Biomedical subjects

Bertrand Thirion

Publications and source records attributed to Bertrand Thirion.

2 recordsLinked to original sources

PubMed2004

Variational, geometric, and statistical methods for modeling brain anatomy and function.

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.

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PubMed2003

Dynamical components analysis of fMRI data through kernel PCA.

In parallel with standard model-based methods for the analysis of fMRI data, exploratory methods--such as PCA, ICA, and clustering--have been developed to give an account of the dataset with minimal priors: no assumption is made on the data content itself, but the data structure is assumed to show some properties (decorrelation, independence) that allow for the detection of structures of interest. In this paper, we present an alternative that tries to take into account some relevant knowledge for the analysis of the dataset, e.g., the experimental paradigm, while keeping the flexibility of exploratory methods: we use a prior temporal modeling of the data that characterizes each voxel time course. Two implementations are proposed: one based on the General Linear Model, the other one on more flexible short-term predictors, whose complexity is controlled by a Minimum Description Length approach. However, our main concern here is the construction of a multivariate model; the latter is performed with the help of a kernel PCA method that builds a redundant representation of the data through the nonlinearity of the kernel. This allows for a refinement in the description of the (temporal) patterns of interest. In particular, this helps in the characterization of subtle variations in the response to different experimental conditions. We illustrate the usefulness of nonlinearity through the analysis of a synthetic dataset and show on a real dataset how it helps to interpret the experimental results.

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