ε3 homozygotes, ε2 and ε4 carriers showed similar connectivitypatterns. Indeed, carriers of the risk and the protective alleles were al-most identical across a number of resting state networks. Thus, whileit is clear from these studies that APOE influences functional connectiv-ity, the effects of the gene do not appear tomanifest in amanner reflec-tive of the link between APOE and Alzheimer's disease.

The COMT gene encodes for the catechol-O-methyltransferase en-zyme that is involved in the extra-neuronal degradation of dopamine,particularly in the prefrontal and temporal cortex (Matsumoto et al.,2003; Tunbridge et al., 2006). The Val158Met allele of COMT is a function-al polymorphism that results in a substitution of valine (Val) by methio-nine (Met) at amino acid 158 of the membrane-bound form of COMT(Lachman et al., 1996). Val homozygotes have a fourfold increase ofCOMT activity relative to Met homozygotes (Chen et al., 2004). Liu etal. (2010) examined the impact of the Val158Met polymorphism onprefrontal functional connectivity in 57 healthy subjects. Comparedwith heterozygotes, Val homozygous has decreased prefrontal-relatedconnectivities, suggesting that COMT's effects on prefrontal dopaminelevels modulate prefrontal default network connectivity.

Table 1 summarizes a list of recent studies focusing on genetics ofthe connectome. These include heritability analyses, candidate geneassociations, validation of new connectome metric methodologies,and genome-wide connectome-wide association scans.

Methodological issues

Imaging genetic methods are evolving, particularly those involvingthe connectome. Some connectome-related association studies usedfunctional data (resting state reviewed above), while others used net-works from diffusion imaging. In this section, we review some commonmethodological approaches for imaging genetic studies, and also presentsome of the more novel, uniquely network based analyses and methodsthat can provide for promising endophenotypes for future geneticstudies.

Almost all methods developed to date for general voxel-, surface-based, or ROI-derived imaging data, may also be applied to the rich phe-notypes computable from connectome data. Here we review some keymethods used for genetic analysis of images, even though not all ofthem have yet been applied to connectome phenotypes. As these meth-odologies have proven extremely successful in other works, the applica-tion to connectome phenotypes holds great promise for the future.

The field of imaging genetics started with candidate gene and can-didate phenotype studies, as it was uncommon, and costly, to geno-type subjects at more than a handful of genetic loci. Prior biologicalknowledge was typically used to select specific, well-studied geneticvariations or a single characteristic measure of brain anatomy, func-tion, or connectivity. This allowed people to test biologically plausiblehypotheses and assess genetic effects on the brain in a range of neurolog-ical and psychiatric disorders. Genetic association studies using imagesmay be broadly categorized into one of the 3 classes: (1) candidate-phenotype candidate-SNP/gene association (e.g., Joyner et al., 2009);(2) candidate-phenotype genome-wide association (e.g., Potkin et al.,2009a; Stein et al., 2010b), which is a traditional GWAS; and (3) brain-wide candidate-SNP/gene association (e.g., Braskie et al., 2011; Filippiniet al., 2009b; Rajagopalan et al., 2012; Roussotte et al., 2013), which is atraditional imaging analysis—performing association tests at each single

Table 1Table of recent genetic studies of brain connectivity, categorized by analysis type and imaging modality.

Study Modality Type of genetic analysis Connectomicmethodology

Finding

1 Braskie et al. (2012) Structural connectivity (HARDI) Candidate gene—NTRK1 Element-wise analysis on cortical connections NTRK1 associated with differences in the density of fiber connections2 Brown et al. (2011) Structural connectivity (DTI) Candidate gene—ApoE4 Nodal and global network measures APOE-4 by age interaction associated with network measures3 Canuet et al. (2012) Resting state EEG Candidate gene—APOE Lagged phase synchronization ApoE4 associated with differences in interhemispheric “alpha”

connectivity4 Chiang et al. (2012) Structural connectivity (DTI) Heritability and GWAS Voxel-wise genetic network of integrity Variance in white matter hubs were influenced by genetic variants

also associating with IQ5 Dennis et al. (2011) Structural connectivity (HARDI) Candidate gene—CNTNAP2 Regional and global network measures CNTNAP2 associated with global and regional network measures6 Duarte-Carvajalino et al.

