Peristaltic transport of a particulate suspension in the small intestine

Food transport through different sections of the gastrointestinal tract for the purposes of digestion and waste removal is an essential physiological function for life. Mechanical and chemical breakdown of food takes place throughout the gastrointestinal tract. Periodic muscular contraction and relaxation of the intestinal walls agitate, mix and propel the multiphase digesta along the intestines. Experimental measurement of flow inside the intestines is difficult therefore understanding of food transport through the majority of the gut is limited. Computational models for predicting the transient behaviour of intestinal content subject to peristaltic activity offer the possibility for assessing the digestive performance of different foods. We present a numerical model for peristalsis in the duodenum using a suspension of rigid particulates in a viscous Newtonian fluid to represent simple digesta. This consists of a thin viscoelastic membrane representing the gut wall coupled to the particle-based methods Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) which are used to predict the motion of liquid and solids content respectively. Peristaltic waves travel along the gut wall resulting in active muscular contractions and relaxations of the gut. The bulk motion of the content shows both phases move together due to the laminar nature of the flow with only very short-term inter-phase differences found in the relaxation region and in the wake of the contraction. Propulsive events were found to cause significant non-homogeneity of the solids distribution along the length of the duodenum. The inclusion of solids mildly modifies the overall propulsive flow behaviour and the retrograde jet in the wake of the contraction. In the absence of solids and connective tissue constraints, a transverse wobbling instability in the fluid filled viscoelastic tube is observed.     

Nonnegative compartment dynamical system modelling with stochastic differential equations

Compartment models are widely used in various physical sciences and adequately describe many biological phenomena. Elements such as blood, gut, liver and lean tissue are characterized as homogeneous compartments, within which the drug resides for a time, later to transit to another compartment, perhaps recycling or eventually vanishing. We address the issue of compartment dynamical system modelling using multidimensional stochastic differential equations, rather than the classical approach based on the continuous-time Markov chain. Pure-jump processes are employed as perturbation to the deterministic compartmental dynamical system. Unlike with the Brownian motion, noise can be incorporated into both outflows and inter-compartmental flows without violating nonnegativity of the compartmental system, under mild technical conditions. The proposed formulation is easy to simulate, shares various essential properties with the corresponding deterministic ordinary differential equation, such as asymptotic behaviors in mean, steady states and average residence times, and can be made as close to the corresponding diffusion approximation as desired. Asymptotic mean-square stability of the steady state is proved to hold under some assumptions on the model structure. Numerical results are provided to illustrate the effectiveness of our formulation.     

基于EV模型ND样本加权和的相合性

本文研究变系数EV模型的ND样本加权和的相合性问题.利用ND序列的Bernstein型不等式和截尾的方法,获得了ND样本加权和sum from i=1 to n(W_(ni)(t_0)Y_i)的强、弱相合性,推广了独立随机变量加权和的相合性.     

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.     

血液中酒精浓度的数学模型

把人体对酒精的吸收、排放简化为一般的房室模型,提出了吸收因子、消除因子的概念.针对短时间饮酒、长时间饮酒以及间断饮酒等情况,分别建立了关于人体体液中酒精浓度的微分方程模型,并且给出了显式解.对于特殊的周期性间断饮酒的模型,给出了更便于计算的叠加公式,并通过分析酒精浓度函数的极限过程,证明了其有界性.对短时间饮酒和长时间饮酒的情况分别计算了酒精浓度的最大值、取得最大值的时间和禁止驾车的时间范围,而且进行了比较,所得结论与实际吻合.     

Modelling and simulation of the nonlinear dose-plasma concentration response of phenylbutazone on periodic multiple oral dosing: A mechanistic approach

The dose-ranging pharmacokinetics of phenylbutazone on periodic multiple oral dosing have previously been shown to be nonlinear, inasmuch as there is a plateauing of steady-state plasma concentrations with increasing dose. The mechanistic hypothesis of saturable protein binding, postulated to explain this behaviour was tested, in the context of whole-body pharmacokinetic modelling of the observed dose dependancy, using the circuit simulation program SPICE2. The alternate hypothesis, operating singly or in tandem, of loss of unabsorbed drug due to gastrointestinal emptying, saturable absorption, change in the volume of distribution of the drug, were also examined. Within the constraints of the proposed whole-body pharmacokinetic model, the absorption kinetics of increasing oral daily doses of phenylbutazone were shown to be saturable in their mechanism.     

BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES

This paper introduces a method of bootstrap wavelet estimation in a nonparametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.     

M-estimation in nonparametric regression under strong dependence and infinite variance

A robust local linear regression smoothing estimator for a nonparametric regression model with heavy-tailed dependent errors is considered in this paper. Under certain regularity conditions, the weak consistency and asymptotic distribution of the proposed estimators are obtained. If the errors are short-range dependent, then the limiting distribution of the estimator is normal. If the data are long-range dependent, then the limiting distribution of the estimator is a stable distribution.     

