Lecturer at the University Paris Diderot (Paris 7), doing his research in the IMNC laboratory, in the team for modeling of biological systems. Formerly post-doc, in the team of Thomas Nattermann. Former PhD student at the LPTENS under the advice of Rémi Monasson.
Campus d'Orsay - Building 440
91405 Orsay CEDEX - France
E-mail: deroulers # imnc.in2p3.fr |
Phone: +33 1 69 15 36 41
Fax: +33 1 69 15 71 96
In international, peer-reviewed journals, or, when indicated, in proceedings of international conferences.
Diffuse low-grade gliomas are characterized by slow growth. Despite
appropriate treatment, they change inexorably into more aggressive
forms, jeopardizing the patient's life. Optimizing treatments, for
example with the use of mathematical modelling, could help to prevent
tumour regrowth and anaplastic transformation. Here, we present a model
of the effect of radiotherapy on such tumours. Our objective is to
explain observed delay of tumour regrowth following radiotherapy and to
predict its duration.
Materials and methods We have used a migration-proliferation model complemented by an equation describing appearance and draining of oedema. The model has been applied to clinical data of tumour radius over time, for a population of 28 patients.
Results We were able to show that draining of oedema accounts for regrowth delay after radiotherapy and have been able to fit the clinical data in a robust way. The model predicts strong correlation between high proliferation coefficient and low progression-free gain of lifetime, due to radiotherapy among the patients, in agreement with clinical studies.
We argue that, with reasonable assumptions, it is possible to predict (precision ~20%) regrowth delay after radiotherapy and the gain of lifetime due to radiotherapy.
Conclusions Our oedema-based model provides an early estimation of individual duration of tumour response to radiotherapy and thus, opens the door to the possibility of personalized medicine.
Background: Digital pathology images are increasingly
used both for diagnosis and research, because slide scanners are
nowadays broadly available and because the quantitative study of
these images yields new insights in systems biology. However, such
virtual slides build up a technical challenge since the images
occupy often several gigabytes and cannot be fully opened in a
computer's memory. Moreover, there is no standard format. Therefore,
most common open source tools such as ImageJ fail at treating them,
and the others require expensive hardware while still being
Results: We have developed several cross-platform open source software tools to overcome these limitations. The NDPITools provide a way to transform microscopy images initially in the loosely supported NDPI format into one or several standard TIFF files, and to create mosaics (division of huge images into small ones, with or without overlap) in various TIFF and JPEG formats. They can be driven through ImageJ plugins. The LargeTIFFTools achieve similar functionality for huge TIFF images which do not fit into RAM. We test the performance of these tools on several digital slides and compare them, when applicable, to standard software. A statistical study of the cells in a tissue sample from an oligodendroglioma was performed on an average laptop computer to demonstrate the efficiency of the tools.
Conclusions: Our open source software enables dealing with huge images with standard software on average computers. They are cross-platform, independent of proprietary libraries and very modular, allowing them to be used in other open source projects. They have excellent performance in terms of execution speed and RAM requirements. They open promising perspectives both to the clinician who wants to study a single slide and to the research team or data centre who do image analysis of many slides on a computer cluster.
Background: Supratentorial diffuse low-grade gliomas in
adults extend beyond maximal visible MRI-defined abnormalities and a
gap exists between the imaging signal changes and the actual tumor
margins. Direct quantitative comparisons between imaging and
histological analyses are lacking even if they are mandatory to
develop realistic models for diffuse glioma growth.
Methods: In this study, we quantitatively compare the cell concentration and the edema fraction from human histological biopsy samples (BSs) performed within and outside imaging abnormalities during serial imaging- based stereotactic biopsy of diffuse low-grade gliomas.
Results: The cell concentration was significantly higher in BSs located inside (1189±378 cell/mm2) than outside (740±124 cell/mm2) MRI-defined abnormalities (p=0.0003). The edema fraction was significantly higher in BSs located inside (mean, 45±23%) than outside (mean, 5±9%) MRI-defined abnormalities (p<0.0001). At the MRI-defined abnormalities borders, the edema fraction corresponded to 20% whereas tumor cells occupied a mean surface of 3%. The cycling cell concentration was significantly higher in BSs located inside (10±12 cell/mm2) than outside (0.5±0.9 cell/mm2) MRI-defined abnormalities (p=0.0001).
