Optimal linear stability condition for scalar differential equations with distributed delay

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillations around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often the only reliable information available about the distribution, it is desirable to find conditions for stability that are independent from the shape of the distribution. We show here that for a given mean delay, the linear equation with distributed delay is asymptotically stable if the associated differential equation with a discrete delay is asymptotically stable. We illustrate this criterion on a compartment model of hematopoietic cell dynamics to obtain sufficient conditions for stability

Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop

A review on local asymptotic stability analysis for mathematical models of hematopoiesis with delay and delay-dependent coefficients

International audienceStability analysis of mathematical models of hematopoiesis (blood cell production process), described by differential equations with delay, needs to locate eigenvalues of characteristic equations that are usually exponential polynomial functions with delay-dependent coefficients. It is then more complicated than for ordinary differential equations to determine conditions for all roots to have negative real parts. We present, on three models of increasing complexity, the tools and method that can be used, with their advantages and their limitations. The method consists in the reduction of the problem to the localization of roots of a real function, these roots giving critical values of the delay for which stability possibly switches

A New Journal in the Field of Pharmaceutical Technology Is Born

Launching a new journal is always an adventure. There are so many tasks, so many people to convince from the publisher to the authors. After many discussions at the GERPAC’s meetings every year in the south of France, we decided that the game was worth the candle. In fact, few journals are dedicated to the field of Pharmaceutical Technology in Hospitals. Very often the scopes of the scientific journals are wider and it is difficult for authors to communicate over much focused technical questions in those papers. This is why Pharmaceutical Technology in Hospital Pharmacy (PTHP) was launched. We are committed to produce a high-quality scientific international journal because our profession really needs it. This journal will be dedicated to all angles of pharmaceutical technologies in hospitals from sterile compounding to electronic devices related to drug production or distribution. Sterilization and radiopharmacy are also considered in this new journal. Detailed aims and scope are provided in this issue along with the instructions to authors. The editorial board of the journal gather hospital pharmacists and scientific researchers all having a strong background in applied research and scientific publishing, holding also a PhD and being for most of them professors of pharmaceutical technology in Universities from European and extra European Universities. [...

Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch

International audienceA nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the trivial steady state. The study of eigenvalues of a second degree exponential polynomial characteristic equation allows to conclude to the existence of stability switches for the unique positive steady state. A numerical analysis of the role of each parameter on the appearance of stability switches completes this analysis

Investigating the role of the experimental protocol in phenylhydrazine-induced anemia on mice recovery

Producción CientíficaProduction of red blood cells involves growth-factor mediated regulation of erythroid progenitor apoptosis and self-renewal. During severe anemia, characterized by a strong fall of the hematocrit followed by a recovery phase, these controls allow a fast recovery of the hematocrit and survival of the organism. Using a mathematical model of stress erythropoiesis and an ad hoc numerical method, we investigate the respective roles of anemia-inducing phenylhydrazine injections and physiological regulation on the organism’s recovery. By explicitly modeling the experimental protocol, we show that it mostly characterizes the fall of the hematocrit following the anemia and its severeness, while physiological process regulation mainly controls the recovery. We confront our model and our conclusions to similar experiments inducing anemia and show the model’s ability to reproduce several protocols of phenylhydrazine-induced anemia. In particular, we establish a link between phenylhydrazine effect and the severeness of the anemia.Ministerio de Economía, Industria y Competitividad (project MTM2014-56022-C2-2-P

Phase transition oscillations induced by a strongly focused laser beam

We report here the observation of a surprising phenomenon consisting in a oscillating phase transition which appears in a binary mixture, PMMA/3-octanone, when this is enlightened by a strongly focused infrared laser beam. PMMA/3-octanone has a UCST (Upper Critical Solution Temperature) which presents a critical point at temperature Tc = 306.6 K and volume fraction $\phi$c = 12.8 % [Crauste et al., ArXiv 1310.6720, 2012]. This oscillatory phenomenon appears because of thermophoretic and electrostriction effects and non-linear diffusion. We analyze these oscillations and we propose a simple model which includes the minimal ingredients to produce the oscillatory behavior. Phase transitions in binary mixtures are still a widely studied subject, specifically near the critical point where several interesting and not completely understood phenomena may appear, among them we recall the critical Casimir forces [2],[3], confinement effects [4], [5] and out-of-equilibrium dynamics after a quench. The perturbation of the binary mixtures by mean of external fields is also an important and recent field of investigation [6]. For example, a laser can induce interesting phenomena in demixing binary mixtures because the radiation pressure can deform the interface between the two phases and it can be used to measure the interface tension [7]. Depending on the nature of the binary mixtures, laser illumination can also lead to a mixing or demixing transition. In ref.[8], focused infrared laser light heats the medium initially in the homogeneous phase and causes a separation in the LCST (Low Critical Solution Temperature) system. The radiation pressure gradients in a laser beam also contribute in the aggregation of polymers , thus producing a phase transition. The local heating may induce thermophoretic forces which attract towards the laser beam one of the binary-mixture components [9]. Other forces like electrostriction can also be involved [10]. In this letter, we report a new phenomenon, which consists in an oscillating phase transition induced by a constant illumination from an infrared laser beam in the heterogeneous region of an UCST (Upper Critical Solution Temperature) binary mixture. Oscillation phenomena in phase transition have already been reported in slow cooling UCST [11],[12] but as far as we know, never induced by a stationary laser illumination. After describing our experimental setup , we will present the results. Then we will use a very simplified model which contains the main necessary physical ingredients to induce this oscillation phenomenon

Study of the heating effect contribution to the nonlinear dielectric response of a supercooled liquid

We present a detailed study of the heating effects in dielectric measurements carried out on a liquid. Such effects come from the dissipation of the electric power in the liquid and give a contribution to the nonlinear third harmonics susceptibility chi_3 which depends on the frequency and temperature. This study is used to evaluate a possible `spurious' contribution to the recently measured nonlinear susceptibility of an archetypical glassforming liquid (Glycerol). Those measurements have been shown to give a direct evaluation of the number of dynamically correlated molecules temperature dependence close to the glass transition temperature T_g~190K (Crauste-Thibierge et al., Phys. Rev. Lett 104,165703(2010)). We show that the heating contribution is totally negligible (i) below 204K at any frequency; (ii) for any temperature at the frequency where the third harmonics response chi_3 is maximum. Besides, this heating contribution does not scale as a function of f/f_{\alpha}, with f_{\alpha}(T) the relaxation frequency of the liquid. In the high frequency range, when f/f_{\alpha} >= 1, we find that the heating contribution is damped because the dipoles cannot follow instantaneously the temperature modulation due to the heating phenomenon. An estimate of the magnitude of this damping is given.Comment: 25 pages, 10 figures, Accepted for publication in Journal of Chemical Physic