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Research Papers

Magnetic Heating of Nanoparticles: The Importance of Particle Clustering to Achieve Therapeutic Temperatures

[+] Author and Article Information
John Pearce

Department of Electrical and Computer Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: jpearce@mail.utexas.edu

Andrew Giustini, P. Jack Hoopes

Thayer School of Engineering,
Dartmouth College,
Hanover, NH 03755;
Geisel School of Medicine,
Dartmouth College,
Hanover, NH 03755

Robert Stigliano

Thayer School of Engineering,
Dartmouth College,
Hanover, NH 03755

1Corresponding author.

Manuscript received November 2, 2012; final manuscript received June 10, 2013; published online July 16, 2013. Assoc. Editor: Malisa Sarntinoranont.

J. Nanotechnol. Eng. Med 4(1), 011005 (Jul 16, 2013) (14 pages) Paper No: NANO-12-1131; doi: 10.1115/1.4024904 History: Received November 02, 2012; Revised June 10, 2013

Hyperthermia therapy for cancer treatment seeks to destroy tumors through heating alone or combined with other therapies at elevated temperatures between 41.8 and 48 °C. Various forms of cell death including apoptosis and necrosis occur depending on temperature and heating time. Effective tumoricidal effects can also be produced by inducing damage to the tissue vasculature and stroma; however, surrounding normal tissue must be spared to a large extent. Magnetic nanoparticles have been under experimental investigation in recent years as a means to provide a favorable therapeutic ratio for local hyperthermia; however, practical numerical models that can be used to study the underlying mechanisms in realistic geometries have not previously appeared to our knowledge. Useful numerical modeling of these experiments is made extremely difficult by the many orders of magnitude in the geometries: from nanometers to centimeters. What has been missing is a practical numerical modeling approach that can be used to more deeply understand the experiments. We develop and present numerical models that reveal the extent and dominance of the local heat transfer boundary conditions, and provide a new approach that may simplify the numerical problem sufficiently to make ordinary computing machinery capable of generating useful predictions. The objectives of this paper are to place the discussion in a convenient interchangeable classical electromagnetic formulation, and to develop useful engineering approximations to the larger multiscale numerical modeling problem that can potentially be used in experiment evaluation; and eventually, may prove useful in treatment planning. We cast the basic heating mechanisms in the framework of classical electromagnetic field theory and provide calibrating analytical calculations and preliminary experimental results on BNF-Starch® nanoparticles in a mouse tumor model for perspective.

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References

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Figures

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Fig. 1

(a) Hysteresis loop in the B-H curve indicates losses. (b) Measured B-H curve at 1 kHz in a 3% Silicon iron alloy (with a small amount of Al and trace of C), generically referred to as 3SiFe. BR = 1.1 (T) and HC = 114 (A m−1) in this material. Plot data kindly provided by Dr. Aleta Wilder.

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Fig. 2

(a) Heating rate in BNF-Starch® (MicroMod 100-00-102), magnetic nanoparticles (Fe3O4) in solution at 150 kHz in applied magnetic fields of H = 24 (kA m−1) and 90 (kA m−1)—300 and 1130 Oe, respectively [14]. (b) SPL versus applied H-field (in peak-to-peak A m−1) for BNF-starch solution. (c) The imaginary relative permeability, μr", versus applied H-field (in peak-to-peak A m−1). (d) Figurative sketch of the structure of a BNF-starch particle. The magnetic material consists of 6.5 × 19 × 49 nm parallelepiped shaped magnetite crystals closely packed into what is effectively a single suspended solid, nominal particle. The coated particle's hydrodynamic diameter is 100 nm [16].

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Fig. 3

(a) Heating rate in “nanomag-D-spio®” super-paramagnetic nanoparticles (Fe3O4) solution at 150 kHz in applied magnetic fields of H = 24 (kA m−1) and 64 (kA m−1)—300 and 800 Oe, respectively [14]. (b) SPL versus applied H-field for BNF-starch (in peak-to-peak A m−1). (c) The relative imaginary permeability, μr" (no units). (d) Figurative sketch of the individually suspended magnetic nanoparticles [16].

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Fig. 4

Magnetic nanoparticle treatment of a murine breast cancer tumor implanted on the flank. (a) Thermal camera image of a mouse during treatment. The bare skin of the tumor (left arrow) and peritumor, adjacent noncancerous tissue (right arrow), are marked. (b) Surface temperature profile across the area of interest, including tumor and nontumor tissue. The temperature distribution along a straight line intersecting points A and B is shown. (c) Maximum recorded surface temperature of tumor and peritumor areas are plotted versus time (recorded at 1 frame/s).