(2012)Structural connectivity (HARDI) Kinship prediction Hierarchical element-wise, regional and global

measuresNetwork measures can be used to predict relatedness amongindividuals

7 Esslinger et al. (2011) Resting state and emotionaltask fMRI

Candidate gene—ZNF804A Right dorsolateral prefrontal cortex connectivity ZNF804A associated with reduced interhemispheric prefrontalconnectivity

8 Filippini et al. (2009a) Resting state and memory task fMRI Candidate gene—APOE Independent components analysis Increased resting state default mode co-activation in e4 carriers9 Fornito et al. (2011) fMRI network measures Heritability Regional and global network measures Global cost efficiency is heritable; the connectivity of some cortical

regions is more heritable than others10 Glahn et al. (2010) Resting state fMRI Heritability Independent components analysis Default-mode network was heritable11 Jahanshad et al. (2012c) Structural connectivity (DTI) Candidate gene—ApoE4 Element-wise analysis; multivariate analysis ApoE4 boosted network association to cognitive scores12 Jahanshad et al. (2012d) Structural connectivity (HARDI) Heritability and candidate gene—CLU Path length distance Path length distance was heritable and associated with CLU variant13 Jahanshad et al. (2012e) Structural connectivity (HARDI) Candidate gene—ApoE4 Element-wise analysis, nodal efficiency and

strengthApoE4 associated with FA based nodal strength

14 Jahanshad et al. (2013b) Structural connectivity (HARDI) Heritability + GWAS Element-wise, nodal, and global Variant in SPON1 found to associate with the density of specificconnections

15 Liu et al. (2010) Resting state fMRI Candidate gene—COMT Default mode network connectivity in ROIs COMT affects resting state prefrontal cortex16 Rudie et al. (2012) Resting state fMRI and DTI Candidate gene—MET Default mode network connectivity seeded in

the PCC and MPFC; TBSSMET associates with functional and structural connectivity intemporo-parietal regions

17 Schmitt et al. (2008) Structural MRI Heritability Global connectivity measures, small worldness Small worldness is implicated using networks based on geneticallycorrelated cortical regions

18 Scott-Van Zeeland et al. (2010) fMRI - Reward guiding learning task Candidate gene—CNTNAP2 Frontal lobe connectivity CNTNAP2 associates to frontal lobe task based connectivity19 Smit et al. (2008) Resting EEG Heritability Global network measures Clustering coefficient and characteristic path length of the EEG

network are heritable20 Trachtenberg et al. (2012) Resting state fMRI Candidate gene—APOE Independent components analysis Several resting state networks differ by genotype group

(e2/e3,e3/e3,e3/e4,e4/e4)21 Tunbridge et al. (2013) Resting state fMRI Candidate gene—COMT Independent components analysis COMT affects resting state prefrontal cortex22 van den Heuvel et al. (2013) Resting state fMRI Heritability Global network measures Global efficiency is heritable in brain networks of children

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Fig. 1. A menu summarizing some of the imaging genetics association studies in the literature. (Originally created by Dr. Andrew J. Saykin).

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voxel to form statistical maps. Eventually, the trend in imaging geneticsmay be to embrace the brain-wide, genome-wide association paradigm,where both the entire genome and entire brain are searched for non-random associations (Hibar et al., 2011; Jahanshad et al., 2013b; Steinet al., 2010a). This brings unprecedented opportunities to identify novelgenetic determinants of imaging measures and generate 3D maps oftheir effects in the brain. Fig. 1 summarizes some of the imaging geneticsassociation studies in the literature.

