Prediction of temperature profiles in the human skin and subcutaneous tissues

Exact mathematical solutions in terms of confluent hypergeometric and Airy's functions are obtained to study the steady state temperature distributions in human skin and subcutaneous tissues (SST). It is assumed that the skin is exposed to an air environment and heat transfer from the skin occurs by convection, radiation and evaporation. A mathematical model of the SST, accounting for heat conduction, perfusion of the capillary beds and metabolic heat productions of the dermis and subcutaneous tissues, has been solved to obtain interface temperatures for a wide range of environmental temperatures, rates of evaporation of sweat, wind speeds and relative humidities. The solutions provide inter-relationships between interface temperatures, thermal conductivities, metabolic heat production, blood perfusion, thicknesses of various layers of SST and ambient temperature.     

Effects of blood flow,curved boundary and environmental conditions on temperature distribution in a two dimensional model of human skin and subcutaneous tissues

A mathematical model for the study of the effects of blood flow, metabolic heat production, various environmental conditions and the presence of a curved boundary on the temperature distribution (TD) in a two dimensional model of human skin and subcutaneous tissues (SST) is presented. Based on physiological properties, the interfaces between epidermis-dermis (IED) and dermis-subcutaneous tissues (IDS) have been considered to be irregular and the regions of these layers have been divided into 109 triangular elements of various sizes which are connected with each other by 70 nodes. The results computed from this thermobiological mathematical model, using Galerkin's finite element technique, have been exhibited graphically. The effects of various environmental conditions, blood flow and metabolic heat production are found to be nonuniform on TD at the nodes situated at the same depth in SST. This nonuniformity in TD almost disappears at the nodes situated in dermis nearest to IDS except for the two of the six combinations, considered in the present study, in which highest values of blood flow and metabolic heat production have been considered. The rate of fall of temperature with respect to thickness (towards the skin surface) is higher at the straight boundary (SB) than at the curved boundary (CB). The temperature increases with respect to width (from SB to CB) in epidermis and dermis but decreases in subcutaneous tissues. This increase or decrease of temperature is more pronounced at the nodes situated near to, or at CB. The trend of these temperature profiles in SST reflects the dependence of TD not only on the environmental conditions and biophysical variables but also on the geometry of SST.     

Temperatures of skin, subcutaneous tissue, muscle and core in resting men in cold, comfortable and hot conditions

To examine the core-shell model of temperature distribution and the possible role of subcutaneous temperature in heat regulation, comprehensive temperature measurements were made on six nude resting men exposed for 2-3 h to comfort (27 degrees C), cold (15 degrees C) and heat (45 degrees C). Cold produced strong shivering and heat caused heavy sweating. Temperatures were recorded every 10 min from: esophagus, rectum and auditory canal; back muscle and thigh muscle at 20 mm and 40 mm depths; 6 subcutaneous sites; and 16 skin sites. Average temperatures at these 29 sites were tabulated at the ends of comfort, hot and cold and the onsets of sweating and shivering. Body temperature changes were slow to develop, the skin temperatures being fastest, and successively deeper tissues progressively slower. There was occasional after-drop and after-rise. The data were consistent with the core-shell concept. The temperature gradient from subcutaneous tissue to skin, which differed substantially with comfort, the onset of shivering and the onset of sweating, could serve as a regulatory signal. The data are now in computer format and may be of interest to biothermal modelers.     

Steady-state heat distribution in epidermis,dermis and subdermal tissues

Steady-state temperature distribution is investigated in human skin and subdermal tissue exposed to a dry and cool environment with negligible insensible perspiration. The mathematical model incorporates the effect of blood mass flow and metabolic heat generation. The rates of the two and the tissue thermal conductivity are assumed to have different values in all the three parts, namely epidermis, dermis and subdermal tissues. A simple variational finite element approach is used to find numerical values of the interface temperatures for a wide range of the values of skin surface temperature and for different thicknesses of the above parts. These values are used to obtain approximate temperature profiles in the whole region. The biological and physical implications of the results are also discussed.     

