A two-temperature model for selective photothermolysis laser treatment of port wine stains

Abstract

Selective photothermolysis is the basic principle for laser treatment of vascular malformations such as port wine stain birthmarks (PWS). During cutaneous laser surgery, blood inside blood vessels is heated due to selective absorption of laser energy, while the surrounding normal tissue is spared. As a result, the blood and the surrounding tissue experience a local thermodynamic non-equilibrium condition. Traditionally, the PWS laser treatment process was simulated by a discrete-blood-vessel model that simplifies blood vessels into parallel cylinders buried in a multi-layer skin model. In this paper, PWS skin is treated as a porous medium made of tissue matrix and blood in the dermis. A two-temperature model is constructed following the local thermal non-equilibrium theory of porous media. Both transient and steady heat conduction problems are solved in a unit cell for the interfacial heat transfer between blood vessels and the surrounding tissue to close the present two-temperature model. The present two-temperature model is validated by good agreement with those from the discrete-blood-vessel model. The characteristics of the present two-temperature model are further illustrated through a comparison with the previously-used homogenous model, in which a local thermodynamic equilibrium assumption between the blood and the surrounding tissue is employed.

Numerical Modeling and Clinical Evaluation of Pulsed Dye Laser and Copper Vapor Laser in Skin Vascular Lesions Treatment

“…18 Relevant laser irradiation settings providing the appropriate heat transfer to dysplastic vessels for the complete obstruction could be determined with the numerical simulation of the photothermal response of skin blood vessels and extravascular components to the exposure to laser light with various wavelength and irradiation time modes. 15 So far, numerical simulation allows comparing features of heat transfer in the SHVM treatment using various laser systems and explaining the observed differences between them in terms of specific optical characteristics of main skin chromophores exposed to laser light irradiation of certain wavelengths and time periods. 19 The blood chromophores absorption of light with a 578 nm wavelength generated by CVL (354 cm -1 ) appears to be almost twice higher, if compared to the absorption of light with a 585 nm wavelength (191 cm -1 ) provided by PDL [14].…”

“…Values of optical characteristics of melanin, oxyhemoglobin and extravascular dermal components as absorption coefficient, scattering coefficient, anisotropy index for the CVL and PDL wavelength and thermal characteristics of skin components -thermal conductivity and specific heat were taken from. 14,15 Blood vessels were considered to have diameters ranging from 30 to 300 μm and located at a distance from skin surface varying from 100 to 300 μm. Vessels were presented in the form of a cylinder of the infinite length located parallel to the surface of the tissue.…”

Theoretical Study on Pressure Damage Based on Clinical Purpura during the Laser Irradiation of Port Wine Stains with Real Complex Vessels

“…A 1.5 mm × 1.5 mm × 1.0 mm computational domain of the skin with a reconstructed blood vessel buried at a depth of 0.5 mm was used. The thicknesses of the epidermis and the dermis were set respectively as H e = 60 µm and H d = 940 µm based on statistical average values [15]. As mentioned in Section 2.1, in validating the damage model, the reconstructed blood vessels in accordance with the DSC model were embedded in the skin without the epidermis.…”

“…The effects of 595 nm PDL transport in the skin with the curved PWS vessel by TMC were studied on the two layered skin model with a domain of 1.5 mm × 1.5 mm × 1.0 mm. The thicknesses of the epidermis and the dermis were set respectively as H e = 60 µm and H d = 940 µm and a reconstructed blood vessel buried in the skin at a depth of 0.5 mm based on statistical average values [15]. Figure 16 shows laser energy deposition in skin with blood vessel of model C (shown in Section 3.3) and melanin content of 3% in epidermis (f m = 3%).…”

“…Blood coagulation and vessel rupture are regarded as thermal damages and modeled by the damage integral Ω, which increases exponentially with tissue temperature [11][12][13][14]. After the temperature field is solved with the bioheat conduction equation, Ω can be obtained by calculating the integral related to temperature, and blood coagulation can be represented as high-Ω regions [15]. As a subsequent effect of blood coagulation, complete vessel constriction has also been modeled by Ω, although its reasonable damage threshold should be clarified [8].…”