Accepted Manuscript Physics responsible for heating efficiency and self-controlled temperature rise of magnetic nanoparticles in magnetic hyperthermia therapy Zhila Shaterabadi, Gholamreza Nabiyouni, Meysam Soleymani PII:
S0079-6107(17)30149-9
DOI:
10.1016/j.pbiomolbio.2017.10.001
Reference:
JPBM 1288
To appear in:
Progress in Biophysics and Molecular Biology
Received Date: 27 June 2017 Revised Date:
28 September 2017
Accepted Date: 5 October 2017
Please cite this article as: Shaterabadi, Z., Nabiyouni, G., Soleymani, M., Physics responsible for heating efficiency and self-controlled temperature rise of magnetic nanoparticles in magnetic hyperthermia therapy, Progress in Biophysics and Molecular Biology (2017), doi: 10.1016/ j.pbiomolbio.2017.10.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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ACCEPTED MANUSCRIPT
Physics responsible for heating efficiency and self-controlled temperature rise of magnetic nanoparticles in magnetic
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hyperthermia therapy Zhila Shaterabadi1, Gholamreza Nabiyouni1∗, Meysam Soleymani2
SC
1. Department of Physics, Faculty of Science, Arak University, Arak, 38156-88349, Iran 2. Department of Chemical Engineering, Faculty of Engineering, Arak University, Arak, 38156-88349, Iran
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Abstract
Magnetic nanoparticles as heat generation nanosources in hyperthermia treatment are still faced with many drawbacks for achieving sufficient clinical potential. In this context, increase in heating ability of magnetic nanoparticles in a safe alternating magnetic field and also approach to
TE D
a precise control on temperature rise are two challenging subjects so that a significant part of researchers’ efforts has been devoted to them. Since a deep understanding of Physics concepts of heat generation by magnetic nanoparticles is essential to develop hyperthermia as a cancer
EP
treatment with non-adverse side effects, this review focuses on different mechanisms responsible
AC C
for heat dissipation in a radio frequency magnetic field. Moreover, particular attention is given to ferrite-based nanoparticles because of their suitability in radio frequency magnetic fields. Also, the key role of Curie temperature in suppressing undesired temperature rise is highlighted.
Keywords: Magnetic hyperthermia therapy (MHT); Heat generation mechanisms; Specific loss power (SLP); Ferrite nanoparticles; Superparamagnetism; Curie temperature ∗
Corresponding author. E-mail address: [email protected]
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Contents
1. Introduction
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2. Heat generation mechanisms 2.1. Eddy current loss 2.2. Hysteresis loss
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2.3. Relaxation loss 2.3.1. Neel relaxation
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2.3.2. Brown relaxation 2.3.3. Predominant mechanism 3. Specific loss power (SLP) 3.1. Definition and optimization 3.2. Calorimetric measurements
optimization
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3.3. The most common candidates with adjustable magnetic properties for SLP
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4. Role of Curie temperature in self-controlled temperature rise 5. Crucial challenges in transition from lab experiments to in-vivo and clinical trials
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6. Conclusion References
2
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1. Introduction
In the recent years, hyperthermia has been introduced as an alternative method for cancer
RI PT
treatment with reduced side effects. This therapeutic procedure is based on temperature rise in cancerous cells above the physiological level. On the other words, the elevation of temperature to the range of 42-45 ℃ induces cell damage in tumors without any harming to healthy tissues [1,
SC
2]. In magnetic hyperthermia therapy (MHT), the required heat for temperature enhancement is generated by magnetic nanoparticles (MNPs) well dispersed in a physiological solution, by
M AN U
exposing to a radio frequency magnetic field [3].
The manner at which magnetic energy is converted by MNPs to thermal energy is determined by magnetic behavior of NPs (i.e. ferro/ferri magnetic or superparamagnetic states), whereas, heating efficiency is mainly tailored by magnetic parameters (saturation magnetization and
TE D
magnetic anisotropy constant), MNPs’ size, and magnetic field characteristics [4-6]. Up to now, many kinds of magnetic structures have been introduced in the literature for MHT. These structures include spinel ferrites ( ; M=Fe [7-9], Co [10-12], Mg [13], Mn [14], Fe/Mn
EP
[15], Co/Ti [16], Mn/Mg [17], Zn/Fe [18], Zn/Ca [19], and Mn/Zn, Co/Zn, Ni/Zn [20]), manganese-based perovskite structures [21-25], as well as some alloys (such as FeCo [26], CuNi
AC C
[27]). Among them, spinel ferrites are attracting considerable interest because of their unique properties such as excellent chemical stability, high electrical and thermal resistance, and also negligible eddy current loss at high frequencies [28]. Since an ideal mechanism for hyperthermia should be non-invasive, specific to the tumor tissue, and enabling precise targeting and localization in depth of tumor, the efforts of researchers have been continued to approach this ideal situation [29-31]. From a safety point of view, hyperthermia demands MNPs with high heating efficiency to achieve the desirable temperature 3
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rise in a very short time with as low as possible concentration of particles [15, 20, 32]. The progress in this context needs a deep magnetic insight into what happens when MNPs are placed in an alternating magnetic field. To this end, this review is focusing on a comprehensive survey
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of possible mechanisms of heat generation by MNPs. We also discuss about a suitable solution to avoid overheating and damaging to healthy tissues using the Curie temperature of MNPs. We especially emphasis on some privileges of superparamagnetic ferrite NPs for hyperthermia
SC
therapy.