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.     

Thermoregulation through skin under variable atmospheric and physiological conditions

Considering three layers of the skin and subcutaneous region, an attempt has been made to obtain the analytical and numerical solutions for temperature distribution of the bioheat equation. The problem is studied under variable physiological parameters and atmospheric conditions. The role of metabolic heat generation, blood mass flow and perspiration in different thicknesses have been noted. The numerical solutions for different parametric values are shown graphically.     

Heat transfer analysis of skin during thermal therapy using thermal wave equation

Specifying exact geometry of vessel network and its effect on temperature distribution in living tissues is one of the most complicated problems of the bioheat field. In this paper, the effects of blood vessels on temperature distribution in a skin tissue subjected to various thermal therapy conditions are investigated. Present model consists of counter-current multilevel vessel network embedded in a three-dimensional triple-layered skin structure. Branching angles of vessels are calculated using the physiological principle of minimum work. Length and diameter ratios are specified using length doubling rule and Cube law, respectively. By solving continuity, momentum and energy equations for blood flow and Pennes and modified Pennes bioheat equations for the tissue, temperature distributions in the tissue are measured. Effects of considering modified Pennes bioheat equation are investigated, comprehensively. It is also observed that blood has an impressive role in temperature distribution of the tissue, especially at high temperatures. The effects of different parameters such as boundary conditions, relaxation time, thermal properties of skin, metabolism and pulse heat flux on temperature distribution are investigated. Tremendous effect of boundary condition type at the lower boundary is noted. It seems that neither insulation nor constant temperature at this boundary can completely describe the real physical phenomena. It is expected that real temperature at the lower levels is somewhat between two predicted values. The effect of temperature on the thermal properties of skin tissue is considered. It is shown that considering temperature dependent values for thermal conductivity is important in the temperature distribution estimation of skin tissue; however, the effect of temperature dependent values for specific heat capacity is negligible. It is seen that considering modified Pennes equation in processes with high heat flux during low times is significant.     

Biophysics of thermal lesions

Experiments on rats showed that thermal irradiation caused a more marked elevation of subcutaneous temperature at the area of the skin separated from the underlying tissues by a felt plate than at the skin area separated from the surrounding and underlying tissues and immediately sutured to its place or the area of the uninjured skin. The authors believe that the data obtained indicated that the blood flow played no significant role in leading the heat from the skin in the action of the radial heat on it. Of much greater significance is the capacity of the underlying tissues to lead off and to accumulate heat.     

Paradox: increased blood perfusion to the face <Emphasis Type="BoldItalic">enhances</Emphasis> protection against frostbite while it <Emphasis Type="BoldItalic">lowers</Emphasis> wind chill equivalent temperatures

A model of facial heat exchange in cold and windy environments is presented. The tissue is depicted as a hollow cylinder and the model includes heat conduction and heat transport by blood circulation from the warmer core. A steady-state solution facilitating the estimation of wind chill equivalent temperature (WCET) as a function of the effective wind velocity, air temperature and blood perfusion rate was obtained. The results quantify and demonstrate the elevation of skin temperatures caused by increased flow of warmer blood from the inner core to the face. Elevated facial temperatures, while enhancing protection against frostbite and other cold-related injuries, also increase heat loss to the colder environment. Paradoxically, such elevated facial temperatures cause WCETs, as estimated by the prevailing definition, to attain lower rather than higher values, indicating, in fact, increased risk of frostbite. The results of this study should be useful in understanding and quantifying the effects of blood perfusion in protection against cold-related injuries. They should also be considered in the re-evaluation and re-formulation of the concept of wind chill, which has been a useful cold weather indicator for decades.     

