Direction des Relations Internationales (DRI)

Programme INRIA "Equipes Associées" 

I. DEFINITION

Présentation détaillée de l'Équipe Associée

1. Objectifs scientifiques de la proposition (1 à 2 pages)

Our main objectives within this research proposal are:

• To develop rigorous mathematical and computational tools for the analysis of Diffusion MRI data
• To improve acquisition techniques and push forward the state-of-the-art in Computational Diffusion MRI achieved through:
  • Joint publications in international conferences and journals dedicated to promoting advances in computational methods for Diffusion MRI analysis and/or use of Diffusion MRI in clinical and neuroscience applications.
  • Development of software packages that will be used at INRIA, NIH and the University of Minnesota's Center for Magnetic Resonance Research in a first stage and then made available to our other partners.
• To help address pressing and challenging clinical and neuroscience questions.

To this end, we have identified a set of important problems related to diffusion tensors, second and higher orders tensors, HARDI data and optimal real-time experimental designs for DWI acquisitions. Our three research groups will closely collaborate to address them. Working on Diffusion MRI data and putting together the expertise and experimental facilities provided by all the partners will help tremendously to solve many of these problems. This will involve putting together the most recent results in Diffusion MRI, such as those obtained at NIH and the University of Minnesota's Center for Magnetic Resonance Resonance Research, with advanced mathematical tools based on variational approaches, Riemannian geometry, probability theory, stochastic calculus, and statistics, such as those developed in the INRIA Odyssée Project-Team and at the University of Minnesota. NIH and the Center for Magnetic Resonance Research will primarily provide the INRIA Odyssée Project-Team with the data and acquisition expertise while Odyssée will lead and coordinate the development of the mathematical and computational tools for the analysis of such data. The tools will be integrated in at least one common software package and will be made available to each partner. Complementary tools related to the handling and batch-processing of large amount of data, as well as visualization of the results will also be developed and distributed to each partner while taking advantage of analysis software already available in the research community, in particular at INRIA with MedINRIA (http://www-sop.inria.fr/asclepios/software/MedINRIA/) and in the US with Slicer 3D (http://slicer.org) and the LONI Pipeline (http://pipeline.loni.ucla.edu/).

More specifically, we will work on the statistical analysis of diffusion tensor fields using, for instance, recent work on non-parametric statistics on Riemannian manifolds. We will also address important problems like the segmentation or registration of DTI data and the design of efficient acquisition schemes for DMRI, with application to HARDI multi-q-shell scans (see Khachaturian & al.). This will be of great help help in constructing atlases of DTI and QBI brain volumes, an extremely important point for population studies and ability to accurately detect abnormalities between patients and control subjects. We will focus on a clinical application for which Dr. Lehéricy (CENIR, Pitie-Salpetriere Hospital, Paris) has developed an extensive expertise (see Delmaire & al.), namely dystonia (and a specific primary form known as Writer's Cramp). Dr. Lehéricy is a close collaborator of both the Odyssée group and Center for Magnetic Resonance Research. Dystonia is a neurological movement disorder in which sustained muscle contractions cause twisting and repetitive movements or abnormal postures. Structural imaging studies have shown the involvement of the sensorimotor circuit in this pathology and Dr. Lehéricy has been using DTI for several years to study the pathophysiology and possible diagnosis of dystonia. This will constitute an excellent working case for our collaboration and help extend our tools to many other neurological disorders.

It is our claim and hope that the complementarity and synergy of our combined efforts and ideas will aid in making significant contributions to the processing and analysis of diffusion weighted imaging data, a task well known to be extremely challenging due to the complex underlying properties of the data. We are also confident that such tools will enable us to more precisely pinpoint abnormalities of the sensorimotor pathway in dystonia, improve our understanding of the disease and help further develop the use of DTI/HARDI in clinical applications.

References:

• Basser, P., Mattiello, J., and Le Bihan, D. (1994). MR diffusion tensor spectroscopy and imaging. Biophysical Journal, 66(1):259-267.
• Basser, P., Mattiello, J., and Le Bihan, D. (1994). Estimation of the effective self-diffusion tensor from the NMR spin echo. Journal of Magnetic Resonance, B(103):247-254.
• Delmaire, C., Vidailhet, M., Wassermann, D., Descoteaux, M., Valabregue, R., Bourdin, F., Lenglet, C., Sangla, S., Terrier, A., Deriche, R., Lehéricy, S. (2008). Diffusion abnormalities in the primary sensorimotor pathways in writer’s cramp. Archives of Neurology, In press.
• Khachaturian, M.H.,Wisco, J.J., and Tuch, D.S. (2007). Boosting the sampling efficiency of q-Ball imaging using multiple wavevector fusion. Magn. Reson. Med. 57(2):289-296
• Le Bihan, D. and Breton, E. (1985). Imagerie de diffusion in vivo par résonance magnétique nucléaire. C. R. Acad. Sci. Paris, 301 Série II:1109-1112.
• Merboldt, K., Hanicke, W., and Frahm, J. (1985). Self-diffusion NMR imaging using stimulated echoes. J. Magn. Reson , 64:479-486.
• Taylor, D. and Bushell, M. (1985). The spatial mapping of translational diffusion coefficients by the NMR imaging technique. Physics in Medicine and Biology, 30(4):345-349.
• Tuch, D. (2002). Diffusion MRI of Complex Tissue Structure. PhD thesis, Harvard University and Massachusetts Institute of Technology.