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2. Heat generation mechanisms
Application of an alternating magnetic field on the magnetic materials causes the dissipation of magnetic energy in the form of thermal energy. Energy conversion is accomplished by
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independent mechanisms of eddy current, hysteresis and relaxation. Relative portion of each mechanism is mainly determined by size, magnetic anisotropy and the fluid viscosity [31].
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2.1. Eddy current loss
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When a material is exposed to an alternating magnetic field, a voltage will be induced in it, which produces circular currents called Eddy currents. These currents react back on the source of the magnetic field and consequently by creating a magnetic field opposite to the original source, waste the magnetic energy as heat. The Eddy current loss is given by the Eq. 1 [33]. = / (1)
4
ACCEPTED MANUSCRIPT Where K is a constant factor depending on the sample geometry, is the maximum induction,
is the frequency, is the smallest dimension transverse to flux, and is resistivity.
In bulk materials, this type of energy loss causes to flatten the hysteresis loop and therefore
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broaden the AC loop compared with DC loop [33]. However, Eddy current losses in the fine NPs can be connived due to their small sizes (d), except in the case of high-frequency magnetic fields [31, 34].
SC
Although such losses may not have a significant portion in heat generation by MNPs in hyperthermia, they can cause unwanted temperature rise in healthy tissues in high frequencies,
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depending on the electrical conductivity of the tissue [35]. The electrical properties of body tissues are influenced by their electrolyte content i.e. ionic salts such as sodium and chlorine [36]. In a simplified modeling of human cross-sectional anatomy, the effects of inhomogeneity in tissue conductivity on the heat produced by eddy currents investigated at field frequency of
TE D
13.56 MHz. The results showed that the maximum heating occurs at the posterior superficial areas as well as in the anterior portion of the lungs, chest wall, and low pelvis [37]. However, to the best of our knowledge, no precise information is available relating to side effects of eddy
EP
currents in the body. The only reported results are limited to disturb the patient comfort and
AC C
cause pain and damage (blistering) in skin [38, 39].
2. 2. Hysteresis loss
Large ferri- or ferro MNPs are multi-domain magnetic materials. When they are exposed to an applied magnetic field, some magnetic domains containing moments parallel to the magnetic field will grow, whereas the others shrink, so long as all of moments align themselves in the same direction as the applied magnetic field. In such a case, saturation magnetization ( ) is 5
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achieved. The required applied field for reaching saturation magnetization is referred to saturation field ( ). Since the magnetization is accompanied by irreversible displacement of domain walls, magnetizing curve when the field amplitude increases is different with the case
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that field decreases. In fact, by removing the magnetic field, magnetization does not completely vanish so that magnetization still remains at zero applied field, called remanence ( ). The remanence is the origin of hysteresis behavior in magnetic materials. A typical hysteresis loop is
SC
illustrated in Fig. 1. In order to reduce the magnetization to zero again, the magnetic field (of opposite sign) is required, called coercive field or simply coercivity ( ).
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By decreasing in particle size, the required energy for formation of domain wall becomes higher than the magnetostatic energy loss due to multi-domain creation. Therefore, in order to minimize total energy, MNPs prefer to be single domain when their sizes are less than a critical value known as single domain limit. The hysteresis behavior remains significantly in single domain
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MNPs even though the mechanism leading to hysteresis is completely different with which for multi-domain particles [40].
The MNPs with hysteresis behavior produce heat through hysteresis loss [6]. The volumetric
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power dissipation is proportional to the field frequency and loop area as Eq. 2. = ∮ (2)
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where and are vacuum magnetic permeability and applied frequency respectively [41]. For low field strengths (H), i.e. for so-called Rayleigh regions, the dependence of hysteresis loss on H is of the third order [40].
Among the main parameters determining loop area ( , , and ), the later one is strongly size dependent, so that goes to a maximum value in the single domain size limit [42]. This situation is illustrated in Fig. 2 [40]. Such a maximum occurs because of the change in
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mechanism of magnetization reversal from domain wall shift in multi-domain MNPs to coherent rotation of whole moments in single domain MNPs. In fact, the latter mechanism is harder than the former [43]. However, there are the incoherent magnetization reversal modes for single
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domain MNPs such as curling or fanning which originate of specific shapes of NPs. These modes, which are not included in the Stoner-Wohlfarth model, consider the shapes of peanut or prolate spheroid for NPs respectively [40].
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With reducing of size in single domain MNPs, hysteresis loop gradually shrinks until coercive field reaches to zero in the region of superparamagnetic size. Superparamagnetism is a specific
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magnetic behavior in which the MNPs behave as a paramagnetic material with huge magnetic susceptibility (compared with paramagnetic susceptibility which is in order of 10-5) [44]. Based on the Stoner-Wohlfarh model, in the single domain MNPs, the coupling of moments (due to exchange interactions) leads to a manner that all moments behave collectively and form a giant moment called superspin [20, 45]. When the MNPs’ size drops below the so-called
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superparamagnetic limit, the thermal energy ( ) would be high enough to overcome the magnetic anisotropy energy ( ). In such situation, the superspin can easily move between two easy axes when the magnetic field is switched off [46]. The related energy diagram is
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schematically illustrated in Fig. 3. In this scheme, energy profile ( (! )) displays two minima
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according to Eq. 3 in which K is the magnetic anisotropy constant, V is the particle volume, and ! is the angle between superspin and the easy axis. Moreover, the term shows the energy barrier separating the magnetization easy axes [35, 47]. (!) = "#$% !
