One of the goals of shape analysis is to model and characterise shape evolution. We focus on methods where this evolution is modeled by the action of a time-dependent diffeomorphism, which is characterised by its time-derivatives: vector fields. Reconstructing the evolution of a shape from observations then amounts to determining an optimal path of vector fields whose flow of diffeomorphisms deforms the initial shape in accordance with the observations. However, if the space of considered vector fields is not constrained, optimal paths may be inaccurate from a modeling point of view. To overcome this problem, the notion of deformation module allows to incorporate prior information from the data into the set of considered deformations and the associated metric. I will present this generic framework as well as the Python library IMODAL, which allows to perform registration using such structured deformations. More specifically, I will focus on a recent implicit formulation where the prior can be expressed as a property that the generated vector field should satisfy. This imposed property can be of different categories that can be adapted to many use cases, such as constraining a growth pattern or imposing divergence-free fields.[-]

Oxygen is essential for burning food and generate energy, but may become limiting for aquatic organisms that rely on gas exchange under water. This is because breathing under water is challenging: the diffusion of oxygen is orders of magnitude lower in water than in air, while the higher density and viscosity of water greatly enhance the cost of breathing. Given that oxygen may be also be a limiting resource, respiration physiology may be relevant to understand energy budgets in aquatic ectotherms.
Traditionally, respiration physiology has focused on the benefits of extracting sufficient amounts of oxygen and thus prevent asphyxiation. However, breathing oxygen is intrinsically dangerous: while a shortage of oxygen quickly leads to asphyxiation, too much oxygen is toxic. Therefore, the ability to regulate oxygen consumption rates (i.e. respiratory control) is at a premium; good respiratory control will enable ectotherms to balance oxygen toxicity against the risk of asphyxiation across a wide range of temperatures.
In this presentation I will focus on the effects of body size and temperature on this balancing act with regard to oxygen uptake and consumption. Body size is intimately tied to oxygen budgets and hence energy budgets through size related changes in oxygen requirements and respiratory surfaces. Furthermore, a larger body size may represent a respiratory advantage that helps to overcome viscosity. Given that viscous forces are larger in cold water, this respiratory advantage represents a novel explanation for the pattern of larger body sizes in cold water, with polar gigantism as the extreme manifestation.
Temperature is also intimately tied to oxygen budgets and hence energy budgets through thermal controls on metabolism and temperature related changes in the availability of dissolved oxygen (notably diffusivity, viscosity and solubility). Thus, differences in temperatures may act more strongly on ectotherms that rely on aquatic rather than on aerial gas exchange. Comparing four different insect orders, I demonstrate that thermal tolerance is indeed affected more by the prevalent oxygen conditions in species with poor respiration control. In conclusion, the ability to regulate gas exchange (i.e. respiratory control) is thus a key attribute of species that helps to explain thermal responses from an oxygen perspective.[-]

We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient.
We motivate our model in relation to experimental data and demonstrate how it correctly reproduces cut and graft experiments. In particular, our system improves on previous models by preserving polarity in regeneration, over orders of magnitude in body size during cutting experiments and growth phases. Our model relies on tristability in cell density dynamics, between head, trunk, and tail. In addition, key to polarity preservation in regeneration, our system includes sensitivity of cell differentiation to gradients of wnt-related signals measured relative to the tissue surface. This process is particularly relevant in a small tissue layer close to wounds during their healing, and modeled here in a robust fashion through dynamic boundary conditions.[-]

Macrophages are a type of immune cells that can be present in high numbers in some solid tumours. The heterogeneity of macrophage populations (with the anti-tumour M1 cells and thepro-tumour M2 cells being the two extreme phenotypes) has led to difficulties in understanding the innate immune responses to tumours. Here we introduce a class of mathematical models for the interactions between a population of tumour-associated macrophages (structured by their phenotype) and a population of cancer cells (that could be structured by their mutation status). We then use this class of models to confirm that the M1 cells kill tumours, while the M2 cells can lead to tumour growth. In addition, we show that macrophages with mixed phenotypes can contribute to either tumour growth or tumour decay. We also show that tumour dormancy is associated not only with an increased heterogeneity of cancer population, but also with an increased heterogeneity of macrophage population.[-]