2. Présentation des partenaires (1 page environ par partenaire)

For the University of Minnesota, Drs. Sapiro (Department of Electrical and Computer Engineering) and Deriche have known each other for many years. During the summer of 2003, Dr. Sapiro visited the Odyssée Project-Team for one month and actively interacted with Dr. Lenglet, who was starting his doctoral studies on Diffusion Tensor MRI at that time, under the joint supervision of Drs. Deriche and Faugeras. This led to multiple visits of Dr. Lenglet at the Center for Magnetic Resonance Research, where he could acquire state-of-the-art diffusion MRI datasets. Both Drs. Sapiro and Basser accepted to be part of Dr. Lenglet's Ph.D. committee. After two years as a Research Scientist at Siemens Corporate Research in Princeton, NJ, he recently joined the University of Minnesota as a Research Associate.

Odyssée Project-Team

• Computational Neurosciences (O. Faugeras & al.)
• Biological and Computational Vision (P. Kornprobst & al.)
• Diffusion Magnetic Resonance Imaging (R. Deriche & al.)
• Electrical and Magnetical Functional Brain Imaging (M. Clerc, T. Papadopoulo & al.)

The Odyssée Project-Team has been very active in the area of the application of mathematics to the design of models for studying brain anatomy and functions. In particular, it has developed variational, PDEs and level-set based frameworks in computer vision for the purpose of image regularization and segmentation. More recently, the Odyssée Project-Team has developed and applied such ideas to brain image analysis.

New algorithms relying on Riemannian geometry, differential geometry, partial differential equations and front propagation techniques have been proposed to correctly and efficiently estimate, regularize, segment and process DTI data and tackle the white matter tractography problem (i.e. constructing a coherent network of the white matter fiber pathways). The Odyssée team has also been very active in studying High Angular Resolution Diffusion Imaging (HARDI) problems and developing a regularized, fast and robust analytical Orientation Distribution Function (ODF) estimation from Q-Ball Imaging (QBI). This method has also been used to study and compare deterministic and probabilistic tractography based on complex fiber orientation distributions. Odyssée's expertise in these research areas, as well as the tools its members have already developed, tested and validated (see the recent related publication in Magnetic Resonance in Medicine 2006, 2007; NeuroImage 2008; IEEE TMI 2007 and 2008; JMIV 2007 and 2008) are very closely related to the main tasks that will be addressed within this Associated Team proposal. They constitute a great preliminary work to help achieve our objectives.

Therefore, the Odyssée Project-Team proposes to bring its expertise within the methodological tasks presented in this proposal and strongly believes that it will contribute to the success of this Associate Team.

The members of the Odyssée Project-Team that will primarily be involved in this Associated Team are Drs. Deriche, Clerc and Papadopoulo, as well as Ph.D. students Demian Wassermann, Aurobrata Ghosh, Emmanuel Carruyer and additional Post-Doctorants, Ph.D. students and intern scholars to be hired during the next three years.

NIH

Core research activities in STBB include studies on the fundamental physical/chemical basis of nerve excitability, the interaction of electrical and magnetic fields with excitable nerve tissue, non-invasive MRI of transport process in the nervous system (such as water diffusion) and clinical applications of quantitative imaging.

There is a strong translational component to Dr. Basser's research group, with STBB attempting to bring new quantitative methods from "bench to bedside". Indeed, Dr. Basser's group is primarily known for the invention, development, and clinical implementation of MR diffusion tensor imaging (DTI), and for explaining the physical basis of magnetic stimulation of nerve fibers.

The section members that will be involved in this Associated Team are : Drs. Peter Basser (CV attached), Carlo Pierpaoli, Sinisa Pajevic, Evren Ozarslan, Guan Koay, Joelle Sarlls and Raisa Freidlin.

University of Minnesota

CMRR was established in 1991 as a result of the rapidly growing and successful in vivo magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) research effort at the University of Minnesota. It is an interdepartmental and interdisciplinary research laboratory that provides state-of-the-art instrumentation, expertise, and infrastructure to carry out biomedical research utilizing the unique capabilities provided by high field MRI and MRS methodology. The central aim of the research conducted in CMRR is to non-invasively obtain functional, physiological, and biochemical information in intact biological systems, and use this capability to probe biological processes in health and disease. CMRR Faculty conducts research in a variety of areas including:

• High field functional brain mapping in humans; methodological developments, mechanistic studies, and neuroscience applications
• Metabolism, bioenergetics, and perfusion studies of human pathological states (tumors, obesity, diabetes, hepatic encephalopathy, cystic fibrosis, and psychiatric disorders)
• Cardiac bioenergetics under normal and pathological conditions
• Automated magnetic field shimming methods that are critical for spectroscopy and ultrafast imaging at high magnetic fields
• Development of high field magnetic resonance imaging and spectroscopy techniques for anatomic, physiologic, metabolic, and functional studies in humans and animal models
• Radiofrequency (RF) pulse design based on adiabatic principles
• Development of magnetic resonance hardware for high fields (e.g. RF coils, pre-amplifiers, digital receivers, phased arrays)
• Development of software for data analysis and display for functional brain mapping.

