# Eigenvector centrality mapping for ultrahigh resolution fMRI data

#### Poster No:

M624

#### Submission Type:

Abstract Submission

#### Authors:

__Gabriele Lohmann__

^{1}

^{,2}, Alexander Loktyushin

^{3}

^{,2}, Johannes Stelzer

^{1}

^{,2}, Klaus Scheffler

^{1}

^{,2}

#### Institutions:

^{1}University Hospital, Tuebingen, Germany,

^{2}Max Planck Institute for Biological Cybernetics, Magnetic Resonance Center, Tuebingen, Germany,

^{3}Max Planck Institute for Intelligent Systems, Tuebingen, Germany

#### Introduction:

Eigenvector centrality mapping (ECM) is a popular technique for analyzing fMRI data of the human brain (Lohmann et al , 2010). It is used to obtain maps of functional hubs in networks of the brain in a manner similar to Google's PageRank algorithm (Langville et al, 2006). Currently, there exist two different implementations ECM, one of which is very fast but limited to one particular type of correlation metric whose interpretation can be problematic. The second implementation supports many different metrics, but it is computationally costly and requires a very large main memory. Here we propose two new implementations of the ECM approach that resolve these issues. The first technique is based on a new correlation metric that we call 'ReLU correlation (RLC)'. The second technique is based on matrix projections. Below, we describe both methods. A more detailed description can be found in (Lohmann et al, 2018).

#### Methods:

ECM attributes a centrality score to each voxel based on its correlations with other voxels. In order to ensure uniqueness of the results, only non-negative correlation metrics are allowed. The ECM score for the i-th voxel is defined as the i-th entry of the principal eigenvector of the correlation matrix f(X X^T) where X is the data matrix and f is a function that maps correlation values to the non-negative range. For f(x) = x+1, a very efficient implementation of ECM is possible (Wink et al, 2012). However, this particular function f maps zero correlations to some intermediate value which makes interpretation of the resulting maps problematic.

Here we introduce two new implementations of ECM. The first is called 'ECM-RLC'. It is based on a new correlation metric that we call 'ReLU correlation coefficient (RLC)'. We define the RLC between two time courses x, y of length m as RLC(x,y) = 1/(2m) Σ

The second method - called 'ECM-project' - approximates the principal eigenvector using matrix projections. Matrix projections were introduced in (Halko et al, 2011) as a technique for computing singular value decompositions. Here we use it for estimating the principal eigenvector in a memory-efficient way. ECM-project requires more computation time than ECM-RLC, but unlike ECM-RLC is applicable for arbitrary correlation metrics. For more details regarding both methods, see (Lohmann et al, 2018).

Here we introduce two new implementations of ECM. The first is called 'ECM-RLC'. It is based on a new correlation metric that we call 'ReLU correlation coefficient (RLC)'. We define the RLC between two time courses x, y of length m as RLC(x,y) = 1/(2m) Σ

_{i}x_{i}y_{i}+ | x_{i}y_{i}|. ECM can be efficiently implemented with this new metric by expanding the data matrix X so that Y = (X,|X|) where we add m columns to X containing componentwise absolute values of X. ECM is then defined as the principal eigenvector of Y Y^T. This data representation allows a very fast and memory-efficient implementation of ECM. Furthermore, it provides more informative ECM scores than the previous implementation that was based on f(x) = x+1, see (Fig. 1).The second method - called 'ECM-project' - approximates the principal eigenvector using matrix projections. Matrix projections were introduced in (Halko et al, 2011) as a technique for computing singular value decompositions. Here we use it for estimating the principal eigenvector in a memory-efficient way. ECM-project requires more computation time than ECM-RLC, but unlike ECM-RLC is applicable for arbitrary correlation metrics. For more details regarding both methods, see (Lohmann et al, 2018).

#### Results:

Resting state fMRI data were acquired at a 9.4T Siemens Magnetom scanner of a single subject (female, 29 yrs). Acquision parameters: spatial resolution: (1.2mm)

^{3}, matrix size: 160x160, 55 slices, 330 volumes, TR=2.03 sec, TE=19ms, flipangle=70. The data were corrected for motion and the baseline drift was removed using a highpass filter with a cutoff frequency of 1/100 Hz. A ROI containing 466462 voxels was manually constructed. The corresponding correlation matrix would require about 405 GByte of main memory making it impracticably large for standard PCs. We applied ECM-RLC and obtained the result shown in Fig 1.#### Conclusions:

We have introduced two new implementations of ECM called ECM-RLC and ECM-project. Both methods are memory efficient so that they are applicable to high-resolution fMRI data acquired at field strength ≥7 Tesla. Even very large data sets containing more than 400,000 voxels can be handled easily. We also introduced a new correlation metric called 'RLC'. It applies a filter for each time point separately so that it may be better suited for capturing dynamically varying connectivity.

#### Imaging Methods:

BOLD fMRI

#### Modeling and Analysis Methods:

fMRI Connectivity and Network Modeling

^{1}
Methods Development

^{2}
Task-Independent and Resting-State Analysis

#### Keywords:

Computational Neuroscience

Data analysis

Design and Analysis

HIGH FIELD MR

MRI

^{1|2}Indicates the priority used for review

#### My abstract is being submitted as a Software Demonstration.

#### Please indicate below if your study was a "resting state" or "task-activationâ€ť study.

#### Healthy subjects only or patients (note that patient studies may also involve healthy subjects):

#### Was any human subjects research approved by the relevant Institutional Review Board or ethics panel? NOTE: Any human subjects studies without IRB approval will be automatically rejected.

#### Was any animal research approved by the relevant IACUC or other animal research panel? NOTE: Any animal studies without IACUC approval will be automatically rejected.

#### Please indicate which methods were used in your research:

#### For human MRI, what field strength scanner do you use?

#### Which processing packages did you use for your study?

#### Provide references using author date format

Langville, A et al (2006), 'Google's PageRank and Beyond: The Science of Search Engine Rankings', Princeton University Press

Lohmann, G. et al. (2010), 'Eigenvector centrality mapping for analyzing connectivity patterns in fMRI data of the human brain', PLoSONE 5(4):e10232

Lohmann, G. et al. (2018), 'Eigenvector centrality mapping for ultrahigh resolution fMRI data of the human brain', bioRxiv, https://doi.org/10.1101/494732

Wink, A.M. (2012) 'Fast eigenvector centrality mapping of voxel-wise connectivity in functional magnetic resonance imaging: implementation, validation, and interpretation', Brain Connectivity, vol. 2, no.5, pp.265-274