Reproducibility of Whole-brain Connectivity Networks

By Christopher Parker

Imaging & Biophysics Unit,UCL Institute of Child Health,30 Guilford Street, London,

WC1N 1EHUnited Kingdom

Thesis for Masters of Science in Medical Image Computing

Supervised by Dr Chris Clark and Dr Jonathan Clayden

August 2011

Words: 9,049

Abbreviations

AD Alzheimer DiseaseCu Cuneus CG Cortical gyrusCV Coefficient of VariationFI Op Frontal inferior opercular FI Or Frontal inferior orbital FI Tr Frontal inferior triagulate FM Frontal middle FS Frontal superior OM Occipital middle Or Orbital OS Occipital superior OT LaFu Occipital temporal lateral fusiform OT MeLi Occipital temporal medial lingual OT MePa Occipital temporal medial parahippocampal PaS Parietal superior PD Ci Post dorsal cingulate PeI An Parietal inferior angular PeI Su Parietal inferior supramar Po Postcentral Pr Precentral Pre Precuneus PV Ci Post ventral cingulate Re Rectus ShIn Insular short Su Subcallosal TI Temporal inferiorTM Temporal middleTS La Temporal superior lateral TS PlPo Temporal superior plan polar TS PlT Temporal superior plan tempo TS Tr Temporal superior transverse

Introduction

Probing the microstructure of the brain in vivo is possible with imaging techniques such as diffusion MRI, which exploit the diamagnetic property of water and its movement over time. Due to thermal energy, water molecules in a medium diffuse according to the random probabilistic nature of Brownian motion. The probable displacement limits of water molecules in 3-dimensional space relative to a point of origin will be spherically bounded with increasing diameter as a function of time. Such diffusion, where there is a uniform average distance travelled in any direction, is termed isotropic. Diffusion of water in biological tissues is not generally isotropic but is commonly restricted due to cellular and sub-cellular components. In areas of biological tissue, preferential diffusion in a given direction will mean that the probable displacement of molecules will be elliptically bounded, with the length of the major and minor axes increasing over time, a property termed anisotropy [Mukherjee et al 2008]. In cellular structures such as white matter axon fibres, water preferentially diffuses in parallel to the direction of the fibre and is relatively restricted perpendicularly. This property allows the differentiation of fibre tracts and their orientation from surrounding tissue based on diffusion anisotropy. Specifically, white matter; where water diffuses parallel to the fibre direction, can be distinguished from grey matter, where there is relatively little diffusion anisotropy. dMRI consequently provides an excellent tool for investigation of the fibre network of the human brain in vivo.

Figure 1. Left: Two streamline tracts arising from seed voxels (marked in dark green) track the likely fibre path by following the principal direction of the diffusion tensor (from [Ciccarelli et al 2008]). Right: A fractional anisotropy map of the human brain showing a colour representation of the principal 3-dimensional direction of the diffusion tensor at each voxel (red: left-right, blue: up-down, green: inwards-outwards, from https://www.ynic.york.ac.uk/events/news/image-of-the-month).

dMRI uses diffusion-sensitising gradients in T2-weighted spin-echo echo-planar sequences [Mascalchi et al 2005] to measure the directional diffusion of water molecules in biological tissues. Voxel measurements obtained from dMRI are derived from the diffusion tensor and include mean diffusivity (the average molecular movement independent of direction) and fractional anisotropy (the deviation from isotropy). dMRI data can provide the direction of maximum diffusion in each voxel of a brain image, which is thought to represent the dominant direction of white matter fibres at that location. These vectors can be used to reconstruct lines of connectivity that are assumed to represent the underlying brain structure, allowing the 3-dimensional reconstruction and analysis white matter fibre connectivity, a procedure termed tractography [Ciccarelli et al 2008].

Conventional, or deterministic streamline tractography examines the principal eigen-vector of the diffusion tensor at each voxel and propagates a streamline, or track through the brain (Fig. 1) which follows connected voxels until a stopping criteria is reached (the change in diffusion angle is too great or fractional anisotropy too low). This technique assumes that water predominantly diffusion along a main direction within each voxel and therefore is insensitive to tracking the correct path through voxels that contain diverging or kissing fibres. One approach to overcome this limitation has been to model the uncertainty in fibre orientation at a voxel level using probabilistic streamline tractography [Behrens et al 2007, Parker et al 2003]. This technique models the uncertainty in tract distribution and produces a distribution of streamlines whereby the streamline density is proportional to the expected density of

nerve fibres at a given voxel. The probabilistic approach provides a more comprehensive estimation/tracking of connectivity between seed and target regions than traditional deterministic methods, as a wider configuration of fibre arrangements are modelled using probability. In agreement with autopsies of human brains, the general organisation of the main fibre tracts, as determined by dMRI tractography, is conserved between healthy individuals, and provides the physical infrastructure for brain function.

The millions of neuronal connections present in the human brain communicate on a macro-structural scale via fibre tracts, to control all levels of physiological and psychological function. In cases of neurological disease, landmarks of neuronal health such as myelination, brain lesions, and connectivity between neurons may be adversely affected. Such changes can affect the local directional diffusion of water, but may also affect the organisation of the brain on a larger scale, as white matter structures may deteriorate or adapt due to a condition. dMRI tractography is a way of measuring these changes and can therefore aid in the examining of neurological health [Ciccarelli et al 2008]. While many studies have looked at single fibre tracts to obtain clinical information, few attempts have been made to characterise the complete brain as a connected network of fibres using dMRI tractography. A definitive method for quantifying the integrity of the whole brain connectivity network has not been determined, nor is it clear how this network might vary both in healthy individuals or in pathological situations.

Grey matter is most abundant in the cortex and contains densely connected dendrites that receive nervous stimulation from white matter nerve fibre bundles originating from other brain structures. The nerve fibres transmit electrical signals along their axons which encode information that collectively coordinates and controls physiological and psychological activity. The wiring of nerve axons therefore forms the physical infrastructure for functional communication between brain regions. Since the organisation of brain fibres at the whole brain level forms a complex network, graph theoretical analysis has recently been employed to investigate aspects of brain network connectivity [3]. Graph theoretical analysis is a concept first developed by Leonhard Euler in 1736 that provides a mathematical framework for the study of interacting elements composing a system (Fig. 2) [Euler 1736]. The technique has recently been applied to study the structural and functional connectivity networks of the brain [Bullmore & Sporns 2009]. Using graph theoretical analysis, nerve fibres can be represented as edges that form connections between regions, or nodes. Subsequently, various measures of complex networks can be applied to whole-brain networks to quantify aspects of its architecture, such as path length (the number of connections traversed to connection two nodes), node degree (the number of connections from a node), clustering (how density of connections between nearest nodes) and global efficiency (inversely proportional to pathlength) [Bullmore & Sporns 2009, Watts and Strogatz 1998]. Structural networks are obtained from dMRI tractography data and are derived from the measurement of diffusion anisotropy occuring along white matter fibres, depicting the organisation of the structural wiring of the brain. Developing measurements of clinical relevance that reflect the global organisation of brain connectivity may provide novel biomarkers of white matter health, which can then be used for diagnosis and prognosis of neurological disease and in identifying different neurological phenotypes.

