Christophe LETELLIER

C. Letellier, F. Denis & L. A. Aguirre
What can be learned from a chaotic cancer model ?
Journal of Theoretical Biology, 322, 7-16, 2013. Online

- Abstract
A simple model of three competing cell populations (host, immune and tumor cells) is revisited by using a topological analysis and computing observability coefficients. Our aim is to show that a non conventional analysis might suggest new trends in understanding the interactions of some tumor cells and their environment. The action of some parameter values on the resulting dynamics is investigated. Our results are related to some clinical features, suggesting that this model thus captures relevant phenomena to cell interactions.

C. Letellier & R. Gilmore
The universal template is a subtemplate of the double-scroll template
Journal of Physics A, 46, 065102, 2013. Online

- Abstract
The double-scroll attractor that can be produced by a wide class of nonlinear electronic circuits is known to contain periodic orbits of all types under certain operating conditions. We identify the branched manifold that describes the double-scroll attractor under these operating conditions. We then show that Ghrist’s universal template is embedded as a subtemplate in the double-scroll template.

C. Letellier, G. G. Rodrigues, J.-F. Muir & L. A. Aguirre
Individuality of breathing patterns in patients under noninvasive mechanical ventilation evidenced by chaotic global models
Chaos, 23 (1), 013137, 2013. Online

- Abstract :
Autonomous global models based on radial basis functions were obtained from data measured from patients under noninvasive mechanical ventilation. Some of these models, which are discussed in the paper, turn out to have chaotic or quasi-periodic solutions, thus providing a first piece of evidence that the underlying dynamics of the data used to estimate the global models are likely to be chaotic or, at least, have a chaotic component. It is explicitly shown that one of such global models produces attractors characterized by a Horseshoe map, two models produce toroidal chaos, and one model produces a quasi-periodic regime. These topologically inequivalent attractors evidence the individuality of breathing profiles observed in patient under noninvasive ventilation.

C. Letellier & L. A. Aguirre
Dynamical analysis of fractional-order Rössler and modified Lorenz systems
Physics Letters A, 377 (28-30), 1707-1719, 2013. Online

- Abstract
This paper is devoted to the dynamical analysis of fractional-order systems, namely the Rössler and a modified Lorenz system. The work here described compares the dynamical regimes of such fractional-order systems to that of the corresponding standard systems. It turns out that most of the chaotic attractors are topologically equivalent to those found in the original integer-order systems, although in some particular (and apparently rare) cases unusual bifurcation patterns and attractors are found.

C. C. R. Sady, U. S. Freitas, A. Portmann, J.-F. Muir, C. Letellier, L. A. Aguirre
Automatic sleep staging from ventilator signals in non invasive ventilation
Computers in Biology and Medicine, 43 (7), 833-839, 2013. online

- Abstract :
Noninvasive ventilation, a recognized treatment for chronic hypercapnic respiratory failure, is predominantly applied at night. Nevertheless, the quality of sleep is rarely evaluated due to the required technological complexity. A new technique for automatic sleep staging is here proposed for patients treated by noninvasive ventilation. This new technique only requires signals (airflow and hemoglobin oxygen saturation) available in domiciliary ventilators plus a photo-plethysmogram, a signal already managed by some ventilators. Consequently, electroencephalogram, electrooculogram, electromyogram, and electrocardiogram recordings are not needed. Cardiorespiratory features are extracted from the three selected signals and used as input to a Support Vector Machine multi-class classifier. Two different types of sleep scoring were investigated : the first type was used to distinguish three stages (wake, REM sleep and nonREM sleep), and the second type was used to evaluate five stages (wake, REM sleep, N1, N2 and N3 stages). Patient-dependent and patient-independent classifiers were tested comparing the resulting hypnograms with those obtained from visual/manual scoring by a sleep specialist. An average accuracy of 91% (84%) was obtained with three-stage (five-stage) patient-dependent classifiers. With patient-independent classifiers, an average accuracy of 78% (62%) was obtained when three (five) sleep stages were scored. Also if the PPG-based and flow features are left out, a reduction of 4.5% (resp. 5%) in accuracy is observed for the three-stage (resp. five-stage) cases. Our results suggest that long-term sleep evaluation and nocturnal monitoring at home is feasible in patients treated by noninvasive ventilation. Our technique could even be integrated into ventilators.