7
(3)
ACCEPTED MANUSCRIPT By applying an external magnetic field at the angle & to the easy axis, the angular dependency of energy is changed to the Eq. 4 [47]. Therefore, by decreasing energy barrier, superspin can easily magnetized in the field direction.
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(! ) = "#$% ! − "()#(& − ! ) (4)
To be more accurate, there is a characteristic timescale defined as the time required for returning the superspin back to equilibrium after it experiences a perturbation. This time constant is known
SC
as Neel relaxation time (+, ) and defined as Eq. 5 in which + is attempt frequency of 10./ s, K
is anisotropy constant, V is particle volume, is Boltzmann constant, and T is temperature
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[48]. In order to appearance of superparamagnetic behavior, +, must be shorter than the
measurement time of M-H curve (+ ). In fact, in such a case, relaxation of superspin within oscillating time of magnetic field causes to average value of zero for magnetization. τ, = +
014 02 3 (5)
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For low energy barriers (∆ / ≪ 1), relaxation time is fast enough, so that, in addition to magnetic relaxation, thermal fluctuation of superspin can also take place. In the high energy barriers (∆ / ≫ 1), as long as the condition of +, ≤ +; is kept, MNPs remains in the
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superparamagnetic regime [35]. However, for relaxation times longer than measurement time,
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Neel relaxation of superspin has a delay with respect to oscillation of magnetic field so that superspin can stay stable in the induced direction by magnetic field [49]. This delay in relaxation is the origin of hysteresis behavior in the single domain NPs with sizes larger than superparamagnetic limit. In this conditions, the Neel relaxation is only referred to superspin thermal fluctuations [31, 35]. As a result, the critical size for superparamagnetic behavior really depends on the magnetic field oscillation time. For radio frequency hyperthermia, with typical frequency of 50-700 kHz, 8
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measurement time should be much shorter than which for conventional methods for measuring M-H curve such as SQUID and VSM analyses. Hence, superparamagnetism in MNPs used in MHT is occurred in smaller sizes [49]. However, in the superparamagnetic regime, remanence
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magnetization vanishes, when magnetic field is removed. Having such property makes superparamagnetic NPs as a good candidates for in vivo applications because the lack of remanence in these materials prevents the risk of embolism in blood vessels [35, 50-52].
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In addition to exhibit superparamagnetic behavior, saturation magnetization gradually decreases by size shrinking into ultra-fine NPs [53-56]. The origin of anomalous reduction in
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magnetization is surface spin disorder which was discussed in detail in our recent work [57].
2.3. Relaxation loss
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In single domain NPs, heat is generated as a result of superspin alignment in the applied magnetic field direction. In fact, the magnetic energy is converted to thermal energy while magnetic field overcomes to an energy barrier that resists against rearrangement of magnetic
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moments. This energy barrier is either the magnetic anisotropy energy of MNPs or viscosity of the fluid, which the particles are dispersed in it. Thus either Neel or Brown relaxation
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mechanism is responsible for heat production in MNPs [58].
2.3.1. Neel relaxation
In the Neel relaxation mechanism, while the physical position of MNP is kept fixed, superspin rotates and orients to the direction parallel to the applied field (Fig. 4 (a)). It this case, the
9
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magnetic energy is dissipated by magnetic anisotropy energy which hinders the reorientation of superspin [31, 59]. The Neel relaxation time was first described by Neel using Eq. 5, then
τ, =
τ 01 => 402 3 (6) 2 "
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modified by Brown as Eq. 6 [60].
Where + is attempt frequency of 10./ s, K is the anisotropy constant, V is the MNP volume,
SC
is the Boltzmann energy.
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2.3.2. Brown relaxation
When a MNP rotates in the fluid by itself, in order to align its superspin in the direction of applied field, undergoes the Brown relaxation (Fig. 4 (b)), while the superspin remains fixed relative to the crystal orientation. In this case, thermal energy is produced by friction arising
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from shear stress in the fluid [26, 31]. Brown relaxation time is given by the Eq. 7 [59]. + =
3A"B (7)
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Where, A is viscosity of the surrounding medium, "B is the particle hydrodynamic volume
(including magnetic core, coating and hydration layers), is the Boltzmann constant and T is
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the temperature.
2.3.3. Predominant mechanism
Both Neel and Brawn mechanisms simultaneously occur for particles, so that the effective relaxation time is given by Eq. 8 [32].
10
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1 1 1 = + (8) + +, +
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However, the effective relaxation time is predominated by the term that has shorter relaxation time. Theoretically, there is a critical size, (strongly dependent on the particle magnetic anisotropy), in which both relaxation times equally contribute in heat generation [41]. In fact, for
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larger particles and fluids with lower viscosity, Brown mechanism is faster mechanism, whereas for smaller particles and viscous fluids, the Neel mechanism is responsible for heat production
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[31, 41]. Figure 5 shows size dependency of relaxation time for magnetite NPs in an aqueous medium with constant viscosity. As can be seen, effective relaxation time (+) for particles with size larger than meeting point of +, and + is due to Brownian mechanism, whereas, that is devoted to Neel mechanism for smaller particles [31].
