一种剪应力作用下ATP调节的血管内皮细胞内钙离子动力学数学模型

考虑剪应力诱导血管内皮细胞钙离子内流主要取决于经由三磷酸腺苷（ATP）门控离子通道P2X4的钙离子内流这一实验事实,提出一个修正的剪应力诱导钙离子内流模型,认为钙离子内流量不仅取决于细胞膜内外钙离子浓度差,而且受细胞表面ATP浓度调节A·D2同时利用文献中公布的实验结果,建立了一个新的静态ATP分泌模型,并将其整合到修正后的钙离子内流模型中,建立了一个描述动脉内皮细胞内非线性钙离子动力学系统．求解整合后动力学系统的控制方程,可获得内皮细胞在剪应力作用下受ATP调节的钙离子响应．结果表明,与文献中其他模型比较,改进后的模型模拟的结果能更真实地反映实验事实．     

Mathematical Mo del for Diab etes Mellitus with Impulsive Injections of Glucose-insulin

Impulsive injections of glucose and insulin analogues are very important strate-gies for the control of diabetes mellitus. We mainly imitate diabetes patients take insulin before eating, and eating approximately as a pulse blood glucose injection, as a result, a new mathematical model with impulsive injections of both glucose and insulin at different fixed times is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we show that the existence and uniqueness of a positive globally asymp-totically stable periodic solution for type Ⅰ diabetes. By impulsive comparison theorem, we obtain the glucose concentration level of the system is uniformly bounded above and below for type Ⅱdiabetes. Numerical analysis verifies our theoretical results.     

A statistical approach to the determination of stability for dynamical systems modelling physiological processes

One of the questions involved in the formulation of a new model for a physiological phenomenon, when the model represents a dynamical system, is that concerning its qualitative behavior. The determination of the stability of a particular dynamical system is usually made analytically, from a linearization of the system around an equilibrium point. This analytic proof may often be very complex or impossible, leading to the imposition of conditions on the relative magnitude of the structural model parameters or to other partial results. We discuss a general technique whereby a probabilistic judgment is made on the stability of a dynamical system, and we apply it to the study of a particular delay differential system modelling the relationship between insulin secretion and glucose uptake. This technique is applicable in case experimental material is available from which to estimate the dispersion of the model parameters. A stability criterion is obtained via the usual linearization around an equilibrium point, it is approximated as a Taylor series in the parameters truncated after the first term, and its variance is then computed from the dispersion of the parameters. While the conclusion is probabilistic in nature, it can be obtained for a wide class of models and from either sample or individual experimental subject's parameter estimates.     

Prediction of a glucose appearance function from foods using deconvolution

The glycaemic response of an insulin-treated diabetic patientgoes through many transitory phases, leading to a steady stateglycaemic profile following a change in either insulin regimenor diet. Most models attempting to model the glucose and insulinrelationship try to model the effect of oral or injected glucoserather than that from the digestion of food. However, it isclear that a better understanding of the glycaemic responsewould arise from consideration of intestinal absorption fromthe gut. It is assumed that this type of absorption can be modelledby a so-called glucose appearance function (systemic appearanceof glucose via glucose absorption from the gut) predicting theglucose load from the food. Much research has been carried outin the areas of hepatic balance, insulin absorption and insulinindependent/dependent utilization. However, little is knownabout intestinal absorption patterns or their correspondingglucose appearance profiles. The strategy under investigation herein is to use deconvolutionor backward engineering. By starting with specific results i.e.blood glucose and insulin therapy, it is possible to work backwardsto predict the glucose forcing functions responsible for theoutcome. Assuming compartmental consistency, this will allowa clearer insight into the true gut absorption process, If successful,the same strategy can be applied to more recent glucose andinsulin models to further our understanding of the food to bloodglucose problem. This paper investigates the Lehmann-Deutsch modified model ofglucose and insulin interaction, created from the model proposedby Berger-Rodbard. The model attempts to simulate the steadystate glycaemic and plasma insulin responses, independent ofthe initial values from which the simulation is started. Glucoseenters the model via both intestinal absorption and hepaticglucose production. We considered a 70kg male insulindependentdiabetic patient with corresponding hepatic and insulin sensitivityparameters of 0.6 and 0.3 respectively. Net hepatic glucosebalance was modelled piecewise by linear and symmetric functions.A first-order Euler method with step size of 15 minutes wasemployed. For the simulation, only Actrapid and NPH injectionswere considered. The injection of insulin and the glucose fluxto the gut were started simultaneously to avoid any delay associatedwith gastric emptying. The systemic appearance of glucose was compared from two viewpoints, not only to assess the strategic principle, but alsoto assess the suitability of the modifications made by Lehmannand Deutsch. The first is a forward prediction using the compartmentalstructure. This analysis involves the rate of gastric emptyingwithout time delay. The second is a backward prediction fromexperimentally observed blood glucose profiles. Investigationsinvolved porridge, white rice and banana containing the samecarbohydrate content (25 g). Results obtained from the firstanalysis were dependent on the rate of gastric emptying, especiallyits ascending and descending branches. Results from the secondanalysis were dependent on the dose and type of insulin administered.Both predicted profiles showed consistency with physiologicalreasoning, although it became apparent that such solutions couldbe unstable. Furthermore, both types of prediction were similarin structure and appearance, especially in simulations for porridgeand banana. This emphasized the consistency and suitabilityof both analyses when investigating the compartmental accuracyand limitations within a model. The new strategic approach was deemed a success within the model,and the modifications made by Lehmann and Deutsch appropriate.We suggest that a gastric emptying curve with a possible gastricdelay is the way forward in regulating the appearance of glucosevia gut absorption. The Lehmann-Deutsch gastric curve is describedby either a trapezoidal or triangular function dependent onthe carbohydrate content of the meal. However, it was clearfrom the results obtained that carbohydrate content is onlyone factor in carbohydrate absorption, and further progressmust inevitably involve other food characteristics and propertiesif we are to improve the glucose flux.     