The Department of Electrical and Computer Engineering was established in 1891 at the University of Minnesota. Its faculty pursue research in a broad spectrum of areas such as signal and image processing, communication systems and information theory, VLSI, systems and controls, digital systems and computer architecture, microelectronics, micro-electromechanical systems (MEMS), nano-electronics, optics and opto-electronics, magnetic storage technology and systems, energy systems and power electronics, and biomedical applications. It is part of the Institute of Technology and greatly benefits from the Minnesota Supercomputing Institute for Advanced Computational Research which enables researchers in physical, biological, medical, mathematical, and computing science to find solutions to problems that could not be otherwise attempted. More specifically, Dr. Lenglet is part of Dr. Sapiro's research laboratory in the Department of Electrical and Computer Engineering, dedicated to research in image sciences and addressing biological and medical questions such as brain data processing, characterization of protein ensembles or understanding the structure of the HIV virus using electron tomography.

The members of the University of Minnesota that will be primarily involved in this proposal are Drs. Christophe Lenglet (Radiology and Electrical and Computer Engineering) and Guillermo Sapiro (Department of Electrical and Computer Engineeringt) as well as Drs. Kamil Ugurbil and Kelvin Lim at the Center for Magnetic Resonance Research (CMRR).

3. Impact 

Our collaborative work will have five major impacts:

1. Push forward the state-of-the-art in Computational Diffusion MRI by tackling and solving a set of important and challenging problems (statistical analysis of high-dimensional data, segmentation, registration, atlas creation and their application to the study of dystonia).
2. Joint publications in international conferences and journals dedicated to promoting advances in computational methods for Diffusion MRI analysis and/or use of diffusion MRI in clinical and neuroscience applications.
3. Development of software packages that will be used at INRIA, NIH and the University of Minnesota's Center for Magnetic Resonance Research in a first stage and then made available to our other partners.
4. Organize an extensive exchange program involving junior as well as senior scientists from all the partners and jointly organise an international workshop or tutorial with invited guest speakers.
5. Organize, strengthen and pursue the collaboration and the strong scientific synergy between the INRIA, NIH and the University of Minnesota.
   

4. Divers :

II. PREVISIONS 2009

Programme de travail

To this end, we have identified a set of important problems related to diffusion tensors, second and higher orders tensors, HARDI data and optimal real-time experimental designs for DWI acquisitions. Our three research groups will closely collaborate to address them. Working on Diffusion MRI data and putting together the expertise and experimental facilities provided by all the partners will help tremendously to solve many of these problems. This will involve putting together the most recent results in Diffusion MRI, such as those obtained at NIH and the University of Minnesota's Center for Magnetic Resonance Resonance Research, with advanced mathematical tools based on variational approaches, Riemannian geometry, probability theory, stochastic calculus, and statistics, such as those developed in the INRIA Odyssée Project-Team and at the University of Minnesota. NIH and the Center for Magnetic Resonance Research will primarily provide the INRIA Odyssée Project-Team with the data and acquisition expertise while Odyssée will lead and coordinate the development of the mathematical and computational tools for the analysis of such data. The tools will be integrated in at least one common software package and will be made available to each partner. Complementary tools related to the handling and batch-processing of large amount of data, as well as visualization of the results will also be developed and distributed to each partner while taking advantage of analysis software already available in the research community, in particular at INRIA with MedINRIA (http://www-sop.inria.fr/asclepios/software/MedINRIA/) and in the US with Slicer 3D (http://slicer.org) and the LONI Pipeline (http://pipeline.loni.ucla.edu/). 3D Slicer (www.slicer.org), is a free, open source software package for visualization and image analysis, developed under the NA-MIC consortium, in which STBB is substantially involved. The Odyssée project has actively collaborated in the development of this software in the last years. The most important contributions of this collaboration are twofold. In the first place, the development of a visualization system for the 3.3 release. This system allows easy integration of complex glyphed datatypes like QBalls and High Order Tensors. Moreover, QBall integration has been performed following (Descoteaux & al.; 2007), currently implementing estimation and visualization (Odyssée QBall plug-in for Slicer3D 3.3). In order to continue this work and turn 3D slicer into a user interface for QBall-based neuroscience research, visualization of QBall scalar measures (Frank; 2002) and connectivity metrics like streamline or probabilistic tractography should be developed. Secondly, the integration of Python development into the Slicer platform has allowed the Odyssée research team to plan the integration of fiber clustering algorithms (Wassermann & al. 2008) and a new statistical framework for the research on white matter biomarkers from diffusion MRI.

The LONI Pipeline is a simple graphical environment for constructing complex scientific analyses of data. It provides a visually intuitive interface to data analysis while also allowing for diverse programs to interact seamlessly. The Pipeline allows researchers to share their methods of analysis with each other easily and provides a simple platform for distributing new programs, as well as program updates, to the desired community. The environment also takes advantage of supercomputing environments by automatically parallelizing data-independent programs in a given analysis whenever possible. Finally, the LONI Pipeline can run in a client-server mode, allowing access to compute servers running analysis software that benefits from a dedicated machine with vast computational resources. The LONI Pipeline is complementary to MedINRIA and Slicer 3D as it essentially provides a simple, efficient and integrated means to process large amount of data by taking advantage supercomputing capabilities. Dr. Lenglet will lead the integration of the computational tools developed within our Associate Team into the LONI pipeline.

