A mathematical model of aging-related and cortisol induced hippocampal dysfunction

<p>Abstract</p> <p>Background</p> <p>The hippocampus is essential for declarative memory synthesis and is a core pathological substrate for Alzheimer's disease (AD), the most common aging-related dementing disease. Acute increases in plasma cortisol are associated with transient hippocampal inhibition and retrograde amnesia, while chronic cortisol elevation is associated with hippocampal atrophy. Thus, cortisol levels could be monitored and managed in older people, to decrease their risk of AD type hippocampal dysfunction. We generated an in silico<it/>model of the chronic effects of elevated plasma cortisol on hippocampal activity and atrophy, using the systems biology mark-up language (SBML). We further challenged the model with biologically based interventions to ascertain if cortisol associated hippocampal dysfunction could be abrogated.</p> <p>Results</p> <p>The in silico<it/>SBML model reflected the in vivo<it/>aging of the hippocampus and increased plasma cortisol and negative feedback to the hypothalamic pituitary axis. Aging induced a 12% decrease in hippocampus activity (HA), increased to 30% by acute and 40% by chronic elevations in cortisol. The biological intervention attenuated the cortisol associated decrease in HA by 2% in the acute cortisol simulation and by 8% in the chronic simulation.</p> <p>Conclusion</p> <p>Both acute and chronic elevations in cortisol secretion increased aging-associated hippocampal atrophy and a loss of HA in the model. We suggest that this first SMBL model, in tandem with in vitro<it/>and in vivo<it/>studies, may provide a backbone to further frame computational cortisol and brain aging models, which may help predict aging-related brain changes in vulnerable older people.</p

A note on asymptotic stability conditions for delay difference equations

We obtain necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation xn+1+p∑j=1Nxn−k+(j−1)l=0, where n=0,1,2,…, is a real number, and k, l, and N are positive integers such that k>(N−1)l

An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control

Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data.
We analyze a non-linear model of the human immunodeficiency virus (HIV) infection that considers the interaction between a replicating virus, CD4+ T-cell and the cytotoxic-lymphocytes (CTL).We then investigate the intracellular delay effect on the stability of the endemically infected steady state. Criteria are given to ensure that the infected steady state is asymptotically stable for all delays. Model analysis also allows the prediction of a critical delay $\tau_c$ below which the effector CTL can play a significant role in the immune control mechanism even when the basic reproduction number is high

A nonlinear mathematical model for pulsatile discharges of luteinizing hormone mediated by hypothalamic and extra-hypothalamic pathways.

A mathematical model of hormone secretion in the hypothalamo-pituitary-gonadal axis in man is extended to incorporate two different neural pathways, which have been suggested by clinical data to be capable of stimulating pulsatile discharges of LH (luteinizing hormone) independently of each other. Analysis of the nonlinear model is carried out through the use of geometric singular perturbation methods. In this way, existence of a limit cycle is proved for certain ranges of the system parameters. When the LH secretion rate independent of the hypothalamus is assumed constant, dropping the hypothalamus stimulated secretion term from the model blocks the hypothalamus pathway, implying that sustained oscillations in the hormone levels may not be attainable. Therefore, a sinusoidal term is incorporated into the model so that the system can still exhibit pulsatile LH secretion independent of the hypothalamus mediation. It is shown, by a construction of a bifurcation diagram, that the pulsatile hormone secretion can develop into chaotic dynamics when the amplitude of oscillation stimulated by extra-hypothalamic structures is high enough to disturb the synchrony of hypothalamic control. The resulting numerical simulation is found to compare well with the clinically observed data. </jats:p

Option pricing under stochastic environment of volatility and market price of risk

Since Black-Scholes model was proposed in 1973, it has been applied widely for option pricing. The aim of this paper is to develop European option pricing model taking into account stochastic volatility and stochastic market price of risk (MPR) under the framework of Black-Scholes. Both volatility and market price of risk are assumed to be stochastic and assumed to follow Ornstein-Uhlenbeck process. By using an analytical approach of Abraham Loui, explicit formulas are derived for European call and put option prices. Sensitivity of option price to model parameters are tested and the simulation results show the strong characteristic of stochastic model

A numerical study of non-Newtonian blood flow in stenosed coronary artery bypass with grafts

We investigate the behaviour of the pulsatile blood flow in a stenosed right coronary artery with a bypass graft. The human blood is assumed as a non-Newtonian fluid and its viscous behaviour is described by the Carreau model. The transient phenomena of blood flow through the stenosed region and the bypass graft are simulated for five cardiac cycles by solving the three dimensional unsteady Navier--Stokes equations coupled with the non-Newtonian model. Effects of the time variations of pulsatile velocity and pulse pressure are taken into account. The influence of the bypass angle on the flow interaction between the jet flow from the native artery and the flow from the bypass graft is investigated. Distributions of velocity, pressure and wall shear stresses are determined under various conditions. The results show that the blood pressure in the stenosed artery drops dramatically in the stenosis area and that high wall shear stresses occur around the stenosis site