Contribution of calcium fluxes to astrocyte spontaneous calcium oscillations in deterministic and stochastic models

Spontaneous Ca²⁺ oscillation is a special kind of astrocyte signal that is crucial in several brain functions. However, the underlying mechanism of its initiation is still unclear. Experimental investigations reveal quite different results of the contribution of Ca²⁺ influxes from the extracellular space. We developed a new biophysical model, which includes two kinds of extracellular Ca²⁺ influx: through voltage gated Ca²⁺ channels and through capacitative Ca²⁺ entry. Besides, two stochastic models are constructed to discuss the influence of channel noise in voltage gated influx and stochastic IP₃ receptor dynamics on the contribution of Ca²⁺ fluxes. Simulation results reveal that the contribution of a given flux can be considerably strengthened or weakened by special cellular states, such as the change of membrane potential, inter-flux feedback; the special cellular condition (e.g. endoplasmic reticulum depletion, other flux inhibition). In stochastic environment, the contribution of fluxes may be strongly altered and the respond of different fluxes varies qualitatively. Our results may help to understand the different results obtained in experiments.     

Optimizing inputs for diagnosis of diabetes. I. Fitting a minimal model to data

A glucose tolerance test was performed on dogs by injecting glucose intravenously and measuring the plasma glucose and insulin concentrations versus time. Various analytical and computational techniques were utilized to fit the data to a minimal model and to estimate the parameters of the blood glucose regulation process. A relatively good fit was obtained in spite of the rather simple model.Animal experiments were funded by the National Institute of Health Grant No. AM-17236 awarded to Dr. R. N. Bergman at U.S.C.     

A mathematical fractional model with nonsingular kernel for thrombin receptor activation in calcium signalling

In calcium signalling, activation of receptor is a very significant aspect. To understand the mechanism of calcium signalling, receptors are the important components. The mobilization of intracellular calcium from intracellular stores depends upon binding of agonist to cell surface receptor. Thrombin is chosen as model ligand. In order to understand thrombin receptor activation, we analyze fractional model incorporating derivative of arbitrary order and nonsingular kernel which can precisely describe the effect of memory and can explain the model in better and more efficient manner as compared with fractional operators with singular kernels. The problem has been solved by perturbation iterative method. Using fixed‐point theorem, it is proved that solution of the system will exist and also it will be unique.     

Modelling and decision support in physiology and medicine: a methodological framework with lllustration

This paper presents a methodological framework for modelling that has found wide application in the complex domains of physiology and medicine. The processes of model validation are centrally embedded within this framework. The parallelism between modelling per se and the development of model-based decision support systems is then considered, showing that it is possible to devise a unified methodological framework which encompasses the requirements both of model validation and decision support system evaluation. The applicability of the framework is demonstrated in the validation of a mathematical model of blood glucose dynamics; and in the development and evaluation of decision support systems such as those which are aimed at addressing the problem of advising the insulin-dependent diabetic patient on the adjustment of insulin dosage     

Enhanced ionization of multi-well quantum systems in intense laser fields

The ionization dynamics of multi-well quantum systems in intense laser fields (~ 10¹⁴W/cm) has been numerically investigated through solving the time-dependent Schrodinger equation. The enhanced ionization effect at a critical inter-well distance is found as a general feature of multi-well quantum systems subjected to intense laser fields. It is well rationalized in terms of.the field-induced over-the-barriers ionization mechanism. With the number of wells increasing the whole ionization peak slightly shifts to small inter-well distance, but the enhanced ionization tendency still keeps. The ionization potential of multi-well systems is not the sole important factor of intense field-ionization of system.     

