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All neonates, whether term or preterm, are prone to hypothermia, which is a major health issue causing many health problems to infants and sometimes even death. Thus, such subjects are imperative to study to help researchers and biologists in neonatology, for developing certain methods, procedures and devices to prevent these abnormal temperature fluctuations to save the neonates from this health threat. To this purpose, a multi-node mathematical model is developed, to provide detailed insights and its applications to study the temperature profiles, thermoregulatory and heat-transfer mechanisms in hypothermic neonates. The model is constructed using the radial form of heat equation along with appropriate boundary and initial conditions. The model solution is obtained with the aid of the variational finite element method followed by the fundamental matrix method. The model outcomes obtained show the temperature fluctuations and tissue responses in hypothermic neonates. Finally, the model outcomes are compared with the published/experimental work to prove the feasibility and validity of the proposed work. Moreover, this work generalizes the several previously published works in the related field. [ABSTRACT FROM AUTHOR]

As an advancement in medical sciences, radioactive tracers are used in nuclear medicine, not only to understand the flow process and to make optimal diagnosis but also for staging, monitoring and evaluation of response to therapy. To this outlook, four mathematical models are devised to study the diffusion phenomena and kinetics of radiotracers injected intravenously into the bloodstream of the human body. The models are developed with the aim of studying and estimating the flow and concentration profiles of the radiotracer in biological tissues and studying the kinetics of reversible and irreversible tracers (i.e. 18F-Fludeoxyglucose), respectively. These profiles are helpful to determine the appropriate dose of the radiotracer to be administered, in positron emission tomography for the diagnostics, anticipation and treatment of various diseases. Finally, the results are simulated graphically and are also compared with the published/experimental work to check the feasibility and validity of the formulated models. [ABSTRACT FROM AUTHOR]

The conduction, perfusion and metabolic heat generation based partial differential equation has been used to study the heat transfer in human head. The main objective of this study is to predict the temperature distribution at the multi-layered human head that results in hypothermic condition. The temperature profiles have been estimated at the interface points of brain, skull and scalp with respect to various parameters including atmospheric temperature, arterial temperature and metabolic heat generation. The variational finite element method and analytical method based on Laplace transform has been employed to establish the solution of the formulated model, and the resulting outcomes are illustrated graphically. Under cold exposure, the blood capillaries around scalp exchange core heat with the external cold environment and experience lowering in the tissue temperature of the blood in the scalp. It is reflected in the graphical view of the model that the prolonged exposure to cold transmits its effect into the deep brain capillaries, wherein the temperature gradually lowers down below the normal body temperature that results hypothermia and hence abnormal body homoeostasis. [ABSTRACT FROM AUTHOR]

Mathematical modelling of oxygen transport in biological tissues played a great role and provides optimal results for advanced biomedical and biophysical research. Conventionally, oxygen is administered to hypoxic patients through pulmonary route. A mathematical model has been proposed to establish an alternative route for oxygen supply, whereby oxygen is administered directly into the target tissue bypassing the lung compartment. Our study aims at evaluating the feasibility of the novel approach using compartment modelling. The model is represented by a system of first order ordinary differential equations and their solution by Cramer’s rule and Laplace transform method. The concentration profiles of oxygen through pulmonary and intravenous routes were estimated in the arterial blood and tissue compartments at different flow rates; and with respect to initial oxygen concentration in the lung compartment and in the injected solution. Our results are in agreement with those arrived at by Lin Gui and Jing Liu (2006) [4]. The method offers a promising alternative to the conventional approach for clinical rescue of hypoxic patients, more so in emergency situations. [ABSTRACT FROM AUTHOR]

In this paper, two mathematical models have been formulated by extending the basic reaction–diffusion model, along with suitable initial and boundary conditions to study the drug delivery and its diffusion in biological tissues from multi-layered capsules/tablets and other drug delivery devices (DDDs), respectively. These devices are either taken orally or through other drug-administration routes. The formulated models are solved using the variational finite element method followed by the fundamental matrix method, to study the drug delivery and its diffusion more efficiently. The main aim of this work is to provide an effective model, using optimal mathematical techniques to help researchers and biologists in medicine in decreasing the endeavours and expenses in designing DDDs. The outcomes obtained are compared with the experimental data to demonstrate the validity and the feasibility of the proposed work. [ABSTRACT FROM AUTHOR]

A mathematical model of oxygen and carbon dioxide transport via blood in the human body has been formulated. The model is represented by four compartments: alveolar tissue, arterial blood, tissue and venous blood. The aim of this study is to estimate the concentration profiles of oxygen and carbon dioxide over alveolar tissue, arterial blood, tissue and venous blood compartments. The formulation is based on the transport of oxygen from atmospheric air to alveolar tissue and subsequently to capillary bed through inspiration and back flow of carbon dioxide through expiration. Ordinary differential equations and balance law have been employed to formulate compartment-wise transport phenomenon of both oxygen and carbon dioxide in the respiratory tract via blood. The solution of the model has been obtained using eigenvalue approach. The model provide the information regarding absorption rate of oxygen and release rate of carbon dioxide at the respective compartments. The results obtained in this study may help clinical and bio-medical sciences to deal with respiratory ailments faced by the people living at high altitudes. The results are in agreement with those arrived at by N. S. Cherniack et al. (1968). In addition, these results may have utility in biomedical engineering and physiological research problems. [ABSTRACT FROM AUTHOR]

A mathematical model based on radial reaction‐diffusion equation has been formulated. An explicit formula of finite difference method based on the forward‐time central‐space (FTCS) scheme has been applied to solve the initial‐boundary‐value problem. The main purpose of this study is to estimate the concentration profiles of oxygen at the biological tissues under variable oxygen tension (oxygen partial pressure (PO2)) in capillaries. The results obtained illustrate the variation of oxygen concentration in biological tissues with respect to temporal and spatial parameters. The results have shown a remarkable change in response to variation in PO2 in the blood capillary relative to that in the interstitial fluid. It has been observed, at fixed values of time period, oxygen concentration as a function of radial distance shows a decrease for PO2 in blood capillary (Pbc) greater than PO2 in interstitial fluid (Pf), that is, for Pbc > Pf, a decrease (approaching zero value) followed by a gradual increase for Pbc < Pf and a constant like behavior for Pbc = Pf. The values estimated in this study may help medical scientists to understand conditions under which hypoxia and other respiratory ailments occur to the biological tissues. [ABSTRACT FROM AUTHOR]