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## Section: New Results

### Computational Anatomy

#### Statistical Analysis of Diffusion Tensor Images of the Brain

Participants : Marco Lorenzi [Correspondent] , Nicholas Ayache, Xavier Pennec.

Image non-linear registration, Longitudinal modeling, Alzheimer's disease

Alzheimer's disease is characterized by the co-occurrence of different phenomena, starting from the deposition of amyloid plaques and neurofibrillary tangles, to the progressive synaptic, neuronal and axonal damages. The brain atrophy is a sensitive marker of disease progression from pre-clinical to the pathological stages, and computational methods for the analysis of magnetic resonance images of the brain are currently used for group-wise (cross-sectional) and longitudinal studies of pathological morphological changes in clinical populations. The aim of this project is to develop robust and effective computational instruments for the analysis of longitudinal brain changes. In particular novel methods based on non-linear diffeomorphic registration have been investigated in order to reliably detect and statistically analyze pathological morphological changes [5] (see Fig.8 ). This project is also focused in the comparison of the trajectories of longitudinal morphological changes [31] estimated in different patients. This is a central topic for the development of statistical atlases of the longitudinal evolution of brain atrophy.

Figure 8. Modeled longitudinal brain changes in normal aging extrapolated from -15 to 18 years, and corresponding observed patient anatomies with estimated morphological age and age shift (biological age in parenthesis). Our modeling framework describes meaningful anatomical changes observed in clinical groups.

#### Statistical Learning via Synthesis of Medical Images

Participants : Hervé Lombaert [Correspondent] , Nicholas Ayache, Antonio Criminisi.

This work has been partly supported by a grant from Microsoft Research-Inria Joint Centre, by ERC Advanced Grant MedYMA (on Biophysical Modeling and Analysis of Dynamic Medical Images)

Statistical learning, Synthesis

Machine learning approaches typically require large training datasets in order to capture as much variability as possible. Application of conventional learning methods on medical images is difficult due to the large variability that exists among patients, pathologies, and image acquisitions. The project aims at exploring how realistic image synthesis could be used, and improve existing machine learning methods.

First year tackled the problem of better exploiting existing training sets, via a smart modeling of the image space (Fig. 9 ), and applying conventional random forests using guided bagging [21] . Synthesis of complex data, such as cardiac diffusion images (DTI), was also done. Synthesis of complex shapes, using spectral graph decompositions, is currently on-going work.

The modeling of shapes also includes novel representations based on the spectral decomposition of images[4] which are more robust to large deformations when comparing multiple patients.

Figure 9. Laplacian Forest, where images are here represented as points, and where decision trees are trained using the spatial organization of these images on a reduced space.

#### Statistical analysis of heart shape, deformation and motion

Participants : Marc-Michel Rohé [correspondent] , Xavier Pennec, Maxime Sermesant.

This work was partly supported by the FP7 European project MD-Paedigree and by ERC Advanced Grant MedYMA (on Biophysical Modeling and Analysis of Dynamic Medical Images)

Statistical analysis, Registration, Reduced order models, Machine learning

The work aims at developping statistical tools to analyse cardiac shape, deformation, and motion. In particular, we are interested in developping reduced order models so that the variability within a population described by a complex model can be reduced into few parameters or modes that are clinically relevant. We use these modes to represent the variability seen in a population and to relate this variability with clinical parameters, and we build group-wise statistics which relate these modes to a given pathology. We focus on cardiomyopathies and the cardiovascular disease risk in obese children and adolescents.

#### Geometric statistics for Computational Anatomy

Participants : Nina Miolane [Correspondent] , Xavier Pennec.

Lie groups, pseudo-Riemannian, Statistics, Computational Anatomy

Figure 10. Structure of Lie groups on which one can define a bi-invariant metric or a bi-invariant pseudo-metric. The black levels of the tree represent the adjoint decomposition of the Lie algebra, the dashed lines represent the possible algebraic types of the substructures. Note the recursive construction in the pseudo-Riemannian case.

#### Statistical Analysis of Diffusion Tensor Images of the Brain

Participants : Vikash Gupta [correspondent] , Nicholas Ayache, Xavier Pennec.

Population specific multimodal brain atlas for statistical analysis of white matter tracts on clinical DTI.

Figure 11. A: Probabilistic parcellation of corpus callosum with blue and red being the maximum and minimum probability regions respectively. B: Multivariate statistics on white matter tracts. The red-yellow sections show statistically significant differences

#### Longitudinal Analysis and Modeling of Brain Development

Participants : Mehdi Hadj Hamou [correspondent] , Xavier Pennec, Nicholas Ayache.

This work is partly funded through the ERC Advanced Grant MedYMA 2011-291080 (on Biophysical Modeling and Analysis of Dynamic Medical Images).

Brain development, adolescence, longitudinal analysis, non-rigid registration algorithm, extrapolation, interpolation

This work is divided into 2 complementary studies about longitudinal trajectories modeling:

• Diffeomorphic registration parametrized by Stationary Velocity Fields (SVF) is a promising tool already applied to model longitudinal changes in Alzheimer's disease. However, the validity of these model assumptions in faithfully describing the observed anatomical evolution needs to be further investigated. In this work, we thus analyzed the effectiveness of linear regression of SVFs in describing anatomical deformations estimated from past and future observations of the MRIs.

• Due to the lack of tools to capture the subtle changes in the brain, little is known about its development during adolescence. The aim of this project is to provide quantification and models of brain development during adolescence based on diffeomorphic registration parametrized by SVFs (see Fig.12 ). We particularly focused our study on the link between gender and the longitudinal evolution of the brain. This work was done in collaboration with J.L. Martinot et H. Lemaître (Inserm U1000).

Figure 12. Pipeline for the longitudinal analysis of brain development during adolescence.