Multiscale modeling of insulin secretion

Insulin secretion from pancreatic beta cells is a fundamental physiological process, and its impairment plays a pivotal role in the development of diabetes. Mathematical modeling of insulin secretion has a long history, both on the level of the entire body and on the cellular and subcellular scale. However, little direct communication between these disparate scales has been included in mathematical models so far. Recently, we have proposed a minimal model for the incretin effect by which the gut hormone glucagon-like peptide 1 (GLP-1) enhances insulin secretion. To understand how this model couples to cellular events, we use a previously published mechanistic model of insulin secretion, and show mathematically that induction of glucose competence in beta cells by GLP-1 can underlie derivative control by GLP-1.     

Multiscale modeling with carbon nanotubes

Technologically important nanomaterials come in all shapes and sizes. They can range from small molecules to complex composites and mixtures. Depending upon the spatial dimensions of the system and properties under investigation computer modeling of such materials can range from equilibrium and non-equilibrium quantum mechanics, to force-field-based molecular mechanics and kinetic Monte Carlo, mesoscale simulation of evolving morphology, and finite-element computation of physical properties. This brief review illustrates some of the above modeling techniques through a number of recent applications with carbon nanotubes: nano electromechanical sensors (NEMS), chemical sensors, metal-nanotube contacts, and polymer-nanotube composites.     

基于小波变换的多尺度建模和估计理论概述

在许多应用领域中,通常要对出现在不同尺度的现象进行分析和辨识,最近引入的多尺度框架使这一分析成为可能.本文简单介绍了多尺度建模和估计理论的发展概况,分析了多尺度模型、平滑误差模型以及两类多尺度实现模型,并指出了目前急需解决的问题.     

Multiscale modeling and estimation of Poisson processes withapplication to photon-limited imaging

Many important problems in engineering and science are well-modeled by Poisson processes. In many applications it is of great interest to accurately estimate the intensities underlying observed Poisson data. In particular, this work is motivated by photon-limited imaging problems. This paper studies a new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform. It is shown that the Haar transform provides a very natural and powerful framework for this problem. Using this framework, a novel multiscale Bayesian prior to model intensity functions is devised. The new prior leads to a simple Bayesian intensity estimation procedure. Furthermore, we characterize the correlation behavior of the new prior and show that it has 1/f spectral characteristics. The new framework is applied to photon-limited image estimation, and its potential to improve nuclear medicine imaging is examined     

数学分析及数学软件在数学建模当中的应用探究

本文分别阐述当前的数学软件类型及其各自存在的特点,从而对当前主流的数学软件在数学建模当中的应用进行梳理。同时以LINGO软件在数学建模中的典型应用进行举例,以此给数学软件在数学建模当中的应用提供应用的实例参考。     

Multiscale FEM modeling of vascular tone: from membrane currents to vessel mechanics

Regulation of vascular tone is a complex process that remains poorly understood. Here, we present our recent efforts for the development of physiologically realistic models of arterial segments for the analysis of vasoreactivity in health and disease. Multiscale modeling integrates intracellular and cell membrane components into whole-cell models of calcium and membrane potential dynamics. Single-cell models of vascular cells are combined into a multicellular model of the vascular wall, and vessel wall biomechanics are integrated with calcium dynamics in the smooth muscle layer. At each scale, continuum models using finite element method can account for spatial heterogeneity in calcium signaling and for nonuniform deformations of a vessel segment. The outlined approach can be used to investigate cellular mechanisms underlying altered vasoreactivity in hypertension.     

关于数学建模与数学实验课程设置方式的思考探究

本文主要探讨了数学建模和数学实验课程的设置方式,将传统的二者单独衔接授课改进成围绕主题目标的综合式教学方式,将数学建模和数学实验的教学放在同一次课程中结合实现,从而达到提高学生数学综合应用能力的目标.     

