The shadowing effect in the laser treatment of port-wine stains modelled mathematically Available to Purchase

The unsightly skin colorations known as port-wine stains are the consequence of a dense mass of fine blood vessels near the surface of the skin. These can be removed by irradiation with a low-power laser beam strong enough to coagulate the capillaries but not so strong that surface scarring occurs, or tissue below the skin is damaged. However, a blood vessel is highly absorbent and therefore casts a shadow behind it with the result that treatment may only be partially successful. A mathematical model is presented here for this shadowing effect, which is investigated by means of the diffusion approximation to the energy transport equation. The obstacle is treated as if it were totally absorbing so that the Marshak boundary condition can be applied as a suitable approximation to the conditions at the interface between the obstacle and the surrounding tissue. The strength of the effect is estimated in the case when the capillary is regarded as a cylindrical obstruction of circular cross section. By way of comparison, a similar calculation is possible for a spherical obstacle. and the effect is found to be less in that case. In both cases there is strong shadowing immediately behind the obstacle, but this effect diminishes as distance behind the obstacle increases.