Mathematical model of skin exposed to thermal radiation

Abstract

SUMIARYPrediction of dermal injury resulting from exposure to thermal energy of any given intensity and duration depends entirely upon the resultant skin temperature-time history. Means are now available for assessing heat transfer by low temperature radiation, convection and conduction to the bare skin and through thin protective coverings of known physical properties.However, thermal effects of nuclear detonations constitute a special problem because much of the radiation lies in the visible range where the optical properties of the skin and its coverings, if any, greatly influence the heating pattern. Blackening of the skin eliminates e:fects due to its optical properties but enhances the ever-present variations in the thermal "constants" of the skin. The present report describes the utilization of a mathematical equation and computer techniques for extracting these variations from empirical data obtained at relatively low levels of radiation (<0.5 Cal /cm 2 sec ), and applying extrapolations of these values in calculations of temperature-time histories at higher levels of irradiance where empirical data are lacking. This procedure is subject to validation by experimentation within a limited range of exposures.If validation is achieved in the blackened skin then the entire system may be utilized in the determination of optical properties of unblackened skin.Sii

Optimum pulse duration and radiant exposure for vascular laser therapy of dark port-wine skin: a theoretical study

“…We used the values A ϭ 1.8 ϫ 10 51 1͞s and ⌬E ϭ 327,000 J͞mol for bulk skin as reported in the literature. 43 Calculations of ⍀ were carried out for a period of time until thermal damage accumulation had ceased. We can approximate threshold temperature for tissue injury, T th , by assuming that the exposure time is equal to the laser pulse duration and that the damage end point occurs when ⍀͑x, z, t͒ ϭ 1 ͑i.e., that 63% of the tissue in that volume has been coagulated͒.…”

Thermal Performance Assessment of Heat Resistant Fabrics Based on a New Thermal Wave Model of Skin Heat Transfer

“…In a burn evaluation, it is regarded that thermal damage begins when the temperature at the basal layer, the interface between the epidermis and dermis, rises above 44 o C [8]. Generally, the Stoll and Chianta curve is used to make estimates of the time it takes for second-degree burn damage to begin to occur for a prescribed exposure.…”

“…Table 3 presents these values developed by Weaver and Stoll [8] providing the best estimation for the time to second-degree burn compared to test data. T is basal layer temperature for first-and seconddegree burns while for third-degree burns, it is temperature at the interface between the dermis and the subcutaneous layers.…”

“…In quantitatively estimating thermal performance of fabrics or garments under hazard conditions, time-to-burn damage of skin beneath a layer of fabric is applied using different skin heat transfer models [8,9,10,11]. Nearly all these models have been based on Pennes' skin model [12], which is expressed as (1) where ρ skin , C s,skin and k skin are the density, specific heat and thermal conductivity of human tissue; � � � � ρ b and C p,b are the density and the specific heat of blood and ω b is blood perfusion rate; q m and q r are volumetric heat due to metabolism and spatial heating; T b is artery temperature and T is human temperature.…”

What is on the Horizon for Hyperthermic Cancer Therapy?

“…It harmonizes well with the presently applied dose concept of Cumulative Equivalent Minutes (CEM) [156]. This conventionally functional dose is based on the thermal characterization measured by the Arrhenius function [157][158][159]. These changes have been experimentally studied by in vitro measurements of necrosis, blistering and burns to skin, or by assessing burn injuries to the skin of humans [160][161][162][163][164].…”