Univariate-imaging univariate-genetic association

The first completely unbiasedwhole-brain whole-genome searchwas a voxel-wise genome-wide association study (vGWAS) (Steinet al., 2010a) (See Fig. 2A). Independent association tests wereperformed for each pair of SNPs and voxels inmaps of local brain volumedifferences calculated by tensor-basedmorphometry (TBM) (Leow et al.,2005). This typical massive univariate approach resulted in a total ofmore than 1010 statistical tests. Only theminimum p-value across the ge-nome was recorded at each voxel to accommodate the huge number ofstatistical tests performed. The p-value distribution for themost associat-ed SNPwas modeled as a Beta distribution, Beta(1, Neff), where Neff is anestimate of the effective number of independent tests performed, ac-counting for the genetic correlation along the genome. The minimump-value at each voxel was then adjusted by the fitted theoretical

distribution, and corrected over the brain using the false discovery ratemethod (FDR) (Benjamini andHochberg, 1995). Thiswork is pioneering,as it showed that a full scan of the genome with brain imaging pheno-types is feasible. However, the drawbacks of this approach are alsoclear. Univariate-imaging univariate-genetic association tests completelyignore the spatial correlation in 3D imaging data and therefore typicallyhave poor reproducibility and low power. Also, with millions of billionsof statistical tests performed, the computational burden is extremelyheavy, and the colossal multiple comparisons correction often leavesno significant associations (Stein et al., 2010a). Clearly, more sophisticat-ed multivariate methods are needed to account for the spatial structurein both the imaging and genetic data.

Univariate-imaging multivariate-genetic association

Multivariate methods can be used tomodel the interaction betweenSNPs or the joint effect of multiple SNPs on imaging traits. SNP sets canbe formed by SNPs located in or near a gene, SNPs locatedwithin a genepathway, SNPs within evolutionary conserved regions, or other a prioribiological information. Alternatively, the grouping may be based on asliding window or the haplotype blocks to cover the entire genome(Wu et al., 2010). Grouping SNPs and performing set-based associationtests can alleviate the stringent multiple comparison correction com-pared to individual-SNP tests. Set-based SNP tests also offer the

Fig. 2. A cartoon figure summarizing univariate and multivariate association methods.

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possibility to accommodate genetic interaction, model joint effects ofSNPs, and test cumulative effects of rare variants. Importantly,multivar-iate methods often have improved reproducibility and increased powerrelative to univariate methods, especially when individual SNPs havesimilar but modest effects.

Early work on set-based tests combined test statistics or p-valuesfrom standard individual-SNP tests, so they suffered from many ofthe same problems as univariate tests (Hoh et al., 2001; Purcell etal., 2007). The simplest and classical way to test the overall effect of

multiple SNPs is to use a multiple linear regression. However, the highLD between co-segregated SNPs in haplotype blocks often produces col-linearity between the SNP regressors and can substantially overestimatethe available degrees of freedom in themodel. If it is reasonable to assumethat the effects of all SNPs are in the same direction andmost of the SNPsare causative, one can collapse all SNPs into a single regressor and per-form a so-called burden test (Li and Leal, 2008; Madsen and Browning,2009;Morgenthaler and Thilly, 2007;Morris and Zeggini, 2010). Alterna-tively, penalized and sparse regression techniques (Wang et al., 2013;Yuan et al., 2012) may be used, including ridge regression (Hoerl, 1985;Kohannim et al., 2011), the least absolute shrinkage and selection opera-tor (LASSO; Kohannim et al., 2012b; Tibshirani, 1996), and elastic net(Kohannim et al., 2012a; Zou and Hastie, 2005). (See Fig. 2B.)

Hibar et al. (2011) used amethod known as principal componentsregression (PCReg) to approach the collinearity problem. They firstperformed PCA on the set of SNPs to extract mutually orthogonal predic-tors that explain the majority of the total genetic variance, and then builta partial-F regression model. By grouping SNPs based on gene member-ship, a voxel-wise gene-wide association study (vGeneWAS) was carriedout, using the same imaging and genetic data as in vGWAS (Hibar et al.,2011; Stein et al., 2010a) showed increased power of their methods al-though no gene survived multiple testing correction, perhaps due to theover-simplification of the empirical and linear method, and the massiveunivariate nature of the method on the images.

