scholarly journals Derivation of a Cell-Based Mathematical Model of Excitable Cells

2020 ◽  
pp. 1-13
Author(s):  
Karoline Horgmo Jæger ◽  
Aslak Tveito
Keyword(s):  
Mathematical Model ◽  
Electrical Properties ◽  
Numerical Methods ◽  
Spatial Models ◽  
Excitable Cells ◽  
Intracellular Space ◽  
Classical Models ◽  
A Cell ◽  
Simulation Results ◽  
Present Text

Abstract Excitable cells are of vital importance in biology, and mathematical models have contributed significantly to understand their basic mechanisms. However, classical models of excitable cells are based on severe assumptions that may limit the accuracy of the simulation results. Here, we derive a more detailed approach to modeling that has recently been applied to study the electrical properties of both neurons and cardiomyocytes. The model is derived from first principles and opens up possibilities for studying detailed properties of excitable cells.We refer to the model as the EMI model because both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model, in contrast to classical spatial models of excitable cells. Later chapters of the present text will focus on numerical methods and software for solving the model. Also, in the next chapter, the model will be extended to account for ionic concentrations in the intracellular and extracellular spaces.

Mathematical modeling of biological tissues electrical conductivity based on the ion electrodiffusion equations

2021 ◽  
Author(s):  
N.V. Kovalenko ◽  
K.V. Sovin ◽  
O.A. Ryabushkin
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Electrical Properties ◽  
Biological Tissue ◽  
Physiological State ◽  
Biological Tissues ◽  
Radiation Heating ◽  
Tissue Degradation ◽  
Simulation Results ◽  
Electrical Properties Of Tissues

Problem formulating. The vital processes of biological tissues are closely related to their electrical properties. An important task is to create a physical and mathematical model that will link the electrical properties of tissues to their physiological state. Goal. Construction of a model of biological tissue electrical properties based on the equations of ion electrodiffusion. Result. The paper presents the model of biological tissue electrical properties based on the ion electrodiffusion equations, and compares the simulation results with the experimental results presented in the literature. Practical meaning. The presented model can be used to describe processes occurring in tissue at the level of concentration and conductivity of ions in individual cells and cell membranes. In particular, the process of tissue degradation during laser radiation heating can be described.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Simulation Tool for Assignment Models: SIMASI

2014 ◽  
Vol 13 (8) ◽  
pp. 4723-4728
Author(s):  
Pratiksha Saxena ◽  
Smt. Anjali
Keyword(s):  
Optimization Procedure ◽  
Simulation Tool ◽  
Optimization Strategy ◽  
Performance Measurements ◽  
Integrated Simulation ◽  
Assignment Model ◽  
Classical Models ◽  
Simulation Results ◽  
User Friendly ◽  
Assignment Models

In this paper, an integrated simulation optimization model for the assignment problems is developed. An effective algorithm is developed to evaluate and analyze the back-end stored simulation results. This paper proposes simulation tool SIMASI (Simulation of assignment models) to simulate assignment models. SIMASI is a tool which simulates and computes the results of different assignment models. This tool is programmed in DOT.NET and is based on analytical approach to guide optimization strategy. Objective of this paper is to provide a user friendly simulation tool which gives optimized assignment model results. Simulation is carried out by providing the required values of matrix for resource and destination requirements and result is stored in the database for further comparison and study. Result is obtained in terms of the performance measurements of classical models of assignment system. This simulation tool is interfaced with an optimization procedure based on classical models of assignment system. The simulation results are obtained and analyzed rigorously with the help of numerical examples. 

Research on Dynamic Balance Method of Precision Centrifuge

2014 ◽  
Vol 945-949 ◽  
pp. 777-780
Author(s):  
Tao Liu ◽  
Yong Xu ◽  
Bo Yuan Mao
Keyword(s):  
Mathematical Model ◽  
Balance Control ◽  
Dynamic Balance ◽  
Dynamic Balancing ◽  
Structure Characteristics ◽  
Balance System ◽  
Simulation Results ◽  
Set Up ◽  
System Controller ◽  
The Mathematical Model

Firstly, according to the structure characteristics of precision centrifuge, the mathematical model of its dynamic balancing system was set up, and the dynamic balancing scheme of double test surfaces, double emendation surfaces were established. Then the dynamic balance system controller of precision centrifuge was designed. Simulation results show that the controller designed can completely meet the requirements of precision centrifuge dynamic balance control system.