Temperature distribution in human skin and subdermal tissues

Temperature profiles have been computed in the skin and subdermal part of a human body for (i) various values of environmental temperature, rate of sweat evaporation and wind velocity, (ii) rate of blood mass flow, (iii) rate of metabolic heat generation and (iv) three different sets of thicknesses of skin layers. The mathematical equations have been considered for a one-dimensional steady-state case. The two important physical parameters, namely rate of blood mass flow and rate of metabolic heat generation, have been assigned position-dependent values. The latter is also taken as linearly dependent on the tissue temperature. Analytic solutions have been obtained for the three layers of the region. These forms of solution facilitate the study of parameter dependence.     

An assessment of skin temperature gradients in a tropical primate using infrared thermography and subcutaneous implants

Infrared thermography has become a useful tool to assess surface temperatures of animals for thermoregulatory research. However, surface temperatures are an endpoint along the body's core-shell temperature gradient. Skin and fur are the peripheral tissues most exposed to ambient thermal conditions and are known to serve as thermosensors that initiate thermoregulatory responses. Yet relatively little is known about how surface temperatures of wild mammals measured by infrared thermography relate to subcutaneous temperatures. Moreover, this relationship may differ with the degree that fur covers the body. To assess the relationship between temperatures and temperature gradients in peripheral tissues between furred and bare areas, we collected data from wild mantled howling monkeys (Alouatta palliata) in Costa Rica. We used infrared thermography to measure surface temperatures of the furred dorsum and bare facial areas of the body, recorded concurrent subcutaneous temperatures in the dorsum, and measured ambient thermal conditions via a weather station. Temperature gradients through cutaneous tissues (subcutaneous-surface temperature) and surface temperature gradients (surface-ambient temperature) were calculated. Our results indicate that there are differences in temperatures and temperature gradients in furred versus bare areas of mantled howlers. Under natural thermal conditions experienced by wild animals, the bare facial areas were warmer than temperatures in the furred dorsum, and cutaneous temperature gradients in the face were more variable than the dorsum, consistent with these bare areas acting as thermal windows. Cutaneous temperature gradients in the dorsum were more closely linked to subcutaneous temperatures, while facial temperature gradients were more heavily influenced by ambient conditions. These findings indicate that despite the insulative properties of fur, for mantled howling monkeys surface temperatures of furred areas still demonstrate a relationship with subcutaneous temperatures. Given that most mammals possess dense fur, this provides insight for using infrared imaging in thermoregulatory studies of wild animals lacking bare skin.     

In vivo thermal conductivity of the human forearm tissues

The effective thermal conductivities of the skin + subcutaneous (keff skin + fat) and muscle (keff muscle) tissues of the human forearm at thermal steady state during immersion in water at temperatures (Tw) ranging from 15 to 36 degrees C were determined. Tissue temperature (Tt) was continuously monitored by a calibrated multicouple probe during a 3-h immersion of the resting forearm. Tt was measured every 5 mm from the longitudinal axis of the forearm (determined from computed-tomography scanning) to the skin surface. Skin temperature (Tsk), heat loss (Hsk), and blood flow (Q) of the forearm, as well as rectal temperature (Tre) and arterial blood temperature at the brachial artery (Tbla), were measured during the experiments. When the keff values were calculated from the finite-element (FE) solution of the bioheat equation, keff skin + fat ranged from 0.28 +/- 0.03 to 0.73 +/- 0.14 W.degrees C-1.m-1 and keff muscle varied between 0.56 +/- 0.05 and 1.91 +/- 0.19 W.degrees C-1.m-1 from 15 to 36 degrees C. The values of keff skin + fat and keff muscle, calculated from the FE solution for Tw less than or equal to 30 degrees C, were not different from the average in vitro values obtained from the literature. The keff values of the forearm tissues were linearly related (r = 0.80, P less than 0.001) to Q for Tw greater than or equal to 30 degrees C. It was found that the muscle tissue could account for 92 +/- 1% of the total forearm insulation during immersion in water between 15 and 36 degrees C.     

Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.     

