SEMINAIRE EN MATHEMATIQUES APPLIQUEES A LA BIOLOGIE
Clair Poignard, INRIA Bordeaux Sud Ouest, Wednesday November 24th, 2021Electroporation at the cell scale
Room 5340, Universite de Montreal, Pavillon Aisenstadt
Electropermeabilization (also called electroporation) is a significant
increase in the electrical conductivity and permeability of the cell
membrane that occurs when pulses of large amplitude (a few hundred
volts per centimeter) are applied to the cells: due to the electric
field, the cell membrane is permeabilized, and then nonpermeant
molecules can easily enter the cell cytoplasm by diffusion through the
electropermeabilized membranes. If the pulse duration is sufficiently
short (a few milliseconds or a few microseconds, depending on the
pulse amplitude), the cell membrane reseals within several tens of
minutes: reversible electroporation, preserves the cell viability and
is used in electrochemotherapy to vectorize the drugs until the cell
inside. If the pulses are too long, too numerous or if their
amplitude is too high, the cell membrane is irreversibly destroyed and
the cells are killed. Irreversible electroporation provides thus a
novel non thermal an minimally invasive ablation therapy.
In this talk I will present the state of the art on the mathematical
models of cell electroporation, and on going work on the modeling of
the micro-tissue response to electrical shocks. I will also illustrate
how numerical models can help interventional radiologists in their
practice of percutaneous tumor ablation by irreversible
electroporation.
SEMINAIRE DE MATHÉMATIQUES APPLIQUÉES DE L’IRL
Vendredi 3 juin 2022
Salle PK-4323 au LACIM (laboratoire du CRM), Université du Québec à Montréal
13h30 Albert COHEN Laboratoire Jacques-Louis Lions, Sorbonne Université
Titre: Optimal sampling in least-squares methods
Recovering an unknown function from finitely many point samples is an ubiquitous task in various applicative settings: non-parametric regression, machine learning, reduced modeling, response surfaces in computer or physical experiments, data assimilation and inverse problems. In this lecture, I will present recent results that are relevant to the context where the user is allowed to select the measurement points, sometimes refered to as active learning. These results allow us to derive an optimal sampling point distribution when the approximation is searched in a linear space of finite dimension n and computed by weigted-least squares.
Here optimal means both that the approximation is comparable to the best possible in this space, and that the sampling budget m barely exceeds n. The main involved tools are Christoffel functions, matrix concentration inequalities, reproducing kernel Hilbert spaces.
Pause
14h25 Viviane PONS, IRL CRM et Laboratoire Informatique pour la Mécanique et les Sciences de l’Ingénieur, Université Paris Saclay
Titre : treillis du s-ordre faible et s-Tamari
Nous présentons deux objets combinatoires classiques : le treillis de l’ordre faible sur les permutations et le treillis de Tamari. Dans les deux cas, le diagramme de Hasse modélisant la relation d’ordre partiel est le squelette d’un polytope : respectivement le permotoèdre et l’associaèdre. On montrera comment on peut généraliser cette construction pour obtenir deux nouveaux treillis et les constructions géométriques associées.
15h00 Claire GUERRIER, IRL CRM et Laboratoire Dieudonné, Université de Nice et de la Côte d’Azur
Titre: Signal propagation in myelinated axons: relating structure to function using mathematical modeling and simulations.
How myelin sheath characteristics influence spike transmission within myelinated axons and vice-versa?To address this question, we develop a model for signal transmission in the myelinated axon where myelin compartments alternates with nodes of Ranvier. The model is based on cable theory and Hodkin-Huxley formalism, and the analysis relies on the heat equation. Using a computational approach coupled to mathematical analysis, we determine the analytical solution corresponding to signal propagation in one myelin compartment, and investigate the signal transmission time for different neuronal morphology.