MATHEMATICAL MODEL FOR THE TRANSPORT OF OXYGEN IN THE LIVING TISSUE THROUGH CAPILLARY BED

2015 ◽  
Vol 15 (04) ◽  
pp. 1550055 ◽  
Author(s):  
M. A. KHANDAY ◽  
AIJAZ NAJAR
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Oxygen Transport ◽  
Human Body ◽  
Oxygen Supply ◽  
Living Tissue ◽  
Capillary Bed ◽  
Living Tissues

Oxygen is essential for the survival of living tissues in the human body. The mechanism of oxygen transport in the human body is a subject of great concern. In the conditions like hypoxia and hypothermia, the amount of oxygen supply in the biological tissue loose homeostasis, thereby the concentration of O 2 and the liberation of CO 2 in the human body demands a special attention. The present study based on finite element method employed to the mass diffusion equation with suitable conditions has been established. The main objective of this work is to understand the behavior of O 2 through various compartments of the capillary bed. The concentration of O 2 at plasma and capillary layers has been estimated which in turn leads to understand the situation of oxygen transport during various situations.

NUMERICAL ESTIMATION OF THE FLUID DISTRIBUTION PATTERN IN HUMAN DERMAL REGIONS WITH HETEROGENEOUS METABOLIC FLUID GENERATION

2015 ◽  
Vol 15 (01) ◽  
pp. 1550001 ◽  
Author(s):  
M. A. KHANDAY ◽  
MIR AIJAZ ◽  
AASMA RAFIQ
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Distribution Pattern ◽  
Human Body ◽  
Radial Diffusion ◽  
Fluid Distribution ◽  
Interface Conditions ◽  
Numerical Estimation ◽  
Normal Functioning

The composition of fluid distribution in human body is consisting of various intra-cellular and extra-cellular fluids. Dehydration and other changes in the system may lead to various disorders and diseases in the normal functioning. It is therefore imperative to study the fluid distribution and its balance in the human body systems. In this study, we estimate the pattern of fluid in human dermal regions with heterogeneous metabolic fluid generation. The model is based on radial diffusion equation with appropriate boundary and interface conditions. The variational finite element method has been used to solve the model. The results of fluid concentrations at the dermal and subdermal regions were calculated and interpreted graphically at various levels of humidities and perspirations.

Tissue necrosis and passage of fluid due to cold stress from the thermally damaged human body peripherals: A mathematical model

2015 ◽  
Vol 04 (02) ◽  
pp. 1550012
Author(s):  
M. A. Khanday ◽  
Fida Hussain ◽  
Khalid Nazir
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Heat Equation ◽  
Cold Stress ◽  
Human Body ◽  
Human Subjects ◽  
Diffusion Equations ◽  
Tissue Necrosis ◽  
Cold Temperatures ◽  
Element Technique

The development of cold injury takes place in the human subjects by means of crystallization of tissues in the exposed regions at severe cold temperatures. The process together with the evaluation of the passage of fluid discharge from the necrotic regions with respect to various degrees of frostbites has been carried out by using variational finite element technique. The model is based on the Pennes' bio-heat equation and mass diffusion equations together with suitable initial and boundary conditions. The results are analyzed in relation with atmospheric temperatures and other parameters of the tissue medium.

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

Model calculations in reconstructions of measured fields

Open Physics ◽  
2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Mihály Makai ◽  
Yuri Orechwa
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Group Theory ◽  
Point Group ◽  
Iterative Solution ◽  
The Finite Element Method ◽  
Technological Systems ◽  
Convergence Problem ◽  
Model Calculations

AbstractThe state of technological systems, such as reactions in a confined volume, are usually monitored with sensors within as well as outside the volume. To achieve the level of precision required by regulators, these data often need to be supplemented with the solution to a mathematical model of the process. The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rule problems. We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.

Hybrid Nodal Integral / Finite Element Method for Time-Dependent Convection Diffusion Equation

2021 ◽  
Author(s):  
Sundar Namala ◽  
Rizwan Uddin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Second Order ◽  
Time Dependent ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Integral Methods ◽  
Element Method

Abstract Nodal integral methods (NIM) are a class of efficient coarse mesh methods that use transverse averaging to reduce the governing partial differential equation(s) (PDE) into a set of ordinary differential equations (ODE). The standard application of NIM is restricted to domains that have boundaries parallel to one of the coordinate axes/palnes (in 2D/3D). The hybrid nodal-integral/finite-element method (NI-FEM) reported here has been developed to extend the application of NIM to arbitrary domains. NI-FEM is based on the idea that the interior region and the regions with boundaries parallel to the coordinate axes (2D) or coordinate planes (3D) can be solved using NIM, and the rest of the domain can be discretized and solved using FEM. The crux of the hybrid NI-FEM is in developing interfacial conditions at the common interfaces between the NIM regions and FEM regions. We here report the development of hybrid NI-FEM for the time-dependent convection-diffusion equation (CDE) in arbitrary domains. Resulting hybrid numerical scheme is implemented in a parallel framework in Fortran and solved using PETSc. The preliminary approach to domain decomposition is also discussed. Numerical solutions are compared with exact solutions, and the scheme is shown to be second order accurate in both space and time. The order of approximations used for the development of the scheme are also shown to be second order. The hybrid method is more efficient compared to standalone conventional numerical schemes like FEM.

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