Multiscale modeling and estimation of motion fields for videocoding

We present a systematic approach to forward-motion-compensated predictive video coding. The first step is the definition of a flexible model that compactly represents motion fields. The inhomogeneity and spatial coherence properties of motion fields are captured using linear multiscale models. One possible design is based on linear finite elements and yields a multiscale extension of the triangle motion compensation (TMC) method. The second step is the choice of a computational technique that identifies the coefficients of the linear model. We study a modified optical flow technique and minimize a cost function closely related to Horn and Schunck's (1981) criterion. The cost function balances accuracy and complexity of the motion compensated predictor and is viewed as a measure of goodness of the motion field. It determines not only the coefficients of the model, but also the quantization method. We formulate the estimation and quantization problems jointly as a discrete optimization problem and solve it using a fast multiscale relaxation algorithm. A hierarchical extension of the algorithm allows proper handling of large displacements. Simulations on a variety of video sequences have produced improvements over TMC and over the half-pel-accuracy, full-search block matching algorithm, in excess of 0.5 dB in average. The results are visually superior as well. In particular, the reconstructed video is entirely free of blocking artifacts.     

Multiscale modeling for image analysis of brain tumor studies

Image-based modeling of tumor growth combines methods from cancer simulation and medical imaging. In this context, we present a novel approach to adapt a healthy brain atlas to MR images of tumor patients. In order to establish correspondence between a healthy atlas and a pathologic patient image, tumor growth modeling in combination with registration algorithms is employed. In a first step, the tumor is grown in the atlas based on a new multiscale, multiphysics model including growth simulation from the cellular level up to the biomechanical level, accounting for cell proliferation and tissue deformations. Large-scale deformations are handled with an Eulerian approach for finite element computations, which can operate directly on the image voxel mesh. Subsequently, dense correspondence between the modified atlas and patient image is established using nonrigid registration. The method offers opportunities in atlas-based segmentation of tumor-bearing brain images as well as for improved patient-specific simulation and prognosis of tumor progression.     

Automated mathematical modeling from experimental data: anapplication to material science

Automated model formulation is a crucial issue in the construction of computational environments that can reason about the behavior of a physical system. The procedure of mathematically modeling a physical system is complex and involves three fundamental entities: the experimental data, a set of candidate models, and rules for determining in such a set the “best” model that reproduces the measured data. The construction of the candidate models is domain dependent and based on specific knowledge and techniques of the application domain. The choice of the best model is guided by the data themselves; a first rough guess is refined through system identification techniques so that the quantitative properties of the observed behavior are assessed. Automating such a procedure requires handling and integrating different formalisms and methods, both qualitative and quantitative. The paper describes a comprehensive environment that aims at the automated formulation of an accurate quantitative model of the mechanical behavior of an actual viscoelastic material in accordance with the observed response of the material to standard experiments. Algorithms and methods for both the generation of an exhaustive library of models of ideal materials and the selection of the most “accurate” model of a real material have been designed and implemented. The model selection phase occurs in two main stages: first the subset of most plausible candidate models for the material is drawn from the library; then, the most accurate model of the material is identified by using both statistical and numerical methods     

箔片转动数学建模及仿真分析

针对箔片在运动过程中存在变角速度的转动现象,对箔片的转动问题进行了研究.首先分析了气动阻尼对箔片转动的影响,建立了箔片的运动模型及转动模型,并应用CFD计算箔片的气动力系数.然后,通过高速相机计算了箔片的转动角速度并与转动模型的仿真结果进行对比,验证了模型的准确性.最后对箔片的转动特性以及箔片云的运动扩散过程进行仿真分...     

数字指南针的数学建模应用研究

机器人的应用离不开传感器,传感器应用成为青少年机器人教育中的一个重要内容.其中,电子指南针的应用非常广泛,但是电子指南针的应用有一定难度,使得广大青少年在使用过程中束手无策.我经过研究发现主要存在以下问题:机器人在需要转向时的方向问题——逆时针转动还是顺时针转动？机器人在转动过程中的速度如何,速度快的话则在目标角度有可能由于机器人控制器来不及处理角度数据而失败(转过头),速度慢的话则大大降低了机器人的运行效率.鉴于以上两个问题,本文就通过建立数学模型,把数字指南针的应用和高中阶段的数学三角函数结合起来,巧妙的解决以上两个问题.     

