Limits of localized heating by electromagnetically excited nanoparticles

Abstract

Based on an analysis of the diffusive heat flow equation, we determine limits on the localization of heating of soft materials and biological tissues by electromagnetically excited nanoparticles. For heating by rf magnetic fields or heating by typical continuous wave lasers, the local temperature rise adjacent to magnetic or metallic nanoparticles is negligible. However, heat dissipation for a large number of nanoparticles dispersed in a macroscopic region of a material or tissue produces a global temperature rise that is orders of magnitude larger than the temperature rise adjacent to a single nanoparticle. One approach for producing a significant local temperature rise on nanometer length scales is heating by high-power pulsed or modulated lasers with low duty cycle.

Electromagnetic absorption mechanisms in metal nanospheres: Bulk and surface effects in radiofrequency-terahertz heating of nanoparticles

“…However, even for the latter case, large collections of nanoparticles can generate significant heating (tens to hundreds of degrees) over macroscopic volumes. 3 Alternately, because of the relatively low penetration depth of radiation at infrared (IR) and visible frequencies, radio frequency (RF) energy has been suggested for biomedical applications because it penetrates easily in the human body, thus reaching important internal organs. A series of papers [4][5][6][7][8][9][10][11][12] has considered RF heating of gold nanoparticles, showing significant heating.…”

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

“…Major work have been done in the past to solve the DHFE equation for a cosine-MF source as can be found in [36,37,49,59]. Keblinski et al [38] found that a laser source having a constant power of 1.4·10 −8 W heating a single MNP with a radius of 65 nm can cause a temperature change of 0.06 K at the particle surface. Moreover, for a cosine-MF heat source the local temperature was found to be even lower, causing a maximum change in temperature of 0.1 m • K for a particle having a radius of 50 nm at a frequency of 2 MHZ [48].…”

“…However, Keblinski et al [38] and others [4,20] solved the DHFE equation only for a constant heat flux having the average power of a cosine-MF, without exploring the temperature temporal behavior. In addition, until now there has not been an explicit mathematical formulation that solves the DHFE equation for other periodic MFPs that can be used as radiation sources for MH treatments.…”

“…This equation was also used by Keblinski et al [38] and Govorov et al [49] for solving nanoscale heat problems.…”

“…By analytically solving the DHFE for different boundary conditions, one can easily describe the dependence of the solution on each parameter composing it, such as the radius of the MNP, the frequency of the MF, and the material properties [38]. This allows us to optimize the solution for better performances, reaching the highest temperature elevation under specific constrains, for example the radius of the MNP.…”