The interaction between laser irradiation and biological tissue has long been a research hotspot in the medical field [1–3]. In the recent years, contact heat-evoked potentials (CHEPs) have become widely used experimental tonic pain model [4, 5]. Pain and associated abnormal sensations (e.g., labor) are usually related to current or potential tissue damage [6–7]. Laser-evoked potentials represent the activation of nociceptors (e.g., \(\text{Aδ}\), C) in the brain in response to laser-induced pain-heat stimulation, which can be used to diagnose neurological disorders. Therefore, lasers were used in various pain studies [8–10]. Lasers of different wavelengths (e.g., infrared, visible) are significant for quantitative sensory testing and time-locked evoked potential recordings [8]. When using a laser for thermal pain stimulation, it should be ensured that the skin is not damaged by the heat. Therefore, the stimulation intensity should be controlled between the nociceptive threshold and the tissue damage threshold [8].
The penetration depth of laser energy into the skin depends on the wavelength [11]. The penetration depth of the \(\text{C}{\text{O}}_{\text{2}}\) laser with a wavelength of 10.6 µm is tiny, 20 µm, because the energy is absorbed by moisture in the stratum corneum and other epidermal layers [9, 12]. Tillman et al. studied the depth of C nociceptive fibers in monkeys and found that the depth in the hairy skin averaged 201 µm. For human hairy skin, the \(\text{Aδ}\) fibers penetrate the epidermis from the dermis. There are usually fewer nociceptor nerves in hairless skin than in hairy skin [14]. Atherton et al. found that fibers within the epidermis are immune to heat-sensitive TRPV1 antibodies, suggesting that heat-sensitive fibers are present in the epidermis. But there is no evidence to support fiber extension into the stratum corneum [15]. Since about 90% of the infrared laser energy is absorbed by the shallow stratum corneum and epidermis, activation of nociceptors is mainly achieved by thermal conduction. Scholars studied laser-evoked responses, such as latency and pain intensity, in hairless and hairy skin with type I and type II fiber populations [10, 16]. The response thresholds for Type I and Type II are 53°C and 46°C, respectively. Treede et al. found that the activation threshold of the C nociceptive fibers was 41℃ [10].
Mathematical models can predict the temperature increase induced by laser stimulation at different depths of skin tissue. Xu et al. used mathematical theory to predict skin tissue temperature rise after laser heating. Simplified one-dimensional heat transfer models were applied to predict temperature [9, 12, 18]. However, these models cannot consider different thermal properties involved in various skin layers, such as the stratum corneum, important epidermis, and dermis [9, 12]. Besides, the one-dimensional model can only predict the temperature distribution below the spot, assuming that the heat is only transferred vertically, not radially. Based on the one-dimensional models, two-dimensional and three-dimensional models were proposed [19–21, 22]. Lu et al. showed that the accuracy of models increased when a 3-D model was used in short-pulse laser studies [23]. Haimi-Cohen et al. developed a theoretical model to study nociceptor activation after laser stimulation. Unfortunately, the model did not consider the different thermal properties of each skin layer, and the analysis results were not experimentally validated [24]. Frahm et al. established a two-dimensional axial biological tissue model and used it to predict the temperature distribution after laser irradiation [25]. Sun et al. established a 5-layer finite element model based on pork belly, but did not subdivide the skin layer [26]. Wang et al. Created a five-layer finite element model based on biological tissue and verified it with experiments [27]. Models that represent the skin as a two-layer (2-D) or three-layer (3-D) constructs have been shown to more accurately predict the temporal and spatial temperature distribution of skin as well as the pain stimulation effects and damage risks [27, 28].
The above studies analyzed the temperature distribution of the skin surface during laser irradiation by simulation and experiments. They contributed to heat pain research but did not systematically analyze the effect of parameters on the temperature distribution. Therefore, it is necessary to establish a reliable mathematical model to predict the three-dimensional temperature field inside the skin during laser irradiation. On this basis, the influence of crucial parameters on the temperature distribution can be accurately and quantitatively analyzed. Also, the parameters can be optimized to improve thermal pain efficacy. The rest of this paper is organized as follows. Section 2 establishes the finite element model of laser thermal pain treatment and verifies the reliability of the model through experiments; Section 3 calculates the model under standard conditions to obtain the distribution characteristics of the temperature field, and then conducts a single factor analysis of different influencing factors. Analyzed and carried out orthogonal test analysis to get the influence degree of different influencing factors on temperature distribution, and finally made some discussions; Section 4 draws some conclusions.