This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick's principle and law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The graphs plotted illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the graphs that the drug concentration decreases in the first compartment and gradually increases in other compartments.
A mathematical model is proposed to study the amount of drug concentration at various regions of human dermal system. The model is based on the mechanism of transdermal drug delivery systems (TDDS) with appropriate boundary conditions. The analytical solution for such problems either does not exist or is too complicated to handle. In this paper, finite element and Crank–Nicholson methods were used to find the solution of the formulated model with greater accuracy.
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.
The human head is one of the most sensitive parts of human body due to the fact that it contains brain. Any abnormality in the functioning of brain may disturb the entire system. One of the disturbing factors of brain is thermal stress. Thus, it is imperative to study the effects of thermal stress on human head at various environmental conditions. For the thermoregulation process, the human head is considered to be a structure of four layers viz.; brain, cerebrospinal fluid (CSF), skull and scalp. A mathematical model has been formulated to estimate the variation of temperature at these layers. The model is based on radial form of bio-heat equation with the appropriate boundary conditions and has been solved by variational finite element method. The rate of metabolic heat generation and thermal conductivity in this study have been assumed to be heterogeneous. The results were compared with the experimental studies for their coincidence and it has been observed theoretically and experimentally that the human head has greater resistance to compete with the thermal stress up to large extent.
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