Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues

Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.     

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.     

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.     

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.     

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.     

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.     

Temperature regulation of marine mammals

A mathematical model of heat loss from an aquatic animal to the surrounding water is presented. Heat is generated in metabolically active tissues and distributed by circulating blood and by conduction. The time dependent radial temperature profile of the animal is numerically solved from heat transfer equations by a computer. The model is applied to large whales, porpoises, and seals. For the whales, blood circulation to the dermal layer below appendage and body skin surfaces proved to be essential for sufficient heat dissipation. When decreasing the blood flow below a certain value (dependent on sea temperature and whale activity) the large whales would overheat. Blubber thickness was found to be of minor importance in whale thermoregulation, because the blubber coat can be bypassed by blood circulation. On the other hand, it is in general not possible for small porpoises and seals to stay warm in the coldest waters using normal mammalian resting metabolic rates, even if the peripheral circulation is shut off (or artery-vein heat exchangers used). Heat loss can be reduced if the outermost tissue layers are allowed to cool. This is achieved by minimizing convective radial heat flow via the circulation. (For large whales even minute radial blood flow raises the muscle temperatures to the core temperature level.) Seasonal acclimatization of harbour seals is explained by changes in their effective insulation thickness. Differences in whale activity induce changes in the temperature profile mainly within the first few centimeters from the skin surface. These superficial temperatures, if known, could be used to estimate whale metabolic rates. Since they drop close to the sea water temperature within minutes after whale death, the measurements should be done of live whales.     

A direct substitution, equation error technique for solving the thermographic tomography problem

A new technique for solving the combined state and parameter estimation problem in thermographic tomography is presented. The technique involves the direct substitution of known skin temperatures into the finite difference form of the bio-heat transfer equation as formulated for solving an initial value problem with a convection boundary condition at the skin surface. These equations are then used to solve the inverse bio-heat transfer problem for the unknown subcutaneous tissue temperatures and physiological parameters. For a small number of nodal points, closed form algebraic solutions are obtained. For larger sets of equations, a hybrid technique is used in which the problem is initially posed as an unconstrained optimization problem in which the model equation error is minimized using the conjugate gradient descent technique to get close to a solution. Then a generalized Newton-Raphson technique was used to solve the equations. A numerical simulation of a one-dimensional problem is investigated both with and without noise superimposed on the input (transient) skin temperature data. The results show that the technique gives very accurate results if the skin temperature data contains little noise. It is also shown that if the physical properties of the tissue and the metabolism are known, that a given set of proper transient skin temperature inputs yields a unique solution for the unknown internal temperatures and blood perfusion rates. However, the similar problem with known blood perfusion rates and unknown metabolisms does not yield a unique solution for the internal temperatures and metabolisms.     

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.     

A 3D thermal model to analyze the temperature changes of digits during cold stress and predict the danger of frostbite in human fingers

The existing computational models of frostbite injury are limited to one and two dimensional schemes. In this study, a coupled thermo-fluid model is applied to simulate a finger exposed to cold weather. The spatial variability of finger-tip temperature is compared to experimental ones to validate the model. A semi-realistic 3D model for tissue and blood vessels is used to analyze the transient heat transfer through the finger. The effect of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between tissues and large vessels are considered in energy balance equations. The current model was then tested in different temperatures and air speeds to predict the danger of frostbite in humans for different gloves. Two prevalent gloves which are commonly used in cold climate are considered for investigation. The endurance time and the fraction of necrotic tissues are two main factors suggested for obtaining the response of digit tissues to different environmental conditions.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

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.     

A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment.     

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.     

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.     

Physiological Responses Of Birds To Flight And Running

1. The energy required for sustained physical activity in flying and running birds is obtained from fatty acids mobilized from adipose stores under the influence of hormones. There is some evidence that glucagon, insulin and growth hormone may be involved in this process. 2. Energy expenditure can increase up to 14 times and 12 times resting values in flying and running birds, respectively. Energy expenditure varies only slightly over the normal range of flight speeds in individual species, but in running birds there is a linear correlation between oxygen consumption and speed. The slope of this relationship is an inverse function of body weight and indicates the energy cost of transport in ml O₂.kg^-1.m^-1. 3. Increased oxygen demands by the working muscles are met by increased ventilation and circulation. Increased oxygen delivery by the blood is achieved by rises in cardiac output and oxygen extraction. Cardiac stroke volume changes relatively little and the increased cardiac output results mainly from an increase in heart rate. Regional blood distribution during exercise may be determined not only by the demands of the locomotory muscles but also by the need to increase heat loss from the skin and respiratory tract. 4. Ventilatory movements during flight are frequently synchronized in a I:I fashion with wing movements. Increased ventilation during flight and running may be stimulated, not only by the need for increased gas exchange, but also in order to raise heat loss by respiratory evaporation. Thermal hyperventilation carries a risk of CO, washout from the lungs and consequent blood alkalosis. The risk is minimized in some species by appropriate alterations in the rate and depth of breathing, which help to confine excess ventilation to the respiratory dead space. 5. Metabolic heat produced during exercise is either lost from the respiratory linings and the skin, or stored by the body with a resultant rise in body temperature. Changes in peripheral blood perfusion and active regulation of the feathers may assist cutaneous heat loss. Respiratory evaporation usually accounts for less than 30% of the total heat loss, even at high air temperatures, and becomes progressively less efficient at higher exercise intensities. At high air temperatures and high exercise intensities, most of the metabolic heat is stored, and exercise duration is limited as the body temperature approaches the upper lethal limit.     

