surface parameterization using Riemann Surface Structure

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Boris A. Gutman, Neda Jahanshad, Derek Hibar, Cassandra Leonardo, Kristian Eschenburg, Talia Nir, Julio Villalon-Reina, Paul M. Thompson

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Continuous Connectomics: An Exploratory Framework for Connectivity Analysis in Brain Imaging

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MRI tractography. Medical Image Analysis 15, 414-425 (2011) [2] Gutman, B.A., et al.: A Family of Fast Spherical Registration Algorithms for Cortical Shapes. Multimodal Brain Image Analysis (MBIA) (2013)

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[1]. Aganj, I., et al.: A Hough transform global probabilistic approach to multiple-subject diffusion

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We have presented a framework for fusing connectivity information with cortical surface anatomy for a joint connectivity analysis. There are four distinct contributions: (1) the definition of a continuous connectome space and a method for estimating continuous kernels from fiber models; (2) an algorithm for defining a mutual connectome shared by two brains; (3) a spatial correspondence search between two connectome kernels, directly registering the brains’ structural connectivities; (4) an adaptation of graph theory measures to the continuous setting.

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• Continuous Clustering Coefficient:

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• Continuous Nodal degree (connectedness): 𝒌 𝒙 = 𝜴 𝑲(𝒙, 𝒚)𝒅𝒚 = 𝑲 𝒙, 𝒙 𝟐𝒕 𝒙

Corrected p-maps for AD-NC difference in (A) clustering coefficient , (B) connectedness, a.k.a. continuous nodal degree

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5. Continuous Connectomics

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4. Connectome-based cortical surface registration

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Both measures passed False Discovery Rate (FDR) correction. Connectedness: q = 1.0x10-3 for the right -3 hemisphere, and q = 1.9x10 for the left. Clustering -3 coefficient: q = 1.7x10 for the right hemisphere and q = 2.5x10-5 for the left.

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• Registering connectomes reduces to multi-channel registration:

Individual improvement 0.098 +/-0.089 0.2 +/-0.089

4. Sensitivity of continuous connectomics to Alzheimer’s Disease

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• By projecting networks of one person’s brain into appropriate eigenspaces of another we can match networks between individual brains. 𝟏 𝟐 Mutual network set: 𝑬𝑴 = 𝒆𝒊𝒌 , 𝒆𝒋 , 𝒘𝒌

Anatomy + connectivity 0.43 +/-0.12 0.12 +/-0.099

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2. Matched eigen-networks (right)

• Treat each fiber as an obseravtion in a connectome space • Use kernel density estimation to compute a continuous connectivity profile for each brain:

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• Tractogaphy with Hough Transform [1] • Cortical Surface extraction with Freesurfer

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• Current connectivity analysis assumes a small discrete graph – not flexible enough for connectome matching

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1. Visualizing individual fiber model contribution to the continuous connectome

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Results

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• Structural connectivity may be a better indicator of functional role of brain regions than gross anatomy alone

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Data

ADNI 2 dataset: 64-direction DTI images & T1-weighed images for cortical surface extraction. 48 Alzheimer’s patients. 50 age-matched controls.

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Motivation: matching connectomes across different brains

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Imaging Genetics Center, Institute for Neuroimaging & Informatics, University of Southern California, Los Angeles, CA, USA.