Yongwimon Lenbury

Modeling of bone formation and resorption mediated by parathyroid hormone: response to estrogen/PTH therapy

Bone, a major reservoir of body calcium, is under the hormonal control of the parathyroid hormone (PTH). Several aspects of its growth, turnover, and mechanism, occur in the absence of gonadal hormones. Sex steroids such as estrogen, nonetheless, play an important role in bone physiology, and are extremely essential to maintain bone balance in adults. In order to provide a basis for understanding the underlying mechanisms of bone remodeling as it is mediated by PTH, we propose here a mathematical model of the process. The nonlinear system model is then utilized to study the temporal effect of PTH as well as the action of estrogen replacement therapy on bone turnover. Analysis of the model is done on the assumption, supported by reported clinical evidence, that the process is characterized by highly diversified dynamics, which warrants the use of singular perturbation arguments. The model is shown to exhibit limit cycle behavior, which can develop into chaotic dynamics for certain ranges of the systems parametric values. Effects of estrogen and PTH administrations are then investigated by extending on the core model. Analysis of the model seems to indicate that the paradoxical observation that intermittent PTH administration causes net bone deposition while continuous administration causes net bone loss, and certain other reported phenomena may be attributed to the highly diversified dynamics which characterizes this nonlinear remodeling process.

Numerical accuracy of magnetotelluric modeling: A comparison of finite difference approximations

To solve for the induced electromagnetic fields in a conductive medium the quasi-static Maxwell’s equations may be reduced to a second order elliptic system, formulated in terms of either the electric or magnetic vector fields. We show with 1-D and 3-D numerical experiments that solutions obtained from equations formulated in terms of the electric fields are less sensitive to grid resolution than those obtained from the magnetic formulation. On a fine enough mesh, solutions from both approaches are nearly identical, while on coarser meshes solutions form the electric field formulation tend to be closer to exact solutions (where available), or fully converged fine mesh solutions.

Modeling seasonal leptospirosis transmission and its association with rainfall and temperature in Thailand using time-series and ARIMAX analyses

OBJECTIVE To study the number of leptospirosis cases in relations to the seasonal pattern, and its association with climate factors. METHODS Time series analysis was used to study the time variations in the number of leptospirosis cases. The Autoregressive Integrated Moving Average (ARIMA) model was used in data curve fitting and predicting the next leptospirosis cases. RESULTS We found that the amount of rainfall was correlated to leptospirosis cases in both regions of interest, namely the northern and northeastern region of Thailand, while the temperature played a role in the northeastern region only. The use of multivariate ARIMA (ARIMAX) model showed that factoring in rainfall (with an 8 months lag) yields the best model for the northern region while the model, which factors in rainfall (with a 10 months lag) and temperature (with an 8 months lag) was the best for the northeastern region. CONCLUSION The models are able to show the trend in leptospirosis cases and closely fit the recorded data in both regions. The models can also be used to predict the next seasonal peak quite accurately.

Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man

A system of three non-linear differential equations with exponential feedback terms is proposed to model the self-regulating cortisol secretion system and explain the fluctuation patterns observed in clinical data. It is shown that the model exhibits bifurcation and chaos patterns for a certain range of parametric values. This helps us to explain clinical observations and characterize different dynamic behaviors of the self-regulative system.

Nonlinear delay differential equations involving population growth

Conditions are given on the function @?, such that population @g(t) given by#x003C7;(t) = @m@g(t) + @?(@g(t - @t)), becomes extinct or remains globally stable. Our theorems are shown to be applicable to the Nicholsons model of blowflies and the population dynamics of baleen whales. In some of these cases, the function @? is unimodal rather than monotone.

Mathematical modeling and application of genetic algorithm to parameter estimation in signal transduction: Trafficking and promiscuous coupling of G-protein coupled receptors

