methods of measuring and predicting SAR for magnetic nanoparticles. ... properties effecting magnetic nanoparticle heating are included in Table 2 and their.
CHAPTER
XX SUPERPARAMAGNETIC IRON OXIDE NANOPARTICLE HEATING: A BASIC TUTORIAL
M.L. Etheridge* N. Manucherabadi* R. Franklin J.C. Bischof * Co-Authors
1. ITRODUCTIO Nanoparticles are being used in a rapidly increasing variety of biomedical applications, including detection, imaging, and treatment of disease. These particles have controllable dimensions in the nanometer range, matching the scale of biological entities and facilitating intimate interactions with cells and molecular constituents. They exhibit remarkable physical properties that can be finely tuned by adjusting the composition, size, and shape. One of the special features of magnetic nanoparticles is their ability to serve as colloidal mediators for heat generation in externally applied, alternating magnetic fields. This application has been termed magnetic fluid hyperthermia (MFH) and has attracted growing research interest for treatment of malignant tumors, due to its potential for highly specific energy delivery through a minimally invasive (or potentially noninvasive) platform. In this method, magnetic particles delivered to tissue induce localized heating when exposed to an alternating magnetic field, leading to thermal damage concentrated to the tumor [1]. Because of the well-demonstrated biocompatibility of iron-oxide nanoparticles, magnetite (Fe3O4) and maghemite (Fe2O3) are the most popular materials for in vivo investigations [2]. In any hyperthermia application, the distribution of temperature elevation due to the specific absorption rate (SAR) is an important factor in determining the therapeutic outcome. SAR for MFH can be estimated experimentally and theoretically, while the exact mechanisms by which heating is derived (eddy current, hysteresis, and relaxation processes) can vary. Experimental, in vitro SAR values previously reported for different magnetic colloids show strong sample/protocol dependence (Table 1). In many other studies, the conditions of the tests (properties of system/tissue, nanoparticles or magnetic field) are not published or are unclear. This wide variability throughout the literature demonstrates the need for standard methods of measuring and predicting SAR for magnetic nanoparticles. The high prevalence of iron oxide in experimental study should also be noted. 1
Table 1: Values of in vitro SAR, as reported for a number of magnetic colloids having different nanoparticle properties [3-10]. The nanoparticles with diameters less than 20 nm are likely heated through relaxation mechanisms, while the larger particles are likely subject to hysteresis losses. The diameter values marked with (*) report only crystallite size and cores may be composed of multilpe crystallites. Core Material
Magnetic Core Diameter (nm)
Coating
Iron Oxide
3.1
Dextran
MnZnFeO
7.6
Maghemite
3-15 10 10 8 6 100-150 100-150 6-12 6-12 10-12 8 3-10 3-10 3-10 7.5 13 46 81
Dextran Surfactant Dextran Uncoated Uncoated Uncoated Dextran Uncoated Uncoated Dextran Dextran Dextran Surfactant Starch Starch Starch Dextran Dextran Dextran Dextran
Magnetite
10
Iron Oxide
11.2* 12.6* 10.5* 11.8*
Magnetite Maghemite Magnetite Ferrite
Magnetite
Magnetite
Suspending Medium
Ha (kA/m)
f (kHz)
Water Dextran Water
0.5
200 - 1000
0.2 - 13.2
520
NA
6.84
1100
Kerosene Ether Water Water
6.5
300
Water
7.2
880
Water
6.5
400
Water
32.5
80
Surfactant
Water Collagen
14
175
Carboxyl Starch Dextran Carboxyl
Water
5.66
900
SAR Fe (W/g Fe)
Reference
0.15 - 0.8 10 - 235 Jordan et al. 1993 0.05 - 0.5 60 Chan et al. 1993 140-370 62 40 Hergt et al. 1998 29 1 mm for magnetite) [19]. For individual iron oxides nanoparticles (10-100 nm), eddy current effects can be neglected.