Recently, Ge et al. (2012) presented a suite of methods to addressthe limitations of the existing whole-brain genome-wide associationstudies. They introduced to imaging genetics a kernel machine-basedmulti-locus model (Liu et al., 2007; Wu et al., 2011) that provides abiologically-informed way to capture the interactions between SNPsand model their joint effect on imaging traits. This method modelsnon-SNP covariates and offers a flexible framework to model epistaticeffects between genetic variants based on the choice of kernels, whoseelements are measures of genetic similarity between pairs of subjects.By using a connection to linear mixed models, the semi-parametricmodel can be fitted efficiently at each voxel, and a standard variancecomponent test can be used to make inference (Lin, 1997), yielding anapproximate chi-squared statistical map whose degrees of freedomcan adapt to the correlation structure of the sets of SNPs (Liu et al.,2007). A fast implementation of voxel- and cluster-wise inferencesbased on random field theory (RFT) (Friston et al., 2006; Ge et al.,2012; Worsley et al., 1996) was then applied to the statistical map,which makes use of the 3D spatial information in the imaging dataand performs multiple testing correction over the brain by implicitlyaccounting for the search volume and smoothness of the statisticimage. A head-to-head comparison to vGWAS (Stein et al., 2010a) andvGeneWAS (Hibar et al., 2011) using the same data set shows boostedstatistical power when combining these methods. Several genes wereidentified with whole-brain whole-genome significance for the firsttime.

Joint multivariate association

In order to respect themultivariate nature of both imaging and geneticdata, joint consideration of the imaging and genetic data appears to bepromising. One candidate for joint multivariate modeling is a regularizedversion of the two-block method, e.g., the canonical correlation analysis(CCA) (Hotelling, 1936) and the partial least squares (PLS) regression(Wold et al., 1983) with an additional l1 or l2 regularization to handlehigh dimensional data and perform variable selection. Both methodshypothesize that imaging and genetic data are linked through twounobserved latent variables, and seek linear combinations of the twodata blocks – as an approximation to the latent variable—that have themaximum correlation with each other (See Fig. 2C). Recently, Le Flochet al. (2012) applied the sparse PLS method in the context of imaginggenetics. Liu et al. (2009) proposed another two-block method knownas parallel independent component analysis (paraICA or PICA), which

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discovers independent components of the imaging and genetic data re-spectively, and at the same time determines and maximizes the correla-tion between the components of the two modalities. One challenge ofthis approach is that it may be hard to recover the contributing SNPsand locate the spatial effect in the brain from large genetic and imagingcomponents, making the results harder to interpret. A slightly differentbut related perspective on joint multivariate modeling is to considera multivariate multiple regression, i.e., regressing the entire imagingdata block on the genetic data, and impose different structures orregularizations on the regression coefficient matrix. Recent work inthis category include group-sparse multi-task regression (Wang et al.,2012a) and sparse multi-modal multi-task regression (Wang et al.,2012b),which used a group-sparse or group-lasso penalty to incorporatethe grouping of SNPs and to enforce a sparse structure across differentSNP groups and imaging modalities. Vounou et al. (2010) introduced asparse reduced-rank regression (sRRR) method. They reduced the rankof the regression coefficient matrix to a number much smaller than thenumber of imaging traits and the number of SNPs, and then factorizedthe coefficient matrix into the product of two small full-rank matrices,which are constrained to be sparse (See Fig. 2D). The method wasapplied to a whole-brain whole-genome data set in a subsequent publi-cation (Vounou et al., 2012).

Joint multivariate methods better capture the multivariate nature ofthe data and significantly reduce the number of statistical tests, alleviat-ing themultiple testing correction problem. Therefore, theymay provideincreased power relative to massive univariate methods. A commondrawback of thesemethods is the overfitting issue, especiallywhenhan-dling very high dimensional data. Currently, in most applications, datareduction is needed before these methods can be applied. Moreover,these complex multivariate methods normally use iterative optimiza-tion procedures, so computational demand is high, especially whenone needs to tune some regularization parameters and to validate theresults through cross-validation or permutation schemes.