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3. Specific loss power (SLP)
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3.1. Definition and optimization
In magnetic hyperthermia therapy, in order to keep injected MNP dose and treatment duration as
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low as possible, the heating efficiency must be as high as possible [6]. Specific loss power (SLP), also referred to as specific absorption rate (SAR), is used as a figure of merit to evaluate heating performance of MNPs. This parameter is defined by heat dissipated per unit time per NPs mass and expressed by Eq. 9. FG =
(9) ∅
11
ACCEPTED MANUSCRIPT Where, P, , and ∅ are volumetric power dissipation, the mass per unit volume of MNPs, and the volume fraction of MNPs in the suspension, respectively [61]. For MNPs with hysteresis behavior, P is given by Eq. 2. However, linear response theory (LRT), = J, is suitable for = > J KK (10)
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calculation of power dissipation in fine MNPs; so that, Eq. 2 is replaced by Eq. 10 [3, 34, 61]: Where, = 4> × 10.M and J KK is the imaginary part of the magnetic susceptibility: Where, J is static susceptibility:
N+ (11) 1 + (N+)
P
W
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J = JO (coth V − )
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J KK = J
Q
Q
(12)
Where, V is Langevin parameter and JO is initial susceptibility: V=
XY ;Z B1 02 3
(13)
given by Eq. 14 [62].
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When magnetic energy barrier is negligible, the case which occurs for the fine MNPs, J is XY ;Z[ 1 P02 3
(14)
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J =
Therefore, by conjugation of Eq. 10, Eq. 11, and Eq. 14, P is given as Eq. 15.
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1 \ ] "/3 + ^ (N+) = (15) 2 1 + (N+)
This equation has a maximum value when the particle relaxation time is matched with the field frequency i.e. N+ = 1. Deviations from this maximum condition (either N+ > 1 or N+ < 1) leads to reduction of heating ability [3, 31]. Moreover, at the low frequencies (well below the optimal frequency i.e. N+ ≪ 1), loss power increases with the square of field frequency while it is field frequency independent for N+ ≫ 1 [31, 63]. 12
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However, for each material (with specific K), the optimum size satisfying the maximum condition strongly depends on the field frequency and medium viscosity [63]. It means that, at a given field frequency and fluid viscosity, position of maximum value of P strongly depends on
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the effective magnetic anisotropy and is determined by MNPs’ structure. Figure 6 shows size dependency of loss power for several MNPs. As can be seen, the maximum value for heating efficiency occurs in different sizes for various MNPs. Moreover, the maximum value depends on
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magnetic compound [3].
When maximum condition (Eq. 15) is satisfied by Neel relaxation i.e. N+, = 1, the optimal
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MNP size is fallen within the transition point of ferro- or ferri magnetic to superparamagnetic region [64, 65]. In such a case, heat generation by the smaller MNPs is weak because of decrease in energy barrier that stands against magnetic field. In fact, production of noticeable heat through the Neel mechanism, requires that the magnetic anisotropy energy significantly be larger than the
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thermal energy [63]. Nevertheless, for magnetic anisotropy energies much bigger than thermal energy, heat generation by the Neel relaxation is suppressed. In fact, for Neel relaxation times longer than time reversal of magnetic field, the magnetic relaxation time is too slow to permit
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MNPs follows the fast oscillations of alternating magnetic field [35]. In this condition, stable state of ferri/ferro magnetic arises from the delay in the Neel relaxation. This delay causes
AC C
hysteresis loss in energy [65]. However, in high magnetic anisotropy barriers for which superspin is strongly coupled to particle, Brown relaxation is the only term in the effective relaxation time (+) [3, 63]. In fact, in single domain MNPs with sizes of larger than superparamagnetic limit, superposition of Brown relaxation loss with hysteresis loss occurs. On the other words, the square law for dependency of loss power on the field strength for the
13
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superparamagnetic regime is changed to the third-order (known as Rayleigh law) for the sizes above the superparamagnetic limit [5, 65]. For optimizing heating efficiency by the Neel mechanism, it needs to simultaneous control of
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particle size, anisotropy constant as well as field frequency. Herein, the field frequency and particle size are determined by experimental conditions. Although magnetocrystalline anisotropy is largely an intrinsic parameter of material, shape anisotropy is strongly affected by synthesize
SC
parameters [20]. Therefore, manipulation of total anisotropy constant (K), through modification of shape anisotropy needs to have a precise control on the shape of all individual particles which
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is really difficult, and in practice, even impossible. Hence, it seems, adjusting K to a desirable value by changing the magnetocrystalline anisotropy is easier. Recently, core-shell structures as a combination of hard and soft magnetic materials have attracted the most attention because the magnetocrystalline anisotropy in these structures can be satisfactorily moderated compared with
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utterly hard or soft magnetic materials. In such core-shell structures, exchange coupling between hard and soft materials results in utilizing of desirable properties of the hard (high magnetocrystalline anisotropy and coercivity) and soft (low magnetocrystalline anisotropy and large magnetization) magnetic materials [66, 67]. Figure 7 shows a schematic of core shell
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structure of () @ % NPs.
