A model for the temperature distribution in skin noxiously stimulated by a brief pulse of CO₂ laser radiation

The application of localized noxious heat stimuli to the skin, generated by brief infrared radiation pulses emitted by a CO₂ laser, is a relatively new experimental technique for the thermal induction of pain in humans and in experimental animals. This study proposes a model for the spatial (3-dimensional) and temporal distribution of the skin temperature during and following a radiation pulse. The heat equation is written and solved, using thermal and optical constants of human skin reported in the literature. The solution is approximated, with a very small error, by a closed form expression, having a simple physical interpretation. This model is applied to analyze a typical set-up currently in use in our laboratory. The results show a significant difference between the temperature of the surface of the skin and that of the border between the epidermis and the dermis, which is the location of the most superficial receptive nerve ends. It is shown that, for the set-up examined, these nerve ends reach a temperature of 45°C, known to be the human pain threshold, 30-40 ms after pulse onset. Moreover, it is also shown that they may remain above threshold temperature for up to a few hundreds of milliseconds (considerably outlasting pulse cessation). In addition, it is shown that the area in which nerve ends reach this threshold is a circle with a very small radius (1-2.5 mm). The implications of the results on the double sensation experienced by humans, and on the exteremly powerful EEG correlates, are discussed.