References:

• M. Descoteaux, E. Angelino, S. Fitzgibbons, and R. Deriche. Regularized, fast and robust analytical Q-ball imaging. Magn Reson Med, 58(3):497–510, 2007.
• Odyssée QBall plug-in for Slicer3D 3.3 http://www-sop.inria.fr/odyssee/en/software/QBallSlicer
• L. R. Frank. Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magn Reson Med, 47(6):1083–1099, Jun 2002.
• D. Wassermann and R. Deriche. Simultaneous Manifold Learning and Clustering: Grouping White Matter Fiber Tracts Using a Volumetric White Matter Atlas, MMI Workshop, MICCAI 2008, NY, USA
• Wassermann, D., Descoteaux, M., Deriche, R.,  " Diffusion Maps Clustering for Magnetic Resonance Q-Ball Imaging Segmentation",  International Journal on Biomedical Imaging, special issue on Recent Advances in NeuroImaging Methodology, 2008
  

WP-1: On Diffusion Tensor Imaging

DTI was introduced in 1994 by Peter Basser, our partner in this proposal, as a rigorous analytical formalism to encapsulate the diffusion properties of water molecules in biological tissues (inside a typical 1-3 cubic mm sized voxel) as an effective self-diffusion tensor given by a symmetric positive definite tensor . It is the only non-invasive imaging technique to resolve the connectivity patterns of the white matter fibers or assess their integrity. As such, it has led to many applications in clinical diagnosis of neurological diseases and disorder, neurosciences applications in assessing connectivity of different brain regions, and more recently, therapeutic applications, primarily in neurosurgical planning.

Diffusion tensor imaging (DTI) thus produces a three-dimensional image containing, at each voxel, a symmetric positive-definite tensor D. The estimation of these tensors requires the acquisition of diffusion weighted images in several non-coplanar encoding directions, at least six, as well as an unweighted image . Because of the signal attenuation, the image noise will affect the measurements and it is therefore important to take into account the nature and the strength of this noise in all the pre-processing steps.

Each tensor can be visualized as an ellipsoid, with the three main axes describing an orthogonal coordinate system. These directions are represented by the eigenvectors and their length the eigenvalues of the tensor. The longest axis of the diffusion ellipsoid represents value and direction of maximum diffusion, whereas the shortest axis denotes value and direction of minimum diffusion. The diffusion is said to be isotropic when the three eigenvalues are equal. In that case, the tensor can be visualized as a sphere.

In an isotropic medium, as in water for instance, water molecules naturally move according to Brownian motion. In biological tissues however the diffusion is very often directionally biased or anisotropic. For example a molecule inside the axon of a neuron has a low probability to cross a myelin membrane. Therefore the molecule will move principally along the axis of the neural fiber. Conversely if we know that molecules locally diffuse principally in one direction, we can make the assumption that this corresponds to a set of fibers. Therefore, from the diffusion tensor D, a neural fiber direction can be inferred from the tensor's main eigenvector while various diffusion anisotropy measures, such as the Fractional Anisotropy (FA), can be computed using the associated eigenvalues to quantify anisotropy, thus describing the inequality of diffusion values among particular directions

In the current state of this technology, a certain number of challenging problems related to DTI have been studied by the three partners in estimation, regularization, segmentation and tractography but many important questions still remain to be answered.

Our first objective here is to take benefit of the added value brought by each partner within this proposal to solve an important segmentation problem combining the results already available at NIH with the Level-Set algorithms developed at Odyssée while Christophe Lenglet, now our partner at the University of Minnesota, was a graduate student at INRIA. Ozarslan & al, 2008, members of Dr. Basser's team at NIH, have shown in controlled experiments using Diffusion MRI and DTI, that in regions containing boundaries between fluids and tissue, the estimated diffusion tensors are oriented to have their least prominent eigen-vectors or 3rd eigen-vectors perpendicular to the boundary. This has been shown in experiments with a cylinder submerged in water. The problem we would like to adress is the following: Given a field of vectors (say the 3rd eigen-vectors from a DTI image), such that some of those vectors are perpendicular to a boundary (or they define a contour), is it possible to extract this boundary or contour using a Level-Set approach? We believe that it is possible to reconstruct the boundary between fluids and tissues from the 3rd eigenvalues of a DTI image. We propose to explore this important issue and, if successful, adapt our technique to segment tissues from surrounding fluids in the brain.

References:

1. Ozarslan, E., Nevo, U. and Basser, P.J. (2008) Anisotropy induced by macroscopic boundaries: Surface normal mapping using diffusion-weighted imaging. Biophys J 94(7):2809-2818
2. Lenglet, C. and Rousson, M. and Deriche, R. (2006) DTI Segmentation by Statistical Surface Evolution, IEEE Transactions on Medical Imaging, 25(6), 685-700, June 2006
3. C. Lenglet, M. Rousson, R. Deriche, O. Faugeras, S. Lehericy, K. Ugurbil.(2005) A Riemannian Approach to Diffusion Tensor Images Segmentation, Proc. Information Processing in Medical Imaging, 591-602, Glenwood Springs, CO, July 11-15, 2005

Another important issue that we would like to jointly explore with our partners at NIH and University of Minnesota is related to the computation of probabilities and statistics of tensor fields and tensor derived quantities. It is necessary to pay particular attention to the following question that still needs to be answered: What distributions properly describe DWI-derived data? Fourth-order covariance tensors between second-order tensors have been proposed by Basser & Pajevic to compute statistics on DTI. This can also be used to compute statistical quantities like the mean tensor and covariance tensor over a region-of-interest (ROI). This can then be used to either segment ROIs or compare similar ROIs across subjects. However, when performing these computations of statistics, is there a correct underlying metric? Knowing that diffusion tensors have to be positive definite, should one use Riemannian metrics to compute the statistics like the mean tensor and the covariance tensor instead of the classical Euclidean metric? This question is however not so much concerned with the estimation process of tensors but rather with the computation of the statistics over a set of tensors.

