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Publicly available brain templates
A template is defined as a gray level image with anatomical labels. It can also be defined as a probabilistic image that gives the probability that the voxel belongs to each tissue. An atlas is defined as a (probabilistic) template together with the deformation metric like in [82]. The construction of digital atlases of the human brain is currently a very important topic, for which a lot of efforts have been spent. In the following we will present three brain templates that are widely used by clinicians: the well known threedimensional Talairach-Tournoux brain template (referred to as Talairach brain Atlas in the literature), the Whole Brain Atlas developed by Harvard Medical School and the Brainweb template developed by McGill University in Canada. Note that the word atlas is sometimes used for template. In the present work, we highlight the complementary information that the atlas carries compared to the template: the geometrical variability.
Talairach brain atlas :
The Talairach Brain Atlas [131] relies on a coordinate system that is based on the anterior-posterior commissural (AC-PC) line. It relies on a grid system to project the brain images into the three-dimensional space. Talairach Brain Atlas was constructed upon postmortem sections of a 59-year-old French woman. The brain specimen was cut every 2-5mm in sagittal direction, then the cross-section of each slice was photographed. Neurologists outlined the contours of the brain structure according to the photographs, and then color filled these contours, the same brain structures having the same color or texture expression. The horizontal and coronal section data were created by the interpolation of sagittal cross-section data. Talairach brain atlas divides the reference brain into 8 parts in the X-axis direction (from the left to the right of the brain), 11 parts in the Y-axis direction (from the front to the back of the brain) and 12 parts in the Z-axis direction (from the button to the top of the brain), see Fig.1.3. The Talairach space provides a cube where the brain should fit in a specified orientation. Since this reference is based on the assumption that the brain is symmetric, it contains only one brain hemisphere.
The interest of this template is that, when compared to a new individual, the localization of brain structures is accurate for areas close to AC-PC, for example, the thalamus. However the template accuracy decreases significantly for cortical areas, especially those that are highly asymmetric between the two hemispheres (e.g., the temporal lobe). Nevertheless, the Talairach brain template is widely accepted by the neuroscientists, because it was historically the first computational template. The neuroscientific literature still often refers to Talairach coordinates. There are however several disadvantages. The first one is its low resolution. The second one is that it makes a strong assumption on the symmetry of the whole brain which is not satisfied and is a rough approximation which may lead to misanalysis of patients. The third one is that it is based on a single subject who may not be representative of the whole population.
Some application of digital brain templates
Teaching of neuroanatomy :
Traditional neural anatomy teaching requires the aid of anatomical charts, books, images and renderings. Due to the very complex structure of the human brain, it is difficult to understand its shape, subcortical structures and the relationships between them. Moreover, brain-structure is, to some extent, subject dependent, which makes the use of a digital brain templates particularly relevant. Some publications and web applications [127, 146] make it possible to observe the brain easily with any translation, rotation or zoom on the region of interest. Moreover, as they are supposed to capture the most common features, they appear useful in brain anatomy understanding.
Surgical planning and reference :
As already mentioned above, digital brain templates can provide accurate and reliable information for surgical planning. It can be used to assess the risk of surgery and choose the best surgical approach. A particular example can be mentioned here with the deep brain stimulation (DBS) [21, 152]. The template is used in order to predefine the coordinate of one point in a subcortical structure where a deep electrode is inserted in order to stimulate a precise territory and cure some disorders. It is important to couple the anatomical and functional images, as this makes it possible to identify some areas that are critical to some essential functions and avoid to lesion those during the surgery Atlas-based segmentation :
Due to the large variability of the human brain, tissue segmentation is particularly difficult. It becomes even more challenging as we have to face the partial volume effect (PVE) issue. In low resolution images, PVE appears at boundaries between tissues, where a given voxel contains several tissue types. This blurs the boundaries between tissues. The atlas information can be used to guide the segmentation using both the template image to indicate the location and shape of the tissues and structures but also using the quantification of the normal geometrical variability to favor particular shapes and spatial organization.