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It is worth to mention that the validity of Eq. 15 and consequently correctness of the SLP maximum condition (N+ = 1) in superparamagnetic materials are confirmed as long as the relation between magnetization (M) and field amplitude (H) remains linear (when
S0079-6107(17)30149-9
DOI:
10.1016/j.pbiomolbio.2017.10.001
Reference:
JPBM 1288
To appear in:
Progress in Biophysics and Molecular Biology
Received Date: 27 June 2017 Revised Date:
28 September 2017
Accepted Date: 5 October 2017
Please cite this article as: Shaterabadi, Z., Nabiyouni, G., Soleymani, M., Physics responsible for heating efficiency and self-controlled temperature rise of magnetic nanoparticles in magnetic hyperthermia therapy, Progress in Biophysics and Molecular Biology (2017), doi: 10.1016/ j.pbiomolbio.2017.10.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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M AN U
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ACCEPTED MANUSCRIPT
Physics responsible for heating efficiency and self-controlled temperature rise of magnetic nanoparticles in magnetic
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hyperthermia therapy Zhila Shaterabadi1, Gholamreza Nabiyouni1∗, Meysam Soleymani2
SC
1. Department of Physics, Faculty of Science, Arak University, Arak, 38156-88349, Iran 2. Department of Chemical Engineering, Faculty of Engineering, Arak University, Arak, 38156-88349, Iran
M AN U
Abstract
Magnetic nanoparticles as heat generation nanosources in hyperthermia treatment are still faced with many drawbacks for achieving sufficient clinical potential. In this context, increase in heating ability of magnetic nanoparticles in a safe alternating magnetic field and also approach to
TE D
a precise control on temperature rise are two challenging subjects so that a significant part of researchers’ efforts has been devoted to them. Since a deep understanding of Physics concepts of heat generation by magnetic nanoparticles is essential to develop hyperthermia as a cancer
EP
treatment with non-adverse side effects, this review focuses on different mechanisms responsible
AC C
for heat dissipation in a radio frequency magnetic field. Moreover, particular attention is given to ferrite-based nanoparticles because of their suitability in radio frequency magnetic fields. Also, the key role of Curie temperature in suppressing undesired temperature rise is highlighted.
Keywords: Magnetic hyperthermia therapy (MHT); Heat generation mechanisms; Specific loss power (SLP); Ferrite nanoparticles; Superparamagnetism; Curie temperature ∗
Corresponding author. E-mail address: [email protected]
1
ACCEPTED MANUSCRIPT
Contents
1. Introduction
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2. Heat generation mechanisms 2.1. Eddy current loss 2.2. Hysteresis loss
SC
2.3. Relaxation loss 2.3.1. Neel relaxation
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2.3.2. Brown relaxation 2.3.3. Predominant mechanism 3. Specific loss power (SLP) 3.1. Definition and optimization 3.2. Calorimetric measurements
optimization
TE D
3.3. The most common candidates with adjustable magnetic properties for SLP
EP
4. Role of Curie temperature in self-controlled temperature rise 5. Crucial challenges in transition from lab experiments to in-vivo and clinical trials
AC C
6. Conclusion References
2
ACCEPTED MANUSCRIPT
1. Introduction
In the recent years, hyperthermia has been introduced as an alternative method for cancer
RI PT
treatment with reduced side effects. This therapeutic procedure is based on temperature rise in cancerous cells above the physiological level. On the other words, the elevation of temperature to the range of 42-45 ℃ induces cell damage in tumors without any harming to healthy tissues [1,
SC
2]. In magnetic hyperthermia therapy (MHT), the required heat for temperature enhancement is generated by magnetic nanoparticles (MNPs) well dispersed in a physiological solution, by
M AN U
exposing to a radio frequency magnetic field [3].
The manner at which magnetic energy is converted by MNPs to thermal energy is determined by magnetic behavior of NPs (i.e. ferro/ferri magnetic or superparamagnetic states), whereas, heating efficiency is mainly tailored by magnetic parameters (saturation magnetization and
TE D
magnetic anisotropy constant), MNPs’ size, and magnetic field characteristics [4-6]. Up to now, many kinds of magnetic structures have been introduced in the literature for MHT. These structures include spinel ferrites ( ; M=Fe [7-9], Co [10-12], Mg [13], Mn [14], Fe/Mn
EP
[15], Co/Ti [16], Mn/Mg [17], Zn/Fe [18], Zn/Ca [19], and Mn/Zn, Co/Zn, Ni/Zn [20]), manganese-based perovskite structures [21-25], as well as some alloys (such as FeCo [26], CuNi
AC C
[27]). Among them, spinel ferrites are attracting considerable interest because of their unique properties such as excellent chemical stability, high electrical and thermal resistance, and also negligible eddy current loss at high frequencies [28]. Since an ideal mechanism for hyperthermia should be non-invasive, specific to the tumor tissue, and enabling precise targeting and localization in depth of tumor, the efforts of researchers have been continued to approach this ideal situation [29-31]. From a safety point of view, hyperthermia demands MNPs with high heating efficiency to achieve the desirable temperature 3
ACCEPTED MANUSCRIPT
rise in a very short time with as low as possible concentration of particles [15, 20, 32]. The progress in this context needs a deep magnetic insight into what happens when MNPs are placed in an alternating magnetic field. To this end, this review is focusing on a comprehensive survey
RI PT
of possible mechanisms of heat generation by MNPs. We also discuss about a suitable solution to avoid overheating and damaging to healthy tissues using the Curie temperature of MNPs. We especially emphasis on some privileges of superparamagnetic ferrite NPs for hyperthermia
SC
therapy.
