## 5 Skin Tissue Modeling
### Inverse Modeling  
Inverse procedures that are useful for estimating thermophysical parameters and growth features of skin lesions are gaining more and more interest due to the increasing development of IR cameras and computational capacity. Indeed, information regarding the thermal properties of a lesion leads to more reliable numerical models, and on the other hand, an accurate estimate of the lesion penetration depth provides relevant information about the tumor stage to which it is related [67], reducing the cases of unnecessary biopsies required for stage characterization. An inverse procedure aimed at estimating the size and location of a skin lesion was applied by [PERSON] and [PERSON] [68] using a dual reciprocity boundary element method coupled with a genetic algorithm. The temperature measurements at the skin surface were obtained from a steady-state 2D model involving a lesion located at different depths, in which both a second and a third-kind boundary condition at the skin surface were applied. The absence of internal nodes, the unnecessary computation of sensitivities, and the unnecessary definition of an initial guess location of the lesion are the main advantages of the suggested procedure [68]. However, the authors reported that very small or deeply located tumors cannot be detected using this procedure as they produce only a small perturbation of the skin temperature. Simplified 2D and 3D skin models based on the steady-state bioheat Pennes equation were used by [PERSON] et al. [69] to estimate the unknown metabolic heat generation or geometrical parameters of a circular or spherical tumor lesion included in the computational domain. A second-order finite difference scheme was applied to obtain the simulated surface temperature distributions used in the inverse procedure, which was based on the Pattern Search algorithm. The authors reported very good estimation accuracy for both 2D and 3D cases, even when the simulated data were affected by a noise level of 5-10%. Two stochastic algorithms (such as the genetic algorithm and simulated annealing) were applied by [PERSON] and [PERSON] [70] for simultaneously estimating the diameter, penetration depth, blood perfusion, and metabolic heat generation of subsurface skin cancers based on the surface temperature variations obtained from a 3D model of human skin. In this work, the forward model required the numerical solution of the Pennes bioheat equation for a multilayer skin (see Figure 7) whose top surface can exchange heat with the external environment by convection, radiation, and evaporation. Also, the cooling phase was simulated by applying a first-kind boundary condition (imposed temperature) to the top surface. The simulated annealing algorithm was found to be superior with respect to the genetic algorithm. In fact, the computing time is shorter, and the retrieved parameters have a higher accuracy when using the former algorithm. The authors concluded that their algorithm, along with a thermal camera, may provide a useful diagnostic tool for the characterization of subsurface skin lesions. [PERSON] et al. [71] estimated the perfusion coefficient, thermal conductivity, and thermal heat capacity of skin tissue using inverse thermal modeling based on the Laplace transform method and the related Nyquist's plots. The time domain thermal response was predicted by a 1D three-layer skin model using the Pennes equation, while the temperature measurements were obtained from a person's forearm by applying dynamic IR thermography. The authors reported a measurement uncertainty of less than 30% and that they were going to apply this approach for screening malignant and benign skin lesions. Later, in 2018, the same authors applied the same procedure to classify psoriatic lesions and healthy skin regions [72]. However, a more complete thermal model involving metabolic heat generation was considered by the authors. [PERSON] et al.