M. Rosalie & C. Letellier
Systematic template extraction from chaotic attractors : I. Genus-one attractors with an inversion symmetry
Journal of Physics A, 46 375101, 2013 On line

- Abstract
Describing the topological properties by a template is a powerful technique to classify chaotic attractors. Most of the time, reduced templates are used, but direct templates—in which all mechanisms (torsions, branch permutation, etc) identified in the attractor are explicitly described without any simplification—are of great interest for a better description of the subtleties of the dynamics. We introduce here two additional conventions for representing in a unique way the reduced template from a given linking matrix. We then propose an addition law for linking matrices which allows us to manipulate (combine) different mechanisms. A direct template can thus be described by using a series of linking matrices. On the other hand, we show how to analytically build the linking matrix associated with an attractor which is the image under an inversion symmetry of an attractor whose linking matrix is known.

F. Denis, L. Viger, A. Charron, E. Voog & C. Letellier
Detecting lung cancer relapse using self-evaluation forms weekly filled at home : the sentinel follow-up
Supportive Care in Cancer, 22 (1), 79-85, 2013. On line

- Abstract

  • Purpose. We aimed to assess if patients’ ratings of symptoms can be used to provide an early indication of disease recurrence or progression in lung cancer. We proposed a simple self-evaluation form made of six clinical parameters weekly scored by patients at home as a follow-up—here named sentinel—to improve relapse detection. Its performances were compared to those of a routine imaging follow-up.
  • Methods. Patients with lung cancer were prospectively recruited to weekly fill a form at home for self-assessing weight, fatigue, pain, appetite, cough, and breathlessness during at least 4 months. Each patient reported weight and assessed the severity of each symptom by grading it from 0 (no symptom) to 3 (major symptom). A score was retrospectively designed for discriminating patients with relapse from those without. Accuracy of relapse detection was then compared to values of the routine planned imaging.
  • Results. Forty-three patients were included in our center and recruited for 16 weeks or more follow-up during which at least one tumor imaging assessment was performed (CT scan or PET-CT). Forty-one completed the form weekly. Sensitivity, specificity, and positive and negative predictive values of sentinel were high (86, 93, 86 % and 93 vs 79, 96, 92, and 90 % for routine imaging—p = ns) and well correlated with relapse (pχ2 > 0.001). Moreover, relapses were detectable with sentinel on average 6 weeks earlier than the planned imaging.
  • Conclusion. This study suggests that a personalized cancer follow-up based on a weekly self-evaluation of six symptoms is feasible and may be accurate for earlier detection of lung cancer relapse, allowing integration in electronic devices for real-time patient outcome follow-up.
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Le Monde October 8, 2013
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Ouest France 0ctober 8, 2013
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Le Maine October 10, 2013

C. Quérel, O. Grondin & C. Letellier
A semi-physical NOx model for diesel engine control
SAE Technical Paper, 2013-01-0356, 2013 Online

- Abstract
In this paper, a new physics-based model for the prediction of NOx emissions produced by diesel engines is presented. The aim of this work is to provide a reference model for the validation of control strategies and NOx estimators. The model describes the NOx production in the burned gas zone where the burned gas temperature sub-model is adapted to be generic and tunable. The model consists of three main sub-models for the estimation of the burned gas temperature, the concentration of the species in the burned gases and the NOx formation, respectively. A new model for estimating the burned gas temperature, known to have a strong impact on thermal NOx formation rate, is proposed. The model depends on the intake burned gas ratio and the combustion phasing computed from the cylinder pressure. This model has a limited number of calibration parameters identified so that NOx model output matches with experimental data measured in a four-cylinder, four-stroke, direct-injection diesel engine. The proposed model is compared with a standard physical zero-dimensional thermodynamic approach. The new burned gas temperature sub-model enables to highly improve NOx estimation accuracy both in steady-state and transient operations, compared to purely physical models.

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