Figure 2. A graphical representation of the network in Euler's seven bridges problem. Land masses are network nodes and lines (or edges) between them represent bridges. Euler's problem was to visit all land masses by traversing each bridge only once. The problem has no solution but led to the concept of graph theory.

A number of studies have examined groups of healthy subjects in order to characterise the normal topology of the structural and functional network. Previous studies have shown that like almost all complex networks, both the structural and functional networks have a small-world topology [Bassett & Bullmore 2006, Watts and Strogatz (1998), Hagmann et al 2008]. Such networks are characterised by a similar global mean pathlength and a higher mean clustering coefficient than equivalent measures in a random network with the same node degree distribution and therefore have a network configuration that

is somewhere between random and a regular lattice. This organisation enables efficient information transfer between any two elements of the system and simultaneously a high degree of local communication. It has been suggested that such configurations are a result of brain evolution that favours the development of neuroanatomical regions that are efficiently wired for self-communication and communication with native regions [Sporns et al 2000]. Analysis of networks derived from dMRI tractography analyses have shown that the structural network contains hubs; regions that are relatively highly connected or highly central to network communication (Fig. 3) [Gong et al 2008, Hagmann et al 2008, Shu 2009]. Occipital and parietal cortical regions are frequently highly connected and contain hub regions such as the left and right precentral cortical gyri and precuneus. The structural network may provide the physical backbone that constrains functional interactions. Techniques such as functional MRI (fMRI), electroencephalography (EEG) and magnetoencephalography (MEG) can be used to measure the strength of a causal relationships occuring over time between regions and therefore to reconstruct the functional brain network. A comparison of diffusion imaging and resting state fMRI data reveals a close relationship between structural and functional connections, including a significant overlap in the hub regions found in structural and functional networks [Hagmann et al 2008].

Figure 3. Hubs of the structural whole-brain network. Blue circles are network nodes and represent brain regions defined in this study [Hagmann et al 2008]. The node size is proportional to the frequency with which the region ranked highly in centrality measures among a small group of subjects.

Brain disease or trauma results in significant damage to the structural network and some disease have been described as disconnection syndromes [Catani & fftyche 2005]. Alzheimer's disease (AD) is a neurodegenerative disorder characterised by progressive patterns of regional brain atrophy and white matter degeneration [Selkoe 2002]. Loss of small-worldness and changes in other network attributes, such as the distribution or abundance of hub regions, have been reported in cases of AD and other neurological diseases such as schizophrenia using a variety of imaging techniques such as dMRI, structural MRI, EEG and MEG [Chun-Yi et al 2010, Stam et al 2007, Stam et al 2009, de Haan et al 2009]. A recent report that compared the structural brain network of a large group of mild AD subjects with that of healthy individuals found an increase in the average pathlength and a decrease in global efficiency in the disease state. Nodal efficiency (which reflects the how easily a particular node can transfer information through the network to other nodes) of frontal cortical regions, such as the superior and inferior frontal gyri, was decreased in mild AD compared with healthy subjects [Chun-Yi 2010]. In addition, global and local efficiency as well as pathlength were highly correlated to cognitive and behavioural scores. Moreover, the overlap found between the regions containing deposition of the toxic amyloid-β protein (the pathological hallmark of AD) and those designated as hubs by network analysis has led to the hypothesis that AD pathology may result from a targeted attack of these highly central cortical regions [Sporns 2011]. Together with other reports, these investigations imply a loss of efficiency of information transfer in the mild AD brain, perhaps as the integrity of white matter connections between cortical regions deteriorates and communication becomes more sparse. These results show that both global and local changes in mild disease states can be revealed through network analysis and can perhaps be employed to detect early changes in the course of neurodegenerative disease. Graph theoretical analysis of structural and functional brain networks may lead to the discovery of biomarkers that are predictive of AD progression in the asymptomatic phase where future treatments will be most effective and where diagnosis is currently problematic.

Distinct patterns of network architecture appear to be associated with development and ageing. Autism is a neurodevelopmental disorder characterised by disturbance of social interaction and

emotional processing with unknown cause. Studies of autism brains using dMRI have found a disorganisation of white matter pathways [Keller et al 2007] and disturbance of the reformation of the default-mode network after periods of psychological activity [Kennedy et al 2006]. Intriguingly, no studies have reported changes in network topology in childhood development, where it may be expected that changes in network structure may reflect rapid physiological, cognitive and psychological maturation. There is evidence that the topology of the network may reflect senescence. For example, functional networks in older people had a lower cost efficiency when compared to a younger age group [Achard, S. & Bullmore 2007]. Such changes could be caused by continual maturation of nerve cells and thus the connections that they bridge between different anatomical regions. It is thought that lower global efficiency or higher mean path length are indicative of a general reduction in nerve fibre connections and may be associated with the cognitive decline that can accompany old age [Bullmore, E. & Sporns 2009].

Despite a number of reports regarding the healthy configuration of the structural network, there remains no definitive method for obtaining the structural connectivity network and methodological variation means that results are not directly comparable between studies. The extent to which patient motion, head position and computational methods used in artefact correction, cortical parcellation, streamline tractography and connection strength measurement affect the reproducibility of network measures within a single subject has not been investigated in detail, despite significant differences in the methods used to obtain and analyse the structural network. A single attempt has been made previously to investigate the reproducibility of graph theoretical measurements obtained from structural networks [Vaessen et al 2010]. The study investigated the effect of the diffusion gradient scheme on reproducibility of small world metrics, but no dependency on reproducibility was found. Another recent report has investigated test-retest reliability of functional network measurements obtained from MEG [Deuker et al 2009]. The study examined a small group of subjects that each had two repeat MEG tests within a small time interval and found high reproducibility of network measures, particularly for networks obtained using lower frequency bandwidths. Identifying and reducing sources of variation in structural networks from a single subject will give greater reliability and robustness to network analyses, facilitating the delineation of group effects on network measures in clinical studies.

