## 5 Skin Tissue Modeling  
### Forward Modeling  
The most common modeling of the skin tissues used in the literature involves a five-layer structure consisting of the epidermis, papillary dermis, reticular dermis, fat layer, and muscle, as shown in Figure 7. One-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) models based on the Pennes equation are encountered in the literature. An exception is the work authored by [PERSON] and [PERSON] [60], who considered a simplified three-layer skin model consisting of a skin, fat, and flesh layer with cancer tissue inside. To reveal the correlation between skin surface temperature and interior human pathophysiology, these authors solved a transient 3D bio-heat transfer problem involving a  
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Figure 7: Schematic of a five-layer skin tissue model with an embedded tumor. non-linear boundary condition at the skin surface (due to simultaneous heat transfer by convection, radiation, and evaporation) using the Monte Carlo method. Different factors affecting the skin temperature and consequently the temperature reading recordable with an IR camera were investigated: skin emissivity, skin humidity, convective heat transfer coefficient, temperature and relative humidity of ambient air, metabolic rate and blood perfusion in the tumor, and lesion size. The authors found that the obtainable thermal contrast is strongly correlated with the lesion size and the metabolic rate in the area affected by the lesion [60]. Irregular-shaped skin lesions were considered by [PERSON] and [PERSON] [61] in a 3D multilayer skin model similar to that depicted in Figure 7. These authors assessed the sensitivity of surface transient thermal responses with respect to the variations in thermophysical properties, metabolic heat generation, blood perfusion rate, and thicknesses of skin layers. Their model involves a constant-temperature boundary condition applied to the skin surface to simulate the cold stimulus, while convective heat transfer on the same surface describes the thermal recovery. A similar 3D model was used by the same authors in [62]. A 2D semi-infinite multilayer skin model involving an elliptical lesion located in the papillary dermis layer was studied by [PERSON] and [PERSON] [33] to investigate the skin cooling effect provided by different cooling methods. A bio-heat transfer model integrated with the momentum and energy conservation equations for non-Newtonian blood flow within multi-layer skin was suggested by [PERSON] et al. [63]. In particular, they considered a 3D multilayer model with counter-current blood vessels in each skin layer, as well as various cancerous lesions with different geometrical, thermal, and physical parameters. Following the dynamic infrared thermography procedure, the rewarming period of the skin was simulated by taking free convection, radiation, and evaporation into account. The evaluation of the skin thermal response highlighted that subsurface blood flow overpowers the response of early-stage melanomas. In order to theoretically evaluate lock-in thermal imaging for the early detection of melanomas, [PERSON] and [PERSON] [64] used a Pennes equation-based 2D axisymmetric multilayer skin model to simulate the steady state and transient surface temperatures. The skin lesion is modeled as a cylindrically shaped region with different thermophysical properties compared to the surrounding healthy tissue. Also, boundary conditions applied to the top surface take convective and radiative heat transfer between the skin and thermally modulated air flow into account. The authors concluded that melanomas can be successfully detected by applying the lock-in demodulation formalism to the transient skin surface temperature. This is also true when the lesion is at the early-stage of development, i.e., when its penetration depth is less than 0.1 mm. [PERSON] et al. [65] developed efficient solvers to compute the steady-state and transient solutions of a bio-heat transfer problem in skin tissue.