Journal of Mathematical Sciences and Modelling, 2019
High speed airflow into the cornea accelerates evaporation and heat transfer. Eyelid blinking inc... more High speed airflow into the cornea accelerates evaporation and heat transfer. Eyelid blinking increases with increased airflow speed into the eye. Increased blinking increases corneal temperature when drops below normal level. In cold climatic condition high speed airflow causes rapid temperature drop. Most often, eye injuries caused by cold exposure occur in individuals who try to force their eyes open in high speed wind and cold weather such as two wheeler rider. The purpose of this study is to investigate the temperature changes in two wheeler rider’s cornea, considering eyelid blinking, in his/her different speed. Thus, in this paper, bio-heat transfer process is simulated using finite element method at rider’s different speed in transient state cases. In still air, blinking increases corneal temperature by $2.74^oC$ at normal ambient temperature $22.5^oC$ than in open eye. At ambient temperature $0^oC$ and rider’s speed $60km=hr$, corneal temperature drops to $5.45^oC $ in open...
The human body is made by 100 trillion cells. The uncontrolled and abnormal growth of cells cause... more The human body is made by 100 trillion cells. The uncontrolled and abnormal growth of cells causes tumors. Due to the presence of tumor, the skin surface temperature of body provides abnormal behavior than normal. Most of the breast tumor develops in lobules and milk ducts of glandular layer. In this study, tumor is assumed in glandular layer. The study of this work is focused to find the temperature distribution in tumor embedded female breast tissue with different tumor location and different tumor size. For this, the finite element method is used to solve two-dimensional Pennes bio heat equation. The results show that the skin surface temperature of breast is higher with nearest tumor from areola. The temperature variation in breast tissue with tumors located at symmetrical position about the central line of the breast are identical.
COVID-19 (Corona Virus Disease) is continuously spreading all over the world from January 2020. I... more COVID-19 (Corona Virus Disease) is continuously spreading all over the world from January 2020. It has been the major public health concern worldwide. In Nepal, the confirmed cases of the dis ease are increasing day by day. Mathematical modeling is one of the best tool to study the transmission dynamics of COVID - 19. In the present work, the transmission dynamics of COVID - 19 in Nepal with isolation is studied by using epidemic compartmental model. The global stability of the equilibrium points of the model are discussed with Lyapunov function. The stability of the disease is dependent on both trans- mission rate of the disease and the progression rate of the infectious state to isolated or hospitalized state. Simulations are made to observe situation of the disease in Nepal using the mathematical results graphically.
Breast cancer is one of the leading cancer and the second leading cause of death in women worldwi... more Breast cancer is one of the leading cancer and the second leading cause of death in women worldwide. It can occur when cancer develops in breast tumor. The tumor tissue has generally higher metabolic and blood perfusion rate than normal tissue. It then causes the temperature rise in the in-vivo breast tissue. Previous researchers have studied the temperature profiles on the breast skin surface only with and without tumor. The aim of the present work is to study the temperature distribution profiles in the layers of breast tissue with and without tumor along the direction from aerola to the body core. Breast tumor can be occurred in any layers of breast tissue but most of the cancer cells are normally developed in glandular layer. So, the study is carried out based on the tumor in glandular layer. Pennes bio-heat equation is used to study the temperature variation in the layers of breast tissue. In the study, it is observed that the location and size of the tumor has significant effe...
Advances in Engineering and Technology: An International Journal, 2021
A modified version of the so called Holling-Tanner prey-predator models with prey dependent funct... more A modified version of the so called Holling-Tanner prey-predator models with prey dependent functional response is introduced. We improved some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems and studied the stability of this model in the deterministic and stochastic environments. The study was focused on three types of stability, namely, stable node, spiral node, and center. The numerical schemes are employed to get the approximated solutions of the differential equations. We have used Euler scheme to solve the deterministic prey-predator model and we used Euler-Maruyama scheme to solve stochastic prey-predator model.
