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Analytical solution to heat equation with magnetic resonance experimental verification for nanoshell enhanced thermal therapy
Author(s) -
Elliott Andrew,
Schwartz Jon,
Wang James,
Shetty Anil,
Hazle John,
Stafford Jason R.
Publication year - 2008
Publication title -
lasers in surgery and medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.888
H-Index - 112
eISSN - 1096-9101
pISSN - 0196-8092
DOI - 10.1002/lsm.20682
Subject(s) - nanoshell , surface plasmon resonance , laser , photothermal therapy , magnetic resonance imaging , thermal , resonance (particle physics) , experimental data , materials science , chemistry , optics , thermodynamics , nanotechnology , atomic physics , nanoparticle , physics , mathematics , radiology , medicine , statistics
Aims The treatment efficacy of laser‐induced thermal therapy is greatly enhanced by the presence gold coated nanoshells within the tissue being treated. The nanoshells are turned to exhibit a surface plasmon resonance at the frequency of the incident laser light, dramatically increasing the therapeutic efficiency of the laser treatment. Accurate modeling of the resulting temperature distributions is essential for treatment planning. Analytic solutions are desirable because they give greater insight into the physical meaning of the different terms that contribute to the problem. Methods The heat equation is solved by application of the Green's function method and the solution is compared to experimental temperature data for gel phantoms containing different concentrations of nanoshells. The experimental temperature data was obtained by using magnetic resonance temperature imaging methods while the gel was being heated with an 810 nm laser. Results Reasonable agreement was obtained between the results of the analytic calculation and the experimental data for the various concentrations of nanoshells and laser outputs tested. This agreement was consistent for both the spatial and temporal domain. On average the disagreement between analytical calculation and experiment was 0.93±0.84°C. Conclusion We hase shown that analytic solutions to the heat equation using the Green's function approach can be used to describe experimental temperature distributions due to the presents of nanoshells for various laser powers and nanoshell concentrations. Lesers Surg. Med. 40:660–665, 2008. © 2008 Wiley‐Liss, Inc.