Modeling laser thermal therapy output for nanoshell heating using a natural coordinate system

Laser induced thermal therapy (LITT) using laser fibers equipped with an optically diffusive tip and surrounded with a water cooled jacket represent an efficient method for greater control of thermal therapy delivery. By combining LITT with magnetic resonance temperature imaging (MRTI) the evolution of the temperature distribution can be monitored in real time. This can be used in conjunction with gold coated spherical silica core nanoshells or gold coated superparamagnetic iron oxide particles that are tuned to exhibit a plasmon resonance at the optical frequency of the incident laser. This results in increased local absorption and heating, even at low applied laser power. Accurate modeling of the thermal distribution is an essential part of the treatment planning process; not only to predict the 3 dimensional spatial distribution but also how the thermal distribution evolves in time. If the diffusing tip of the fiber was a true line source the thermal distribution would be ellipsoidal in nature. But it has also been demonstrated that the thermal distribution can approximate an ovaloid[1, 2] with the smaller end pointing along the direction of the fiber, this break in ellipsoidal symmetry is due to the directional nature of the photons being transported along the fiber. Both ellipsoidal, ovaloid as well as other coordinates such as limacon are difficult to model in. To alleviate this situation in 2 dimensions the Pennes equation is first solved in circular polar coordinates with appropriate boundary conditions. Conformal mapping is then used to transform the solution into the desired coordinates.