Characterising intra-subject variation is a necessary pre-requisite for understanding network variation occuring in health and disease and reduction of such variation may give insights into a best-practice technique for network analysis. This project examines repeat diffusion-weighted imaging data from 3 individuals to characterise the reproducibility of various network measures obtained from graph theoretical analysis. Developing reproducible network measurements of clinical relevance may provide novel biomarkers of white matter health that may be used for investigation of connectivity in neurodevelopment, neurological disease or in healthy subjects.

Methods

Subjects and Image Acquisition

Three healthy subjects (subjects 1, 2 and 3 were all females with age 26, 25 and 26 respectively) were scanned at Great Ormand Street Hospital, London. T1-weighted images of (1mm)3 resolution were acquired with a 3D FLASH sequence (TR = 11ms,TE = 4.94ms ,α = 15o ) on a 1.5T Siemens Avanto MRI scanner. A diffusion-weighted echo planar sequence (TR = 7300ms, TE = 81ms) with 60 orthogonal diffusion directions (b= 1000s/mm2) was used to acquire DTI images of (2.5mm)3. The diffusion-weighted sequence was repeated three times for each subject.

Image Processing

Pre-processing

In order to reduce image acquisition artefacts and to determine diffusion tensor characteristics, the raw T1-weighted and diffusion acquisition data were pre-processed using the diffusion-specific FSL-FDT algorithm implemented in TractoR [Clayden et al 2011, Behrens et al 2007].

The processing pipeline consists of five stages. The first stage converts DICOM files into a 4D NIFTI volume. The second corrects the images for eddy current induced distortions. This is followed by the creation of a brain mask, which enables the extraction of only brain voxels. Next, the diffusion tensor characteristics such as principal eigenvectors and FA values are calculated. The BEDPOSTX (Bayesian Estimation of Diffusion Parameters Obtained using Sampling Techniques) algorithm [Behrens et al 2007] was then performed using a 2 fibre model at each voxel. The BEDPOSTX algorithm uses Markov chain Monte Carlo sampling to estimate diffusion MRI parameters, creating from the raw data the necessary precursor files for probabilistic streamline tractography.

Cortical Parcellation

In order to identify regions of interest, Freesurfer was used to completely parcellate the cortical surfaces of the T1-weighted image. The parcellation scheme automatically assigns a neuroanatomical label to each location on a cortical surface model of the image based on probabilistic information from a manually labeled training set [Desikan et al 2006, Fischl et al 2004,http://surfer.nmr.mgh.harvard.edu/]. Following parcellation, TractoR was used to extract all 58 cortical gyri volumes of interest from the T1-weighted volume.

Registration

In order to segment the cortical structures of interest in the diffusion-weighted images and to enable spatial normalisation of diffusion images from multiple scans, the TractoR implemented FSL affine co-registration algorithm (FLIRT) was used to co-register the T1-weighted volume and b=0 diffusion-weighted scan [Jenkinson & Smith 2004], from which the co-registration of extracted cortical gyri regions were also determined. The registration algorithm used a correlation ratio cost function with 9 degrees of freedom. Trilinear interpolation was used to estimate voxel intensities between voxels occuring due to sub-voxel transformations. The transformation matrix that produced the best measure of correspondence between the images was used to inversely transform each extracted cortical region to the T1-weighted image space.

Streamline tractography

Binarised forms of each transformed cortical region were used for streamline tractography. Conventional probabilistic streamline tractography [Behrens et al 2007], performed with the FSL

ProbTrack algorithm implemented in TractoR, was used to estimate the density of white matter fibre trajectories arising from each cortical region. The stopping criteria employed for streamlines prevent them from leaving the brain, from passing through a voxel that has already been visited, or from curving by more than 80 degrees. This procedure for generating streamlines is repeated a large number of times for a particular seed point, generating a spatial distribution for the tract running through the seed point. 100 streamlines per voxel were seeded for all voxels in each parcellated cortical region and the total number of streamlines passing through each voxel in the entire brain volume were recorded.

Graph theoretical analysis

In graph theoretical analysis, cortical regions are represented as network nodes (or vertices) and connections between them as edges (or links). Whole-brain and single region connectivity measures can subsequently be obtained using graph theory.

Although DTI does not observe the direction of fibre pathways at the voxel level, it may be argued that some directionality may be inferred by examining the distribution of streamlines seeded from one region to another when compared with streamlines seeded in the opposite direction. For example if there is a strong nerve fibre linking two regions then streamlines seeded from both will have approximately equal streamline intensity in each end region, and it may be argued that these regions are mutually connected with equal connection strength. However, when a nerve fibre originating from region A becomes increasingly less coherent as it nears the target region B, it may be considered likely that the strength of connection is directionally asymmetrical. Such a situation is commonly represented by streamline tractography data, where the directional strength of connection is higher for seed regions with that have more coherent fibres branching to, than from the target region. In this analysis, the less commonly used directed graph is employed to study cortical network reproducibility.

A directional measure of connection strength between each cortical region was determined using one of two measures: the maximum streamline density in the target region t of streamlines seeded from the starting region f (measure 1); and the mean streamline density in the target region divided by the distance between the regions (measure 2). Performing this calculation between N cortical regions produces an N-by-N directional association matrix of connection strengths between all regions. Cortical regions that are connected with a connection strengths (S) above the threshold are considered connected (Cft = 1) whereas those equal or less are not considered connected (Cft = 0). For a threshold T, this can be described as:

If Sft > T, Cft = 1 connectedIf Sft =< T, Cft = 0 not connected

Applying a threshold to the adjacency matrix produces a binary adjacency matrix where only the desired number of strongest connections form the edges of the network (Fig. 4).

The connection density of a graph describes the fraction of edges that exist in the network as a proportion of the total possible connections present before thresholding. A connection strength threshold can be chosen by using a percentage of the maximum connection strength found in the association matrix, or by using a percentage that produces a desired connection density, where connection density was calculated as the number of connections after thresholding as a fraction of the total number of possible connections (considered as N2 – N). Since using a fixed percentage of the maximum connection strength is particularly sensitive to outlying connection strengths, networks were constructed to contain a given percentage of the strongest connections (percentages are described below).

Fig. 4. An image representation of an adjacency matrix. With the matrix origin in the top-left corner, entries describe the presence of a connection between the seed region (matrix column) and target region (matrix row). Matrix entries of 0 and 1 are displayed as black and white, respectively. The matrix is asymmetrical either side of the diagonal as not all connections are reciprocated.

In a directed network, three scenarios exist for a single connection C between any two nodes f and t. These are that both are connected to each other (ie Cft = 1 and Ctf = 1), or either one is connected to the other but the other does not reciprocate the connection (for example, Cft = 1 and Ctf = 0).