The Study of p-n and Schottky Junction for Magnetodiode

2011 ◽  
Vol 378-379 ◽  
pp. 663-667 ◽  
Author(s):  
Toempong Phetchakul ◽  
Wittaya Luanatikomkul ◽  
Chana Leepattarapongpan ◽  
E. Chaowicharat ◽  
Putapon Pengpad ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electrical Properties ◽  
Simulation Model ◽  
Hall Effect ◽  
Schottky Junction ◽  
Field Sensitivity ◽  
Field Response ◽  
Type Semiconductor ◽  
Simulation Results ◽  
P Type

This paper presents the simulation model of Dual Magnetodiode and Dual Schottky Magnetodiode using Sentaurus TCAD to simulate the virtual structure of magneto device and apply Hall Effect to measure magnetic field response of the device. Firstly, we use the program to simulate the magnetodiode with p-type semiconductor and aluminum anode and measure electrical properties and magnetic field sensitivity. Simulation results show that sensitivity of Dual Schottky magnetodiode is higher than that of Dual magnetodiode.

Identification and Model Predictive Position Control of Two Wheeled Inverted Pendulum Mobile Robot

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Amir A. Bature ◽  
Salinda Buyamin ◽  
Mohamad N. Ahmad ◽  
Mustapha Muhammad ◽  
Auwalu A. Muhammad
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Mobile Robot ◽  
Inverted Pendulum ◽  
Position Control ◽  
Superior Performance ◽  
System A ◽  
Wheeled Inverted Pendulum ◽  
Simulation Results ◽  
Real Plant

In order to predict and analyse the behaviour of a real system, a simulated model is needed. The more accurate the model the better the response is when dealing with the real plant. This paper presents a model predictive position control of a Two Wheeled Inverted Pendulum robot. The model was developed by system identification using a grey box technique. Simulation results show superior performance of the gains computed using the grey box model as compared to common linearized mathematical model. 

Research on Flux Damping Control Strategy of DFIG during Grid Voltage Dips

2015 ◽  
Vol 713-715 ◽  
pp. 756-759
Author(s):  
Xu Guang Zhang ◽  
Zhen Xie
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Grid Voltage ◽  
Damping Control ◽  
Simulink Simulation ◽  
Voltage Dips ◽  
Simulation Results ◽  
Stator Flux ◽  
Natural Component ◽  
Simplified Mathematical Model

A flux damping control strategy was proposed to accelerate the decay of stator flux and restrain stator, rotor current and torque oscillation caused by grid voltage dips. Firstly, this paper analyzes the simplified mathematical model of DFIG during symmetrical voltage dips. Then, the mechanism of flux damping control strategy to restrain stator, rotor current oscillation and increase flux damping was analyzed. The flux damping control strategy can increase the damping of stator side, which accelerates the decay of the stator flux natural component and improve the dynamic LVRT performance of DFIG. The correctness and effectiveness of this method is verified by MATLAB/Simulink simulation results.

scholarly journals SETI, Evolution and Human History Merged into a Mathematical Model

2013 ◽  
Vol 12 (3) ◽  
pp. 218-245 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Mathematical Model ◽  
Exponential Growth ◽  
Numerical Estimate ◽  
Mean Value ◽  
Darwinian Evolution ◽  
Human History ◽  
The Galaxy ◽  
Positive Time ◽  
A Cell ◽  
Geometric Locus

AbstractIn this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

The Impact Analysis of Revolute Pair Clearance to the End Pose Accuracy of Welding Robot

2015 ◽  
Vol 778 ◽  
pp. 259-263
Author(s):  
Fa Jun Zhang ◽  
Lin Zi Li ◽  
Hui Lin ◽  
Yin Lin Pu ◽  
Zhu Xin
Keyword(s):  
Mathematical Model ◽  
Impact Analysis ◽  
Joint Clearance ◽  
Welding Robot ◽  
Movement Characteristic ◽  
Movement Stability ◽  
Simulation Results ◽  
The Impact ◽  
The Mathematical Model ◽  
Welding Position

Various uncertain factors affect the movement of the welding robot, thus welding gun tend to deviate from the theory of welding position which reduces the welding accuracy, of which the revolute pair clearance have an greater effect on the movement of the welding robot. In order to study the influence of revolute pair clearance to the end pose accuracy of welding robot, the mathematical model of revolute pair clearance was established, and the software SolidWorks was used for establishing the welding robot model, making simulations of the mechanical arm with joint clearance and no joint clearance. At last, the movement characteristic of the hinge shaft is attained. The simulation results showed that the shaft velocity and displacement of mechanical arm with joint clearance has a certain degree of fluctuation, which affecting the end pose accuracy of welding robot , and reducing the movement stability and the welding accuracy of welding robot.

Sign in / Sign up

Export Citation Format

Share Document