A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments

The genesis of the present research paper is to develop a revised exact analytical solution of thermal profile of 1-D Pennes’ bioheat equation (PBHE) for living tissues influenced in thermal therapeutic treatments. In order to illustrate the temperature distribution in living tissue both Fourier and non-Fourier model of 1-D PBHE has been solved by ‘Separation of variables’ technique. Till date most of the research works have been carried out with the constant initial steady temperature of tissue which is not at all relevant for the biological body due to its nonhomogeneous living cells. There should be a temperature variation in the body before the therapeutic treatment. Therefore, a coupled heat transfer in skin surface before therapeutic heating must be taken account for establishment of exact temperature propagation. This approach has not yet been considered in any research work. In this work, an initial condition for solving governing differential equation of heat conduction in biological tissues has been represented as a function of spatial coordinate. In a few research work, initial temperature distribution with PBHE has been coupled in such a way that it eliminates metabolic heat generation. The study has been devoted to establish the comparison of thermal profile between present approach and published theoretical approach for particular initial and boundary conditions inflicted in this investigation. It has been studied that maximum temperature difference of existing approach for Fourier temperature distribution is 19.6% while in case of non-Fourier, it is 52.8%. We have validated our present analysis with experimental results and it has been observed that the temperature response based on the spatial dependent variable initial condition matches more accurately than other approaches.     

Prediction of mean skin temperature in warm environments

The data collected by the authors in four experimental series have been analysed together with data from the literature, to study the relationship between mean skin temperature and climatic parameters, subject metabolic rate and clothing insulation. The subjects involved in the various studies were young male subjects, unacclimatized to heat. The range of conditions examined involved mean skin temperatures between 33 degrees C and 38 degrees C, air temperatures (Ta) between 23 degrees C and 50 degrees C, ambient water vapour pressures (Pa) between 1 and 4.8 kPa, air velocities (Va) between 0.2 and 0.9 m.s-1, metabolic rates (M) between 50 and 270 W.m-2, and Clo values between 0.1 and 0.6. In 95% of the data, mean radiant temperature was within +/- 3 degrees C of air temperature. Based on 190 data averaged over individual values, the following equation was derived by a multiple linear regression technique: Tsk = 30.0 + 0.138 Ta + 0.254 Pa-0.57 Va + 1.28.10(-3) M-0.553 Clo. This equation was used to predict mean skin temperature from 629 individual data. The difference between observed and predicted values was within +/- 0.6 degrees C in 70% of the cases and within +/- 1 degrees C in 90% of the cases. It is concluded that the proposed formula may be used to predict mean skin temperature with satisfactory accuracy in nude to lightly clad subjects exposed to warm ambient conditions with no significant radiant heat load.     

The influence of hypoxia on the thermal sensitivity of skin colouration in the bearded dragon, Pogona vitticeps

One physiological mechanism used by reptiles to remain within thermal optima is their ability to reversibly alter skin colour, imparting changes in overall reflectance, and influencing the rate of heat gain from incident radiation. The ability to lighten or darken their skin is caused by the movement of pigment within the dermal chromatophore cells. Additionally, lizards, as ectotherms, significantly lower their preferred body temperatures when experiencing stressors such as hypoxia. This decrease in preferred temperature has been proposed to be the result of a downward adjustment of the thermal set-point, the temperature around which the body temperature is typically defended. We tested the hypothesis that lightening of the skin in lizards would be modified by hypoxia in a manner consistent with the known reduction in preferred temperatures. Skin colouration values of the dorsal skin of bearded dragons were analysed at three different levels of oxygen (20.8, 9.9 and 4.9 kPa) and at temperatures spanning the preferred temperature range (30, 32, 34, 36, 38 and 40 C). Hypoxic lizards lightened their skin at lower ambient temperatures more than normoxic ones, and in an oxygen-dependent fashion. The orchestrated adjustment of skin reflectance suggests that this physiological trait is being regulated at a new and lower set-point. Evidence from this study demonstrates that skin colouration plays a role in body temperature regulation and that the reduction in temperature set-point so prevalent in hypoxia is also manifested in this physiological trait.     

