Synthesis report for the years 2014-2017
Here you can find the general presentation of the team: Mamba presentation – 2014 to 2017
and you may download the synthesis report: MAMBA synthesis report – 2014 to 2017
Context and overall objectives of the project-team
The MAMBA (Modelling and Analysis in Medical and Biological Applications) team is the continuation of the BANG (Biophysics, Numerical Analysis and Geophysics) team, which itself was a continuation of the former project-team M3N. Historically, the BANG team, headed by Benoît Perthame during 11 years (2003-2013), has developed models, simulations and numerical algorithms for two kinds of problems involving dynamics of Partial Differential Equations (PDEs).
The dynamics of complex physical or biophysical phenomena involves many agents, e.g. proteins or cells – which can be seen as active agents. Mathematically, they can be represented either explicitly as individuals with their dynamics modelled e.g. through branching trees and piecewise deterministic Markov processes (PDMP), or stochastic differential equations, or under certain conditions be grouped or locally averaged, in which case their dynamics is mimicked by Ordinary or Partial Differential Equations (ODEs/PDEs).
Biology and medicine presently face the difficulty to make sense of the data newly available by means of recent signal acquisition methods. Modelling through agent-based or continuous models is a unique way to explain (model) the observations and then compute, control and predict the consequences of the mechanisms under study. These are the overall goals of Mamba.
Last activity report : 2017
Analysis and control for population dynamics
Time asymptotics for nucleation, growth and division equations
We revisited the well-known Lifshitz-Slyozov model, which takes into account only polymerisation and depolymerisation, and progressively enriched the model. Taking into account depolymerisation and fragmentation reaction term may surprisingly stabilisde the system, since a steady size-distribution of polymers may then emerge, so that “Ostwald ripening” does not happen [article].
Cell population dynamics and its control
The question of optimal control of the population dynamics, that naturally arises when dealing with anticancer drug delivery optimisation, has been specifically the object of [article], work led in common with E. Trélat (LJLL and Inria team CAGE) and published in the J. Maths. Pures Appl.
The asymptotic behaviour of interacting populations in a nonlocal Lotka-Volterra way is also, independently of any control, studied for two populations in this article, and for many in [article].
Mathematical models of infectious diseases
Reaction and motion equations for living systems
Mathematical modelling for chemotaxis
A new kinetic model of chemotaxis for angiogenesis has been developed [article].
Free boundary problems for tumour growth.
Motivated by numerical observations from D. Drasdo using agent-based modelling, the article [article] studies the interfaces between two cell populations described by continuous models with different motilities and recovers interface instabilities.
Model and parameter identification combining stochastic and deterministic approaches in nonlocal and multi-scale models
Data assimilation and stochastic modelling for protein aggregation
Following Carola Kruse’s post-doc [article], in collaboration with Tom Banks, Aurora Armiento’s Ph.D [article], co-supervised with Philippe Moireau, was devoted to the question of adapting data assimilation strategies to the specific context and difficulties of protein aggregation.
In parallel with the statistical approach to growth and division processes, the deterministic approach has been continued in collaboration with Magali Tournus [article].
Estimating cellularity and tumour heterogeneity from Diffusion-Weighted MRI based on histological data
In [article] we developed, in close collaboration with the University of Heidelberg and DKFZ, together with I. Vignon-Clementel (Inria team REO), a procedure to estimate tumour heterogeneity and cellularity from Diffusion-Weighted Imaging (DWI) with calibration using histological data. The estimate is based on the intravoxel incoherent motion (IVIM) model that relates the DWI signal to water diffusion within each image voxel, as well as on an image processing and analysis procedure we developed for automated cell counting in large histological samples after tumour removal. We recently showed that biopsies routinely taken are likely to be sufficient to construct a calibration curve to relate DWI diffusion coefficient to cell density, and thus to infer the whole tumour heterogeneity. The biopsies have to be taken in regions of largely different diffusion values.
Focus on cancer
Modelling Acute Myeloid Leukaemia (AML) and its control by anticancer drugs by PDEs and Delay Differential equations
The collaboration with the DISCO team at Inria-Saclay has been continued in conference papers [article], [article]. In one of these papers, the concept of dormancy in cancer as a state of coexistence between tumour and healthy stem cell populations is studied using a new model.
Adaptive dynamics setting to model and circumvent evolution towards drug resistance in cancer by optimal control
This topic, main subject in Camille Pouchol’s ongoing PhD thesis, has already been mentioned about Axis 1. It has led to the publication [article].
The general question of drug resistance in cancer, from biological observations to mathematical modelling and optimal control, has been reviewed in [article], [article] and presented in various international conferences and workshops.
Senescence modelling by telomere shortening
This work, following Sarah Eugène’s PhD thesis, has been continued in collaboration with Zhou Xu at IBPC [article].
Growth, evolution and regeneration in populations and tissues
Making use of data assimilation and statistical methods [article], we proposed new models and mechanisms and most recently we predicted the existence of several coexisting species of protein fibrils [article].
The release of Wolbachia-infected mosquitoes in Dengue infested zones and the study of their propagation may be represented by spatial reaction-diffusion models. When implementing such a method, an important issue concerns the spatial propagation of the mosquitoes: on releasing infected mosquitoes in a given domain (which can be part of a city), the hope is to invade the whole area. The study of this propagation phenomena falls into the study of existence of travelling waves. We proposed in [article] a mathematical model to study such phenomena and have simplified it to recover a well-known simple bistable system for which existence of traveling wave is known. The study of the probability of success of spatial invasiveness has been performed in [article], and [article] is devoted to the blocking of the propagation in heterogeneous environment presenting strong enough population gradient. In the previous works, the invasion is installed by large enough impulsive deliveries. Another approach, consisting in igniting the propagation by feedback control, has been studied in [article], [article].
Toxicity extrapolation from in vitro to in vivo
The investigation of this field has been continued by Géraldine Cellière, leading to her PhD defense in June 2017 [article].