Conclusions: We show that the margins of T2-weighted signal changes are mainly correlated to the edema fraction. In 62.5% of patients, the cycling tumor cell fraction (defined as the ratio of the cycling tumor cell concentration to the total number of tumor cells) was higher at the inner limits of the MRI-defined abnormalities than inside the tumor center. In the remaining patients, the cycling tumor cell fraction increased towards the center of the tumor.
Objectives: Here we present a model aiming to provide an
estimate of time from tumour genesis, for grade II gliomas. The
model is based on a differential equation describing the
diffusion-proliferation process. We have applied our model to
situations where tumour diameter was shown to increase linearly with
time, with characteristic diametric velocity.
Materials and methods: We have performed numerical simulations to analyse data, on patients with grade II gliomas and to extract information concerning time of tumour biological onset, as well as radiology and distribution of model parameters.
Results and conclusions: We show that the estimate of tumour onset obtained from extrapolation using a constant velocity assumption, always underestimates biological tumour age, and that the correction one should add to this estimate is given roughly by 20/v (year), where v is the diametric velocity of expansion of the tumour (expressed in mm/year). Within the assumptions of the model, we have identified two types of tumour: the first corresponds to very slowly growing tumours that appear during adolescence, and the second type corresponds to slowly growing tumours that appear later, during early adulthood. That all these tumours become detectable around a mean patient age of 30 years could be interesting for formulation of strategies for early detection of tumours.
We present a model aiming at the description of intercellular communication on the invasive character of gliomas. We start from a previous model of ours based on a cellular automaton and develop a new version of it in a three-dimensional geometry. Introducing the hydrodynamic limit of the automaton we obtain a macroscopic model involving a nonlinear diffusion equation. We show that this macroscopic model is quite adequate for the description of realistic situations. Comparison of the simulations with experimental results shows agreement with the finding that the inhibition of intercellular communication (through gap junctions) tends to decrease migration. As an application of our model we estimated the possible increase in life expectancy, due to reduced cell migration mediated by the inhibition of intercellular communication, on patients suffering from gliomas. We find that the obtained increase may amount to a 20% gain in the case of unresectable tumours.
Background: Imaging determinations of the spatial extent of
diffuse low-grade gliomas (DLGGs) are of paramount importance in
evaluating the risk-to-benefit ratio of surgical resection. However,
it is not clear how accurately preoperative conventional MRI can
Methods: We report a retrospective histologic and imaging correlation study in 16 adult patients who underwent serial stereotactic biopsies for the diagnosis of untreated supratentorial well-defined and non-contrast-enhanced DLGG, in whom biopsy samples were taken within and beyond (OutBSs) MRI-defined abnormalities.
Results: Thirty-seven OutBSs that extended from 10 to 26 mm beyond MRI-defined abnormalities were studied. Immunostaining revealed MIB-1-positive cells (i.e., cycling cells) in all but 2 of the OutBSs. None of the MIB-1-positive cells coexpressed glial fibrillary acidic protein, and all of them coexpressed OLIG2. MIB-1-positive cells were cycling isolated tumor cells, because 1) their morphologic characteristics reflected those of tumor cells, 2) the number of MIB-1-positive cells per square centimeter was significantly higher than that of controls, 3) the number of MIB-1-positive cells per square centimeter was positively correlated with the tumor growth fraction (p = 0.012), and 4) the number of MIB-1-positive cells per square centimeter in OutBSs decreased with distance from the tumor (p = 0.003).
Conclusions: This study demonstrates, using a multiscale correlative approach, that conventional MRI underestimates the actual spatial extent of diffuse low-grade gliomas (DLGGs), even when they are well delineated. These results suggest that an extended resection of a margin beyond MRI-defined abnormalities, whenever feasible in noneloquent brain areas, might improve the outcome of DLGGs.
Twelve pregnancies in 11 adult women harboring World Health Organization (WHO) grade II gliomas (GIIGs) prior to pregnancy were reviewed to address whether pregnancy affects tumor growth using a quantitative approach of the radiological velocity of diametric expansion (VDE) on successive magnetic resonance images. VDE was significantly increased during pregnancy as compared to prepregnancy (p < 0.001) and to postdelivery (p = 0.012) periods. Pregnancy increases the radiological growth rates of GIIGs. An increase in seizure frequency was observed concomitantly in 40% of cases and further oncological treatment was started after delivery in 25% of cases.
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.