Node out-degree and in-degree

Node degree is the simplest measure of node connectivity. Node out-degree; O, counts the total number of outgoing connections from a particular node, whereas in-degree; I, counts the number of incoming connections. For the nth node, the out-degree and in-degree were calculated as follows:

Clustering coefficient

The clustering coefficient of a graph measures the extent to which the connections from a particular node are themselves inter-connected. Specifically, it is calculated as the number of connections existing between the nearest neighbours of a node divided by the total number of possible connections between neighbours given their node out-degrees [Watts & Strogatz 1998]. The clustering coefficient of the nth node was calculated by considering outgoing connections, as follows:

Mean Pathlength and efficiency

A path exists between two nodes that can be connected by some combination of edge traversal. The path length P between two nodes (Pft) is calculated as the minimum total number of edges traversed to travel through the network from one node to another [Watts & Strogatz 1998]. This describes how close the nodes are in terms of network topology. The mean path length of a node (Ṕn) is the average of path lengths that connect this node to all other nodes;

The average mean pathlength of all nodes in the network gives a general indication of the mean number of paths travelled to connect any two nodes in the network and is calculated as follows:

The efficiency of a node (Ef) measures how directly connected the node is integrated in the network and is inversely proportional to the average mean pathlength. The general efficiency (En) of the network is the average of all node effiencies, or the inverse of the average mean pathlength across all nodes [24]. A high efficiency (or low average mean pathlength) describes a network that is configured to allow effective communication between any two nodes by traversing only a small number of edges. The calculation was as follows:

Where

Betweenness Centrality

Betweenness centrality (X) (referred to hereafter as centrality), is a measure of how essential a given node is as an intermediate node in all minimum paths between other nodes in the network [Freeman 1977]. It is the cumulative fraction of shortest paths between all other nodes in the network that pass through the given node, divided by the total number of connections in the network and is calculated for the nth node as follows:

Network hubs are nodes that are important for mediating a large proportion of communications within the graph and are defined as a node with high degree or centrality [Bullmore & Sporns 2009]. In this report, a node with centrality above 1 standard deviation of the mean was classified as a network

hub. For each network configuration produced, hubs were classified and recorded.

Small worldness

The small world phenomenon is a commonly reported characteristic in complex networks and signifies a network architecture which is somewhere between a random network and a regular lattice [Watts & Strogatz 1998]. A random network will have a relatively short mean pathlength and low clustering coefficient compared to a regular lattice, which will exhibit higher mean path length and higher clustering. A small world has both a shorter mean pathlength than a random network and higher clustering. The small-worldness of a network can be calculated as the ratio of clustering coefficient to mean pathlength after both measures have been normalised by their equivalent values found in random networks with the same connection density and degree distribution. To make this calculation, networks of the same connection density but containing a completely random combination of connections were generated and their mean mean pathlength and mean clustering coefficient computed. An index greater than 1 indicates that the network has small-world properties [Humphries et al 2006]. The small-world index was then calculated as follows:

SWIn =

All graph theoretical analyses used in this investigation were developed in R (v2.13.0).

Reproducibility of graph theoretical measures

Availability of repeat diffusion weighted scans of a single subject allows the assessment of reproducibility in graph theoretical measures. Graph theoretical analysis was applied to repeat diffusion-weighted scans from three individuals. While a large amount of data was generated in this analysis, reproducibility analysis attempts to focus on the measures deemed most significant for clinical research and for describing the existing variation and sources of such variation. These are the connection strength measure, per-node network measures, global network measures and the classification of functional nodes such as hubs.

Connection strength measure

The reproducibility of network measures was first investigated in three repeat scans of a single subject (subject 1) using two different measures of connection strength. A graph containing 30% of the strongest connections in the network was derived from repeat scans using connection strength measure 1 and 2. The standard deviation and coefficient of variation (CV) of each node network measure (such as node outdegree, indegree, mean pathlength, clustering coefficient and centrality) across repeat scans was calculated for subject 1. These mean node measures and corresponding CVs were then averaged over the total number of nodes, in order to give a general indication of the reproducibility of per-node measures. Additionally, the reproducibility of global network measures (such as mean node degree, mean mean pathlength, global efficiency and the small world index) was calculated across repeat scans for subject 1. The connection strength measure that produced networks with the best overall reproducibility was then used in subsequent analyses that investigated intra and inter-subject reproducibility in more detail.

Intra-subject

Networks were examined over a range of densities from 10% to 40%, since these represent the strongest connections and cover the range that has been reported in the literature. At each connection density, the average CV for each graph measure and the CV of mean graph measures were computed

and compared, as described before. The reproducibility in the classification of hubs according to previously mentioned criteria was also examined.

Regardless of the connection density chosen, it can be appreciated that the major source of variation for network measurements is the reproducibility of the connection strength measure between two regions. Intra-subject variation in connection strength matrices was therefore examined for connection strength measure 1 and 2.

Inter-subject

Intra-subject reproducibility analysis was repeated for all three subjects and reproducibility of global and mean node measurements across three scans were compared at a variety of connection densities in order to examine whether aspects of general variability observed in subject 1 was observed in other subjects undergoing repeat scans.

Results

It was first determined that the second measure of connection strength was more reproducible than the first for subject 1. The source of existing variation was then characterised by looking at the connection strength matrix for this subject for these two connection strength measures. Next, reproducibility of graph measures and network hubs is described across a range of densities in all subjects for connection strength 2. Finally, a potential underlying cause of variation if presented.

Connection Strength Measure

In subject 1, a number of highly reproducible connections (either present or absent in all scans) were found using both connection strength measures (Fig. 5). 2971 of 3306 connections were the same across repeat scans in adjacency matrices derived from measure 1 and a total of 335 connections were absent in one or both scans. Using measure 2, a total of 3063 of 3306 connections were completely reproduced whereas 243 had varying configuration between repeat scans. These differences are summarised in Fig. 5.

Figure 5. Reproducibility of network edges at 30% connection density, obtained by thresholding association matrices constructed using two different measures of connection strength. White and black entries represent the presence of absence of a directional connection between cortical regions (direction is from the column to row index) found in all repeat scans of subject 1 using both measures of connection strength. Red entries depict connections present in all adjacency matrices derived from connection strength measure 2 but absent in all from measure 1, whereas yellow entries represent connections present in all adjacency matrices using measure 1 but absent in all using measure 2. Connections that have varying presence/absence between repeat scans from measure 1 are shown in blue and from measure 2 are shown in purple. Connections that had varying presence/absence in using both connection strength measures are shown in green. Cortical region abbreviations are described in the Abbreviations section.