A new continuous model for multiple re-entrant manufacturing systems

The semiconductor manufacturing systems that involve a large number of products and many steps can be modeled through conservation laws for a continuous density variable on production processes. In this paper, the basic partial differential equation (PDE) models for single-product re-entrant manufacturing systems are proposed first. However, through the validation of numerical examples, the basic continuous models do not perform well for single-product re-entrant systems. Then, a new state equation that takes into account the re-entrant degree of a product is introduced to improve the basic continuous models. The applicability of the modified continuous model is illustrated through numerical examples. The influence of the influx variation on the outflux is also discussed. With the changes of influx, the outflux has a reverse phenomenon. Based on the new state equation, the continuous model for multi-product re-entrant systems with different priorities is established, and an example is provided to illustrate the applicability of the new continuous model.     

Chaotic attractor generation and critical value analysis via switching approach

The generation of novel chaotic funnel-shaped attractors is introduced and the analysis of related critical values is given with a proposed switching method in this paper. The underlying mechanism involves a simple three-dimensional switched system and a hysteretically switching signal. Moreover, theoretic analysis is carried out to study the attractor generation and the corresponding critical values by fully utilizing the specific structure of the non-smooth system. Based on carefully derivation, the critical values and related stability regions of the created attractors are estimated explicitly, which is usually impossible for general non-smooth dynamics. In addition, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable system parameters.     

Dynamical Probing of the Mechanisms Underlying Calcium Oscillations

Oscillations in the concentration of free intracellular calcium ([Ca²⁺]) play an important role in many cell types. Thus, understanding the mechanisms underlying Ca²⁺ oscillations is of significant scientific import. There are two basic classes of mechanism that cause these oscillations: (1) positive and negative feedback from calcium to the inositol trisphosphate (IP₃) receptor, and (2) positive and negative feedback from calcium to IP₃ metabolism. These two classes can be distinguished experimentally by their different responses to pulses of IP₃. In general most cells will have both types of mechanism present simultaneously. We show that, when Ca²⁺ oscillations are driven by these two mechanisms at the same time, one mechanism is dominant. As the strength of each mechanism is varied, the response of the cell exhibits a threshold phenomenon, being governed either by one mechanism or the other, with no ambiguity in the response to a pulse of IP₃. We interpret these results, and other responses to IP₃ pulses, in terms of a fast-slow time scale analysis of the calcium dynamics, where calcium transport across the cell membrane occurs on a slow time scale.     

Reorganization of the configuration manifold and critical systems

When the dynamics of holonomic mechanical systems are described in redundant coordinates with parameter-dependent constraints, some special features arise. At certain (critical) values of the parameters, the configuration manifold of the system may have, for example, self-intersections; in the neighbourhood of such a singular submanifold one cannot introduce Lagrangian coordinates of the system and it becomes difficult (even impossible) to define the orbits of the “critical” system correctly by taking limits with respect to the parameter. In such cases the classical Poincaré theory of bifurcation of equilibria in conservative systems also needs some adjustment. As an example, a crank-gear mechanism is considered.     

Wave–Mean-Flow Interactions in a Forced Rossby Wave Packet Critical Layer

This paper describes the nonlinear critical layer evolution of a zonally localized Rossby wave packet forced in mid-latitudes and propagating horizontally on a beta plane in a zonal shear flow. The wave packet has an amplitude that varies slowly in the zonal direction. Numerical solutions of the governing nonlinear equations show that the wave–mean-flow interactions differ from those that would result with a monochromatic forcing. With the localized forcing, the net absorption of the disturbance at the critical layer continues for large time, because there is an outward flux of momentum in the zonal direction. Further insight into the mechanism for this and other aspects of the evolution of the critical layer is obtained through an approximate asymptotic analysis which is valid for large time.     

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system was studied by using a mesoscopic stochastic model. When the stimulus was too weak to fire calcium spikes for the cell, separately, we found that calcium spikes could be induced by the external noise or internal noise, and internal signal stochastic resonance (ISSR) or internal noise stochastic resonance (INSR) occurred, respectively, so that the cell system could detect the weak stimulus through intracellular calcium spikes with the help of external noise or internal noise. When considering both of the noises, we found that internal noise could suppress ISSR, while external noise could enhance INSR in a certain range of external noise intensity. Interestingly, when the INSR occurs, the optimal size matched well with the real cell size, this was of significant biological meaning.     