References:

1. Basser, P. & Pajevic, S. A normal distribution for tensor-valued random variables: applications to diffusion tensor MRI IEEE Transactions in Medical Imaging, 2003, 22, 785-794
2. Basser, P. J. & Pajevic, S. Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI Signal Processing, 2007, 87, 220-236
3. Lenglet, C.; Rousson, M.; Deriche, R. & Faugeras, O. Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing Journal of Mathematical Imaging and Vision, 2006, 25, 423-444
4. Pasternak, O.; Verma, R.; Sochen, N.; and Basser, P.J. (2008) On What Manifold Do Diffusion Tensors Live? MICCAI Workshop - Manifolds in Medical Imaging: Metrics, Learning and Beyond, 2008.

WP-2: On High Order Diffusion Tensor Imaging

The Odyssée Project-Team has already started to contribute towards these objectives and its recent work deals with the development of local reconstruction methods, segmentation and tractography algorithms able to infer multiple fiber bundles from diffusion data. To do so, high angular resolution diffusion imaging (HARDI) is used to measure diffusion images along several directions. Q-ball imaging (QBI) is a recent HARDI technique that reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima aligned with the underlying fiber directions at every voxel. QBI and the diffusion ODF play a central role in our work focused on the development of a robust and linear spherical harmonic estimation of the HARDI signal and in our regularized, fast and robust analytical QBI solution which outperforms the state-of-the-art ODF numerical technique available. These contributions are fundamental and have already started to make a significant impact on the Diffusion MRI, HARDI and Q-Ball Imaging community. They are the basis of our probabilistic and deterministic tractography algorithms, which exploit the full distribution of the fiber ODF.

It is well known that DTI, using second-order tensors, can not properly model complex anisotropic diffusion phenomenon like fiber crossings. It is limited to a single dominant direction (one major eigenvector), and in the case of crossing fibers the tensors become oblate or spherical. Generalized DTI (GDTI) developed by Ozarslan & al. overcomes this shortcoming by estimating the diffusion function with High Order Tensors (HOT). However, HOTs in GDTI are also estimated using the linearized Least-Squares approach which doesn't guarantee a positive diffusion function. Diffusion is a non-negative quantity. Negative diffusion doesn't correspond to anything physical. The problem of guaranteeing positive diffusion using HOTs is difficult because of the increased multi-linearity of the tensors. The Odyssée team has recently proposed to extend the Riemannian framework they developed for second-order tensors to the space of fourth-order tensors by mapping a fourth-order 3D tensor to a second-order 6D tensor which is a 6x6 matrix. Then they proceed to use the Riemannian framework for in the space to guarantee a positive diffusion function. The three partners are very interested in pursuing these studies and explore together new solutions to these important problems. Diffusion being a physical phenomenon, negative diffusion is not physical. However, in the presence of noisy data straightforward linear Least Squares approximation can result in a non-positive diffusion function. Therefore, this should be tackled as carefully as possible.

The recent work by the Odyssée group on extracting the maxima of an antipodally symmetric spherical function written either in the spherical harmonic basis (SH), or in the symmetric tensor basis (ST) constrained to the sphere, or the homogeneous polynomial (HP) basis constrained to the sphere, can be applied to the Diffusion orientation transform (DOT) framework, developed by Ozarslan & al, 2006. The DOT is a function that maps the apparent diffusion coefficient (ADC) profile to the diffusion PDF. The key idea is that the Fourier transform can be done using the Rayleigh expansion of a plane wave in spherical coordinates. The approach developed by the Odyssée group has demonstrated it can extract the maxima of the analytical ODF written in the SH basis. This can be equally applied to the DOT, to not only extract fiber directions but also quantify the quality of the estimation. We propose to quantify the quality of the estimation of the DOT on synthetic and/or phantom data with known ground truth and explore the possibility of examining the orientation resolution of the DOT, by decreasing the angle between the known diffusion directions. This could be done as a function of the rank of the SH series and could be further used to compare the estimations of the DOT to that of the ODF.