Data reduction methods

Due to the ultra-high dimensionality of both the imaging and geneticdata, comprehensive modeling of whole-brain voxel-wise and genome-wide data remains challenging andmay cause a number of statistical andcomputational problems. Therefore, a balance is often needed betweenpure discovery methods and those that invoke data reduction. A prioribiological information may be used to restrict the analysis to someparticular brain regions or a wide list of possibly associated SNPs andgenes. Alternatively, various softwares and templates may be used tosplit the brain into a number of cortical and subcortical regions of interest(ROI), and extract a summarized measure from each ROI to get a coarsecoverage of the entire brain. Such parcellation is easy to perform andconsistent across subjects, but has the risk of missing patterns of effectsthat lie only partially within the chosen ROIs. Data-driven feature ex-traction approaches such as principal component analysis (PCA)and independent component analysis (ICA) may be used to avoidthese problems. Recently, Chiang et al. (2012) proposed a novel ap-proach to data reduction on voxel-wise data. Specifically, they selectedhighly genetically influenced voxels and then clustered these voxelsinto ROIs based on their genetic correlationwithin images. This approachcan potentially be applied to any imagingmodalities that show pleiotro-py. As for the dimension reduction of the whole-genome data, a prelim-inary univariate filtering is commonly applied. Multivariate methodsmay also be used iteratively, removing the lowest ranked variables ateach iteration (Guyon et al., 2002). Iterative sure independence screen-ing (Fan and Lv, 2008; Fan and Song, 2010) iterates a univariate screen-ing procedure, conditional on the previously selected features to captureimportant features that are marginally uncorrelated with response. Thismay be a promising method for data reduction and has been applied togenome-wide association studies (He and Lin, 2011).

Connectome methodologies

The human brain connectome can be represented as a matrix, or agraph, containing regions of interest as nodes and connections or corre-lations between them as edges. Based on this matrix or graph, manytopological graph theorymeasures can be evaluated on the connectome.These more abstract measures provide complementary information tothe more traditional imaging features, including details regarding themore global organization of structural and functional connections inthe brain. The genetic influences on these organizational propertiesmay reflect gene effects that are involved in a host of biological pathwayshaving global effects on the brain, rather than just those with an effect atthe cellular level or an effect on the integrity of brain tissues. Combininginformation on anatomical and functional integrity with measures ofnetwork organization will allow a more comprehensive understandingof genetic effects on the brain. As mentioned previously, one of severalpublically available toolboxes for calculating these measures is theBrain Connectivity Toolbox (Rubinov and Sporns, 2010). While ge-netic analyses on more standard and readily available measures suchas path length, efficiency, clustering coefficient, and small-worldnesshave been described previously, other measures to analyze and morerobustly understand the network are being continually developed andproposed.

Evaluation of measures on the structural “backbone”, or core, of thematrix by thresholding out low density connections can yield highersignal-to-noise and hence more stable results than including smallnoisy connections in the topological measures (Hagmann et al., 2008).This network core at a range of thresholds can also be used to describea ‘rich-club’ network, defining the set of high-degree nodes that aremore densely interconnected among themselves than nodes of alower degree (Daianu et al., 2013; van den Heuvel and Sporns, 2011);once genetic analyses are performed at these levels, this increasedsignal-to-noise could then facilitate more robust analyses and the op-portunity for successful replication studies. On another hand, othermethods are being adapted to the connectome to devise a multi-scaleframework to model the connectome at all the possible thresholdsusing filtration methods (Lee et al., 2012). These works improving andexpanding connectome-specific analyses methods are potential targetsfor the variety of genetic analyses described above.

Replication and future directions

As can already be seen, the connectome offers a rich and promis-ing target for genetic analysis. Some analyses have already screenedconnectomes from hundreds of twins and others for hundreds offamily members. They discovered genes that may affect our risk forAlzheimer's disease (Jahanshad et al., 2013b). Others have foundthat functional networks are heritable, with several promising candidategene findings. Even so, most genetic analyses consider a single trait—such as a diagnosis of Alzheimer's disease or schizophrenia. Clearly, inthe case of imaging—and connectomics in particular—we need to adaptgenetic methods to cope with networks, graphs, connectivity matrices,and other unusual data types (such as path lengths in networks(Jahanshad et al., 2012d)). In this review we have summarizedsome of the efforts to cope with the high dimension of genomicand imaging data at the same time, which will be vital in connectomics,as connectivity is essentially an N × N signal storing information onconnections between all pairs of brain regions.

