Modeling the color perception of port wine stains and its relation to the depth of laser coagulated blood vessels

To find the maximal depth of an ecstatic vessel in the dermis that contributes to the abnormal color of a port wine stain (PWS), "normal" and "laser treated PWS skin" are modeled, respectively, as a two-layer plane parallel geometry consisting of an epidermis and a dermis, and as a three-layer geometry consisting of an epidermis, a dermis without additional blood (the "treated" part of the stain, assumed identical to the "normal" dermis), and a layer of dermis containing 5% or 10% of blood per volume (the untreated part of the PWS). Spectral remittances were calculated for various wavelengths using the diffusion approximation to the transport equation for light propagation. These remittances were transformed into the CIE 1976 (L*a*b*)-color system. Color differences between "normal" and PWS skin as a function of the dermal depth of "injured" ecstatic blood vessels were calculated. The maximal depth where ecstatic blood vessels just contribute to the abnormal PWS color is predicted as 0.9 mm for a "normally" pigmented epidermis (60 microns thick) and a 5% or 10% blood per volume content. For a darker pigmented epidermis (60 microns thickness) and again at both 5% and 10% blood per volume content, this depth was found to be 0.8 mm