We propose a simple cellular automaton model for the description of the evolution of a colony of Bacillus subtilis. The originality of our model lies in the fact that the bacteria can move in a pool of liquid. We assume that each migrating bacterium is surrounded by an individual pool, and the overlap of the latter gives rise to a collective pool with a higher water level. The bacteria migrate collectively when the level of water is high enough. When the bacteria are far enough from each other, the level of water becomes locally too low to allow migration, and the bacteria switch to a proliferating state. The proliferation-to-migration switch is triggered by high levels of a substance produced by proliferating bacteria. We show that it is possible to reproduce in a fairly satisfactory way the various forms that make up the experimentally observed morphological diagram of B. subtilis. We propose a phenomenological relation between the size of the water pool used in our model and the agar concentration of the substrate on which the bacteria migrate. We also compare experimental results from cutting the central part of the colony with the results of our simulations.
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 million 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 detail 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.
Motivated by recent experiments on nanowires and carbon nanotubes, we study theoretically the effect of strong, point-like impurities on the linear electrical resistance R of finite length quantum wires. Charge transport is limited by Coulomb blockade and cotunneling. ln R is slowly self-averaging and non Gaussian. Its distribution is Gumbel with finite-size corrections which we compute. At low temperatures, the distribution is similar to the variable range hopping (VRH) behaviour found long ago in doped semiconductors. We show that a result by Raikh and Ruzin does not apply. The finite-size corrections decay with the length L like 1/ln L. At higher temperatures, this regime is replaced by new laws and the shape of the finite-size corrections changes strongly: if the electrons interact weakly, the corrections vanish already for wires with a few tens impurities.
The probability Psuccess(α, N) that stochastic greedy algorithms successfully solve the random SATisfiability problem is studied as a function of the ratio α of constraints per variable and the number N of variables. These algorithms assign variables according to the unit-propagation (UP) rule in presence of constraints involving a unique variable (1-clauses), to some heuristic (H) prescription otherwise. In the infinite N limit, Psuccess vanishes at some critical ratio α_H which depends on the heuristic H. We show that the critical behaviour is determined by the UP rule only. In the case where only constraints with 2 and 3 variables are present, we give the phase diagram and identify two universality classes: the power law class, where Psuccess[αH (1+ε N-1/3), N] ∼ A(ε)/Nγ; the stretched exponential class, where Psuccess[αH (1+ε N-1/3), N] ∼ exp[-N1/6 Φ(ε)]. Which class is selected depends on the characteristic parameters of input data. The critical exponent γ is universal and calculated; the scaling functions A and Φ weakly depend on the heuristic H and are obtained from the solutions of reaction-diffusion equations for 1-clauses. Computation of some non-universal corrections allows us to match numerical results with good precision. The critical behaviour for constraints with >3 variables is given. Our results are interpreted in terms of dynamical graph percolation and we argue that they should apply to more general situations where UP is used.
The probability P(α, N) that search algorithms for random Satisfiability problems successfully find a solution is studied as a function of the ratio α of constraints per variable and the number N of variables. P is shown to be finite if α lies below an algorithm-dependent threshold α_A, and exponentially small in N above. The critical behaviour is universal for all algorithms based on the widely-used unitary propagation rule: P[ (1 + ε) αA , N] ∼ exp[-N1/6 Φ(ε N1/3) ]. Exponents are related to the critical behaviour of random graphs, and the scaling function Φ is exactly calculated through a mapping onto a diffusion-and-death problem.
A quantum field theoretic formulation of the dynamics of the Contact Process on a regular graph of degree z is introduced. A perturbative calculation in powers of 1/z of the effective potential for the density of particles φ(t) and an instantonic field ψ(t) emerging from the quantum formalism is performed. Corrections to the mean-field distribution of densities of particles in the out-of-equilibrium stationary state are derived in powers of 1/z. Results for typical (e.g. average density) and rare fluctuation (e.g. lifetime of the metastable state) properties are in very good agreement with numerical simulations carried out on D-dimensional hypercubic (z=2D) and Cayley lattices.
We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional, rather than activated, dynamics. We also look at the distribution of relaxation times among different samples, finding different results for the two q values. For q=3 the relative variance of the relaxation time tau at the critical point is finite. However, for q=24 this appears to diverge in the thermodynamic limit and it is ln(tau) which has a finite relative variance. We speculate that this difference occurs because the transition of the corresponding pure system is second order for q=3 but first order for q=24.
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