Numerical treatment of cardiac diseases using optimal control theory

AbstractWe propose a mathematical modelization and optimization of the action of some drugs such as β-blockers—a particular drug (tertatolol) studied in Servier laboratories is specially examined. Linear compartmental models are first tried but they are not convenient for explaining the experimental data. Then a dose effect relation is directly seeked. One obtains a nonlinear relationship between the dose, the plasmatic concentration and the drug's effect. Using some optimal control methods allows one to define an optimal therapeutic giving the optimal doses and possibly the optimal times optimizing some given criteria

Nonequilibrium Fluctuations, Travelling Waves, and Instabilities in Active Membranes

The stability of a flexible fluid membrane containing a distribution of mobile, active proteins (e.g. proton pumps) is shown to depend on the structure and functional asymmetry of the proteins. A stable active membrane is in a nonequilibrium steady state with height fluctuations whose statistical properties are governed by the protein activity. Disturbances are predicted to travel as waves at sufficiently long wavelength, with speed set by the normal velocity of the pumps. The unstable case involves a spontaneous, pump-driven undulation of the membrane, with clumping of the proteins in regions of high activity.Comment: 4 two-column pages, two .eps figures included, revtex, uses eps

Factors Responsible for the Stability and the Existence of a Clean Energy Gap of a Silicon Nanocluster

We present a critical theoretical study of electronic properties of silicon nanoclusters, in particular the roles played by symmetry, relaxation, and hydrogen passivation on the the stability, the gap states and the energy gap of the system using the order-N [O(N)] non-orthogonal tight-binding molecular dynamics and the local analysis of electronic structure.Comment: 26 pages including figure

Generic phase diagram of active polar films

We study theoretically the phase diagram of compressible active polar gels such as the actin network of eukaryotic cells. Using generalized hydrodynamics equations, we perform a linear stability analysis of the uniform states in the case of an infinite bidimensional active gel to obtain the dynamic phase diagram of active polar films. We predict in particular modulated flowing phases, and a macroscopic phase separation at high activity. This qualitatively accounts for experimental observations of various active systems, such as acto-myosin gels, microtubules and kinesins in vitro solutions, or swimming bacterial colonies.Comment: 4 pages, 1 figur

Undulation Instability of Epithelial Tissues

Treating the epithelium as an incompressible fluid adjacent to a viscoelastic stroma, we find a novel hydrodynamic instability that leads to the formation of protrusions of the epithelium into the stroma. This instability is a candidate for epithelial fingering observed in vivo. It occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Our work provides physical insight into a potential mechanism by which interfaces between epithelia and stromas undulate, and potentially by which tissue dysplasia leads to cancerous invasion.Comment: 4 pages, 3 figure

Active Membrane Fluctuations Studied by Micropipet Aspiration

We present a detailed analysis of the micropipet experiments recently reported in J-B. Manneville et al., Phys. Rev. Lett. 82, 4356--4359 (1999), including a derivation of the expected behaviour of the membrane tension as a function of the areal strain in the case of an active membrane, i.e., containing a nonequilibrium noise source. We give a general expression, which takes into account the effect of active centers both directly on the membrane, and on the embedding fluid dynamics, keeping track of the coupling between the density of active centers and the membrane curvature. The data of the micropipet experiments are well reproduced by the new expressions. In particular, we show that a natural choice of the parameters quantifying the strength of the active noise explains both the large amplitude of the observed effects and its remarkable insensitivity to the active-center density in the investigated range. [Submitted to Phys Rev E, 22 March 2001]Comment: 14 pages, 5 encapsulated Postscript figure

Energy Transduction of Isothermal Ratchets: Generic Aspects and Specific Examples Close to and Far from Equilibrium

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.Comment: 16 pages, 10 figure

Observation of the Smectic C -- Smectic I Critical Point

We report the first observation of the smectic C--smectic I (C--I) critical point by Xray diffraction studies on a binary system. This is in confirmity with the theoretical idea of Nelson and Halperin that coupling to the molecular tilt should induce hexatic order even in the C phase and as such both C and I (a tilted hexatic phase) should have the same symmetry. The results provide evidence in support of the recent theory of Defontaines and Prost proposing a new universality class for critical points in layered systems.Comment: 9 pages Latex and 5 postscript figures available from [email protected] on request, Phys.Rev.Lett. (in press