Differing edge configuration between repeat scans leads to slightly different intra-subject network topologies. The reproducibility of per-node and global network measures, their standard deviation and coefficient of variation, give a summary of the main characteristics of the network and are shown for these two measures in Table 1.

Networks from subject 1 using connection strength measure 1 and 2 had similar architectures, as shown by their similar global network properties. Mean node degree was identical for both connection strength measures, as the connection density was fixed at 30%. The per-node averaged node degree CV was reduced from 6.17% to 5.71% using the second measure of connection strength. Reduction in average per-node CV was found for all graph theoretical measures apart from indegree and centrality, which were increased slightly.

The reproducibility of all global network measures was increased for connection strength measure 2. The largest change in CV was observed for the mean clustering coefficient (from 1.189% to 0.224%) and small world index (from 1.122% to 0.46%). In subject 1, average per-node CV, which was less than 6.5% for all graph measures apart from centrality (which was 15.15%), was generally orders of magnitude higher than the CV of mean graph measures, which was less than 1.2% for all graph measures.

Subject1* 1 2 3

μ ± σ CV (%) μ ± σ CV (%) μ ± σ CV (%) μ ± σ CV (%)

Per-nodeNode degree 17.4 ± 1.0 6.17 17.4 ± 0.1 5.71 17.4 ± 2.5 14.69 17.4 ± 1.1 6.04

Indegree 17.4 ± 0.9 5.48 17.4 ± 0.9 5.54 17.4 ± 2.5 14.21 17.4 ± 0.9 5.79Mean Pathlength 1.81 ± 0.04 2.29 1.82 ± 0.04 2.05 1.82 ± 0.09 5.15 1.80 ± 0.04 2.23

Clustering Coefficient 0.62 ± 0.03 4.37 0.62 ± 0.03 4.11 0.60 ± 0.04 7.16 0.55 ± 0.02 3.72Centrality 0.0149 ± 0.0017 15.14 0.0153 ± 0.0017 15.6 0.0154 ± 0.0016 12.67 0.0149 ± 0.0018 17.22

GlobalMean Mean pathlength 1.81 ± 0.01 0.422 1.82 ± 0.00.. 0.174 1.82 ± 0.01 0.976 1.80 ± 0.00.. 0.271

Mean Clustering Coefficient 0.62 ± 0.01 1.189 0.62 ± 0.00.. 0.224 0.60 ± 0.02 2.74 0.55 ± 0.00.. 0.362

Mean Centrality 0.0149 ± 3.12x105 0.021 0.0153 ± 3.1x105 0.020 0.0154 ± 1.56x105 0.101 0.0149 ± 0.0018 0.521Global Efficiency 0.55 ± 0.00.. 0.344 0.55 ± 0.00.. 0.140 0.549 ± 0.0044 0.802 0.56 ± 0.00.. 0.221Small World Index 1.90 ± 0.02 1.122 1.96 ± 0.01 0.460 1.88 ± 0.03 1.950 1.89 ± 0.02 0.800

Table 1. Intra-individual reproducibility of whole-brain and per-node graph theoretical measures. Networks of 30% density were obtained by thresholding connection strength matrices. Upper: Per-node reproducibility. Average (over all nodes) mean graph measures ± average standard deviation (μ ± σ) over three repeat scans and their average coefficient of variation (CV) for subjects 1, 2 and 3 are shown in the top half of the table. The average CV for node degree, mean pathlength, clustering coefficient, global efficiency and small world index were reduced using the second measure of connection strength, whereas indegree and centrality were increased. All subjects have similar averaged measures. Measures obtained from repeat scans of subject 2 appear more variable. Lower: Global reproducibility. The bottom half shows the intra-subject mean, standard deviation of the mean and CV for all subjects. A larger reduction in CV of global measures than per-node measures was found using the second measure of connection strength. The ‘*’ symbol denotes networks obtained using the first measure of connection strength.

In the second measure of connection strength, whereas averaged CV of node degree was 5.71% in subject 1, node CVs ranged from 0% to 16.7% with the highest CV found in the right Po CG and no variation found in 8 nodes (8 10 14 26 30 32 48 and 50), including 8 and 30. Indegree CV ranged from 0% (found in four regions, for example in the left and right Re CG) to 17.61% (right TI CG). Pathlength CV of all nodes ranged from 0% (left FS CG) to 6.50% (right OT MeLi CG). Clustering coefficient

ranged from 0.51% (left Su CG) to 11.39% (right OT LaFu CG) and centrality ranged from a highest CV of 100.69% (left TS Tr CG) to a lowest of 0.19% (right Po CG). Between nodes, a weak correlation was found between the CV of one graph measure and that of another (clustering coefficient vs pathlength r=0.57, node degree and pathlength r = 0.62). Of all graph measures, centrality was the least reproducible per-node measure, with a mean CV of 15.60% in subject 1. Reproducibility of global network measures was high for subject 1, with CV less than 0.5% for all global measures examined.

Connection Strength Matrix

There is currently no definitive method for measuring connection strength between two regions using diffusion-weighted imaging. It is however a necessary and important pre-requisite to graph theoretical analysis and an important factor in determining network reproducibility since different measures of connection strength may be more or less sensitive to variation in streamline density data.

Differing network architectures between scans were ultimately derived from the thresholding of connection strength matrices that had some degree of inter-scan variation. A different distribution of connection strengths leads to different threshold when using a percentage of the maximum, and thus to a different configuration of edges between scans. Figure 6 demonstrates the variation existing in connection strengths using measure 2 in all edges of the network, before thresholding. Both measures had a similar general pattern of variation; a relatively high CV for inter-regional connections and a lower CV for intra-regional connections. Measure 1 had a mean CV of 38.72% over all connections. Inter-hemisphere mean CV was 46.76% whereas intra-hemispheric connection CV was 30.68%. Using measure 1, the lowest CV (0.9%) was found between region L TM CG and L TI CG. The highest CV (141.42%) and therefore least reproducible connection using this measure was found in a total of 164 different connections (between region the left PD Ci CG and left FI Op CG, for example). The mean CV for all connections using measure 2 was 40.94%, with a mean inter-hemispheric connection strength CV of 53.36% and an intra-hemispheric connection strength CV of 28.52%. For measure 2, the lowest CV (0.19%) was found connecting region right TS PlPo CG to right TS LaCG whereas the highest CV was found in 82 connections. For example, between the right PV Ci CG to the left FI Or CG (CV of 141.42%). Both measures had a similar distribution of connection strength CV, with an overall correlation of r=0.827 between the CV of all connections in measure 1 and measure 2.

