Implementation of a multisource model for gold nanoparticle-mediated plasmonic heating with near-infrared laser by the finite element method

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The use of optically tunable gold nanoparticles (GNPs) in conjunction with near-infrared (NIR) laser has emerged as an attractive option for laser-induced thermal therapy (LITT), as it capitalizes on plasmonic heating of GNPs tuned to absorb light strongly in the NIR region. Previously, the authors developed a multisource model to predict the temperature change in a GNP-laden tissue-like medium illuminated by NIR laser and implemented it by a linear superposition (LS) method combining analytic and finite element method (FEM) solutions. While it is intuitive and straightforward, the LS approach might be somewhat cumbersome to implement for realistic LITT cases because it requires separate calculations of the temperature change due to individual GNP heat sources and the laser heat source. Therefore, the current investigation aimed to develop a simpler yet mathematically more elegant and computationally more efficient method solely based on FEM to implement the authors’ multisource model.


A multisource FEM model was developed to calculate the full spatiotemporal temperature distribution due to all heat sources (i.e., individual GNPs and the laser heat source) by solving the heat diffusion equation with multiple heat sources using FEM. This model was tested for its validity using two computational phantoms, a two-layer GNP-laden cylindrical phantom and a breast phantom with a GNP-laden microcavity. For comparison, the results for the two phantom cases were also obtained from the LS method.


For the two-layer phantom case, the FEM approach resulted in a maximum temperature increase of 16.4 °C at a depth of 1.35 cm, 2.5 mm below the interface between the two layers, while the LS method produced a maximum temperature increase of 16.7 °C at a depth of 1.3 cm, 2 mm below the interface between the two layers. A comparison of the depth versus temperature changes obtained from the two approaches showed reasonably good agreement within 6%. In the breast phantom case, the LS results show a maximum temperature increase of 16.35 °C at a depth of 2.17 cm, 0.3 mm away from the center of the cavity in the direction closer to the laser. The FEM results show the same characteristics as those obtained via the LS method with a maximum temperature increase of 16.2 °C at a depth of 2.16 cm, 0.4 mm away from the center of the cavity in the direction closer to the laser. The two methods produced good agreement within 2% for the depth versus temperature distributions.


The current multisource FEM model not only reproduced the results from the previous LS model, but also dramatically reduced computation time by 2 orders of magnitude, despite a generally more stringent requirement for computer memory. With further experimental validation, the FEM model can be used to predict the distinct plasmonic heating characteristics expected from NIR laser illumination of tissue-like media filled with GNPs, while offering the capability of handling heterogeneous spatial distribution of GNPs for realistic clinical cases.

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