The human body is made by 200 different types of cells, which are separated by voids. Blood suppl... more The human body is made by 200 different types of cells, which are separated by voids. Blood supplies the nutrients and minerals to all cells within the tissue through these voids. The breast tissue is treated as a porous media in the study. Tumor includes the vascular (blood) and the extra-vascular (solid) regions. The porosity of a tumor is higher than normal tissue. The present work deals with the temperature variation of normal and tumorous breast tissue based on porous media. The finite element method is used to solve the two-dimensional bio-heat equation. The results show that the temperature profile of normal breast tissue in the porous media model is almost identical with the conventional bio-heat model at correction factor is equal to 0:6. The temperature of tumor region in the porous media model is slightly lower than the conventional bio-heat model. When the porosity is increased, the temperature of normal breast tissue is increased. But in tumorous breast tissue, the temp...
Corresponding Author: Kabita Luitel Department of Mathematics, Bhaktapur Multiple Campus, Nepal E... more Corresponding Author: Kabita Luitel Department of Mathematics, Bhaktapur Multiple Campus, Nepal Email: [email protected] Abstract: Clothing plays a major role in protecting the human body from cold and hot environment by working as an insulator. The physical factors such as conduction, convection, radiation, evaporation and the physiological factors such as blood flow and metabolism within the body together with clothing system help to maintain human thermal comfort and the human thermoregulatory system. On the other hand, body is continuously losing a small amount of heat from the air gap between skin surface and protective clothes. This paper studies the role and effect of the insulations of clothes and air for dry heat loss and the moisture transfer due to air velocity along with walking speed and observes how they work together for temperature distribution in human body. Pennes’ bioheat equation is taken as a model and Backward in Time and Central in Space (BTCS) scheme is...
Dengue is an infectious disease affecting tropical and subtropical regions worldwide. It is trans... more Dengue is an infectious disease affecting tropical and subtropical regions worldwide. It is transmitted to person through the biting of infectious aedes mosquitoes. In the paper, SIR model is used to describe the spread of dengue disease due to different biting rates of mosquitoes. The host (human) population is divided into three compartments: susceptible, infected and recovered. The mosquito population is divided into two compartments: susceptible and infected. Associated basic reproduction number is calculated and a sensitivity analysis is performed to determine the relative importance of model parameters to the disease transmission.
Lasers have been widely used in ophthalmology. Refractive errors are some of the most common opht... more Lasers have been widely used in ophthalmology. Refractive errors are some of the most common ophthalmic abnormalities worldwide. Laser refractive surgery was developed to correct refractive errors myopia, hyperopia and astigmatism. Two types of laser surgical techniques: lamellar and thermal are available to reshape the corneal curvature. Ultraviolet (UV) emitting argon fluoride (ArF) excimer laser is used to sculpt cornea in lamellar procedures, whereas, infrared (IR) emitting holmium yttrium aluminum garnet (Ho: YAG) laser is used to shrink cornea in thermal procedure. Tissue heating is common in all types of laser surgical techniques. Hence, in this paper, a finite element model is developed to investigate the temperature distribution of cornea in different laser refractive surgeries. Characteristics of optical and thermal processes and influence of the parameters of radiation and tissues on the results of laser action are investigated. The results of mathematical modeling in dif...
Sweat evaporation is the principal process of dissipating heat energy in a hot environment and du... more Sweat evaporation is the principal process of dissipating heat energy in a hot environment and during activities. Sweat loss is significantly affected by the level of energy expenditure, hormones, and the number of sweat glands. The thickness of the skin layer plays a vital role to maintain body temperature. The rate of sweat evaporation varies with ambient temperature and activity level. On increasing both metabolism and ambient temperature, sweat rate loss also increases and controls the body in the thermoregulatory system. The evaporative sweat release rate has a linear behavior. The appropriate physical and physiological parameters that affect thermoregulation have been incorporated into the model. The study presents the temperature distribution in three layers: epidermis, dermis, and subcutaneous tissue (SST) of the human dermal parts during cooking, cleaning, and walking. The solution is obtained by using the finite element method. The results demonstrate that the body mechani...
