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Quantifying Human Brain Connectivity from Diffusion Tensor MRI

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Abstract

A new approach for quantifying the degree of connectivity between human brain regions from Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data is presented. To this aim, a functional is proposed and its theoretical properties are shown. The connectivity between pairs of white matter points is quantified by minimizing the weighted length of the curves within white matter connecting the points to each other. The weighting factor is a decreasing function of the diffusion coefficient along the curve tangent. This coefficient is a linear function of the diffusion tensor components, which are estimated from DT-MRI data. As a by-product of the analysis, the minimizing curves connecting the two points are provided. The solution of the minimization problem is obtained numerically by approximating the functional on a lattice and then solving a shortest path problem on an undirected weighted graph. The presented method is global and therefore not affected by problems due to fiber branching and crossing. It is also automatic and fast. Some results obtained from the implementation of this method on real data in physiological and simulated pathological conditions are illustrated.

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Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo, “Mauro Picone”, CNR, Rome, Italy

    Giovanni Sebastiani, Francesco de Pasquale & Piero Barone

  2. I.R.C.C.S. Fondazione Santa Lucia, Rome, Italy

    Francesco de Pasquale

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  1. Giovanni Sebastiani
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  2. Francesco de Pasquale
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  3. Piero Barone
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Correspondence to Giovanni Sebastiani.

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Giovanni Sebastiani is currently senior researcher at Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Rome, Italy. In 1998, he received the title of Doctor Philosophiae in Mathematics from the University of Science and Technology, Trondheim, Norway. His scientific interests mainly belong to Probability, Statistics and Physics applied to Medicine and Biology. His web page is at http://www.iac.rm.cnr.it/∼sebast/

Francesco de Pasquale received his Ph.D. in Applied Statistics from the University of Plymouth, United Kingdom in 2004 discussing a thesis on Bayesian and Template based methods for image analysis. Since his degree in Physics obtained at the University of Rome, “La Sapienza” in 1999 his work has been focused on developing models and methods for Magnetic Resonance Imaging, in particular image restoration, classification and segmentation in a Bayesian framework. After being appointed a two-year position as a Lecturer at the University of Plymouth from 2003–2004 he is now a post-doc researcher at IAC, an Institute of the Italian National Research Council, Rome, Italy. He is currently involved with Prof. Gian Luca Romani in a project on Functional MRI with the University of Chieti.

Piero Barone was born in Rome, Italy, in 1949. He received the “laurea” degree in mathematics from the University of Rome “La Sapienza” in 1972. He joined the Istituto per le Applicazioni del Calcolo (IAC) of the italian National Research Council in 1975. In 1992 he was appointed research director at IAC where leads a group of biomedical image and signal processing. His current research interests are in stochastic Pade’ and Bayesian methods applied to spectral analysis and in fast image regularization and classification. Magnetic Resonance spectroscopy, relaxometry, dosimetry and dynamic and diffusion tensor MRI are typical application fields. In the past he worked on space-time processes related to electrocardiac studies (body surface potential mapping), on deconvolution problems, stochastic algorithms and orthogonal transforms. Dr. Barone coauthored more than ninety papers on international journals and an european patent. He served as a project referee for the National Science Foundation and the Norvegian Research Council.

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Sebastiani, G., de Pasquale, F. & Barone, P. Quantifying Human Brain Connectivity from Diffusion Tensor MRI. J Math Imaging Vis 25, 227–244 (2006). https://doi.org/10.1007/s10851-006-6896-0

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