2014

F. Denis, L. Viger, A. Charron, E. Voog, O. Dupuis, Y. Pointreau & C. Letellier
Detection of lung cancer relapse using self-reported symptoms
transmitted via an Internet Web-application : pilot study
of the sentinel follow-up
Support Care Cancer, 22 (6), 1467-1473, 2014. Online

 Abstract
Purpose We aimed to investigate whether patient selfevaluated
symptoms transmitted via Internet can be used
between planned visits to provide an early indication of disease
relapse in lung cancer.

Methods Between 2/2013 and 8/2013, 42 patients with lung
cancer having access to Internet were prospectively recruited
to weekly fill a form of 11 self-assessed symptoms called
“sentinel follow-up”. Data were sent to the oncologist in
real-time between planned visits. An alert email was sent to
oncologist when self-scored symptoms matched some
predefined criteria. Follow-up visit and imaging were then
organized after a phone call for confirming suspect symptoms.
Weekly and monthly compliances, easiness with which patients
used the web-application and the accuracy of the sentinel
follow-up for relapse detection were assessed and compared
to a routine visit and imaging follow-up.

Results Median follow-up duration was 18 weeks (8–32).
Weekly and monthly average compliances were 79 and
94 %, respectively. Sixty percents of patients declared to be
less anxious during the few days before planned visit and
imaging with the sentinel follow-up than without.
Sensitivity, specificity, positive, and negative predictive
values provided by the sentinel (planned imaging) follow-up
were 100 %(84 %), 89 %(96 %), 81 %(91 %), and
100 %(93 %), respectively and well correlated with relapse
(pχ2<0.001). On average, relapses were detectable 5 weeks
earlier with sentinel than planned visit.

Conclusion An individualized cancer follow-up that schedule
visit and imaging according to the patient status based on
weekly self-reported symptoms transmitted via Internet is
feasible with high compliance. It may even provide earlier
detection of lung cancer relapse and care.

Paper awarded by Les Trophées de l’Hospitalisation Privée (Paris, May 20, 2014).

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Martin Rosalie & Christophe Letellier
Toward a general procedure for extracting templates from chaotic attractors bounded by high genus torus
International Journal of Bifurcation and Chaos, 24 (4), 1450045, 2014.
Online

 Abstract
The topological analysis of chaotic attractor by means of template is rather well established for simple attractors as solution to the Rössler system. Lorenz-like attractors are already slightly more complicated because they are bounded by a genus-3 bounding torus, implying the necessity to use a two-component Poincaré section. In this paper, we enriched the concept of linking matrix to correctly describe an algebraic template for an attractor with (g−1) components of Poincaré section and whose bounding torus has g interior holes aligned. An example with g=5 — a multispiral attractor — is explicitly treated.

Erratum : The third equation of system (16) should be replaced by " -beta y - gamma z".

S. Mangiarotti, L. Drapeau & C. Letellier
Two chaotic global models for cereal crops cycles observed from
satellite in northern Morocco
Chaos, 24, 023130, 2014. Online

 Abstract
The dynamics underlying cereal crops in the northern region of Morocco is investigated using a global modelling technique applied to a vegetation index time series derived from satellite measurements, namely, the normalized difference vegetation index from 1982 to 2008. Two three-dimensional chaotic global models of reduced size (14-term and 15-term models) are obtained. The model validation is performed by comparing their horizons of predictability with those provided
in previous studies. The attractors produced by the two global models have a complex foliated structure—evidenced in a Poincar e section—rending a topological characterization difficult to perform. Thus, the Kaplan-Yorke dimension is estimated from the synthetic data produced by our global models. Our results suggest that cereal crops in the northern Morocco are governed by a weakly dissipative three-dimensional chaotic dynamics.

L. Viger, F. Denis, M. Rosalie & C. Letellier
A cancer model for the angiogenic switch
Journal of Theoretical Biology, 360, 21-33, 2014. Online

 Abstract
The occurrence of metastasis is an important feature in cancer development. In order to have a one-site model taking into account the interactions between host, effector immune and tumor cells which is not only valid for the early stages of tumor growth, we developed in this paper a new model where are incorporated interactions of these three cell populations with endothelial cells. These latter cells are responsible for the neo-vascularization of the tumor site which allows the migration of tumor cells to distant sites. It is then shown that, for some parameter values, the resulting model for the four cell populations reproduces the angiogenic switch, that is, the transition from avascular to vascular tumor.

E. Fresnel, J.-F. Muir & C. Letellier
Realistic human muscle pressure for driving a mechanical lung,
EPJ Nonlinear Biomedical Physics, 2, 7, 2014,
Online

 Abstract
Background An important issue in noninvasive mechanical ventilation consists in understanding the origins of patient-ventilator asynchrony for reducing their incidence by adjusting ventilator settings to the intrinsic ventilatory dynamics of each patient. One of the possible ways for doing this is to evaluate the performances of the domiciliary mechanical ventilators using a test bench. Such a procedure requires to model the evolution of the pressure imposed by respiratory muscles, but for which there is no standard recommendations.
Methods In this paper we propose a mathematical model for simulating the muscular pressure developed by the inspiratory muscles and corresponding to different patient ventilatory dynamics to drive the ASL 5000 mechanical lung. Our model is based on the charge and discharge of a capacitor through a resistor, simulating contraction and relaxation phases of the inspiratory muscles.
Results Our resulting equations were used to produce 420 time series of the muscle pressure with various contraction velocities, amplitudes and shapes, in order to represent the inter-patient variability clinically observed. All these dynamics depend on two parameters, the ventilatory frequency and the mouth occlusion pressure.
Conclusion Based on the equation of the respiratory movement and its electrical analogy, the respiratory muscle pressure was simulated with more consistency in regards of physiological evidences than those provided by the ASL 5000 software. The great variability in the so-produced inspiratory efforts can cover most of realistic patho-physiological conditions.

C. Letellier & J.-M. Malasoma
Universalities in the chaotic generalized Moore & Spiegel equations
Chaos, Solitons & Fractals, 69, 40-49, 2014. Online

 Abstract
By investigating the topology of chaotic solutions to the generalized Moore and Spiegel equations, we address the question how the solutions of nonlinear dynamical systems are dependent on the nature of the nonlinearity. In these generalized jerk equations, the single nonlinear term has a parity which depends on uⁿu̇. The system has an inversion symmetry when n is even and no symmetry property when n is odd. It is shown that the topology of chaotic solutions only depends on the parity of n, that is, on the symmetry properties and not on the degree of nonlinearity. The value of n only affects the possibility to develop the chaotic solution, that is, to increase the number of unstable periodic orbits within the attractor.