References:

1. Ghosh, A. & Descoteaux, M. & Deriche, R. Riemannian Framework for estimating Symmetric Positive Definite 4th Order Diffusion Tensors, Medical Image Computing and Computer Assisted Intervention , New York, USA, pp. 858-865, 2008
2. Ghosh, A. & E.Tsigaridas & Descoteaux, M. & Comon, P. & B.Mourrain & Deriche, R. A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the Orientation Distribution Function in Diffusion MRI, MICCAI:08 Workshop on Computational Diffusion MRI, New York, USA
3. Ozarslan, E. & Shepherd, T. & Vemuri, B. & Blackband, S. & Mareci, T. Resolution of Complex Tissue Microarchitecture Using the Diffusion Orientation Transform (DOT) NeuroImage, 2006, 31, 1086-1103

WP-3: On High Angular Resolution Diffusion Imaging

In the first case, a large number of q-space points are taken over the discrete grid () and the inverse Fourier transform of the measured DWI signal is taken to obtain an estimate of the diffusion PDF. This is Diffusion Spectrun Imaging (DSI), introduced by Wedeen & al, 2000. The method requires very strong imaging gradients ( s/mm) and a long time for acquisition (15-60 minutes) depending on the number of sampling directions. To infer fiber directions of the diffusion PDF at every voxel, people either take an isosurface of the diffusion PDF for a certain radius or compute the diffusion ODF. The diffusion ODF contains the full angular information of the diffusion PDF. Q-Ball Imaging was shown to reconstruct a smoothed version of this diffusion ODF with a single shell HARDI acquisition and the Odyssée team has been very active in studying high angular resolution diffusion imaging (HARDI) problems and recently developed a regularized, fast and robust analytical ODF estimation from Q-Ball Imaging (See the recent related publications at Magnetic Resonance in Medicine 2006 and 2007, IEEE TMI 2008; 2008).

During Dr. Descoteaux's thesis defense, Dr. Basser visited the Odyssée group and we discussed the problem of registration of DWI and HARDI data. Within this proposal, we would like to explore the idea of registering slices of HARDI data using Spherical Harmonics. This is definitely an important problem and the idea is worth pursuing. NIH and CMRR can provide Odyssée with the diffusion weighted MRI data and acquisition expertise. The Odyssée group can perform, in collaboration with Dr. Lenglet, the ODF analysis and define what criteria are needed to perform the registration of the DWI. This will also be of great interest to NIH.

Second, and as it has been explained above, Q-Ball imaging only deals with a single-shell and it is only very recently that the development in multiple-shell acquisition schemes has started (Khachaturian & al. 2007). We think that this issue is extremely important and could provide a much better and accurate solution to the problem of recovering the Diffusion PDF from the large number of data provided by HARDI. Therefore this problem will also be tackled by INRIA, NIH and the University of Minnesota.

Finally, a large number of clinical studies use simple scalar diffusion measurements such as fractional anisotropy (FA) and/or mean diffusivity to characterize the structural abnormalities present along a given fiber pathway to identify pathologies and compare patients with healthy control. An open problem that will be explored by INRIA, NIH and the University of Minnesota is the one related to the quantities, scalar or not, that could be retrieved from HARDI techniques like Q-Ball or Diffusion Kurtosis Imaging or from the Ensemble Average Propagator to better describe and characterize the biological tissue being analyzed. For instance, we recently obtained preliminary data in 25 patients with Writer's Cramp compared to 25 healthy control subjects suggesting that FA was reduced in the putamen of patients with Writer's Cramp. These results suggest that microstructural abnormalities are present along the sensorimotor cortico - striatal fiber tracts of these patients. Better tools, such as those that will be developed by the Associate Team, are therefore needed to undertake a more systematic study of these abnormalities. Improvement is expected in several domains: Reconstruction of the face and lower limb portions of the cortico - striatal bundle, new methods to obtain statistics on the tensor characteristics or on diffusion orientation using Q-ball imaging, classification algorithms based on the properties of the ODF. Many perspectives also exist to apply these techniques and tools to other pathologies, such as Tourette syndrome, or diseases of other fiber tracts, such as the pyramidal tract in amyotrophic lateral sclerosis or the cingulate bundle in patients with Mild Cognitive Impairment. By combining our expertise in the aforementioned approaches, we believe to have excellent prospects of achieving our goals.

References:

1. C. Lenglet, J.S.W. Campbell, M. Descoteaux, G. Haro, P. Savadjiev, D. Wassermann, A. Anwander, R. Deriche, G.B. Pike, G. Sapiro, K. Siddiqi, P. Thompson. (2008) Mathematical Models for Diffusion MRI Processing, Neuroimage - Special Issue on Mathematics in Brain Imaging (in press)
2. M. Descoteaux and R. Deriche. (2008) High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution. Journal of Mathematical Imaging in Vision, special issue on Mathematics in Image Analysis , in press 2008
3. M. Descoteaux, E. Angelino, S. Fitzgibbons, R. Deriche Regularized, Fast and Robust Analytical Q-Ball Imaging, Magnetic Resonance in Medicine, Volume 58, Issue 3. Pages 497-510.
4. M. Descoteaux, R. Deriche, T. Knoesche and A. Anwander. (2008) Deterministic and Probabilistic Tractography Based on Complex Fiber Orientation Distributions. IEEE Transactions in Medical Imaging, accepted July 6th 2008,
5. A. Ghosh, M. Descoteaux and R. Deriche. Riemannian Framework for estimating Symmetric Positive Definite 4th Order Diffusion Tensors, Medical Image Computing and Computer Assisted Intervention (MICCAI) 2008, New York, USA, September 2008
6. Khachaturian, M.H.,Wisco, J.J., and Tuch, D.S. (2007). Boosting the sampling efficiency of q-Ball imaging using multiple wavevector fusion. Magn. Reson. Med. 57(2):289-296

