Abstracts

Sylvain Arguillère  (Thursday, 9.30-10.10)  Shape analysis through flows of diffeomorphisms. 

The domain of Shape Analysis is the quantitative comparison of shapes in a way that takes into account their geometric properties. The end goal is to give a nice framework for the statistical analysis of shapes and images, particularly medical data, in order to accurately identify which area of the brain is affected by certain diseases for example. In this talk, I will describe a method introduced by Alain Trouvé, which allows to compare shapes through flows of diffeomorphisms with minimal energy, using tools from differential geometry and optimal control.

Irène Kaltenmark  (Thursday, 10.10-10.50)  Geometrical growth models for Computational Anatomy. Shape analysis of the cortical surface

In the first part of this talk, I will present a growth model for longitudinal shape analysis. It generalizes the diffeomorphometric framework based on the idea that the similarity between two shapes can be quantified by the amount of deformation required to match them. The specificity of this model is to relax the central hypothesis of one-to-one correspondences between shapes which may not apply when modeling highly heterogeneous growth processes.

The second part of this talk will focus on the morphological analysis of the cortical surface at the group level. I will present an algorithm to create a labeling system of cortical surface parcellations. The regions of these parcellations, called sulcal basins, are the geometric components of the cortical folding.

Amine Bohi (Thursday, 11.20-12.00)  Global Perturbation of Initial Geometry in a Biomechanical Model of Cortical Morphogenesis

Cortical folding pattern is a main characteristic of the geometry of the human brain which is formed by gyri (ridges) and sulci (grooves). Several biological hypotheses have suggested different mechanisms that attempt to explain the development of  cortical folding and its abnormal evolutions. Based on these hypotheses, biomechanical models of cortical folding have been proposed. In this work, we compare biomechanical simulations for several initial conditions by using an adaptive spherical  parameterization approach. Our approach allows us to study and explore one of the most potential sources of reproducible cortical folding pattern: the specification of initial geometry of the brain.

Jessica Dubois (Thursday, 12.00-12.40)  The early development of the human brain: MRI studies of the growth and folding patterns in newborns and infants

The development of the human brain is very intense during the last weeks of pregnancy and the first post-natal months. Brain networks are organized and gradually mature, depending on the child's sensory, motor and cognitive acquisitions. The developmental mechanisms that take place at the microscopic and mesoscopic scales (e.g. cell proliferation, growth and maturation of connections, etc.) are accompanied by important morphological changes: brain size growth and cortex folding with the appearance of gyri and sulci. Over the last twenty years, magnetic resonance imaging (MRI) combined with sophisticated image processing and modeling tools have enabled the precise and quantitative analysis of these forms in vivo. In this presentation, we will describe several recent studies conducted in collaboration between several teams on the evolution of folding during development. First, we will detail how gyrification progresses with age in successive waves [1]. Then we will look at the differences observed between fetuses and premature infants [2], and at the relationships between folding, clinical factors and neurodevelopmental  outcome in children [3,4]. Finally, we will focus on the development of the central sulcus and its asymmetries of shape between cerebral hemispheres [5]. These various studies suggest that folding patterns can serve as potential markers of the brain functional development.

Benjamin Charlier (Thursday, 14.00-14.40)  KeOps: Kernel Operations on the GPU, with autodiff, without memory overflows

The KeOps library lets you compute generic reductions of large 2d arrays whose entries are given by a mathematical formula.  It is perfectly suited to the computation of convolutions(or more generally to Kernel dot products) and the associated gradients (with an automatic differentiation engine).

KeOps is fast as it allows you to compute Gaussian convolution up to 40 times faster than a standard tensor algebra library that use GPU.  KeOps is scalable and can be used on large data (typically from n=10^3 to n=10^7 number of rows/columns): it combines a tiled reduction scheme and works even when the full kernel matrix does not fit into the GPU memory. Finally, KeOps is easy to use as it comes with its Matlab, Python (NumPy or PyTorch) and R (coming soon) bindings.

Web site: http://www.kernel-operations.io

Main authors: B. Charlier, J. Feydy, J. Glaunès

Arezki Boudaoud (Thursday, 15.10-15.50)  Dynamics and robustness of plant form

How does a living organism reach its final form? What makes morphogenesis robust against internal and external perturbations? In order to address these questions, we are developing methods to quantify plant form, to reconstruct the dynamics of organ morphogenesis, and to assess variability in shape. During the talk, I will give a survey of our main approaches and results.

Roberto Toro (Thursday, 15.50-16.30)  Neocortical morphogenesis through development and evolution

 The neocortex is the thin external layer of the cerebrum. The neurones it hosts, together with their profuse reciprocal connections, constitute most of brain volume. In humans, the neocortex is recognised as the substrate of cognitive functions such as language, decision making and creativity. We will discuss the development and evolution of the neocortex from the perspective of mechanical morphogenesis. We will aim at understanding biological processes such as cell proliferation and especialisation, within the context of the mechanical forces induced by growth of the elastic brain tissue. I will present our analyses of the development of brain folding and connectivity in ferrets, as well as our analyses of the evolution of neocortical folding in primates.