基于布尔对OUPA的数学建模及优化

基于在低压电力系统中的OUPA只有物理实体,没有数学模型的前提下,首次提出使用布尔代数对其进行描述,从数学建模的角度补充了OUPA在理论上的空白;在建立数学模型之后,对其模型进行优化,主要解决目前长期存在于低压线路中由功率因数变化引起继电器误动的问题,以逻辑门电路为基础,高速微低功耗处理器为核心重新设计新一代OUPA模型,为三相线路下智能互联OUPA的同步控制奠定理论基础。     

Rigorous mathematical modeling techniques for optimal delivery of macromolecules to the brain

Several treatment modalities for neurodegenerative diseases or tumors of the central nervous system involve invasive delivery of large molecular weight drugs to the brain. Despite the ample record of experimental studies, accurate drug targeting for the human brain remains a challenge. This paper proposes a systematic design method of administering drugs to specific locations in the human brain based on first principles transport in porous media. The proposed mathematical framework predicts achievable treatment volumes in target regions as a function of brain anatomy and infusion catheter position. A systematic procedure to determine the optimal infusion and catheter design parameters that maximize the penetration depth and volumes of distribution will be discussed. The computer simulations are validated with agarose gel phantom experiments and rat data. The rigorous computational approach will allow physicians and scientists to better plan the administration of therapeutic drugs to the central nervous system.      

New approach to the mathematical modeling of thermal regimes for electronic equipment

A mathematical model is constructed for simulating thermal regimes of typical electronic building blocks. It describes convective heat transfer in an air-filled cavity having finitely thick heat-conducting walls and containing a heat source. On this basis, flow patterns, temperature fields, and vorticity-vector fields are computed that characterize the convective heat transfer over a range of natural-convection parameters found in practice. Nonstationarity is shown to be a determinant of thermal regimes attained by the system. Computational relations are derived representing the variation of the average Nusselt number with the Grashof number for the boundary of the cavity.     

A mathematical foundation for linear lumped modeling techniques

The mathematical foundation for a linear lumped transistor model is developed from the nonlinear regional model proposed by Schilling. A one-dimensional model is described with simple analytic equations representing carrier density and electric field profiles and stored charge across the base and collector regions of a bipolar transistor. The regional boundaries are derived as simple functions of the device parameters, e.g., impurity profile, and operating conditions at its terminals. A one-to-one correspondence between these physical device parameters and lumped model elements is provided by the model. The linear regional model is demonstrated to be equivalent to its nonlinear counterpart, consequently to Gummel's charge control model.     

Multiscale autoregressive processes. II. Lattice structures forwhitening and modeling

For pt.I see ibid., vol.40, no.8, p.1915-34 (1992). Lattice structures for the whitening and modeling of isotropic processes on trees are developed, and a result relating the stability properties of these models to the reflection coefficient sequence introduced in pt.I is presented. This framework allows one to obtain a detailed analysis of the Wold decomposition of processes on trees. One interesting aspect of this is that there is a significantly larger class of singular processes on dyadic trees than on the integers     

Multiscale modeling of circular and elliptical particles in laminar shear flow

Drug delivery systems for cancer prevention and pain management have been improved related to classical cancer chemotherapy. Nanotechnology with nanoparticles offers new ways in transport of drug molecules and contrast agents by the blood flow through the circulatory system. In this study, we use multiscale mesoscopic bridging procedure of the finite elements (FE) coupled with dissipative particle dynamics (DPD) and lattice Boltzmann (LB) method to model the motion of circular and elliptical particles in a 2-D laminar flow. Four examples are considered: 1) one sedimenting cylinder in a channel, 2) two sedimenting cylinders in a channel, 3) motion of four elliptical particles in a linear shear flow, and 4) motion of circular and elliptical particle in the arterial bifurcation geometry. A good agreement with solution from the literature available was found. These results show that the multiscale approach with coupled FE and DPD/LB methods can effectively be applied to model motion of micro/nanoparticles for a drug delivery system.     

Multiscale modeling and simulation of the cardiac fiber architecture for DMRI

Cardiac fiber architecture plays an important role in the study of mechanical and electrical properties of the wall of the human heart, but still remains to be elucidated. This paper proposes to investigate, in a multiscale manner, how the arrangement patterns and morphological heterogeneity of cardiac myocytes influence the fibers orientation. To this end, different virtual cardiac fiber structures are modeled, and diffusion tensor imaging at multiple scales are simulated using the Monte Carlo method. The results show that the proposed modeling and simulation allow us to quantitatively describe the variation of the measured tissue properties (fiber orientation and fractional anisotropy) as a function of the observation scale.