S. Mangiarotti, F. Le Jean, M. Huc & C. Letellier
Global modeling of aggregated and associated chaotic dynamics
Chaos, Solitons & Fractals, 83, 82-96, 2016. Online

- Abstract Spatially distributed systems are rather difficult to investigate due to two distinct problems which can be sometimes combined. First, the spatial extension is taken into account by monitoring the system evolution at different locations. Second, the dynamics cannot always be continuously tracked in time, and segments of data – sometimes recorded at different places – are only available. When the dynamics underlying a single marker is under consideration – as for instance the normalized difference vegetation index which can be used for assessing the vegetation canopy of a given area – a global model can be obtained from a single scalar time series built by aggregating the available time series recorded at different places and/or associating the segments of data recorded at different times (and possibly at different locations). We investigated how these two data preprocessing – common in environmental studies – may affect the model dynamics by using a system of spatially distributed Rössler systems which are phase synchronized or not.

L. A. Aguirre & Letellier
Controllability and synchronizability : Are they related ?
Chaos, Solitons & Fractals, 83, 242-251, 2016. Online

- Abstract In the two last decades the concept of observability has been formally linked to that of embedding in the context of nonlinear dynamics. Such a concept has been shown to play an important role in global modeling, data analysis and filtering, to mention a few examples. Preliminary results suggested that observability, at least in some cases, has some influence in synchronization problems. Could the dual concept of controllability also be important in such problems ? In the context of synchronization, in general, the role played by controllability properties may not be as relevant as observability is for data analysis. In this work we compute controllability coefficients analogous to the observability ones, now established in the literature, and evaluate their importance in synchronization problems. Two benchmarks have been used in the simulations : the Rössler and the cord systems. The following schemes were investigated : synchronization to external sinusoidal force, complete replacement, uni- and bi-directional coupling of identical oscillators. The results discussed in this work show that controllability and synchronizability are not related in general.

A. Kerfourn, B. Lamia, J.-F. Muir & C. Letellier
A dynamical model for heart remodeling during the two phases of pulmonary arterial hypertension
EPJ Nonlinear Biomedical Physics, 4, 1, 2016. Online

- Abtract Background. Pulmonary arterial hypertension is a rare and lethal disease affecting small diameter pulmonary arteries and leading to a progressive increase of the right vascular resistances. Patients with such a disease have no specific symptom, a feature which delays the diagnosis by 18 months to 2 years in average. In most cases, pulmonary arterial hypertension is diagnosed when the cardiac output is already reduced, inevitably leading to death when the disease is not efficiently treated. During the evolution of the disease, the right ventricle is clearly affected in two different ways : first the thickness of its walls increases (compensation) and second the ventricle inflates (decompensation). The latter phase remained unexplained.
Methods. We developed a dynamical model of the cardiovascular system in order to explain such a feature by regulation mechanisms. Since pulmonary arterial hypertension is a slowly evolving pathology, we took into account long-term regulation mechanisms as the myocardial development (muscular heart development) ; we only considered the heart rate variations among the short-term regulation mechanisms.
Results. Using a static model, we showed that the two phases observed during the evolution of pulmonary arterial hypertension can be explained by the interplay between the right and left ventricles. We then showed that our dynamical model can reproduce the heart remodeling during these two phases (compensation and decompensation of the right ventricle). After the compensation phase, the right ventricle can no longer maintain the cardiac output without the help of the left ventricle, which produces a part of the required work with the side effect of inflating the right ventricle.
Conclusion. By taking into account slow regulation mechanisms, the cardiac remodeling during pulmonary arterial hypertension was reproduced. We thus showed that the two phases observed during the increase in the pulmonary arterial resistance result from an interplay between the left and right ventricles.

F. Denis & C. Letellier,
Is high cancer rate in human due to a weakness in biology resulting from the rapid increase in lifetime expectancy ?
Bulletin du Cancer, 103 (3), 224-226, 2016. Online

- Introduction Keane et al. recently showed that specific genes related to cell cycle and DNA repair of bowhead whale may explain the very low lifespan cancer rate measured in this cetacean [1], a particularity selected during million years of evolution. In the other hand, Tomasetti et al. reported that variations in cancer risk among tissues can be correlated to the number of stem cell divisions during the average lifetime of humans : longer one lives, greater his cancer risk [2]. There are thus two puzzling aspects in carcinogenesis that are i) the lack of correlation between body size (the number of cells in an organism) and the incidence of cancer (Peto’s paradox), and ii) the lifetime cancer rate significantly greater in humans than in any other wild mammals.