Thermal insulation and body temperature wearing a thermal swimsuit during water immersion

This study evaluated the effects of a thermal swimsuit on body temperatures, thermoregulatory responses and thermal insulation during 60 min water immersion at rest. Ten healthy male subjects wearing either thermal swimsuits or normal swimsuits were immersed in water (26 degrees C or 29 degrees C). Esophageal temperature, skin temperatures and oxygen consumption were measured during the experiments. Metabolic heat production was calculated from oxygen consumption. Heat loss from skin to the water was calculated from the metabolic heat production and the change in mean body temperature during water immersion. Total insulation and tissue insulation were estimated by dividing the temperature difference between the esophagus and the water or the esophagus and the skin with heat loss from the skin. Esophageal temperature with a thermal swimsuit was higher than that with a normal swimsuit at the end of immersion in both water temperature conditions (p<0.05). Oxygen consumption, metabolic heat production and heat loss from the skin were less with the thermal swimsuit than with a normal swimsuit in both water temperatures (p<0.05). Total insulation with the thermal swimsuit was higher than that with a normal swimsuit due to insulation of the suit at both water temperatures (p<0.05). Tissue insulation was similar in all four conditions, but significantly higher with the thermal swimsuit in both water temperature conditions (p<0.05), perhaps due to of the attenuation of shivering during immersion with a thermal swimsuit. A thermal swimsuit can increase total insulation and reduce heat loss from the skin. Therefore, subjects with thermal swimsuits can maintain higher body temperatures than with a normal swimsuit and reduce shivering thermo-genesis.     

Parametric studies on the three-layer microcirculatory model for surface tissue energy exchange

The new three-layer microvascular mathematical model for surface tissue heat transfer developed in, which is based on detailed vascular casts and tissue temperature measurements in the rabbit thigh, is used to investigate the thermal characteristics of surface tissue under a wide variety of physiological conditions. Studies are carried out to examine the effects of vascular configuration, arterial blood supply rate, distribution of capillary perfusion, cutaneous blood circulation and metabolic heat production on the average tissue temperature profile, the local arterial-venous blood temperature difference in the thermally significant countercurrent vessels, and surface heat flux.     

Effects of color temperature of fluorescent lamps on body temperature regulation in a moderately cold environment

A study on the effects of different color temperatures of fluorescent lamps on skin and rectal temperatures in a moderately cold environment involving (i) changes in skin temperature of 7 male subjects exposed to an ambient temperature ranging from 28 degrees C to 18 degrees C (experiment I) and (ii) changes in skin and rectal temperatures and metabolic heat production of 11 male subjects exposed to ambient temperature of 15 degrees C for 90 min (Experiment II) was conducted. In Experiment I, the reduction of mean skin temperature from the control value was significantly greater under 3000 K than under 5000 K or 7500 K lighting. In Experiment II, the reductions in mean skin temperature and rectal temperature were respectively greater and smaller under 3000 K than those under 5000 K or 7500 K lighting. However, metabolic heat production was not affected by color temperature conditions. The relationships between morphological and physiological parameters revealed that no significant relation of rectal temperature to body surface area per unit body weight was found only under 3000 K. Furthermore, while the mean skin temperature was independent on the mean skinfold thickness under 3000 K, a significant negative correlation between the rectal and mean skin temperatures was observed. Therefore, body heat loss might be suppressed effectively by increasing the vasoconstrictor tone under a color temperature of 3000 K, and the body shell was dependent only on morphological factors under 5000 K and 7500 K lighting.     

Shivering onset, metabolic response, and convective heat transfer during cold air exposure

The onset and intensity of shivering of various muscles during cold air exposure are quantified and related to increases in metabolic rate and convective heat loss. Thirteen male subjects resting in a supine position and wearing only shorts were exposed to 10 degrees C air (42% relative humidity and less than 0.4 m/s airflow) for 2 h. Measurements included surface electromyogram recordings at six muscle sites representing the trunk and limb regions of one side of the body, temperatures and heat fluxes at the same contralateral sites, and metabolic rate. The subjects were grouped according to lean (LEAN, n = 6) and average body fat (NORM, n = 7) content. While the rectal temperatures fluctuated slightly but not significantly during exposure, the skin temperature decreased greatly, more at the limb sites than at the trunk sites. Muscles of the trunk region began to shiver sooner and at a higher intensity than those of the limbs. The intensity of shivering and its increase over time of exposure were consistent with the increase in the convective heat transfer coefficient calculated from skin temperatures and heat fluxes. Both the onset of shivering and the magnitude of the increase in metabolic rate due to shivering were higher for the LEAN group than for the NORM group. A regression analysis indicates that, for a given decrease in mean skin temperature, the increase in metabolic rate due to shivering is attenuated by the square root of percent body fat. Thus the LEAN group shivered at higher intensity, resulting in higher increases in metabolic heat production and convective heat loss during cold air exposure than did the NORM group.