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Fig. 5

Dispersed uncoated nanoparticle numerical model results for three uniformly distributed particles, particle temperature = Tp. The distance to the isothermal bottom surface is 1.5 μm. (a) 36 nm diameter at Qgen = 1016 (W m−3) within the NP, Tp = 52 °C (scale 37 °C to 52 °C) (b) 50 nm at Qgen = 1016, Tp = 72 °C (scale to 72 °C), and (c) 80 nm at Qgen = 1015, Tp = 50 °C (scale to 50 °C). Figure 5 originally appeared in Ref. [21].

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Fig. 6

In vivo transmission electron micrograph of intracellular BNF-starch-coated iron oxide magnetic nanoparticles (black arrows) adjacent to the nuclear envelopes (white arrows) of murine breast adenocarcinoma cells. This image was taken three hours after an intra-tumoral injection of nanoparticles at a concentration of 2.5 mg Fe/cm3 tumor. The scale bar in the top right is 1 μm. The larger particle cluster is approximately 2 μm in effective (hydrodynamic) radius.

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Fig. 7

3-D FEM model space simulating a 10 μm cuboidal cell with 4 μm simulated nucleus. (a) As previously, the bottom face is isothermal at 37 °C and the other faces are 0-flux. (b) Close up view of dextran coated nanoparticle placement (not to scale). Figure 7 originally appeared in Ref. [22].

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Fig. 8

3-D FEM model results at an applied volume power density Qgen = 3 × 1016 (W m−3) and t = 10 min. (a) Horizontal X-Y plane through the nanoparticles at the level corresponding to Z = 0 in Fig. 7(b), color scale 37 °C to 55 °C and the particle temperature is 55 °C. This display plane only intersects the three particles in the center of the cluster. (b) Vertical X-Z plane just behind the nanoparticles at the surface of the simulated nucleus, color scale 37 °C to 48 °C. Figure 8 originally appeared in Ref. [22].

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Fig. 9

A cluster of 45 dextran coated magnetic NPs of 50 nm diameter in two layers, viewed from above, at a uniform mNP volume power density of Qgen = 3 × 1015 (W m−3), Tmax = 44 °C. The NP cluster measures approximately 720 × 620 nm. The display plane is an X-Z plane through the top layer of nanoparticles (the layer exposed to the cytosol). The 43 °C contour extends to a radius of approximately 208 nm, i.e., it remains within the NP cluster dimensions.

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Fig. 10

A cluster of 90 dextran coated magnetic NPs of 50 nm diameter in four layers at a volume power density of Qgen = 3 × 1015 (W m−3), Tmax = 49 °C. The coated NP cluster measures approximately 750 × 650 nm × 500 nm tall. The display plane is an X-Z plane through the same layer of nanoparticles as in Fig. 8 (this layer is now an interior layer). The 43 °C contour extends to a radius of approximately 450 nm (∼200 nm to 300 nm outside of the cluster).

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Fig. 11

Eight prolate ellipsoids in 2 X-Y planes with equivalent volumes of 90 (2 ea.), 270 (4 ea.), and 360 (2 ea.) magnetic NPs of 50 nm diameter with dextran coating at a volume power density of Qgen = 1.5 × 1014 (W m−3) has Tmax = 42 °C. The model space simulates a total of 1980 NPs. The total coupled power is 19.5 mW, virtually the same as for the single ellipsoid in Fig. 11. The display planes are X-Y through the centers of the ellipsoids.

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Fig. 12

A single prolate ellipsoid with equivalent volume to the 90 magnetic NPs of 50 nm diameter with dextran coating at a volume power density of Qgen = 3 × 1015 (W m−3) has Tmax = 59.5 °C. The coated NP ellipsoid measures approximately 391 × 391 nm × 586 nm tall. The display plane is an X-Z plane through the center of the ellipsoids. The 43 °C contour extends to an X-semi-axis of approximately 356 nm (∼160 nm outside of the dextran ellipsoid).

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Fig. 13

Four cells stacked vertically, each with eight prolate ellipsoids, as in Fig. 12. The applied volume power density has been reduced to Qgen = 1 × 1014 (W m−3) resulting in Tmax = 59 °C in the uppermost cell. The total coupled power is 13 μW per cell. (a) Eight X-Y display planes through the centers of the ellipsoids. (b) A single X-Z plane through the central pair of ellipsoids. (c) Eight cell model each with duplicate NP distributions, a total of 15,840 NPs heated with Qgen = 1 × 1013 (W m−3) reaches a steady state temperature of 45 °C in less than 1 s.

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Fig. 14

(a) A single heated cell containing a single 81,000 mNP cluster with four unheated neighbor cells. NP Qgen = 3 × 1011 (W m−3) in the model. The X-Z display plane is through the center of the ellipsoidal NP cluster. Note the volume of the NP cluster relative to the nucleus and cell volumes. The steady state temperature distribution was reached in 0.1 s. (b) X-Z display plane for four similarly loaded cells (81,000 NPs each) with four unheated neighbors (not shown) at Qgen = 3 × 1010 (W m−3). Again, steady state was reached at about t = 0.15 s.

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