Refractive errors are the most common causes of vision impairment worldwide and laser refractive ... more Refractive errors are the most common causes of vision impairment worldwide and laser refractive surgery is one of the most frequently performed ocular surgeries. Clinical studies have reported that approximately 10.5% of patients need an additional procedure after the surgery. The major complications of laser surgery are over/under correction and dry eye. An increase in temperature may be a cause for these complications. The purpose of this study was to estimate the increase in temperature during laser refractive surgery and its relationship with the complications observed for different surgical techniques. In this paper, a finite element model was applied to investigate the temperature distribution of the cornea when subjected to ArF excimer laser at a single spot using various beam delivery systems (broad beam, scanning slit, and flying spot). The Pennes bio-heat equation was used to predict the temperature values at different laser pulse energies and frequencies. The maximum temperature increase by ArF laser (500Hz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$500\mathrm{ Hz}$$\end{document} frequency and 0.5J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5\mathrm{ J}$$\end{document} pulse energy) at a single spot was 33.94∘C,15.86∘C,12.48∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$33.94^{\circ} \mathrm{C}, 15.86^{\circ} \mathrm{C}, 12.48^{\circ} \mathrm{C}$$\end{document} for 6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$6$$\end{document} diopter correction (65.4μm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$65.4 \upmu \mathrm{m}$$\end{document} of ablation of corneal stroma) using broad beam, scanning slit, and flying spot beam delivery approaches respectively. The peak temperature due to a single pulse was estimated to be 234.14∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$234.14 ^{\circ} \mathrm{C}$$\end{document}. Although the peak temperature (sufficient energy to break intermolecular bonds) exists for a very short time (10-30ns\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10-30\mathrm{ ns}$$\end{document}) compared to the thermal relaxation time (2000-10,000μs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2000-10,000 \upmu \mathrm{s}$$\end{document}), there is some thermal energy exchange between corneal tissues during a laser refractive surgery. Heating may cause collagen denaturation, collagen shrinkage, and more evaporation and hence proposed to be a risk factor for over/under correction and dry eye.
The human thermal comfort is the state of mind, which is affected not only by the physical and bo... more The human thermal comfort is the state of mind, which is affected not only by the physical and body’s internal physiological phenomena but also by the clothing properties such as thermal resistance of clothing, clothing insulation, clothing area factor, air insulation, and relative humidity. In this work, we extend the one-dimensional Pennes’ bioheat transfer equation by adding the protective clothing layer. The transient temperature profile with the clothing layer at the different time steps has been carried out using a fully implicit Finite Difference (FD) Scheme with interface condition between body and clothes. Numerically computed results are bound to agree that the clothing insulation and air insulation provide better comfort and keep the body at the thermal equilibrium position. The graphical representation of the results also verifies the effectiveness and utility of the proposed model.
The human thermal comfort is affected by the body’s heat exchange mechanism conduction, convectio... more The human thermal comfort is affected by the body’s heat exchange mechanism conduction, convection, radiation, and evaporation. The mode of heat transfer between the body and environment depends upon the human internal physiological phenomena, together with the boundary conditions. The present paper provides the comprehensive overview of the thermoregulatory system of human body and studies the numerical solution of unsteady-state one dimensional Pennes bio-heat equation with appropriate boundary conditions. The solution is used to observe the temperature profiles at different thermal conductivities, and different heat transfer coefficients in the living tissue at the various time steps. Various physical and physiological factors across the cylindrical living tissue have been incorporated in the model.
A novel coronavirus disease (COVID-19) is an infectious viral disease caused by SARS-CoV-2. The d... more A novel coronavirus disease (COVID-19) is an infectious viral disease caused by SARS-CoV-2. The disease was first reported in Wuhan, China, in December 2019, and it has been epidemic in more than 110 countries. The first case of COVID-19 was found in Nepal on 23 January, 2020. Now the number of confirmed cases is increasing day by day. Thus, the disease has become a major public health concern in Nepal. The propose of this study is to describe the development of outbreak of the disease and to predict the outbreak in Nepal. In the present work, the transmission dynamics of the disease in Nepal is analyzed mathematically with the help of SIR compartmental model. Reported data from June 1 st to June 17 th 2020 of Nepal are used to identify the model parameters. The basic reproduction number of COVID-19 outbreak in Nepal is estimated. Predictions of the peak epidemic time and the final size of the epidemic are made using the model. Our work predicts that, after 125 days from June 1 the infection will reach the peak. In this work, a good correlation between the reported data and the estimation given by our model is observed.