G-protein-coupled receptors (GPCRs) constitute a large and diverse family of proteins whose primary function is to transduce extracellular stimuli into intracellular signals. These receptors play a critical role in signal transduction, and are among the most important pharmacological drug targets. Upon binding of extracellular ligands, these receptor molecules couple to one or several subtypes of G-protein which reside at the intracellular side of the plasma membrane to trigger intracellular signaling events. The question of how GPCRs select and activate a single or multiple G-protein subtype(s) has been the topic of intense investigations. Evidence is also accumulating; however, that certain GPCRs can be internalized via lipid rafts and caveolae. In many cases, the mechanisms responsible for this still remain to be elucidated. In this work, we extend the mathematical model proposed by Chen et al. [Modelling of signalling via G-protein coupled receptors: pathway-dependent agonist potency and efficacy, Bull. Math. Biol. 65 (5) (2003) 933-958] to take into account internalization, recycling, degradation and synthesis of the receptors. In constructing the model, we assume that the receptors can exist in multiple conformational states allowing for a multiple effecter pathways. As data on kinetic reaction rates in the signalling processes measured in reliable in vivo and in vitro experiments is currently limited to a small number of known values. In this paper, we also apply a genetic algorithm (GA) to estimate the parameter values in our model.

Stochastic cellular automata model and Monte Carlo simulations of CD4+ T cell dynamics with a proposed alternative leukapheresis treatment for HIV/AIDS

Acquired Immunodeficiency Syndrome (AIDS) is responsible for millions of deaths worldwide. To date, many drug treatment regimens have been applied to AIDS patients but none has resulted in a successful cure. This is mainly due to the fact that free HIV particles are frequently in mutation, and infected CD4(+) T cells normally reside in the lymphoid tissue where they cannot (so far) be eradicated. We present a stochastic cellular automaton (CA) model to computationally study what could be an alternative treatment, namely Leukapheresis (LCAP), to remove HIV infected leukocytes in the lymphoid tissue. We base our investigations on Monte Carlo computer simulations. Our major objective is to investigate how the number of infected CD4(+) T cells changes in response to LCAP during the short-time (weeks) and long-time (years) scales of HIV/AIDS progression in an infected individual. To achieve our goal, we analyze the time evolution of the CD4(+) T cell population in the lymphoid tissue (i.e., the lymph node) for HIV dynamics in treatment situations with various starting times and frequencies and under a no treatment condition. Our findings suggest that the effectiveness of the treatment depends mainly on the treatment starting time and the frequency of the LCAP. Other factors (e.g., the removal proportion, the treatment duration, and the state of removed cells) that likely influence disease progression are subjects for further investigation.

Bifurcation analysis of a product inhibition model of a continuous fermentation process

SummaryA product inhibition model of a continuous fermentation process is considered. If the yield term is a variable function of ethanol concentration, oscillation in the cell and ethanol concentrations is shown to be a Hopf bifurcation in the underlying system of nonlinear, ordinary differential equations which comprises the model.

Controllability and stability of the perturbed Chen chaotic dynamical system

In this paper, we study perturbed Chen chaotic dynamical system. Firstly, we study the sufficient conditions of parameters which guarantee that the equilibrium points of perturbed Chen chaotic dynamical system are asymptotically stable. Secondly, we study methods for controlling chaos such as feedback control and bounded feedback control that suppress the chaotic behavior to unstable equilibrium points. Finally, we present chaos synchronization of perturbed Chen chaotic dynamical system by using active control and adaptive control.

Bariatric surgery and T2DM improvement mechanisms: a mathematical model

BackgroundConsensus exists that several bariatric surgery procedures produce a rapid improvement of glucose homeostasis in obese diabetic patients, improvement apparently uncorrelated with the degree of eventual weight loss after surgery. Several hypotheses have been suggested to account for these results: among these, the anti-incretin, the ghrelin and the lower-intestinal dumping hypotheses have been discussed in the literature. Since no clear-cut experimental results are so far available to confirm or disprove any of these hypotheses, in the present work a mathematical model of the glucose-insulin-incretin system has been built, capable of expressing these three postulated mechanisms. The model has been populated with critically evaluated parameter values from the literature, and simulations under the three scenarios have been compared.ResultsThe modeling results seem to indicate that the suppression of ghrelin release is unlikely to determine major changes in short-term glucose control. The possible existence of an anti-incretin hormone would be supported if an experimental increase of GIP concentrations were evident post-surgery. Given that, on the contrary, collected evidence suggests that GIP concentrations decrease post-surgery, the lower-intestinal dumping hypothesis would seem to describe the mechanism most likely to produce the observed normalization of Type 2 Diabetes Mellitus (T2DM) after bariatric surgery.ConclusionsThe proposed model can help discriminate among competing hypotheses in a context where definitive data are not available and mechanisms are still not clear.