WP-4: Optimal Real-Time Experimental Designs for DWI Acquisitions

Recently Poupon & al., 2008 addressed this issue and proposed an algorithm for real-time estimation of the diffusion tensor and the orientation distribution function (ODF) using the Kalman filtering framework. Basser & al., 1994, were the first to mention the idea of using the Kalman Filtering in the process of Diffusion Tensor estimation. However, until the recent paper by Poupon & al., no one to our knowledge developed this idea, implemented it or put it in practice. The Diffusion Tensor model, without any positivity constraint, is linear and easily fits into the Kalman filtering framework. However, the important question of how to take into account the positivity constraint within this real-time Kalman framework remains open. Also open is the question of how to incrementally and optimally estimate the ODF within this framework. Poupon & al. made some adjustments that can be shown to lead to a sub-optimal solution for the estimated ODF. We would like to revisite this Kalman framework, develop an optimal ODF estimation and also combine it with an incremental way to select the gradient directions during the scans.

Adding to all these very important questions, the observation noise is usually assumed Gaussian distributed. However, it is well known that the Gaussian assumption is only good when the SNR is high and some other parameters as the - or - value is small. When dealing with HARDI measurements, this is not always the case. Many people perform these DWI acquisitions at -values in which the DWIs suffer from significant signal attenuation. Here, the background noise is mostly Rician. Therefore, one of the objectives to be tackled within this proposal is to reformulate the Kalman filtering problem using a Rician observation noise distribution. if successful, this will open new perspectives since many other applications that use magnitude data as the basis for detection (like Radar detection, for instance) would actually be improved by such a distribution.

Other challenging problems that could be of great interest to be tackled are those related to the practical need to correct the motion induced by the patients during the scan and the need to take into account the different eddy current distortions that are introduced in different DWIs depending on the applied gradient direction and strength. This is usually solved separately by assembling all the DWIs into brain volumes and co-register them to a common template to correct for these artifacts after all of the MRI scans are performed. Therefore, it will be of great interest to explore how the the Kalman Filtering framework could be dynamically reformulated to correct for artifacts on the fly such as eddy currents and patient motion, including cardiac pulsation and respiratory motion.

Those topics will be discussed, developed and validated in close collaboration with our partners. The validation of these techniques will be performed on the set of data that will be acquired and produced at NICHD for 3T and CMRR for 7T.

Reference:

1. Basser, P., Mattiello, J., and Le Bihan, D. (1994). Estimation of the effective self-diffusion tensor from the NMR spin echo. Journal of Magnetic Resonance, B(103):247-254.
2. Descoteaux, M., Wiest-Daesslé, M., Prima, S., Barillot, C., and Deriche, R. (2008). Impact of Rician Adapted Non-Local Means Filtering on HARDI, Medical Image Computing and Computer Assisted Intervention (MICCAI) 122-130.
3. Poupon, C., Poupon, F., Roche, A., Cointepas, Y., Dubois, J., Mangin, J.F. (2007) Real-Time MR Diffusion Tensor and Q-Ball Imaging Using Kalman Filtering. Medical Image Computing and Computer Assisted Intervention (MICCAI) (1): 27-35.
4. Poupon, C., Roche, A., Dubois, J., Mangin, J.F., Poupon, F. (2008) Real-Time MR Diffusion Tensor and Q-Ball Imaging Using Kalman Filtering. Medical Image Analysis, 21(5) 527-534.

WP-5: Electrical conductivity, Diffusion MRI and MEEG problems

Knowledge of electrical conductivity of nerves and muscles is essential to understand not only how impressed electric and magnetic fields affect tissue, but how electric and magnetic field generated by excitable tissues can be detected non-invasively (see Basser & al (2000)). For instance, magneto-encephalography measures magnetic fields produced by action currents in the brain, but localizing the source of these currents relies on a "forward model" of magnetic field generation that is highly dependent on the accuracy and distribution of the electrical conductivity assumed throughout the brain.

Non-invasively estimating electrical conductivity tensor from Diffusion MRI is an additional activity we would like to explore within the framework of this Associate Team. Tuch & al (2001) already proposed a mathematical framework for estimating the conductivity tensor from the diffusion tensor, that predicts a linear relationship between the eigenvalues of the two tensors, supported by reports exhibiting comparable anisotropy of the two tensors in white matter. Using an effective medium approach, Tuch & al show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self diffusion tensor as measured by DT-MRI.

In this work-package, we would like to study and pursue this idea of estimating the conductivity tensor from Diffusion MRI. The road map we propose to follow is (a) Implement and reproduce the results provided by Tuch & al (b) Revisite and study in more details the derivations of the equations provided by Tuch, in particular with respect to the hypothesis and simplifications done (c) Study if it is possible to provide more complete and accurate models of electrical conductivity using HARDI data and not just Diffusion Tensor data as done by Tuch & al. and finally (d) : If (a) and (b) and (c) are successful steps, then we propose to use the estimated electrical conductivity tensor into electro/magneto-encephalography (MEEG) source reconstruction algorithms. This will allow to better study the influence of anisotropic conductivity on MEG/EEG source reconstructions and to provide hopefully better (MEG/EEG) source reconstruction algorithms.