Metabolisms play a vital role in thermoregulation in the human body. The metabolic rate varies wi... more Metabolisms play a vital role in thermoregulation in the human body. The metabolic rate varies with the activity levels and has different behaviors in nature depending on the physical activities of the person. During the activity, metabolic rate increases rapidly at the beginning and then increases slowly to become almost constant after a certain time. So, its behavior is as logistics in nature. The high metabolic rate during activity causes the increase of body core temperature up to 39˚C [1] [2]. The logistic model of metabolic rate is used to remodel Pennes' bioheat equation for the study of temperature distribution in three layered human dermal parts during carpentering, swimming and marathon. The finite element method is used to obtain the solution of the model equation. The results demonstrate that there is a significant change in tissue temperature due to sweating and ambient temperature variations.
Mathematical formulation for heat transfer in living tissue is different than an inert material, ... more Mathematical formulation for heat transfer in living tissue is different than an inert material, and is a current growing research interest area for many researchers due to its wide applications in many medical therapies and physiological studies. This interest stems from the rapid advancement of computational technology and advanced numerical mathematical techniques. The paper focuses on review on basic formulations of bio-heat equation proposed so far by several authors in the living tissue and its some applications.
Hemodialysis is the process of purifying the blood which removes the waste product such as urea ... more Hemodialysis is the process of purifying the blood which removes the waste product such as urea from blood through the semi-permeable membrane of dialyzer. In dialyzer, the rate of blood flow velocity is maintained around five times less than the dialyzed flow velocity during hemodialysis. The study focuses on the urea concentration distribution in the blood during dialysis using partial differential equation of diffusion process developed by J. N. Kapur, assuming blood is Newtonian, and laminar flow. The solution of urea concentration is obtained using Galerkin approximation method associated with appropriate boundary conditions.
Journal of Mathematical Sciences and Modelling, 2019
High speed airflow into the cornea accelerates evaporation and heat transfer. Eyelid blinking inc... more High speed airflow into the cornea accelerates evaporation and heat transfer. Eyelid blinking increases with increased airflow speed into the eye. Increased blinking increases corneal temperature when drops below normal level. In cold climatic condition high speed airflow causes rapid temperature drop. Most often, eye injuries caused by cold exposure occur in individuals who try to force their eyes open in high speed wind and cold weather such as two wheeler rider. The purpose of this study is to investigate the temperature changes in two wheeler rider’s cornea, considering eyelid blinking, in his/her different speed. Thus, in this paper, bio-heat transfer process is simulated using finite element method at rider’s different speed in transient state cases. In still air, blinking increases corneal temperature by $2.74^oC$ at normal ambient temperature $22.5^oC$ than in open eye. At ambient temperature $0^oC$ and rider’s speed $60km=hr$, corneal temperature drops to $5.45^oC $ in open...
The human body is made by 100 trillion cells. The uncontrolled and abnormal growth of cells cause... more The human body is made by 100 trillion cells. The uncontrolled and abnormal growth of cells causes tumors. Due to the presence of tumor, the skin surface temperature of body provides abnormal behavior than normal. Most of the breast tumor develops in lobules and milk ducts of glandular layer. In this study, tumor is assumed in glandular layer. The study of this work is focused to find the temperature distribution in tumor embedded female breast tissue with different tumor location and different tumor size. For this, the finite element method is used to solve two-dimensional Pennes bio heat equation. The results show that the skin surface temperature of breast is higher with nearest tumor from areola. The temperature variation in breast tissue with tumors located at symmetrical position about the central line of the breast are identical.