Failures to reproduce findings

Early work by Potkin and others emphasized the sample sizes need-ed to detect and replicate a genetic effect of a SNP on a brainmeasure, orany other quantitative trait. Gene effects tend to be orders ofmagnitudesmaller thanmany other statistical effects on brain images—such as theeffect of a cognitive or behavioral task on brain activity in functional

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MRI, or the effect of a neurological disease such as Alzheimer's diseaseor epilepsy on brain measures such as hippocampal volumes. In clinicalstudies, a degenerative diseasemay reduce themean volume of a struc-ture (such as the hippocampus) by 10-15% on average, but large-scalegenetic studies (such as those by the ENIGMA and CHARGE consortia)suggest that it is rare for a SNP to affect hippocampal volume by morethan about 1% per allele. Even the most credible and highly replicatedfindings fromENIGMA influenced brain phenotypes by around one per-cent. Although a one percent difference in volumemay be highly signif-icant to an individual (equivalent to 3–4 years of aging), it stands toreason that most studies finding a much larger SNP effect than that, insamples of a few hundred subjects or fewer are somewhat suspicious,as power considerations suggest that such studies can pick up onlymoderate to large effects.

If a study reports a high effect size in a small sample, some skepticismis warranted, because small effect sizes are much more common.Although some published findings may be false positives or errors(Ioannidis, 2005), other more subtle phenomena such as the “winner'scurse” arewell known in quantitative genetics, where the effect size of afinding is often not as strong in a replication sample as it is in the initialdiscovery sample. With the development of large neuroimaging genet-ics consortia combining data from many cohorts worldwide, the risk ofspurious findings should be progressively lowered, and the chance ofa false positive effect remaining credible for a long time is greatly re-duced. The same meta-analysis approach may be able to resolve someof the controversies regarding very small but subtle effects on brainmeasures in psychiatry (Hibar et al., 2013b; Turner et al., 2013).

Replication and meta-analysis

One of the early disappointments in psychiatric genetics was thatgenes discovered to affect risk for schizophrenia and depression, wereoften not replicated in future studies, leaving the literature full ofun-replicated findings whose reliability and credibility is now unclear(Flint et al., 2010). In psychiatry, the issue of non-replication wasaddressed by forming very large consortia to pool data from many co-horts, often involving discovery and replication samples in the tens ofthousands (Sullivan, 2010). In addition, there has been a good deal ofdebate as to exactly what constitutes replication and what needs to bereplicated. For GWAS studies of common variants, the gold standardhas been replication of the exact variant in the exact direction in a sep-arate sample. As the field moves to examining rare variants, what con-stitutes replication is changing, as it is often not possible to replicate aspecific rare variant. Indeed, for findings based on rare variants, gene-level replication, based on a burden test, is considered acceptable.Ultimately, the goal of replication is to show that one's findings arenot spurious or unique to a single sample. In this context, the require-ment for biological validation of linkage/GWAS/sequence results pro-vides additional support for a finding.

In 2009, the ENIGMA Consortium (http://enigma.loni.ucla.edu) wasfounded to help pool data from imaging genetics studies worldwide,and perform studies with enough power to find single common variantsin that affect the brain. One such effort pooled data on hippocampal vol-ume, and intracranial volume, from 21,151 individuals scanned at 125institutionsworldwide, and discovered several common genetic variantsaffecting these brain measures (Stein et al., 2012). A follow-up effortscreening the genome for effects on all subcortical structures is under-way (Hibar et al., 2013a) and working groups studying brain connectiv-ity and integrity are harmonizing phenotypes to allow data pooling(Jahanshad et al., 2013a; Kochunov et al., 2012). For these efforts to suc-ceed, there needs to be a common effort to agree on brainmeasures thatcan be consistently computed from brain images worldwide. Promisingtargets for genetic analysis must be heritable, and reproducible to mea-sure. Zhan et al. (2013b) and Dennis et al. (2012) studied the stabilityof connectomic measures at different field strengths and their

repeatability over time; Jahanshad et al. (2012b) studied diffusion imag-ing protocol effects on genome-wide scanning results.

