Traveling wave solution and the stability of critical points of an enzyme-inhibitor system under diffusion effects: with special reference to dimer molecule.

Enzymes are absolutely essential biological catalysts in human body that catalyze all cellular processes in physiological network. However, there are certain low molecular weight chemical compounds known as inhibitors, that reduce or completely inhibit the enzyme catalytic activity. Mathematical modeling plays a key role in the control and stability of metabolic enzyme inhibition. Enzyme stability is an important issue for protein engineers, because of its great importance and impact on optimal utility of material in biological tissues. In this outlook, we have first determined the existence of traveling wave solution for the enzyme-inhibitor system and then emphasized the stability of critical points that arise in the reactions. The study of traveling wave solution of an enzyme-inhibitor system with reaction diffusion equations involve quite complex mathematical analysis. The results obtained in this model indicate that the traveling wave solution may give a well explained method for improving enzyme kinetic stability. The present study will be helpful in understanding the stability of critical points of an enzyme-inhibitor system to give an idea about the inhibition of less stable enzymes. Moreover, the role of diffusion on the enzyme activity has been exhaustively discussed using mathematical tools related to eigen values and eigen function analysis.

Impact of radiation therapy on healthy and cancerous cell dynamics: a Mathematical analysis.

This study proposes a novel therapeutic model for cancer treatment with radiation therapy by analyzing the interactions among cancer, immune and healthy cells through a system of three ordinary differential equations. In this model, the natural influx rate of mature immune cells is assumed constant and is denoted by, a. The overall effect of radiation therapy on cancer cells is represented by a parameter, s; which is the surviving fraction of cells as determined by the Linear Quadratic (LQ) model. Conditions for the stability of equilibria in the interaction model modified to include the surviving fraction, are systematically established in terms of the dose and model parameters. Numerical simulations are performed in Wolfram MATHEMATICA software, investigating a spectrum of initial cell population values irradiated with 60Co γ-ray Low-LET radiation and High-LET 165 keV/µm Ni-ion radiation to facilitate improved visualization and in-depth analysis. By analyzing the model, this study identifies threshold values for the absorbed dose D for particular values of the model and radiation parameters for both High Linear Energy Transfer (high-LET) and Low Linear Energy Transfer (low-LET) radiations that ensure either eradication or minimization of cancer cells from a patient's body, providing valuable insights for designing effective cancer treatments.

Heat distribution and the condition of hypothermia in the multi-layered human head: A mathematical model.

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.

Mathematical analysis of oxygen and carbon dioxide exchange in the human capillary and tissue system.

Human body has a great ability to maintain homeostasis and the respiratory system plays a pivotal role in physiological processes. In this paper, a mathematical model of oxygen and carbon dioxide transport in the human body through capillary and tissue system has been formulated. The model is given by four ordinary differential equations for the oxygen and carbon dioxide transport, two equations for the capillary and other two for the tissue. An analytic approach based on Taylor's series method has been presented in this paper to obtain a computable approximate solution of the differential equation to model the oxygen and carbon dioxide diffusion in a spherical tissue. The concentration profiles at the capillary and tissue regions has been estimated in relation with partial pressure as the main driving force. The results are in agreement with the literature data those arrived at by Whiteley et al. (2005). The results obtained may help bio-medical sciences to deal with hypoxia and other respiratory ailments faced by the people living at high altitudes. Moreover, facilitated diffusion due to haemoglobin has been presented.

A mathematical model to study thermoregulation and heat-transfer processes in hypothermic neonates under variable physiological parameters.

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.

Mathematical modelling of drug-diffusion from multi-layered capsules/tablets and other drug delivery devices.

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.

Variational finite element approach to study heat transfer in the biological tissues of premature infants.

The body temperature of newborn preterm infants depends on the heat transfer between the infant and the external environment. Factors that influence the heat exchange include the temperature and humidity of the air and the temperature of surfaces in contact with and around the infant. Neonatal thermoregulation has a different pattern as they have an immature thermoregulatory system. For this purpose, mathematical models can provide detailed insights for the heat transfer processes and its applications for clinical purposes. A new multi-compartment mathematical model of the neonatal thermoregulatory system is presented. The formulation of the model is based on the Pennes' bio-heat equation with suitable boundary and initial conditions. The variational finite element method has been employed to determine heat transfer and exchange in the biological tissues of premature infants. The results obtained in this paper have shown that premature infants are unable to maintain a constant core temperature and resemble the empirically obtained results, proving the validity and feasibility of our model. AMS (2010): SUBJECT CLASSIFICATION: 92BXX, 92CXX, 92C35, 92C50, 46N60.