Analysis and Validation of a Mathematical Model for Intracranial Pressure Dynamics

Lumped parameter, compartmental models provide a promising Method for mathematically studying the dynamics of human intracranial pressure. In this modeling approach, a system of fully time-dependent differential equations for interacting compartmental pressures is obtained by considering the intracranial system to be confined within the almost-rigid skull and developing continuity equations associated with conservation of mass. Intracranial volumes and flows are related to compartmental pressure differences through compliance and resistance parameters. In the nonlinear case where compliances are not constant, there is a lack of physical information about these parameters. Consequently, it is vital that any mathematical model with an assumed pressure-dependent compliance be validated through comparison with experimental data. The present work develops a logistic representation for the compliance between the cerebrospinal fluid and brain matter compartments. The nonlinear mathematical model involving this logistic compliance is validated here by comparing its predicted response for bolus injections of cerebrospinal fluid to laboratory data generated in an animal model. Comparison with the animal studies fully supports the validity of the mathematical model with the logistic compliance.     

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.     

Delay in ATP-dependent calcium inflow may affect insulin secretion from pancreatic beta-cell

Any dysfunction in the secretion of insulin and/or in its use is critical in the development of type 2 diabetes. Calcium plays a very important role in the insulin secretion mechanism from beta-cell. In this paper, we studied the dynamic interaction of glucose-induced insulin secretion mechanism through glucose metabolism and ATP-dependent calcium influx. We proposed and analyzed a four dimensional system of nonlinear delay differential equations to give insights into different possible mechanisms for maintaining plasma glucose homeostasis through calcium-induced insulin secretion. The time duration between ATP formation and subsequent calcium influx through cell membrane has been found to be critical in maintaining insulin homeostasis. How variational effects of system parameters lead to various glycemic states are demonstrated. Possibility of new potential drug therapies is also discussed through parameter recalibration.     

Stabilization analysis for economic compartmental switched systems based on quadratic Lyapunov function

The compartmental model is one of the important applications in economic and social dynamic systems which are made of numbers of units-subsystems. Stabilization of economic compartmental switched systems with compartmental subsystems is studied in this paper. A quadratic Lyapunov function is introduced to construct switching law in order to stabilize these kinds of mathematical economic and social models. Necessary and sufficient conditions of stabilization are presented for both asynchronous and synchronous switching. Precisely, after a proper change in state space, stabilization conditions can be expressed in terms of matrix inequalities. At the same time, definitions, theorems and corollaries as well as a detailed simulation result of one example are presented to show the effectiveness of the main result obtained.     

Migratory effect of middle predator in a tri‐trophic food chain model

A tri‐trophic food chain model in a two‐patch environment is considered. Although tri‐trophic food chain model is well studied, the study considering migration of middle predator is lacking. To the best of our knowledge, the present investigation is the first study in this direction. Both prey and predator density‐dependent migrations are considered to observe the effects on stability and persistence of the system. We observe that migration of middle predator has the ability to control chaos in tri‐trophic food chain model. Our results indicate that the chance of predator extinction enhances for prey density‐dependent middle predator migration. Copyright © 2010 John Wiley & Sons, Ltd.     

Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction

Cardinal and ordinal inconsistencies are important and popular research topics in the study of decision making with pair-wise comparison matrices (PCMs). Few of the currently-employed tactics are capable of simultaneously dealing with both cardinal and ordinal inconsistency issues in one model, and most are heavily dependent on the method chosen for weight (priorities) derivation or the obtained closest matrix by optimization method that may change many of the original values. In this paper, we propose a Hadamard product induced bias matrix model, which only requires the use of the data in the original matrix to identify and adjust the cardinally inconsistent element(s) in a PCM. Through graph theory and numerical examples, we show that the adapted Hadamard model is effective in identifying and eliminating the ordinal inconsistencies. Also, for the most inconsistent element identified in the matrix, we develop innovative methods to improve the consistency of a PCM. The proposed model is only dependent on the original matrix, is independent of the methods chosen to derive the priority vectors, and preserves most of the original information in matrix A since only the most inconsistent element(s) need(s) to be modified. Our method is much easier to implement than any of the existing models, and the values it recommends for replacement outperform those derived from the literature. It significantly enhances matrix consistency and improves the reliability of PCM decision making.     

基于随机参照点的均值-风险分析

本文依据参照依赖偏好模型提出了基于随机参照点的风险度量方法,进而构建了均值-风险模型,并讨论了该决策方法与随机占优之间的一致性。研究发现,该决策方法不仅与一级随机占优是一致的而且与二级随机占优也是一致的。由于二级随机占优与期望效用理论的一致性,因而所构建的均值-风险模型与期望效用理论也是一致的。     

Two compartmental fractional derivative model with fractional derivatives of different order

This study presents a new two compartmental model that contains fractional derivatives of different order. The model is so formulated that the mass balance is preserved. In this way we give an answer on a claim that such a model is not possible. The generalization that includes nonlinear terms and fractional order dynamics between compartments is also discussed. We derived a physically correct two compartmental system (i.e., the one preserving the mass balance) by the use of the Taylor expansion formula. Moreover, we derived in the Appendix such a system preserving the mass balance without the use of the Taylor formula but by the use of mass balance for systems with equal order fractional derivatives.     

基于NOD误差的非参数回归模型估计的渐近性质（英文）

In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.     

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.     

附加信息下的局部线性估计

在回归模型中，对一类因变量函数的条件期望方程的附加信息，我们提出了基于极大经验似然方法的局部线性点估计，在一定条件下证明了这些估计的相合性和渐近正态性，而且估计的方差小于通常不带附加信息核估计的方差．模拟结果也显示了估计的优良性．