M AN U
2. Heat generation mechanisms
Application of an alternating magnetic field on the magnetic materials causes the dissipation of magnetic energy in the form of thermal energy. Energy conversion is accomplished by
TE D
independent mechanisms of eddy current, hysteresis and relaxation. Relative portion of each mechanism is mainly determined by size, magnetic anisotropy and the fluid viscosity [31].
EP
2.1. Eddy current loss
AC C
When a material is exposed to an alternating magnetic field, a voltage will be induced in it, which produces circular currents called Eddy currents. These currents react back on the source of the magnetic field and consequently by creating a magnetic field opposite to the original source, waste the magnetic energy as heat. The Eddy current loss is given by the Eq. 1 [33]. = / (1)
4
ACCEPTED MANUSCRIPT Where K is a constant factor depending on the sample geometry, is the maximum induction,
is the frequency, is the smallest dimension transverse to flux, and is resistivity.
In bulk materials, this type of energy loss causes to flatten the hysteresis loop and therefore
RI PT
broaden the AC loop compared with DC loop [33]. However, Eddy current losses in the fine NPs can be connived due to their small sizes (d), except in the case of high-frequency magnetic fields [31, 34].
SC
Although such losses may not have a significant portion in heat generation by MNPs in hyperthermia, they can cause unwanted temperature rise in healthy tissues in high frequencies,
M AN U
depending on the electrical conductivity of the tissue [35]. The electrical properties of body tissues are influenced by their electrolyte content i.e. ionic salts such as sodium and chlorine [36]. In a simplified modeling of human cross-sectional anatomy, the effects of inhomogeneity in tissue conductivity on the heat produced by eddy currents investigated at field frequency of
TE D
13.56 MHz. The results showed that the maximum heating occurs at the posterior superficial areas as well as in the anterior portion of the lungs, chest wall, and low pelvis [37]. However, to the best of our knowledge, no precise information is available relating to side effects of eddy
EP
currents in the body. The only reported results are limited to disturb the patient comfort and
AC C
cause pain and damage (blistering) in skin [38, 39].
2. 2. Hysteresis loss
Large ferri- or ferro MNPs are multi-domain magnetic materials. When they are exposed to an applied magnetic field, some magnetic domains containing moments parallel to the magnetic field will grow, whereas the others shrink, so long as all of moments align themselves in the same direction as the applied magnetic field. In such a case, saturation magnetization ( ) is 5
ACCEPTED MANUSCRIPT
achieved. The required applied field for reaching saturation magnetization is referred to saturation field ( ). Since the magnetization is accompanied by irreversible displacement of domain walls, magnetizing curve when the field amplitude increases is different with the case
RI PT
that field decreases. In fact, by removing the magnetic field, magnetization does not completely vanish so that magnetization still remains at zero applied field, called remanence ( ). The remanence is the origin of hysteresis behavior in magnetic materials. A typical hysteresis loop is
SC
illustrated in Fig. 1. In order to reduce the magnetization to zero again, the magnetic field (of opposite sign) is required, called coercive field or simply coercivity ( ).
M AN U
By decreasing in particle size, the required energy for formation of domain wall becomes higher than the magnetostatic energy loss due to multi-domain creation. Therefore, in order to minimize total energy, MNPs prefer to be single domain when their sizes are less than a critical value known as single domain limit. The hysteresis behavior remains significantly in single domain
TE D
MNPs even though the mechanism leading to hysteresis is completely different with which for multi-domain particles [40].
The MNPs with hysteresis behavior produce heat through hysteresis loss [6]. The volumetric
EP
power dissipation is proportional to the field frequency and loop area as Eq. 2. = ∮ (2)
AC C
where and are vacuum magnetic permeability and applied frequency respectively [41]. For low field strengths (H), i.e. for so-called Rayleigh regions, the dependence of hysteresis loss on H is of the third order [40].
Among the main parameters determining loop area ( , , and ), the later one is strongly size dependent, so that goes to a maximum value in the single domain size limit [42]. This situation is illustrated in Fig. 2 [40]. Such a maximum occurs because of the change in
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mechanism of magnetization reversal from domain wall shift in multi-domain MNPs to coherent rotation of whole moments in single domain MNPs. In fact, the latter mechanism is harder than the former [43]. However, there are the incoherent magnetization reversal modes for single
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domain MNPs such as curling or fanning which originate of specific shapes of NPs. These modes, which are not included in the Stoner-Wohlfarth model, consider the shapes of peanut or prolate spheroid for NPs respectively [40].
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With reducing of size in single domain MNPs, hysteresis loop gradually shrinks until coercive field reaches to zero in the region of superparamagnetic size. Superparamagnetism is a specific
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magnetic behavior in which the MNPs behave as a paramagnetic material with huge magnetic susceptibility (compared with paramagnetic susceptibility which is in order of 10-5) [44]. Based on the Stoner-Wohlfarh model, in the single domain MNPs, the coupling of moments (due to exchange interactions) leads to a manner that all moments behave collectively and form a giant moment called superspin [20, 45]. When the MNPs’ size drops below the so-called
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superparamagnetic limit, the thermal energy ( ) would be high enough to overcome the magnetic anisotropy energy ( ). In such situation, the superspin can easily move between two easy axes when the magnetic field is switched off [46]. The related energy diagram is
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schematically illustrated in Fig. 3. In this scheme, energy profile ( (! )) displays two minima
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according to Eq. 3 in which K is the magnetic anisotropy constant, V is the particle volume, and ! is the angle between superspin and the easy axis. Moreover, the term shows the energy barrier separating the magnetization easy axes [35, 47]. (!) = "#$% !