Figure 6. Inter-scan coefficient of variation in the second measure of connection strength between cortical regions (left) and seed region averages (right) for all connections (gray bars), intra-hemispheric connections (blue) and inter-hemispheric connections (red). Connection strength CV ranged from 0 (red) to 141.42% (white).

While the general trend of higher CV for inter-hemispheric connections exists, it was not true of connections arising from all seed regions. By examining the mean CV of connections arising from each cortical region, fig 6 (right) shows that connections derived from some seed regions are more variable than others. The largest mean CV for all connected regions was found in connections from the left FI Or CG (56.31%), whereas the smallest was from the right PaS CG (23.99%). The seed region with the largest mean CV for inter-hemispheric connections was the left FI Or CG (84.82%) whereas the smallest inter-hemispheric mean CV was from region the right FS CG (23.82%). For intra-hemispheric connections, connections from the left PD Ci CG were least reproducible, with a CV of 57.29%, whereas connections from the right TS La CG were most highly reproducible on average, with a mean CV of 14.26%. Regions that formed variable strength inter-hemispheric connections did not tend to also form variable intra-hemispheric connections (correlation between mean CV for intra and inter-hemispheric connections was r = – 0.2).

Reproducibility Across Densities and Subjects

Reproducibility was then investigated in subjects 2 and 3. Since network architecture and therefore graph theoretical measures depends upon the connection density chosen, reproducibility was analysed for a range of connection densities across all subjects.

In all subjects, mean node outdegree and indegree increased linearly from 5.81 to 23.22 over a range of 10-40% connection densities (Fig. 7). This is because mean node outdegree and indegree are mathematically pre-defined by the connection density. Averaged outdegree and indegree CV was widely variable over these connection densities (Fig. 8), but was highest in subject 2 across all densities.

Figure 7. Reproducibility of global graph measures for three subjects across connection densities of 10-40%, +- their standard error. Subjects have similar mean global measures over the range of connection densities shown. Mean node outdegree and indegree are mathematically pre-defined by the connection density and therefore appear as a perfect linear relationship across subjects with a standard error of 0. For all global graph measures apart from small-world index, CV was below 3% across all densities. The small-world index CV was below 5% for densities 15-40% but had wider variation of 9.6% and 27.7% CV for subjects 2 and 3 respectively at 10% density.

Figure 8. Reproducibility of per-node graph measures. Mean Per-node CV is plotted over connection densities of 10-40% for node degree, clustering coefficient, mean pathlength and centrality for subjects 1, 2 and 3. Mean per-node mean CVs are more variable than global network measures. Subject 2 has higher mean per-node CV over all densities for all graph measures apart from centrality.

The average of mean clustering coefficients also increased as density increased from approximately 0.44 to 0.65. Similarly, subject 2 had the highest average per-node CV for all densities. The variation in the mean clustering coefficients was less than 3% in all subjects and densities. Subject 2 had the highest mean clustering coefficient CV over all densities. The average of mean pathlengths decreased from 3.2 to 1.5 across densities of 10% to 40% in an inverse exponential pattern. Again, subject 2 had the highest averaged CV for all densities. Mean mean pathlength CV was less than 2% in all subjects and densities and subject 2 had higher CV over all densities.

Centrality measures of individual nodes has been widely reported. When considering per-node variation, Table 1 and Fig. 8 shows that centrality is a relatively highly variable graph theoretical measure, in comparison to measures such as node degree and mean pathlength. In all subjects, the averaged mean centrality across all nodes decreased from 0.041 at 10% density to 0.011 at 40% density (Fig. 7). The averaged CV was highly variable between both subjects and densities (Fig. 8). The

averaged centrality CV was lowest for 10% densities in all subjects (11.02%, 9% and 11% CV for subject 1, 2 and 3, respectively). The highest average CV was at 15% density for subjects 1 and 2 (19% and 13.7% respectively). Poor reproducibility was found for densities of 30% in subject 3 (average CV 17.22%). When considering mean centrality across repeat scans, CV is very low, being less than 1.5% across all densities (not shown).

The categorising of networks with small-world architecture was a highly reproducible metric (CV ranged from 0.2% to 4.24% for densities 15% to 40%). Across all subjects, scans and densities the network obtained exhibited small-world properties in comparison with a random network generated at the same connection density (Fig. 7). The CV was more widely variable at 10% density in all subjects, being highest for subject 3 at 27.7% (not shown). The mean small-world index decreased from approximately 3.6 to 1.6 in all subjects (Fig. 7), with a small CV across scans. Subject SWI CV was 3% or less in subject 1 and less than 10% in subject 2 across all scans. High CV for subject 2 and 3 was found at 10% density whereas at densities from 15-40% CV was less than 5%. Similarly to other graph measures, subject 2 had the highest CV over densities of 15-40%.

The identification of hubs and their reproducibility across multiple scans is summarised in table 2 for hubs identified according to criteria described earlier (single density and single subject occurrences are not shown). The most highly reproducible hubs are the L and R MOT CG, which were found in all subjects and all scans for densities of 10% and 20%. The L and R PreCG also showed relatively high reproducibility at 20% and 30% connection density but lower reproducibility at 10%.

Subject 1 2 3 1 2 3 1 2 3Density 0.1 0.2 0.3

Left

OT MePa CG 3 3 3 3 3 3 3 2 2

Pre CG 1 0 1 0 3 2 2 2 3

FS CG 1 3 0 3 2 3 2 3 1

PaS CG 0 1 3 0 1 3 2 2 3

Right

OT MePa CG 3 3 3 3 3 3 3 0 2

Pre CG 0 1 3 1 3 3 3 2 3

FS CG 2 1 0 1 3 2 3 2 1

Table 2. Reproducibility of network hubs across densities of 10-30% in subjects 1, 2 and 3. Numbers count the number of repeat scans that the region was classified as a hub. A total of 21 different hubs were identified across this range of densities in all subjects. The most reproducible classifications are shown. The left and right OT MePa CG are the most reproducible of all hubs, whereas the left and right Pre CG were less reproducible but still identified in a high proportion of repeat scans.

Figure 9. Reproducibility of network hubs in subject 1 across a range of densities. Left: the mean centrality ± standard error of the regions indicated, plotted with the mean ± standard deviation (black line and grey region). Right: CV for four hubs identified as having a high amount of reproducibility over a range of connection densities. The left and right OT MePa are generally more highly reproducible than the left and right precuneus and the centrality of these regions remains significantly above the mean + 1 standard deviation over the range of densities 10-40%.