References:

1. David S. Tuch and Van J. Wedeen and Anders M. Dale and John S. George and John W. Belliveau. Conductivity tensor mapping of the human brain using diffusion tensor MRI - PNAS September 25, 2001 vol. 98 no. 20 11697-11701
2. Basser, P.J. and Roth, B.J. (2000) New currents in electrical stimulation of excitable tissues. Annu Rev Biomed Eng. 02:377-397.
3. Jan Kybic, Maureen Clerc, Olivier Faugeras, Renaud Keriven, Théo Papadopoulo. Generalized head models for MEG/EEG: boundary element method beyond nested volumes Physics in Medicine and Biology, vol. 51, pp. 1333-1346, March 2006.

WP-6: Software Packages and Visualization Tools

• Second and higher order diffusion tensor and Orientation Diffusion Functions estimation from DWI
• DTI and HARDI segmentation methods by statistical surface evolution
• Deterministic and stochastic DTI and HARDI tractography algorithm as well as the Geodesic Connectivity Mapping technique already freely available here: http://gcm.gforge.inria.fr/

Reference:

1. Odyssée QBall plug-in for Slicer3D 3.3 http://www-sop.inria.fr/odyssee/en/software/QBallSlicer
2. The INRIA Odyssé Geodesic Connectivity Mapping Library http://gcm.gforge.inria.fr/index.html

Programme d'échanges avec budget prévisionnel

1. Echanges

The following visits are scheduled :

Total requested : 33510 Euros

The ticket  from Nice to Washington, economy : 660 Euros / person
The ticket  from Nice to Minneapolis economy : 850 Euros / person
The ticket  from Nice to Washingtion and Minneapolis economy : 1040 Euros / person
The IJ (cost par day) related to the US is 170 Euros (http://pauillac.inria.fr/~leifer/ijeuro/) / person

From NIH to INRIA : 9420 Euros
Visit of senior scientists Peter Basser, Carlo Pierpaoli and Sinisa Pajevic for a week at Sophia : ( 660 + 6*170 ) * 3 =  5040 Euros
Visit of Post Doctorant Evren Ozarslan for 2 weeks at Sophia : 660 + 12 * 170 = 660 + 3060 = 2700 Euros
Visit of Post Doctorant Raisa Freidlin for a week at Sophia : 660 + 6* 170 = 1680 Euros

From INRIA to NIH and UofM :  16440 Euros
Visit of senior scientists Rachid Deriche, Maureen Clerc and Théo Papadopoulo for a week at NIH and UofM : 3* (1040+ 6*170 ) = 6180 Euros
Visit of PhD student Aurobrata Ghosh for three weeks : 1040 + 18 * 170 = 4100 Euros
Visit of PhD students Emmanuel Carruyer and Demian Wassermann for two weeks : 2 * ( 1040 + 12 * 170) = 2 * 3080 = 6160 Euros

From UofM to INRIA : 7650 Euros
Visit of senior scientists Guillermo Sapiro and Kamil Ugurbil for a week at Sophia : 2 * (850 + 6*170) = 3740 Euros
Visit of research scientist Christophe Lenglet for 3 weeks : 850 + 18*170 = 3910 Euros

From UofM to INRIA : Supported by UofM
Visit of senior scientist Guillermo Sapiro for a week at Sophia (Scheduled for June 2009).
Visit of research scientist Christophe Lenglet for 2 weeks at Sophia (Scheduled for January 2009).

2. Cofinancement

Following the INRIA-NIH workshop at the NIH's main campus in Bethesda, MD, co-organized by Drs. Basser and Deriche, The INRIA European and International Relations Department (DREI) decided to help the Odyssée Project-team to initiate collaborations between the two groups. The main purpose of this funding was to support exchanges and initiate a collaborative scheme that will lead to the creation of an Associate Team. It is thanks to this help from the DREI that Peter Basser was invited to visit the Odyssée research group and serve on the Ph.D. committee of Maxime Descoteaux. It's also thanks to this help from DREI that Aurobrata Ghosh, a PhD student under the supervision of R. Deriche, at INRIA Sophia Antipolis - Méditerranée, spent two weeks visiting Dr. Basser's lab at NIH, learning about various aspects of DWI acquisition and analysis from a more practical point of view, and hearing about clinical and biological problems that are of interest in the neuroradiology and neuroscience communities.

The University of Minnesota's Department of Electrical and Computer Engineering and Center for Magnetic Resonance Research have a longstanding collaborative relation with the Odyssée Project-Team, which has been jointly supported between 2003 and 2006 by the INRIA European and International Relations Department (DREI) and NSF grant 0404617. As stated above, this allowed multiple visits to the University of Minnesota by Drs. Deriche and Lenglet. The University of Minnesota will help and support this collaboration. Dr. Lenglet has already planned to visit INRIA for two weeks early January 2009, which will be fully supported by the Department of Electrical and Computer Engineering. Another visit by Dr. Sapiro is also planned for mid-june 2009, which will also be supported by the University of Minnesota.

3. Demande budgétaire

The total amount exceeds the maximum of 20KE. This is partly due to the fact that we are three partners, 2 located in the US and one located in Sophia Antipolis - Méditerranée. The visits from INRIA to NIH and UofM have been mutualised in order to include a visit for both sites at the same time for all the PhD students. It should be noticed also that the emphasis is made on exchanges and visits mainly involving senior and junior scientists among which Professors, Post-Doctorants and PhD students. The second and third year will involve more exchanges and visits including intern scholars and PhD students.

© INRIA - mise à jour le 11/08/2008