Combining data augmentation,EDAs and grammatical evolution for blood glucose forecasting

The ideal solution for diabetes mellitus type 1 patients is the generalization of artificial pancreas systems. Artificial pancreas will control blood glucose levels of diabetics, improving their quality of live. At the core of the system, an algorithm will forecast future glucose levels as a function of food ingestion and insulin bolus sizes. In previous works several evolutionary computation techniques has been proposed as modeling or identification techniques in this area. One of the main obstacles that researchers have found for training the models is the lack of significant amounts of data. As in many other fields in medicine, the collection of data from real patients is not an easy task, since it is necessary to control the environmental and patient conditions. In this paper, we propose three evolutionary algorithms that generate synthetic glucose time series using real data from a patient. This way, the models can be trained with an augmented data set. The synthetic time series are used to train grammatical evolution models that work together in an ensemble. Experimental results show that, in a scarce data context, grammatical evolution models can get more accurate and robust predictions using data augmentation. In particular we reduce the number of potentially dangerous predictions to 0 for a 30 min horizon, 2.5% for 60 min, 3.6% on 90 min and 5.5% for 2 h. The Ensemble approach presented in this paper showed excellent performance when compared to not only a classical approach such as ARIMA, but also with other grammatical evolution approaches. We tested our techniques with data from real patients.     

一类反应扩散方程的孤立周期波和局部临界周期分支

研究了一类含有五次非线性反应项和常数扩散项的反应扩散方程的小振幅孤立周期波解,以及它的行波方程局部临界周期分支问题.运用行波变换将反应扩散方程转换为对应的行波系统,应用奇点量方法和计算机代数软件MATHEMATICA计算出该系统的前8个奇点量,得到该系统奇点的两个中心条件,并证明行波系统原点处可分支出8个极限环,对应的...     

Hopf bifurcations in a predator–prey system with a discrete delay and a distributed delay

A delayed Lotka–Volterra two-species predator–prey system with discrete hunting delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. It is found that under suitable conditions on the parameters the positive equilibrium is asymptotically stable when the hunting delay is less than a certain critical value and unstable when the hunting delay is greater than this critical value. Meanwhile, according to the Hopf bifurcation theorem for functional differential equations (FDEs), we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the hunting delay crosses through a sequence of critical values. In particular, by applying the normal form theory and the center manifold reduction for FDEs, an explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions occurring through Hopf bifurcations is given. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.     

Bifurcation problems in nonlinear parametric programming

The nonlinear parametric programming problem is reformulated as a closed system of nonlinear equations so that numerical continuation and bifurcation techniques can be used to investigate the dependence of the optimal solution on the system parameters. This system, which is motivated by the Fritz John first-order necessary conditions, contains all Fritz John and all Karush-Kuhn-Tucker points as well as local minima and maxima, saddle points, feasible and nonfeasible critical points. Necessary and sufficient conditions for a singularity to occur in this system are characterized in terms of the loss of a complementarity condition, the linear dependence of the gradients of the active constraints, and the singularity of the Hessian of the Lagrangian on a tangent space. Any singularity can be placed in one of seven distinct classes depending upon which subset of these three conditions hold true at a solution. For problems with one parameter, we analyze simple and multiple bifurcation of critical points from a singularity arising from the loss of the complementarity condition, and then develop a set of conditions which guarantees the unique persistence of a minimum through this singularity. The research of this author was supported by National Science Foundation through NSF Grant DMS-85-10201 and by the Air Force Office of Scientific Research through instrument number AFOSR-ISSA-85-00079.     

Influences of Attack Angles on Aerodynamic Derivatives and Flutter Characteristics of Flat Box Girders北大核心CSCD

以南京第四长江大桥扁平箱梁为研究对象,通过节段模型自由振动风洞试验详细测试了模型在不同风攻角下的颤振响应,探讨了系统非稳态及稳态临界振幅随风速的演化规律.首先,基于颤振响应振幅包络,结合Hilbert变换,识别了系统振幅依存的模态阻尼,并初步阐释了颤振形态随风攻角转变的机理.其次,提取了系统在不同风攻角下的模态参数,基于双模态耦合闭合解法,识别了断面在不同风攻角下的非线性颤振导数,研究了关键颤振导数振幅依存性随风攻角变化的规律及对断面颤振形态和特性的潜在影响.最后,通过逐项拆解模态阻尼,深入剖析了风攻角对非耦合及耦合气动阻尼的影响,并阐明了分项阻尼导致系统颤振性能差异性的动力学机理.