Differential heating of metal nanostructures at radio frequencies

Abstract

Nanoparticles with strong absorption of incident radio frequency (RF) or microwave irradiation are desirable for remote hyperthermia treatments. While controversy has surrounded the absorption properties of spherical metallic nanoparticles, other geometries such as prolate and oblate spheroids have not received sufficient attention for application in hyperthermia therapies. Here, we use the electrostatic approximation to calculate the relative absorption ratio of metallic nanoparticles in various biological tissues. We consider a broad parameter space, sweeping across frequencies from 1 MHz to 10 GHz, while also tuning the nanoparticle dimensions from spheres to high-aspect-ratio spheroids approximating nanowires and nanodiscs. We find that while spherical metallic nanoparticles do not offer differential heating in tissue, large absorption cross sections can be obtained from long prolate spheroids, while thin oblate spheroids offer minor potential for absorption. Our results suggest that metallic nanowires should be considered for RF- and microwave-based wireless hyperthermia treatments in many tissues going forward.

Figure 1:

(a) Schematic of differential heating induced by RF/microwave application to cells targeted by metal nanostructures. (b) Orientation of RF/microwave interaction with nanomaterials. The relative absorption ratio is averaged over the 3 propagating waves shown (with equal magnitudes) to account for a collection of randomly oriented spheroids. (c) Negative real component of the dielectric function for metals considered in this manuscript. Dashed curves include scattering rate corrections for spherical nanoparticles with 10 nm radius (NP = nanoparticle). (d) Imaginary component of the dielectric function for metals considered in this manuscript. Dashed curves include scattering rate corrections for spherical nanoparticles with 10 nm radius. (e) Real component of the dielectric function for tissues considered in this manuscript. Data from reference [37]. (f) Imaginary component of the dielectric function for tissues considered in this manuscript. Data from reference [37].

Figure 2:

(a) Labelling the tunable variables in relative absorption ratio calculations for spherical nanoparticles. (b)-(i) Relative absorption ratio F_abs for metallic nanospheres in tissue as a function of radius (R) and incident electromagnetic wave frequency (f). (b) Pancreas and Au. (c) Pancreas and Ag. (d) Pancreas and Pt. (e) Pancreas and Cu. (f) Cervix and Pt. (g) Breast and Pt. (h) Brain and Pt. (i) Breast and Au. Semi-axes (i.e., radii in the case of spheres) that violate the electrostatic approximation are excluded from all plots, thus these results represent lower bounds of differential heating.

Figure 3:

(a) Labelling the tunable variables in relative absorption ratio calculations for prolate spheroids. (b)-(h) Relative absorption ratio F_abs for metallic prolate spheroids in tissue as a function of spheroid diameter (D), spheroid length (L), and incident electromagnetic wave frequency (f). (b) Pancreas and Au, D = 10 nm. (c) Pancreas and Au, D = 100 nm. (d) Pancreas and Pt, D = 10 nm. (e) Pancreas and Pt, D = 100 nm. (f) Pancreas and Cu, D = 10 nm. (g) Pancreas and Cu, D = 100 nm. (h) Pancreas and Ag, D = 10 nm. (i)-(p) Relative absorption ratio F_abs for metallic prolate spheroids in tissue at f = 1 GHz, as a function of spheroid diameter (D) and spheroid length (L). (i) Breast and Au. (j) Breast and Ag. (k) Breast and Pt. (l) Breast and Cu. (m) Brain and Au. (n) Brain and Ag. (o) Brain and Pt. (p) Brain and Cu. Semi-axes that violate the electrostatic approximation are excluded from all plots, thus these results represent lower bounds of differential heating.

Figure 4:

(a) Labelling the tunable variables in relative absorption ratio calculations for oblate spheroids. (b)-(h) Relative absorption ratio F_abs for metallic oblate spheroids in tissue as a function of spheroid diameter (D), spheroid thickness (T), and incident electromagnetic wave frequency (f). (b) Pancreas and Au, T = 10 nm. (c) Pancreas and Au, T = 100 nm. (d) Pancreas and Pt, T = 10 nm. (e) Pancreas and Pt, T = 100 nm. (f) Pancreas and Cu, T = 10 nm. (g) Pancreas and Cu, T = 100 nm. (h) Pancreas and Ag, T = 10 nm. (i)-(p) Relative absorption ratio F_abs for metallic oblate spheroids in tissue at f = 1 GHz, as a function of spheroid diameter (D) and spheroid thickness (T). (i) Breast and Au. (j) Breast and Ag. (k) Breast and Pt. (l) Breast and Cu. (m) Brain and Au. (n) Brain and Ag. (o) Brain and Pt. (p) Brain and Cu. Semi-axes that violate the electrostatic approximation are excluded from all plots, thus these results represent lower bounds of differential heating.

Figure 5:

Relative absorption ratio for spherical nanoparticles (a)-(d), prolate spheroids (e)-(h), and oblate spheroids (i)-(l) in breast and brain cancerous tissues at 1 GHz. (a), (e), and (l) Brain cancer and Au. (b), (f), and (j) Breast cancer and Au. (c), (g), and (k) Brain cancer and Pt. (d), (h), and (l) Breast cancer and Pt. Dielectric properties of cancerous tissues are taken from Ref. [45] for breast cancer and Ref. [44] for brain cancer. Dashed lines in (a)-(d) represent the boundary of the electrostatic approximation.