7
(3)
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(! ) = "#$% ! − "()#(& − ! ) (4)
To be more accurate, there is a characteristic timescale defined as the time required for returning the superspin back to equilibrium after it experiences a perturbation. This time constant is known
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as Neel relaxation time (+, ) and defined as Eq. 5 in which + is attempt frequency of 10./ s, K
is anisotropy constant, V is particle volume, is Boltzmann constant, and T is temperature
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[48]. In order to appearance of superparamagnetic behavior, +, must be shorter than the
measurement time of M-H curve (+ ). In fact, in such a case, relaxation of superspin within oscillating time of magnetic field causes to average value of zero for magnetization. τ, = +
014 02 3 (5)
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For low energy barriers (∆ / ≪ 1), relaxation time is fast enough, so that, in addition to magnetic relaxation, thermal fluctuation of superspin can also take place. In the high energy barriers (∆ / ≫ 1), as long as the condition of +, ≤ +; is kept, MNPs remains in the
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superparamagnetic regime [35]. However, for relaxation times longer than measurement time,
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Neel relaxation of superspin has a delay with respect to oscillation of magnetic field so that superspin can stay stable in the induced direction by magnetic field [49]. This delay in relaxation is the origin of hysteresis behavior in the single domain NPs with sizes larger than superparamagnetic limit. In this conditions, the Neel relaxation is only referred to superspin thermal fluctuations [31, 35]. As a result, the critical size for superparamagnetic behavior really depends on the magnetic field oscillation time. For radio frequency hyperthermia, with typical frequency of 50-700 kHz, 8
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measurement time should be much shorter than which for conventional methods for measuring M-H curve such as SQUID and VSM analyses. Hence, superparamagnetism in MNPs used in MHT is occurred in smaller sizes [49]. However, in the superparamagnetic regime, remanence
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magnetization vanishes, when magnetic field is removed. Having such property makes superparamagnetic NPs as a good candidates for in vivo applications because the lack of remanence in these materials prevents the risk of embolism in blood vessels [35, 50-52].
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In addition to exhibit superparamagnetic behavior, saturation magnetization gradually decreases by size shrinking into ultra-fine NPs [53-56]. The origin of anomalous reduction in
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magnetization is surface spin disorder which was discussed in detail in our recent work [57].
2.3. Relaxation loss
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In single domain NPs, heat is generated as a result of superspin alignment in the applied magnetic field direction. In fact, the magnetic energy is converted to thermal energy while magnetic field overcomes to an energy barrier that resists against rearrangement of magnetic
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moments. This energy barrier is either the magnetic anisotropy energy of MNPs or viscosity of the fluid, which the particles are dispersed in it. Thus either Neel or Brown relaxation
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mechanism is responsible for heat production in MNPs [58].
2.3.1. Neel relaxation
In the Neel relaxation mechanism, while the physical position of MNP is kept fixed, superspin rotates and orients to the direction parallel to the applied field (Fig. 4 (a)). It this case, the
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magnetic energy is dissipated by magnetic anisotropy energy which hinders the reorientation of superspin [31, 59]. The Neel relaxation time was first described by Neel using Eq. 5, then
τ, =
τ 01 => 402 3 (6) 2 "
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modified by Brown as Eq. 6 [60].
Where + is attempt frequency of 10./ s, K is the anisotropy constant, V is the MNP volume,
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is the Boltzmann energy.
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2.3.2. Brown relaxation
When a MNP rotates in the fluid by itself, in order to align its superspin in the direction of applied field, undergoes the Brown relaxation (Fig. 4 (b)), while the superspin remains fixed relative to the crystal orientation. In this case, thermal energy is produced by friction arising
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from shear stress in the fluid [26, 31]. Brown relaxation time is given by the Eq. 7 [59]. + =
3A"B (7)
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Where, A is viscosity of the surrounding medium, "B is the particle hydrodynamic volume
(including magnetic core, coating and hydration layers), is the Boltzmann constant and T is
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the temperature.
2.3.3. Predominant mechanism
Both Neel and Brawn mechanisms simultaneously occur for particles, so that the effective relaxation time is given by Eq. 8 [32].
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1 1 1 = + (8) + +, +
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However, the effective relaxation time is predominated by the term that has shorter relaxation time. Theoretically, there is a critical size, (strongly dependent on the particle magnetic anisotropy), in which both relaxation times equally contribute in heat generation [41]. In fact, for
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larger particles and fluids with lower viscosity, Brown mechanism is faster mechanism, whereas for smaller particles and viscous fluids, the Neel mechanism is responsible for heat production
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[31, 41]. Figure 5 shows size dependency of relaxation time for magnetite NPs in an aqueous medium with constant viscosity. As can be seen, effective relaxation time (+) for particles with size larger than meeting point of +, and + is due to Brownian mechanism, whereas, that is devoted to Neel mechanism for smaller particles [31].
