70 research outputs found
Exclusion processes: short range correlations induced by adhesion and contact interactions
We analyze the out-of-equilibrium behavior of exclusion processes where
agents interact with their nearest neighbors, and we study the short-range
correlations which develop because of the exclusion and other contact
interactions. The form of interactions we focus on, including adhesion and
contact-preserving interactions, is especially relevant for migration processes
of living cells. We show the local agent density and nearest-neighbor two-point
correlations resulting from simulations on two dimensional lattices in the
transient regime where agents invade an initially empty space from a source and
in the stationary regime between a source and a sink. We compare the results of
simulations with the corresponding quantities derived from the master equation
of the exclusion processes, and in both cases, we show that, during the
invasion of space by agents, a wave of correlations travels with velocity v(t)
~ t^(-1/2). The relative placement of this wave to the agent density front and
the time dependence of its height may be used to discriminate between different
forms of contact interactions or to quantitatively estimate the intensity of
interactions. We discuss, in the stationary density profile between a full and
an empty reservoir of agents, the presence of a discontinuity close to the
empty reservoir. Then, we develop a method for deriving approximate
hydrodynamic limits of the processes. From the resulting systems of partial
differential equations, we recover the self-similar behavior of the agent
density and correlations during space invasion
Automatic quantification of the microvascular density on whole slide images, applied to paediatric brain tumours
Angiogenesis is a key phenomenon for tumour progression, diagnosis and
treatment in brain tumours and more generally in oncology. Presently, its
precise, direct quantitative assessment can only be done on whole tissue
sections immunostained to reveal vascular endothelial cells. But this is a
tremendous task for the pathologist and a challenge for the computer since
digitised whole tissue sections, whole slide images (WSI), contain typically
around ten gigapixels.
We define and implement an algorithm that determines automatically, on a WSI
at objective magnification , the regions of tissue, the regions
without blur and the regions of large puddles of red blood cells, and
constructs the mask of blur-free, significant tissue on the WSI. Then it
calibrates automatically the optical density ratios of the immunostaining of
the vessel walls and of the counterstaining, performs a colour deconvolution
inside the regions of blur-free tissue, and finds the vessel walls inside these
regions by selecting, on the image resulting from the colour deconvolution,
zones which satisfy a double-threshold criterion. A mask of vessel wall regions
on the WSI is produced. The density of microvessels is finally computed as the
fraction of the area of significant tissue which is occupied by vessel walls.
We apply this algorithm to a set of 186 WSI of paediatric brain tumours from
World Health Organisation grades I to IV. The segmentations are of very good
quality although the set of slides is very heterogeneous. The computation time
is of the order of a fraction of an hour for each WSI on a modest computer. The
computed microvascular density is found to be robust and strongly correlates
with the tumour grade.
This method requires no training and can easily be applied to other tumour
types and other stainings
Modeling tumor cell migration: from microscopic to macroscopic
It has been shown experimentally that contact interactions may influence the
migration of cancer cells. Previous works have modelized this thanks to
stochastic, discrete models (cellular automata) at the cell level. However, for
the study of the growth of real-size tumors with several millions of cells, it
is best to use a macroscopic model having the form of a partial differential
equation (PDE) for the density of cells. The difficulty is to predict the
effect, at the macroscopic scale, of contact interactions that take place at
the microscopic scale. To address this we use a multiscale approach: starting
from a very simple, yet experimentally validated, microscopic model of
migration with contact interactions, we derive a macroscopic model. We show
that a diffusion equation arises, as is often postulated in the field of glioma
modeling, but it is nonlinear because of the interactions. We give the explicit
dependence of diffusivity on the cell density and on a parameter governing
cell-cell interactions. We discuss in details the conditions of validity of the
approximations used in the derivation and we compare analytic results from our
PDE to numerical simulations and to some in vitro experiments. We notice that
the family of microscopic models we started from includes as special cases some
kinetically constrained models that were introduced for the study of the
physics of glasses, supercooled liquids and jamming systems.Comment: Final published version; 14 pages, 7 figure
Modeling origin, natural evolution and response to radiotherapy of gliomas
Diffuse low-grade gliomas are slowly growing tumors. After tens of years, they transform inexorably into more aggressive forms, jeopardizing the patientâ s life. Mathematical modeling could help clinicians to have a better understanding of the natural history of these tumors and their response to treatments.
We present here different models of these tumors: the first one is discrete and describes the appearance of the first glioma cells and the genesis of a tumor. The second model is continuous and consists in a PDE that describes the evolution of the cell density. This model can describe the natural evolution of gliomas, their response to treatments such as radiotherapy and the changes in their dynamics in pregnant women. The discrete and the continuous models are designed to be close to the biological reality. The results are quantitatively compared with either biological data or clinical data, at the cellular level (histological samples) and at the tissue level (MRI scans).Non UBCUnreviewedAuthor affiliation: Paris Diderot UniversityFacult
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Renewable Energy and Flexibility Integration on the Electricity Market
Electricity is the most common way to transport, transform and consume energy. However, the total electricity generation accounts for 40% of worldwide CO2 emissions. With the threat of climate change, it is crucial to lowering emissions related to electricity generation and grid operation. While renewable energy sources provide a solution to decarbonize the electric grid, they bring new challenges due to their inherent volatility. The grid requires balancing capacity to maintain a stable frequency and storage to adapt generation hours to consumption hours. Meanwhile, 54% of the world's electricity consumption happens in countries that rely on competitive markets for efficient dispatch [4]. Therefore, it is essential to provide correct incentives and dispatch mechanisms on the electricity markets to integrate renewable energies and develop new market mechanisms for balancing renewable energy variability. This dissertation explores methods to integrate flexible resources into the electricity market. First, we develop an optimal bidding strategy for grid-scale storage on a wholesale electricity market. The specific role of the storage system creates market power which challenges the design of the bidding algorithm.Secondly, the dissertation focuses on flexible resources located on the distribution grid. Indeed, the simplest way to lower overall CO2 emissions with a decarbonized grid is to electrify all energy use. This electrification entails the deployment of electric vehicles, electric heaters, or electric stoves. In addition, rooftop solar panels, household batteries, and other local energy resources are installed on the distribution grid, known as distributed energy resources (DERs). As a result, the distribution grid faces dramatic changes and requires precise monitoring and maintenance. Controlling DERs and integrating them into the electricity market could provide new flexibility to the grid. This dissertation introduces a new market dispatch model for the day-ahead wholesale electricity market where DERs are integrated as stochastic sources of flexibility. However, the control and integration of DERs on the distribution grid rely on having a complete and accurate distribution grid model. Because the distribution grid lacks sensors and monitoring equipment, developing a detailed grid model is challenging for the system operator. Research on this subject is recent but provides diverse solutions dependent on modeling assumptions and data acquisition. In order to give future researchers a good understanding of existing methods and challenges left to tackle, this dissertation provides a detailed review and analysis of methods to estimate distribution grid topology
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