Statistical Model
We consider here n individual MR images from n patients. This set (yi)16i6n of images are observed on a grid of voxels embedded in a continuous domain D ⊂ R3. We denote xj ∈ D the location of voxel j ∈ . We consider that each image is composed of voxels belonging to one class among K, corresponding to K tissues types. We assume that the signal in the K tissue classes is normally distributed with class dependent means (μk)16k6K and variances (σ2 k)16k6K as proposed in [20]. Therefore the probability of observing a data with intensity yj i for the ith image in the jth voxel given that it belongs to the kth class (cj i = k) is defined as follows: P(yj i |cj i = k, μk, σ2 k) ∼ N(yj i ; μk, σ2 k),
Table of contents :
Acknowledgements
1 Introduction.
1.1 The human brain and its shape
1.1.1 Brain anatomy
1.1.2 Brain imaging techniques
1.1.3 Computational neuroanatomy
1.1.4 Publicly available brain templates
1.1.5 Some application of digital brain templates
1.2 Segmentation and registration
1.2.1 Registration
1.2.1.1 Non-rigid registration methods
1.2.1.2 Application of brain image registration
1.2.1.3 Non-rigid registration algorithms
1.2.2 Segmentation
1.2.2.1 Methods of segmentation
1.3 Template estimation
1.4 Algorithms used in this work
1.4.1 Gradient descent
1.4.2 Stochastic algorithms
1.5 Contributions of this work
1.5.1 Generative Statistical Model
1.5.2 Statistical Learning Procedure
1.5.3 Segmentation of new individuals
2 Probabilistic Atlas and Geometric Variability Estimation.
2.1 Introduction
2.2 The Observation Model
2.2.1 Statistical Model
2.2.2 Parameters and likelihood
2.2.3 Bayesian Model
2.3 Estimation
2.3.1 Existence of the MAP estimation
2.3.2 Consistency of the estimator on our model
2.4 Estimation Algorithm using Stochastic Approximation Expectation-Maximization
2.4.1 Model factorization
2.4.2 Estimation Algorithm
Step 1: Simulation step.
Step 2: Stochastic approximation step.
Step 3: Maximization step.
2.4.3 Convergence analysis
2.5 Experiments and Results
2.5.1 Simulated data
2.5.2 Real data
2.6 Conclusion and discussion
2.7 Proof of Theorem 2.1
2.8 Proof of Theorem 2.3
2.8.1 Proof of assumption (A1’).
2.8.2 Proof of assumption (A2)
2.8.3 Proof of assumption (A3’)
3 Bayesian Estimation of Probabilistic Atlas for Tissue Segmentation
3.1 Introduction
3.2 Material
3.3 Methods
3.3.1 Statistical Model.
3.3.2 Estimation Algorithm.
3.3.3 Segmentation of new individuals.
3.4 Experiments and Results
3.5 Conclusion and Discussion
4 Bayesian Estimation of Probabilistic Atlas for Anatomically-Informed Functional MRI Group Analyses.
4.1 Introduction
4.2 Methods
4.2.1 Statistical Model.
4.2.2 Estimation Algorithm.
4.3 Experiments and Results
4.3.1 Simulated data.
4.3.2 In-vivo data.
4.4 Conclusion
5 Including Shared Peptides for Estimating Protein Abundances: A Significant Improvement for Quantitative Proteomics.
5.1 Introduction
5.2 Method
5.3 Material
5.4 Results
5.5 Conclusion
6 Conclusion and Discussion.
6.1 Summary
6.2 Large deformations for deformable template estimationContents vi
6.3 Multicomponent generalization of the models
6.4 Other remarks
6.4.1 Extension of the multi-modal atlas
6.4.2 Kernel choice
6.4.3 Algorithm implementation optimization
6.4.4 Bias field correction
A Definition of the most used similarity measures.
Bibliography
