Mathematical Methods for procesing and analyzing in-vivo fluorescence images of embryo development

The reconstruction and quantitative characterization of organogenesis during the development of living species is an area of great interest in the field of bio-medicine: What are the processes underlying animal embryogenesis where a single cell (a zygote) transforms into a multi-cellular organism comprising a rich diversity of cells in a detailed spatiotemporal organization?. Recent advances in microscopy techniques combined with the application of biological markers have now enabled the capture of in-vivo 3D image sequences of animal models, at the scale of individual cells, as they undergo embryogenesis. Robust and efficient computational techniques are required to meet the challenge of quantitatively processing and analyzing the huge amount of data provided by such in-vivo observations. In this context, this PhD Thesis contributes to the design of mathematical methods that aim automatically to digitally reconstruct the embryogenesis of animal models (mainly zebrafish) from 3D+time data acquired with state-of-the-art microscopy technologies. To accomplish this long-standing goal, the multiscale integration of cell dynamics must be combined with the molecular dynamics that occur within that spatio-temporal context. Towards this goal, on the one hand, cell dynamics can be explored from lineage tree information combined with information concerning cell shape and structure; and on the other, molecular dynamics can be gleaned from the analysis of spatio-temporal patterns of gene expression data. This PhD thesis comprises four parts that cover different aspects of the multiscale digital reconstruction of embryogenesis; it relies upon the use of various distinct methodologies, ranging from image processing to quantitative data analysis for biological interpretations. The first two parts explore the reconstruction of cell dynamics during zebrafish embryogenesis. In the first part, entitled 'In-toto reconstruction of early zebrafish embryogenesis from multiharmonic imaging', a dedicated image processing pipeline (mitosis tracking, membranes segmentation) for digitizing the first three hours of zebrafish development has been implemented. This strategy is employed to produce the lineage trees in a group of six embryos including complete division timings, coordinates, and cell shapes with minute temporal accuracy and micrometer spatial resolution. The analysis of this data shows the existence of a metasynchronous mitotic wave during the first cleavages in zebrafish development. In the second part 'Towards the spatio-temporal atlas of gene expression in zebrafish embryo development', a prototype of the image registration and data quantification workflows needed to generate a gene expression atlas of zebrafish development from fluorescence in-situ hybridization images is shown. The viability of the proposed approach is illustrated with a proof-ofconcept example that aligns and quantifies five gene expression patterns on a zebrafish template at the beginning of gastrulation. In the next two parts, new generic tools for reconstructing cell dynamics are presented. The third part, entitled 'Spatio-temporal mathematical morphology processing for in-vivo embryogenesis imaging', explores the extension of morphological image processing to 4D datasets. The definition of the basic spatio-temporal structuring elements (hypersegment, hypersphere, hypertube, hyperhorn) allows to present several applications (filtering, tracking, segmentation) dedicated to the analysis of 4D datasets of embryogenesis acquired with different microscopy techniques. Working directly in 4D spaces provides more spatio-temporal coherence than classical methods. Finally, in the fourth part -entitled 'Measuring the cell lineage tree'- a quantitative method that characterizes cell lineage tree data is presented. Because of the lack of mathematical formalisms in this field (usually only qualitative descriptions are provided), the Morphogenetic Entropy measure is defined. It allows one to quantify the informational content of a cell inside a lineage tree, concerning pluripotency and behavior during cell division (proliferation, diversification, stem cell mode). Morphogenetic Entropy measurements can be broadly applied to research on embryogenesis and stem cells. Overall, this PhD Thesis presents mathematical methods that when applied to in-vivo images from animal models (e.g. zebrafish, sea urchin) allow the quantitative description of embryogenesis processes at a cellular scale. The proposed methods analyze structural information, cell lineage trees and gene expression data. From a broader perspective, the use of these methods should contribute to fill the gap between genetics and epigenetics by providing a deeper understanding of embryogenesis.