Figure 9 shows that the mean centrality measure of the L and R OT MP CG and PreCG varies widely over the range of densities analysed. In addition, CV is also highly variable over these densities. When considering the mean centrality of these nodes across three scans, The L and R PreCG (red and orange lines) nodes are classified as hubs only at densities above at 30% or above compared to the L and R OT MP CG which are classified as hubs over all connection densities. Also, CV is highly variable for these hubs but is highest for the L and R PreCG compared with the L and R OT MP CG.

Tract Reproducibility

Variation in graph measures is derived from between scan variation in the connection strength measure used to obtain the adjacency matrix. The biggest contributor to connection strength variation was streamline density; with the distance between regions having a low average CV between scans (0.285%, 0.257% and 0.372% for subject 1, 2 and 3 respectively). To investigate tract density reproducibility, voxel-wise spatial streamline density CV maps were examined for connections with high CV (for example, between 2 and 48 of 141.42% connection strength CV) and low CV (for example, between 54 and 53 of 1.876%) in subject 1. Figure 10 shows the general trend of increasing CV with increasing distance from the seed region. Increasing CV generally coincides with a lower streamline density and therefore weaker connections. There was a trend observed that tracts with high average connection strength CVs were composed largely of longer distance connections and were mainly inter-hemispheric as opposed to intra-hemispheric. Low CV connections were frequently located in close proximity to the seed region, where streamline densities between scans was relatively more homogenous (Fig. 10).

Figure 10. An axial view of voxel-wise streamline density CV (subject 1) is shown overlaid on the subjects un-weighted diffusion image. Left: a high CV connection strength (from the left PV Ci CG to right Sh In CG). Right: a low CV connection strength (from the right TS PlPo CG to the right Su CG). The seed region is marked in green and the target region in blue. Voxel-wise CV values range from 0 to maximum (white). Between scan variation in graph theoretical measures of whole-brain connectivity are derived from variation in connection strengths between two regions.

Discussion

Graph theoretical analysis has recently been employed as a powerful technique for the analysis of functional and structural connectivity. Reproducibility of diffusion-weighted images is imperfect as a result of factors such as partial volume effects, acquisition noise, patient motion and image artefacts, leading to inaccuracies in the reconstruction of diffusion tensor images and therefore structural connectivity networks that can be derived. In addition, a wide range of methodologies are available for processing diffusion-weighted images and for obtaining the connectivity matrix and this can lead to further variation in measures of connectivity networks. This study has used data from three repeat diffusion-weighted scans, with reference to subjects’ structural images, to examine the reproducibility of graph theoretical measures in three healthy subjects. Identifying and reducing sources of variation can lead to greater power for clinical studies and more accurate resolution of phenotypic variation in the structural network.

Brain structural networks are derived by thresholding a matrix of connection strengths between all regions. This analysis first characterised the inter-scan variation existing for all connections, using two different measures of connection strength. Although it was found that measure 2 (the average streamline density divided by the distance between the regions) resulted in smaller values of averaged per-node CV and global measure CV (Table 1, Fig. 7) than measure 2 (the maximum streamline density in the target region), a significant amount of variation existed in graph measures using both measures of connection strength. Per-node variation was highest for centrality (average per-node CV of 15.6%) and lowest for mean pathlength (avera ge per-node CV of 2.05%) using measure 2. Global measures were more reproducible than per-node measures in general, and had the largest increase in reproducibility using connection strength measure 2.

The source of network variation was the connection strength matrix, which had large values of CV compared with network measures. Inter-hemispheric variation was larger than intra-hemispheric variation. By examining spatial variation in streamline density, it could be appreciated that streamline density variation itself increased with distance (Fig. 6 and 10), accounting for higher inter-hemispheric variation. This may have been a major source of reproducibility for of graph theoretical measures of the structural network. However, although long distance connections were more variable, they were also weak connections, many of which were eliminated from network analysis after thresholding. Figure 5 shows that in fact an almost equal mixture of inter and intra-hemispheric connections are variable across scans. This variation may be partly caused by partial volume effects, by seeding from regions with low fractional anisotropy and the limitation in the ability to distinguish crossing or kissing fibres. In addition, the exlusion of overlapping regions and seeding of streamlines from cortical surfaces may reduce the intra-scan variation in graph theoretical measures of structural networks found in this study.

The connection strength measure used should be both a good estimation of the structural connectivity between a pair of regions and relatively unsusceptible sources of variation in imaging acquisition and/or post-processing. A number of different measures of connection strength have been proposed recently. One study using probabilistic streamline data obtained from diffusion-weighted-MRI, used three different measures to quantify connection strengths between grey matter regions, considering connectivity occurring only between surface voxels of region pairs [Iturria-Medina et al 2007]. The first measure considered the cross-section of fibre bundles shared by both regions, while the second considered the fraction of surface area on each region that is connected to the other. The final measure was the probability that the regions are connected by atleast a single connection. A further method used to quantify connectivity has been the derivation of cross-correlations in cortical thickness or volume, although this does not explicitly utilise diffusion MRI data [He et al 2007]. The network variation using such measures has not been reported and a comprehensive review of the reproducibility and biological plausibility of alternative measures of connection strength would be an ideal reference for graph theoretical investigations seeking to minimise sources of variability.

A number of observations were made regarding inter-scan reproducibility. Reproducibility was higher in subjects 1 and 3 than in subject 2, as based on the CV of averaged per-node measures and global measures across repeat scans. A wide range of variation existed in the averaged per-node CV between different graph theoretical measures and across a range of connection densities. The pre-defined connection density of the network did not have a large influence on averaged per-node CV and this was generally highest for measures of betweenness centrality in all subjects. The global measure of mean centrality however, had high reproducibility across all densities and subjects.

Previous studies that have attempted to characterise the whole-brain connectivity network in healthy individuals have found repeatable measurable characteristics such as short relative mean pathlength and high clustering coefficient when compared with random networks at the same connection density [Gong et al 2008, Vaessen et al 2010, Bullmore & Sporns 2009]. The relationship between these measures is known as a small-world architecture and describes a wiring of connections that favours local specialisation and efficient long distance communication. Disruptions in small-world architecture have been reported in cases of neurological disease. All networks examined in this analysis exhibited small-world properties (as small-world index was greater than 1), although the exact index had some degree of variation between scans (see Table 1, Fig. 7).