COVID-19 (Corona Virus Disease) is continuously spreading all over the world from January 2020. I... more COVID-19 (Corona Virus Disease) is continuously spreading all over the world from January 2020. It has been the major public health concern worldwide. In Nepal, the confirmed cases of the dis ease are increasing day by day. Mathematical modeling is one of the best tool to study the transmission dynamics of COVID - 19. In the present work, the transmission dynamics of COVID - 19 in Nepal with isolation is studied by using epidemic compartmental model. The global stability of the equilibrium points of the model are discussed with Lyapunov function. The stability of the disease is dependent on both trans- mission rate of the disease and the progression rate of the infectious state to isolated or hospitalized state. Simulations are made to observe situation of the disease in Nepal using the mathematical results graphically.
Breast cancer is one of the leading cancer and the second leading cause of death in women worldwi... more Breast cancer is one of the leading cancer and the second leading cause of death in women worldwide. It can occur when cancer develops in breast tumor. The tumor tissue has generally higher metabolic and blood perfusion rate than normal tissue. It then causes the temperature rise in the in-vivo breast tissue. Previous researchers have studied the temperature profiles on the breast skin surface only with and without tumor. The aim of the present work is to study the temperature distribution profiles in the layers of breast tissue with and without tumor along the direction from aerola to the body core. Breast tumor can be occurred in any layers of breast tissue but most of the cancer cells are normally developed in glandular layer. So, the study is carried out based on the tumor in glandular layer. Pennes bio-heat equation is used to study the temperature variation in the layers of breast tissue. In the study, it is observed that the location and size of the tumor has significant effe...
Advances in Engineering and Technology: An International Journal, 2021
A modified version of the so called Holling-Tanner prey-predator models with prey dependent funct... more A modified version of the so called Holling-Tanner prey-predator models with prey dependent functional response is introduced. We improved some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems and studied the stability of this model in the deterministic and stochastic environments. The study was focused on three types of stability, namely, stable node, spiral node, and center. The numerical schemes are employed to get the approximated solutions of the differential equations. We have used Euler scheme to solve the deterministic prey-predator model and we used Euler-Maruyama scheme to solve stochastic prey-predator model.
The human body is made by 200 different types of cells, which are separated by voids. Blood suppl... more The human body is made by 200 different types of cells, which are separated by voids. Blood supplies the nutrients and minerals to all cells within the tissue through these voids. The breast tissue is treated as a porous media in the study. Tumor includes the vascular (blood) and the extra-vascular (solid) regions. The porosity of a tumor is higher than normal tissue. The present work deals with the temperature variation of normal and tumorous breast tissue based on porous media. The finite element method is used to solve the two-dimensional bio-heat equation. The results show that the temperature profile of normal breast tissue in the porous media model is almost identical with the conventional bio-heat model at correction factor is equal to 0:6. The temperature of tumor region in the porous media model is slightly lower than the conventional bio-heat model. When the porosity is increased, the temperature of normal breast tissue is increased. But in tumorous breast tissue, the temp...
Corresponding Author: Kabita Luitel Department of Mathematics, Bhaktapur Multiple Campus, Nepal E... more Corresponding Author: Kabita Luitel Department of Mathematics, Bhaktapur Multiple Campus, Nepal Email: [email protected] Abstract: Clothing plays a major role in protecting the human body from cold and hot environment by working as an insulator. The physical factors such as conduction, convection, radiation, evaporation and the physiological factors such as blood flow and metabolism within the body together with clothing system help to maintain human thermal comfort and the human thermoregulatory system. On the other hand, body is continuously losing a small amount of heat from the air gap between skin surface and protective clothes. This paper studies the role and effect of the insulations of clothes and air for dry heat loss and the moisture transfer due to air velocity along with walking speed and observes how they work together for temperature distribution in human body. Pennes’ bioheat equation is taken as a model and Backward in Time and Central in Space (BTCS) scheme is...
Dengue is an infectious disease affecting tropical and subtropical regions worldwide. It is trans... more Dengue is an infectious disease affecting tropical and subtropical regions worldwide. It is transmitted to person through the biting of infectious aedes mosquitoes. In the paper, SIR model is used to describe the spread of dengue disease due to different biting rates of mosquitoes. The host (human) population is divided into three compartments: susceptible, infected and recovered. The mosquito population is divided into two compartments: susceptible and infected. Associated basic reproduction number is calculated and a sensitivity analysis is performed to determine the relative importance of model parameters to the disease transmission.