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3. Specific loss power (SLP)
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3.1. Definition and optimization
In magnetic hyperthermia therapy, in order to keep injected MNP dose and treatment duration as
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low as possible, the heating efficiency must be as high as possible [6]. Specific loss power (SLP), also referred to as specific absorption rate (SAR), is used as a figure of merit to evaluate heating performance of MNPs. This parameter is defined by heat dissipated per unit time per NPs mass and expressed by Eq. 9. FG =
(9) ∅
11
ACCEPTED MANUSCRIPT Where, P, , and ∅ are volumetric power dissipation, the mass per unit volume of MNPs, and the volume fraction of MNPs in the suspension, respectively [61]. For MNPs with hysteresis behavior, P is given by Eq. 2. However, linear response theory (LRT), = J, is suitable for = > J KK (10)
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calculation of power dissipation in fine MNPs; so that, Eq. 2 is replaced by Eq. 10 [3, 34, 61]: Where, = 4> × 10.M and J KK is the imaginary part of the magnetic susceptibility: Where, J is static susceptibility:
N+ (11) 1 + (N+)
P
W
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J = JO (coth V − )
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J KK = J
Q
Q
(12)
Where, V is Langevin parameter and JO is initial susceptibility: V=
XY ;Z B1 02 3
(13)
given by Eq. 14 [62].
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When magnetic energy barrier is negligible, the case which occurs for the fine MNPs, J is XY ;Z[ 1 P02 3
(14)
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J =
Therefore, by conjugation of Eq. 10, Eq. 11, and Eq. 14, P is given as Eq. 15.
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1 \ ] "/3 + ^ (N+) = (15) 2 1 + (N+)
This equation has a maximum value when the particle relaxation time is matched with the field frequency i.e. N+ = 1. Deviations from this maximum condition (either N+ > 1 or N+ < 1) leads to reduction of heating ability [3, 31]. Moreover, at the low frequencies (well below the optimal frequency i.e. N+ ≪ 1), loss power increases with the square of field frequency while it is field frequency independent for N+ ≫ 1 [31, 63]. 12
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However, for each material (with specific K), the optimum size satisfying the maximum condition strongly depends on the field frequency and medium viscosity [63]. It means that, at a given field frequency and fluid viscosity, position of maximum value of P strongly depends on
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the effective magnetic anisotropy and is determined by MNPs’ structure. Figure 6 shows size dependency of loss power for several MNPs. As can be seen, the maximum value for heating efficiency occurs in different sizes for various MNPs. Moreover, the maximum value depends on
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magnetic compound [3].
When maximum condition (Eq. 15) is satisfied by Neel relaxation i.e. N+, = 1, the optimal
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MNP size is fallen within the transition point of ferro- or ferri magnetic to superparamagnetic region [64, 65]. In such a case, heat generation by the smaller MNPs is weak because of decrease in energy barrier that stands against magnetic field. In fact, production of noticeable heat through the Neel mechanism, requires that the magnetic anisotropy energy significantly be larger than the
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thermal energy [63]. Nevertheless, for magnetic anisotropy energies much bigger than thermal energy, heat generation by the Neel relaxation is suppressed. In fact, for Neel relaxation times longer than time reversal of magnetic field, the magnetic relaxation time is too slow to permit
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MNPs follows the fast oscillations of alternating magnetic field [35]. In this condition, stable state of ferri/ferro magnetic arises from the delay in the Neel relaxation. This delay causes
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hysteresis loss in energy [65]. However, in high magnetic anisotropy barriers for which superspin is strongly coupled to particle, Brown relaxation is the only term in the effective relaxation time (+) [3, 63]. In fact, in single domain MNPs with sizes of larger than superparamagnetic limit, superposition of Brown relaxation loss with hysteresis loss occurs. On the other words, the square law for dependency of loss power on the field strength for the
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superparamagnetic regime is changed to the third-order (known as Rayleigh law) for the sizes above the superparamagnetic limit [5, 65]. For optimizing heating efficiency by the Neel mechanism, it needs to simultaneous control of
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particle size, anisotropy constant as well as field frequency. Herein, the field frequency and particle size are determined by experimental conditions. Although magnetocrystalline anisotropy is largely an intrinsic parameter of material, shape anisotropy is strongly affected by synthesize
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parameters [20]. Therefore, manipulation of total anisotropy constant (K), through modification of shape anisotropy needs to have a precise control on the shape of all individual particles which
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is really difficult, and in practice, even impossible. Hence, it seems, adjusting K to a desirable value by changing the magnetocrystalline anisotropy is easier. Recently, core-shell structures as a combination of hard and soft magnetic materials have attracted the most attention because the magnetocrystalline anisotropy in these structures can be satisfactorily moderated compared with
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utterly hard or soft magnetic materials. In such core-shell structures, exchange coupling between hard and soft materials results in utilizing of desirable properties of the hard (high magnetocrystalline anisotropy and coercivity) and soft (low magnetocrystalline anisotropy and large magnetization) magnetic materials [66, 67]. Figure 7 shows a schematic of core shell
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structure of () @ % NPs.
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It is worth to mention that the validity of Eq. 15 and consequently correctness of the SLP maximum condition (N+ = 1) in superparamagnetic materials are confirmed as long as the relation between magnetization (M) and field amplitude (H) remains linear (when