Perhaps the most significant finding is that variation in global network measures such as global efficiency and small world index are highly reproducible compared with measures at the node scale, such as betweenness centrality. Individual node graph theoretical measures (excluding centrality) have an average CV of below 6%, compared with global efficiency and small world index which have a CV of generally less than 1%. Global network measures are derived from averaging graph measures over all nodes in the network and therefore are less affected by variation in network configuration at the node scale occurring due to sources of methodological image quality variation between scans. These global measures are therefore more likely to provide more reliable biomarkers for the integrity of the structural network. A recent study examined the effect of different gradient sets of reproducibility of graph theoretical measures [Vaessen et al 2010]. Similarly to this analysis, the study found that the CV of connection strengths was magnitudes higher than the pooled within group coefficient of variation of graph measures, which were obtained from thresholding the connection strength matrix. In addition, the study found that global network measures such as small world architecture, were very highly reproducible (<3.8% in Vaessen et al 2010). High reproducibility of the small world index was found in this study, and the agreement in high reproducibility of global measures such as these are likely due to the averaging of variation across nodes. The per-node CV has relatively low reproducibility, varying in the range of 0 to 10% for mean pathlength and clustering coefficient across all densities and subjects. High reproducibility at the node scale is desirable since these graph measurements may provide biomarkers that depict the alteration in the connectivity of single regions that global measures may not reveal.

Measures of betweeness centrality have been employed to identify and characterise the extent to which network nodes are important for network communication and therefore to designate the presence of hub regions. Previous studies using diffusion-weighted imaging to obtain structural networks, have shown that the left and right precuneus play an essential role in network communication [Iturria-Medina et al 2008, Gong et al 2008, Hagmann et al 2008]. Reproducibility of hubs is of particular importance since differences in the distribution of hubs has been linked to cases of neurological disease such as Alzheimer disease. This analysis demonstrates that although per-node reproducibility in centrality is relatively low between scans (average CV 15.4% at 30% density), reproducibility in the classification of certain hub regions is high for some regions. The left and right OT MePa CG were the most highly reproducible hubs over all subjects and connection densities (Fig. 9). In fact, the reproducibility is higher for these nodes than for other previously extensively reported network hubs such as the left and right precuneus. The left and right precuneus were frequently classified as hubs, although at some densities in some subjects they were not identified in any subjects (Table 2). Fig 8 shows that these nodes have a higher CV over a wide range of densities when compared to more reproducible hubs such as the left and right OT MePa CG. The left and right MePa CG are therefore ideal candidates for

biomarkers of disruptions in neuronal organisation, such as occurs during Alzheimer disease [Chun-Yi et al 2010].

A number of methodological issues may have affected reproducibility independently of variation connection strength, such as the segmentation and registration. Segmentation and registration was performed using Freesurfer and FSL. Inaccuracies in segmentation are difficult to quantify, although between scans they may be responsible for misalignment of seed region voxels with the anatomical area of interest. Accuracy of the registration process can also lead to mis-classification of voxel labels. These effects were difficult to quantify but could have lead to significant differences in the reconstruction of nerve fibers. The CV for between regions was low (< 0.5%), suggesting that mis-registration or segmentation had not occurred. However, when comparing image data from diseased and healthy subjects combined methodological issues such as choices of atlas, registration and segmentation scheme may become more important as methods that can perform these techniques will need to consider the deviation of structures from that of healthy neurological anatomy.

A further source of methodological variation may have been the labelling system used for cortical regions. Fig 11 shows an axial plane view of labelled cortical regions from subject 1. Due to the interpolation of voxel positions during co-registration, when all transformed binarised regions are considered in the same brain volume there was some overlap in the voxel region ownership. Since streamlines were generated from voxels in these binarised seed regions, target regions that overlapped with the seed region were automatically connected with a high connection strength. This effect may have been exaggerated for regions that are large. To overcome this, future work should use a binarising procedure that allows exclusive partitions to separate neighbouring regions. Since segmentation and registration reproducibility were relatively high compared with that of connection strength, the effect of region overlap on reproducibility may have been small. However, it would have given overestimations to the measurement of connection strength between neighbouring regions, creating an increased likelyhood of neighbouring regions being connected.

Figure 11. Structural connectivity network for subject 1 overlaid upon the subjects unweighted diffusion image with cortical labels. Labels are probabilistic and therefore overlap to some degree between regions, creating a possible source of methodological inaccuracy in quantification of connection strength between regions, which was derived from streamlines seeded for all voxels for every seed region.

One limitation of this study may be the hypothesis that longer distance connections would be more weakly connected [Braitenberg & Schuz 1998], and thus the measure of connection strength involved a division by the distance between these regions. It could be argued that this was unnecessary since such information may be reflected by a lower average streamline density. When assessing reproducibility, it was deemed unlikely that including the distance metric influenced reproducibility significantly, since CV of distances was very low, however it is a relatively simple measurement that is perhaps not the best

biological representation of connectivity. Another possible limitation of the current study was the formulation of a directed network. dMRI data does not give information relating to the direction of white matter tracts and therefore the likely direction of information flow. Studies in the past have employed a non-directed graph to study the brain network. It was determined that an average of only 12.1% of connections were not reciprocated, agreeing with previous studies that a small degree of connections cannot be tracked in both directions [Young et al 1993].

Using acquisition techniques that are better able to determine the fibre orientation in more complex scenarios may be important factors in intra-subject reproducibility of the connection matrix. Q-ball imaging and diffusion spectrum imaging have been employed recently for obtaining diffusion tensor information that is able to distinguish these non-trivial fibre configurations [Tuch 2004, Kuo et al 2008]. In addition, increasing the field strength would provide a number of advantages. The spatial resolution would be improved, allowing a more detailed reconstruction of the network. Also, the signal to noise ratio would increase, meaning the measures of diffusion direction more accurately represent the whiter matter orientation and streamline tracts would be less hampered by noisy voxels.

This work provides an overview of the reproducibility of graph theoretical measures in structural networks obtained by probabilistic tractography. Reproducibility was firstly increased by considering connection strength as the spatial mean of streamline densities as opposed to the spatial maximum. Using this measure, global network measures were highly reproducible in all subjects and densities, whereas per-node reproducibility was lower. The source of network variation was variation in the inter-region connection strength between scans. This variation was highest for inter-hemispheric connections, due to the increasing uncertainty in tract distribution with increasing distance from the seed region. The tractography approach should therefore be carefully considered before network analysis in clinical studies. The use of alternative measures of connection strength, aswell as improving the image resolution and the ability of to reconstruct complex fibre pathways may allow a reconstruction of a highly accurate and detailed structural network. Investigation of other graph theoretical measurements and increasing the per-region reproducibility will expand upon the array of potential biomarkers that this emerging field is beginning to provide. It is to be hoped that not only will accurate construction of the structural network be beneficial for the basic understanding of the human brain, but that these potential biomarkers may be able to accurately predict or reflect psychological or neurological abnormalities, thus identifying important brain system targets for drug intervention.

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