While efforts to identify common variants influencing brain connec-tivity are progressing, far fewer studies have attempted to examine theimpact of functional rare variation on these traits. Yet, there is growingrecognition that rare variation is important for human disease andnormal variation. Given that rare variants are uncommon in the gen-eral population, family studies offer an advantage over studies ofunrelated individuals, as related individuals are more likely to sharerare variants. To our knowledge, there are currently no efforts designedto develop imaging genetics consortia dedicated to the study of rarevariants.

An alternative line of work is exploring how disease risk genes affectthe brain, and how they affect measures derived from neuroimaging,including connectivity measures. As noted earlier, brain connectivityappears to differ in people who carry some common Alzheimer's dis-ease risk genes (CLU; Braskie et al., 2011) or risk genes for schizophrenia(NTRK1; Braskie et al., 2012) or autism (CNTNAP2; Dennis et al., 2011).Carriers of disease risk genes and people with the disease may alsohave common network abnormalities (Engel et al., 2013; Toga andThompson, 2013). Some of the larger psychiatric genetic efforts areunearthing SNPs that appear to confer disease risk in schizophreniaand autism, and efforts are underway to screen connectomic andother neuroimaging data to see what these variants do to the brain. Toease the search, informatics tools can make it easier to look up riskgenes or common variants and see how they affect brain phenotypesin various cohorts worldwide (e.g., ENIGMA-Vis; Novak et al., 2012). Amajor line of discovery will be possible once connectomic data can besearched and meta-analyzed with genome-wide, connectomic-widescreens. Such an effort will combine many of the methods discussedin our review, as well as others not yet conceived or imagined.

Freely available datasets

One recent benefit to the imaging genetics community is theavailability of some freely available datasets with MRI, DTI, GWAS,and other biomarker data. ADNI, for example (adni.loni.ucla.edu), freelyprovides both GWAS and MRI data to any interested and qualified re-searcher. There is no doubt that freely available datasets can lead tomany more published findings—if many analysis groups study the samedataset, they also greatly increase the scrutiny of the data for errors,which is helpful for data quality control and curation andpromotes scien-tific integrity. As not all neuroimaging data is made freely available, it isalso important to consider solutions for datasets that are restricted tousers at one site. Sometimes, restrictions on thedisseminationof personalgenetic datamay be imposed at the outset of a study, in a human subjectsconsent form, for example. Intermediate solutionsmay involve the send-ing of software and analysis protocols to many remote sites, and thereporting of statistical summaries or aggregates to aworking group. Rath-er than the sending of all imaging data to a centralized repository, thisdistributed processing approach has been adopted by consortia such asENIGMA; it is also computationally efficient as it draws on the computa-tional and personal resources of many sites in parallel, while respectingconstraints on the wider dissemination of scans or personal geneticinformation.

Conclusion

To summarize, connectome genetics is still a nascentfield. Yet even inits infancy, the connectome is proving to offer highly favorable pheno-types as genetic associationsmade or evendiscovered in the connectomehave already been replicated. In several cases, genetic variants associatedwith brain connectivity have been shown to affect other brainmeasures,or risk for disease. Clearly, future studies using meta-analytic methodsmay be required tomake stronger statements about genetic associationsthat are robust across multiple cohorts. Statistical approaches are

486 P.M. Thompson et al. / NeuroImage 80 (2013) 475–488

rudimentary compared to imaging-only or genetic-only methods. Thefield is moving towards a complete discovery science, seeking newand credible associations between whole-connectome genome-widedatawithout any a priori assumptions. Computationally efficient, biolog-ically plausible, and statistically powerful methods are urgently neededto tackle the ultra-high dimensional imaging andgenetic datawith com-plex covariance and noise structures.

Acknowledgments

P.M.T. is supported, in part, by NIH R01 grants NS080655, MH097268,AG040060, EB008432, MH089722, HD050735 and P41 EB015922. D.C.G.is supported, in part, by NIH R01 grants MH078143, MH083824,MH080912, HL113323, and MH097940. T.E.N. is supported by NIHR01 EB015611-01 & U54MH091657-03.

Conflict of interest

The authors have no conflicts of interest to disclose.

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