Thermal behavior of human eye in relation with change in blood perfusion, porosity, evaporation and ambient temperature.

Extreme environmental and physiological conditions present challenges for thermal processes in body tissues including multi-layered human eye. A mathematical model has been formulated in this direction to study the thermal behavior of the human eye in relation with the change in blood perfusion, porosity, evaporation and environmental temperatures. In this study, a comprehensive thermal analysis has been performed on the multi-layered eye using Pennes' bio-heat equation with appropriate boundary and interface conditions. The variational finite element method and MATLAB software were used for the solution purpose and simulation of the results. The thermoregulatory effect due to blood perfusion rate, porosity, ambient temperature and evaporation at various regions of human eye was illustrated mathematically and graphically. The main applications of this model are associated with the medical sciences while performing laser therapy and other thermoregulatory investigation on human eye.

REM sleep modulation by perifornical orexinergic inputs to the pedunculo-pontine tegmental neurons in rats.

Rapid eye movement sleep (REMS) is regulated by the interaction of the REM-ON and REM-OFF neurons located in the pedunculo-pontine-tegmentum (PPT) and the locus coeruleus (LC), respectively. Many other brain areas, particularly those controlling non-REMS (NREMS) and waking, modulate REMS by modulating these REMS-related neurons. Perifornical (PeF) orexin (Ox)-ergic neurons are reported to increase waking and reduce NREMS as well as REMS; dysfunction of the PeF neurons are related to REMS loss-associated disorders. Hence, we were interested in understanding the neural mechanism of PeF-induced REMS modulation. As a first step we have recently reported that PeF Ox-ergic neurons modulate REMS by influencing the LC neurons (site for REM-OFF neurons). Thereafter, in this in vivo study we have explored the role of PeF inputs on the PPT neurons (site for REM-ON neurons) for the regulation of REMS. Chronic male rats were surgically prepared with implanted bilateral cannulae in PeF and PPT and electrodes for recording sleep-waking patterns. After post-surgical recovery sleep-waking-REMS were recorded when bilateral PeF neurons were stimulated by glutamate and simultaneously bilateral PPT neurons were infused with either saline or orexin receptor1 (OX1R) antagonist. It was observed that PeF stimulation increased waking and decreased NREMS as well as REMS, which were prevented by OX1R antagonist into the PPT. We conclude that the PeF stimulation-induced reduction in REMS was likely to be due to inhibition of REM-ON neurons in the PPT. As waking and NREMS are inversely related, subject to confirmation, the reduction in NREMS could be due to increased waking or vice versa. Based on our findings from this and earlier studies we have proposed a model showing connections between PeF- and PPT-neurons for REMS regulation.

Explicit formula of finite difference method to estimate human peripheral tissue temperatures during exposure to severe cold stress.

During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, -5 °C and -10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure.

Perifornical orexinergic neurons modulate REM sleep by influencing locus coeruleus neurons in rats.

Activation of the orexin (OX)-ergic neurons in the perifornical (PeF) area has been reported to induce waking and reduce rapid eye movement sleep (REMS). The activities of OX-ergic neurons are maximum during active waking and they progressively reduce during non-REMS (NREMS) and REMS. Apparently, the locus coeruleus (LC) neurons also behave in a comparable manner as that of the OX-ergic neurons particularly in relation to waking and REMS. Further, as PeF OX-ergic neurons send dense projections to LC, we argued that the former could drive the LC neurons to modulate waking and REMS. Studies in freely moving normally behaving animals where simultaneously neuro-chemo-anatomo-physio-behavioral information could be deciphered would significantly strengthen our understanding on the regulation of REMS. Therefore, in this study in freely behaving chronically prepared rats we stimulated the PeF neurons without or with simultaneous blocking of specific subtypes of OX-ergic receptors in the LC while electrophysiological recording characterizing sleep-waking was continued. Single dose of glutamate stimulation as well as sustained mild electrical stimulation of PeF (both bilateral) significantly increased waking and reduced REMS as compared to baseline. Simultaneous application of OX-receptor1 (OX1R) antagonist bilaterally into the LC prevented PeF stimulation-induced REMS suppression. Also, the effect of electrical stimulation of the PeF was long lasting as compared to that of the glutamate stimulation. Further, sustained electrical stimulation significantly decreased both REMS duration as well as REMS frequency, while glutamate stimulation decreased REMS duration only.