Lasers have been widely used in ophthalmology. Refractive errors are some of the most common opht... more Lasers have been widely used in ophthalmology. Refractive errors are some of the most common ophthalmic abnormalities worldwide. Laser refractive surgery was developed to correct refractive errors myopia, hyperopia and astigmatism. Two types of laser surgical techniques: lamellar and thermal are available to reshape the corneal curvature. Ultraviolet (UV) emitting argon fluoride (ArF) excimer laser is used to sculpt cornea in lamellar procedures, whereas, infrared (IR) emitting holmium yttrium aluminum garnet (Ho: YAG) laser is used to shrink cornea in thermal procedure. Tissue heating is common in all types of laser surgical techniques. Hence, in this paper, a finite element model is developed to investigate the temperature distribution of cornea in different laser refractive surgeries. Characteristics of optical and thermal processes and influence of the parameters of radiation and tissues on the results of laser action are investigated. The results of mathematical modeling in dif...
Sweat evaporation is the principal process of dissipating heat energy in a hot environment and du... more Sweat evaporation is the principal process of dissipating heat energy in a hot environment and during activities. Sweat loss is significantly affected by the level of energy expenditure, hormones, and the number of sweat glands. The thickness of the skin layer plays a vital role to maintain body temperature. The rate of sweat evaporation varies with ambient temperature and activity level. On increasing both metabolism and ambient temperature, sweat rate loss also increases and controls the body in the thermoregulatory system. The evaporative sweat release rate has a linear behavior. The appropriate physical and physiological parameters that affect thermoregulation have been incorporated into the model. The study presents the temperature distribution in three layers: epidermis, dermis, and subcutaneous tissue (SST) of the human dermal parts during cooking, cleaning, and walking. The solution is obtained by using the finite element method. The results demonstrate that the body mechani...
Refractive errors are the most common causes of vision impairment worldwide and laser refractive ... more Refractive errors are the most common causes of vision impairment worldwide and laser refractive surgery is one of the most frequently performed ocular surgeries. Clinical studies have reported that approximately 10.5% of patients need an additional procedure after the surgery. The major complications of laser surgery are over/under correction and dry eye. An increase in temperature may be a cause for these complications. The purpose of this study was to estimate the increase in temperature during laser refractive surgery and its relationship with the complications observed for different surgical techniques. In this paper, a finite element model was applied to investigate the temperature distribution of the cornea when subjected to ArF excimer laser at a single spot using various beam delivery systems (broad beam, scanning slit, and flying spot). The Pennes bio-heat equation was used to predict the temperature values at different laser pulse energies and frequencies. The maximum temperature increase by ArF laser (500Hz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$500\mathrm{ Hz}$$\end{document} frequency and 0.5J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5\mathrm{ J}$$\end{document} pulse energy) at a single spot was 33.94∘C,15.86∘C,12.48∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$33.94^{\circ} \mathrm{C}, 15.86^{\circ} \mathrm{C}, 12.48^{\circ} \mathrm{C}$$\end{document} for 6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$6$$\end{document} diopter correction (65.4μm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$65.4 \upmu \mathrm{m}$$\end{document} of ablation of corneal stroma) using broad beam, scanning slit, and flying spot beam delivery approaches respectively. The peak temperature due to a single pulse was estimated to be 234.14∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$234.14 ^{\circ} \mathrm{C}$$\end{document}. Although the peak temperature (sufficient energy to break intermolecular bonds) exists for a very short time (10-30ns\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10-30\mathrm{ ns}$$\end{document}) compared to the thermal relaxation time (2000-10,000μs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2000-10,000 \upmu \mathrm{s}$$\end{document}), there is some thermal energy exchange between corneal tissues during a laser refractive surgery. Heating may cause collagen denaturation, collagen shrinkage, and more evaporation and hence proposed to be a risk factor for over/under correction and dry eye.