(ii) Hysteresis loss: Typical magnetic materials demonstrate unique domains of magnetism (areas of parallel magnetic moments), separated by narrow zones of transition termed domain walls. Domains form to minimize the overall magnetostatic energy of the material, but as dimensions approach the nanoscale, the energy reduction provided by multiple domains is overcome by the energy cost of maintaining the domain walls and it becomes energetically favorable to form a single magnetic domain. A number of methods for estimating the critical radius for single-domain behavior have been proposed [29,27], and the results can vary notably depending on the approach. Some estimated values from literature have been included in Figure 3, with typical diameters on the order of tens of nanometers. Hysteresis loss can occur in multidomain particles. Ferro- and ferrimagnetic materials, when placed in an alternating magnetic field, will produce heat due to hysteresis losses. When exposed to the external field, the magnetic moments tend to align in the direction of the applied field. This is the phenomena of magnetization. Essentially, domain walls can move in the presence of an applied magnetic field such that many single domains combine and create larger domains (domain growth). In other words, those domains whose magnetic moments are along the external field expand at the expense of the other surrounding domains. This domain wall displacement continues until the point of magnetic saturation (Ms), where the domain walls are maximally displaced. Figure 2 presents the relationship between magnetic field strength (Ha) and magnetization (M). If the relationship between the two is plotted for increasing levels of field strength, the magnetization will increase up to a point, then saturate. This condition is called magnetic saturation. If the magnetic field is now reduced linearly, the plotted relationship will follow a different part of the curve back to zero field strength at which point it will be offset from the original curve by an amount called the remnant magnetization (Mr) or remnance. If this relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop. The width of the middle section describes the amount of hysteresis, related to the coercivity of the material. The amount of heat generated is directly related to the area of the hysteresis loop [26]. Although much of the initial research has focused on superparamagnetic relaxation heating, Hergt et al. utilized experimental data for various magnetic particles ranging in size from 30 to 100 nm, to produce expressions which closely predicted losses based on the applied field parameters and particle size distributions [35]. The experimental values and theoretical predictions offered heating rates comparable to those of superparamagnetic nanoparticles and this is likely going to be an area of further development.
7
(iii) Relaxation loss: In addition to single-domain behavior, magnetic nanoparticles exhibit another type of unique behavior, superparamagnetism, in which thermal motion causes the magnetic moments to randomly flip directions, eliminating any remnant magnetization in the absence of an applied field. Thus, a normally ferro- or ferrimagnetic material will only exhibit magnetism under an applied field. This behavior arises because below a critical volume, the anisotropic energy barrier (KuVm) of the magnetic crystal is reduced to the point where it can be overcome by the energy of random thermal motion (kBT). The definition of superparamagnetism is somewhat ambiguous, in that it relies on the choice of a measurement time (τm), for which the behavior is observed and is generally taken to be 100 seconds. The approximate critical radius (rc) for superparamagnetic behavior can be determined by assuming a spherical geometry ( = 4 /3) and modifying the equation describing the probability of thermal relaxation [26]:
= exp
! "# $
% r& = '− )* ln %
.
"# $ /
(2a, 2b)
where τ0 is the attempt time (generally taken to be 10-9 seconds), Vm is the volume of magnetic material, kB is Boltzmann’s constant, and T is the absolute temperature. The approximate critical radii for superparamagnetism for several common magnetic nanoparticle materials are included in Figure 3. Although remnant magnetization and hysteresis behavior are eliminated in superparamagnetic particles, significant losses can still occur through moment relaxation mechanisms. The physical mechanisms of relaxation leading to losses in superparamagnetic iron-oxide nanoparticles are reviewed by Rosensweig [32]. These losses fall into two modes: Brownian and Néelian. The Brownian mode represents the rotational friction component in a given suspending medium. As the whole particle oscillates towards the field, the suspending medium opposes this rotational motion resulting in heat generation. The Néelian mode represents the rotation of the individual magnetic moments towards the alternating field. Upon application of an alternating magnetic field, the magnetic moment rotates away from this crystal axis towards the field to minimize its potential energy. The remaining energy is released as heat into the system. The theoretical contribution of each relaxation mechanism is described in more detail below.
2.3
Relaxation time constants:
Brownian relaxation is due to orientation fluctuations of the grain itself in the carrier fluid, assuming the magnetic moment is locked onto the crystal anisotropy axis. The time taken for a magnetic nanoparticle to align with the external magnetic field is given by the Brownian relaxation time constant (τB): τ1 =
2 !3 "# $
(3)
where η is the fluid viscosity and VH is the hydrodynamic volume of the particle (including coatings). Néelian relaxation refers to the internal thermal rotation of the particle’s magnetic moment within the crystal, which occurs when the anisotropy energy barrier is overcome. The typical 8
time between orientation change is given by the Néelian relaxation time. Néelian rotation occurs even if the particle movement is blocked. The relaxation time of such a process will follow: τ4 =
√*
τ
67
√8
, Γ=
!; "# $
4
where Γ is the ratio of anisotropy energy to thermal energy. As these two relaxation processes are occurring in parallel, the overall behavior can be described by an effective relaxation time (τ), given by: τ=
#