Impact of Cattaneo-Christov Heat Flux in Jeffrey Fluid Flow with Homogeneous-Heterogeneous Reactions

Two-dimensional stretched flow of Jeffrey fluid in view of Cattaneo-Christov heat flux is addressed. Effects of homogeneous-heterogeneous reactions are also considered. Suitable transformations are used to form ordinary differential equations. Convergent series solutions are computed. Impact of significant parameters on the velocity, temperature, concentration and skin friction coefficient is addressed. Analysis of thermal relaxation is made. The obtained results show that ratio of relaxation to retardation times and Deborah number have inverse relation for velocity profile. Temperature distribution has decreasing behavior for Prandtl number and thermal relaxation time. Also concentration decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.     

A canine thermal model for simulating temperature responses of military working dogs

Military working dogs (MWDs) are often required to operate in dangerous or extreme environments, to include hot and humid climate conditions. These scenarios can put MWD at significant risk of heat injury. To address this concern, a two-compartment (core, skin) rational thermophysiological model was developed to predict the temperature of a MWD during rest, exercise, and recovery. The Canine Thermal Model (CTM) uses inputs of MWD mass and length to determine a basal metabolic rate and body surface area. These calculations are used along with time series inputs of environmental conditions (air temperature, relative humidity, solar radiation and wind velocity) and level of metabolic intensity (MET) to predict MWD thermoregulatory responses. Default initial values of core and skin temperatures are set at neutral values representative of an average MWD; however, these can be adjusted to match known or expected individual temperatures. The rational principles of the CTM describe the heat exchange from the metabolic energy of the core compartment to the skin compartment by passive conduction as well as the application of an active control for skin blood flow and to tongue and lingual tissues. The CTM also mathematically describes heat loss directly to the environment via respiration, including panting. Thermal insulation properties of MWD fur are also used to influence heat loss from skin and gain from the environment. This paper describes the CTM in detail, outlining the equations used to calculate avenues of heat transfer (convective, conductive, radiative and evaporative), overall heat storage, and predicted responses of the MWD. Additionally, this paper outlines examples of how the CTM can be used to predict recovery from exertional heat strain, plan work/rest cycles, and estimate work duration to avoid overheating.     

Modeling of processes of heat transfer in whole-body hyperthermia

The method of whole-body hyperthermia in which the body temperature for a short time reaches values up to 43-44 degrees C holds currently much promise. However, at body temperatures above 42 degrees C, the risks associated with the hemodynamic instability and the appearance of arrhythmia in the patient increase. A model of heat transfer has been created to increase the efficiency and safety of the immersion-convectional method of whole-body hyperthermia. This model takes into account changes in the skin blood flow and the dynamics of pulse rate depending on body temperature. The model of heat transfer adequately reflects processes of heating of the organism and can form a basis for the calculation of distribution of heat inside the organism.     

Ambient temperature effect on changes in heat exchange and skin and coat thermoisolation induced with nembutal in guinea pigs

The experiment was carried out on adult male guinea pigs not adapted to cold at temperatures of 29 degrees, 20 degrees and 12 degrees C. During 150 minutes after nembutal injection the following values were recorded: oxygen consumption, subcutaneous, cutaneous and hair-coat temperatures. Using Hatfield's disc heat loss from the body surface by radiation and convection was measured. Nembutal not only inhibited thermogenetic processes at low ambient temperature, but decreased also heat production in a thermoneutral environment. This effect increased with decreasing ambient temperature. At the same time, there was a reduction in heat loss, although in a lower degree. The final result was a fall of the rectal temperature (even by 10 degrees C in a cold environment). Following nembutal administration skin thermoinsulation decreased slightly but the thermoinsulating activity of the hair-coat increased (the pilomotor response was more pronounced than in waking animals). Thermoregulation disturbances induced by nembutal included mainly thermogenesis impairment. The effect of general anaesthesia on heat loss was without any greater importance for maintenance of thermic homeostasis of the organism.