C. Letellier & J.-M. Malasoma,
Architecture of chaotic attractors for flows in the absence of any singular point
Chaos, 26, 063115, 2016. Online

- Abstract Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain—in the particular case of the Wei system—such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2x2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in the neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system.

E. Fresnel, J.-F. Muir & C. Letellier
Performances of domiciliary ventilators compared by using a parametric procedure
EPJ Nonlinear Biomedical Physics, 4, 6, 2016. Online

- Abstract
Background Noninvasive mechanical ventilation is sufficiently widely used to motivate bench studies for evaluating and comparing performances of the domiciliary ventilators. In most (if not in all) of the previous studies, ventilators were tested in a single (or a very few) conditions, chosen to avoid asynchrony events. Such a practice does not reflect how the ventilator is able to answer the demand from a large cohort of patients with their inherent inter-patient variability. We thus developed a new procedure according which each ventilator was tested with more than 1200 “simulated” patients.
Methods Three lung mechanics (obstructive, restrictive and normal) were simulated using a mechanical lung (ASL 5000) driven by a realistic muscular pressure. 420 different dynamics for each of these three lung mechanics were considered by varying the breathing frequency and the mouth occlusion pressure. For each of the nine ventilators tested, five different parameter settings were investigated. The results are synthesized in colored maps where each color represents the ventilator (in)ability to synchronize with a given muscular pressure dynamics. A synchronizability ε is then computed for each map.
Results The lung model, the breathing frequency and the mouth occlusion pressure strongly affect the synchronizability of ventilators. The Vivo 50 (Breas) and the SomnoVENT autoST (Weinmann) are well synchronized with the restrictive model (ε=86 and 78 %, respectively), whereas the Elisée 150 (ResMed), the BiPAP A40 and the Trilogy 100 (Philips Respironics) better fit with an obstructive lung mechanics (ε=87, 86 and 86 %, respectively). Triggering and pressurization performances of the nine ventilators present heterogeneities due to their different settings and operating strategies.
Conclusion Performances of domiciliary ventilators strongly depend not only on the breathing dynamics but also on the ventilator strategy. One given ventilator may be more adequate than another one for a given patient.

I. Sendińa-Nadal, S. Boccaletti, & C. Letellier
Observability coefficients for predicting the class of synchronizability from the algebraic structure of the local oscillators
Physical Review E, 94, 042205, 2016. online

- Abstract
Understanding the conditions under which a collective dynamics emerges in a complex network is still an open problem. A useful approach is the master stability function --- and its related classes of synchronization --- which offers a necessary condition to assess when a network successfully synchronizes. Observability coefficients, on the other hand, quantify how well the original state space of a system can be observed given only the access to a measured variable. The question is therefore pertinent : given a generic dynamical system (represented by a state variable x) and given a generic measure on it h(x) (which may be either an observation of an external agent, or an output function through which the units of a network interact), are classes of synchronization and observability actually related to each other ? We explicitly address this issue, and show a series of non trivial relationships for networks of different popular chaotic systems (Rössler, Lorenz and Hindmarsh-Rose oscillators). Our results suggest that specific dynamical properties can be evoked for explaining the classes of synchronizability.

L. Viger, F. Denis, C. Draghi, T. Ménard & C. Letellier
Spatial avascular growth of tumor in a homogeneous environment,
Journal of Theoretical Biology, 416, 99-112, 2016. online

- Abstract
Describing tumor growth is a key issue in oncology for correctly understanding the underlying mechanisms leading to deleterious cancers. In order to take into account the micro-environment in tumor growth, we used a model describing — at the tissue level — the interactions between host (non malignant), effector immune and tumor cells to simulate the evolution of cancer. The spatial growth is described by a Laplacian operator for the diffusion of tumor cells. We investigated how the evolution of the tumor diameter is related to the dynamics (periodic or chaotic oscillations, stable singular points) underlying the interactions between the different populations of cells in proliferation sites. The sensitivity of this evolution to the key parameter responsible for the immuno-evasion, namely the growth rate of effector immune cells and their inhibition rate by tumor cells, is also investigated.

[1] M. Keane, J. Semeiks, B. Thomsen, J. P. de Magalhaes, Insights into the Evolution of longevity from the Bowhead Whale Genome, Cell Reports, 10, 1-11, 2015.

[2] C. Tomasetti & B. Vogelstein, Variation in cancer incidence among tissues can be explained by the number of stem cell divisions, Science, 347, 78, 2015.

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