The human thermal comfort is the state of mind, which is affected not only by the physical and bo... more The human thermal comfort is the state of mind, which is affected not only by the physical and body’s internal physiological phenomena but also by the clothing properties such as thermal resistance of clothing, clothing insulation, clothing area factor, air insulation, and relative humidity. In this work, we extend the one-dimensional Pennes’ bioheat transfer equation by adding the protective clothing layer. The transient temperature profile with the clothing layer at the different time steps has been carried out using a fully implicit Finite Difference (FD) Scheme with interface condition between body and clothes. Numerically computed results are bound to agree that the clothing insulation and air insulation provide better comfort and keep the body at the thermal equilibrium position. The graphical representation of the results also verifies the effectiveness and utility of the proposed model.
The human thermal comfort is affected by the body’s heat exchange mechanism conduction, convectio... more The human thermal comfort is affected by the body’s heat exchange mechanism conduction, convection, radiation, and evaporation. The mode of heat transfer between the body and environment depends upon the human internal physiological phenomena, together with the boundary conditions. The present paper provides the comprehensive overview of the thermoregulatory system of human body and studies the numerical solution of unsteady-state one dimensional Pennes bio-heat equation with appropriate boundary conditions. The solution is used to observe the temperature profiles at different thermal conductivities, and different heat transfer coefficients in the living tissue at the various time steps. Various physical and physiological factors across the cylindrical living tissue have been incorporated in the model.
A novel coronavirus disease (COVID-19) is an infectious viral disease caused by SARS-CoV-2. The d... more A novel coronavirus disease (COVID-19) is an infectious viral disease caused by SARS-CoV-2. The disease was first reported in Wuhan, China, in December 2019, and it has been epidemic in more than 110 countries. The first case of COVID-19 was found in Nepal on 23 January, 2020. Now the number of confirmed cases is increasing day by day. Thus, the disease has become a major public health concern in Nepal. The propose of this study is to describe the development of outbreak of the disease and to predict the outbreak in Nepal. In the present work, the transmission dynamics of the disease in Nepal is analyzed mathematically with the help of SIR compartmental model. Reported data from June 1 st to June 17 th 2020 of Nepal are used to identify the model parameters. The basic reproduction number of COVID-19 outbreak in Nepal is estimated. Predictions of the peak epidemic time and the final size of the epidemic are made using the model. Our work predicts that, after 125 days from June 1 the infection will reach the peak. In this work, a good correlation between the reported data and the estimation given by our model is observed.
Metabolisms play a vital role in thermoregulation in the human body. The metabolic rate varies wi... more Metabolisms play a vital role in thermoregulation in the human body. The metabolic rate varies with the activity levels and has different behaviors in nature depending on the physical activities of the person. During the activity, metabolic rate increases rapidly at the beginning and then increases slowly to become almost constant after a certain time. So, its behavior is as logistics in nature. The high metabolic rate during activity causes the increase of body core temperature up to 39˚C [1] [2]. The logistic model of metabolic rate is used to remodel Pennes' bioheat equation for the study of temperature distribution in three layered human dermal parts during carpentering, swimming and marathon. The finite element method is used to obtain the solution of the model equation. The results demonstrate that there is a significant change in tissue temperature due to sweating and ambient temperature variations.
Mathematical formulation for heat transfer in living tissue is different than an inert material, ... more Mathematical formulation for heat transfer in living tissue is different than an inert material, and is a current growing research interest area for many researchers due to its wide applications in many medical therapies and physiological studies. This interest stems from the rapid advancement of computational technology and advanced numerical mathematical techniques. The paper focuses on review on basic formulations of bio-heat equation proposed so far by several authors in the living tissue and its some applications.
Hemodialysis is the process of purifying the blood which removes the waste product such as urea ... more Hemodialysis is the process of purifying the blood which removes the waste product such as urea from blood through the semi-permeable membrane of dialyzer. In dialyzer, the rate of blood flow velocity is maintained around five times less than the dialyzed flow velocity during hemodialysis. The study focuses on the urea concentration distribution in the blood during dialysis using partial differential equation of diffusion process developed by J. N. Kapur, assuming blood is Newtonian, and laminar flow. The solution of urea concentration is obtained using Galerkin approximation method associated with appropriate boundary conditions.
Uploads
Papers by Dil Gurung