Leander Lacroix (Thursday, 17.00-17.40) A modular approach to incorporate prior knowledge in shape registration

Alexandre Bône (Friday, 9.30-10.10) Learning the spatio-temporal variability of longitudinal shape data sets

Longitudinal shape data sets are collections of arbitrarily sampled individual processes of geometrical alterations, which naturally arise in the field of medical imaging for instance, and more generally in computer vision. In such data sets, two types of variability can be distinguished: (i) the temporal variability that encode the dynamical differences between comparable processes (e.g. faster or slower); (ii) the spatial variability that remains once the individual dynamics are quotiented out, encoding the static characteristics of the considered geometrical objects (e.g. larger or smaller). The analysis of such data sets is a complex task in practice for two main reasons: (i) subtle temporal individual changes are masked by the spatial static variability; (ii) no common time-line is explicitly available. Building on the large deformation diffeomorphic metric mapping framework, this paper introduces a unified modeling approach that jointly learns a mean progression pattern along with temporal and geometrical variance estimates from unaligned temporal progressions of imaging measurements. Normal distributions of shape trajectories are defined as generative and hierarchical statistical models, which are learned by an original calibration algorithm. The proposed method is validated on a simulated data set, illustrated on a facial expression recognition task, and applied to hippocampi shape progression modeling in Alzheimer's disease.

Emre Baspinar (Friday, 10.10-10.50) A sub-Riemannian cortical model with frequency-phase and its application to image enhancement

Our objective is to develop a geometrical model of the primary visual cortex and employ the model geometry for image enhancement. Our departure point is the visual cortex model of the orientation selective cortical neurons, which was presented in [1]. We spatially extend this model to a five dimensional sub-Riemannian geometry and provide a novel geometric model of the visual cortex which models orientation-frequency selective, phase shifted cortical cell behavior and the associated neural connectivity. The model extracts orientation, spatial frequency and phase information of the objects in any given two dimensional input image. Such information provides a characterization of the shapes and textures in the input image. We develop an image enhancement algorithm which uses a multi-frequency Laplace-Beltrami flow in the sub-Riemannian framework of the model.
References
[1] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,” Journal of Mathematical Imaging and Vision, vol. 24, no. 3, pp. 307–326, 2006.

Luba Tchertanov  (Friday, 11.20-12.00) Conformational Variability of Proteins: Trait of Nature and Headache of Research

The great majority of biologically functional proteins are versatile molecules existing as an ensemble of reversible conformations and it is believed that nature has created such flexibility for specific functions that require large structural flexibility under physiological conditions. Numerical simulation of molecular dynamics is essential research instrument that reproduces the motion of a protein and generates its conformational space, non-accessible by the empirical techniques. The comprehensive and rigorous decoding of the simulation data helps to fill the gap from numerical atomistic description to biophysics and to biofunctions. Nevertheless, despite a great number of the available methods for the simulation data analysis, many aspects of molecular motion in modular multi-domain proteins are not accessible and the understanding of their dynamically-related functions is still restricted. Focusing on the receptor tyrosine kinase KIT [1, 2], the NMDA receptor [3], VKOR [4], and Hsp70 [5] which were studied (or are currently under the study) to explain their functional motion and its role in the vital physiological process − signal transduction, channel gating enzymatic catalysis and activity control − we will demonstrate some successful analysis and also illustrate the problems limiting our research.

References

1. Chauvot de Beauchêne I. and Tchertanov L. (2016). How Missense Mutations in Receptors Tyrosine Kinases impact Constitutive Activity and alternate Drug Sensitivity: Insights from Molecular Dynamics Simulations. Invited Research highlight for Receptors & Clinical Investigation. Vol.3, e1372. doi: 10.14800/rci.1372.
2. Inizan F., Hanna M., M. Stolyarchuk, A. Trouvé, Chauvot de Beauchêne I., Tchertanov L. (2019). The First 3D Structure of the KIT cytoplasmic domain reveals a New Look for an Old receptor. PlosONE. Will be submitted in Oct. 2019
3. Palmai Z., Houenoussi K., Cohen-Kaminsky, Tchertanov L. (2018). How does Binding of Agonist Ligands Control Intrinsic Molecular Dynamics in Human NMDA Receptors? PLOS ONE. 13(8). doi: 10.1371/journal.pone.0201234.
4. Chatron N., Chalmond B., Trouvé A., Benoît E., Caruel H., Lattard V., Tchertanov L. (2017). Identification of the Functional States of Human Vitamin K Epoxide Reductase from Molecular Dynamics Simulations. RSC Advances, 7, 52071 – 52090.
5. Arlet J.B., Ribeil J. A., Hazoume A., Demarest S., Chauvot de Beauchêne I., Negre O., Dussiot M., Moura I. C., Sevin M., Maciel T. T., Auclair C., Belaid-Choucair Z., Leboulch P., Beuzard Y., Baudin-Creuza V., Tchertanov L., Garrido C., Hermine O., Courtois G. (2014). Hsp70 cytosolic sequestration by excess of free α-globin promotes ineffective erythropoiesis in β-thalassemia. Nature. 514(7521):242. doi: 10.1038/nature13614.

Christopher Fallaize (Friday, 12.00-12.40) Shape Analysis with Applications in Bioinformatics

In this talk, I will discuss some recent advances in statistical shape analysis which have been motivated by applications in structural bioinformatics. Examples of such applications include drug discovery, where shapes of molecules are key to biological activity, and protein bioinformatics, where shape similarities help to determine evolutionary histories which aid, for example, prediction of functionality. Statistical challenges include the identification of clusters of molecular shapes with similar substructures, and the matching of "unlabelled" shapes (unlabelled shape analysis).