|Year : 2019 | Volume
| Issue : 4 | Page : 156-164
Heat generation from magnetic fluids under alternating current magnetic field or induction coil for hyperthermia-based cancer therapy: Basic principle
Rashmi Joshi1, Ramaswamy Sandeep Perala2, Manas Srivastava3, Bheeshma Pratap Singh2, Raghumani Singh Ningthoujam1
1 Chemistry Division, Bhabha Atomic Research Centre; Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra, India
2 Chemistry Division, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India
3 Department of Mechanical Engineering, MVPS's Karmaveer Adv. Baburao Ganpatro Thakare College of Engineering, Nashik, Maharashtra, India
|Date of Submission||05-Feb-2020|
|Date of Acceptance||06-Feb-2020|
|Date of Web Publication||14-Feb-2020|
Dr. Raghumani Singh Ningthoujam
Chemistry Division, Bhabha Atomic Research Centre; Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra
Source of Support: None, Conflict of Interest: None
Superparamagnetic particles (SUPs) have been used in many applications in the area of hyperthermia-based cancer treatment, as a magnetic resonance imaging contrast agent, as a carrier for drug, in the removal of toxic ions, etc. When SUPs are dispersed in liquid, they can experience Brownian motion and Néel's spin relaxations. In the presence of direct current magnetic field, SUPs do not show a hysteresis loop. Because of this, they are unable to produce heat. However, in alternating current magnetic field (AMF) of a few kHz and small magnetic fields, they can generate heat. For the treatment of cancer, hyperthermia temperature of 43°C is required, at which temperature cancer cells can be killed selectively, but normal cells can survive. The theory behind heat generation from SUPs in the presence of AMF will be discussed in this work.
Keywords: Brownian motion and Néel's spin relaxations, cancer treatment, hyperthermia approach, hysteresis loop, magnetic fluids, superparamagnetic particles
|How to cite this article:|
Joshi R, Perala RS, Srivastava M, Singh BP, Ningthoujam RS. Heat generation from magnetic fluids under alternating current magnetic field or induction coil for hyperthermia-based cancer therapy: Basic principle. J Radiat Cancer Res 2019;10:156-64
|How to cite this URL:|
Joshi R, Perala RS, Srivastava M, Singh BP, Ningthoujam RS. Heat generation from magnetic fluids under alternating current magnetic field or induction coil for hyperthermia-based cancer therapy: Basic principle. J Radiat Cancer Res [serial online] 2019 [cited 2020 Sep 23];10:156-64. Available from: http://www.journalrcr.org/text.asp?2019/10/4/156/278412
| Introduction|| |
Over the last 12 years, our group has been working on the treatment of cancer and diagnosis using various nanoparticles – magnetic, luminescent, and metallic.,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Among various methods employed for the treatment of cancer, one approach is hyperthermia-based treatment. This requires a temperature of ~42°C, which is slightly more than the physiological temperature of the human body (37°C). There are many ways to bring hyperthermia temperature: extracellular and intracellular methods [Figure 1]. In case of the extracellular method, infrared, microwave, and water bath are used. However, it has disadvantages because it affects the surrounding environment consisting of healthy tissues and cells. Blisters, burns, unwanted rise in heat in the healthy cells, swelling, blood clots, and bleeding in clinical conditions are common side effects of this approach. In case of the intracellular method, alternating current (AC) magnetic field (AMF) (a few kHz) is applied to particles (magnetic or metallic particles), which are located inside the cancer cells. The temperature up to 42°C is generated to kill cancer cells selectively without affecting the surrounding normal cells. As compared to metallic particles (e.g., Co, Ni, CoNi, FePt, CoPt, and FePd), magnetic metal oxide particles (e.g., Fe3O4, g-Fe2O3, and AB2O4 ferrites [A = Co, Ni, Mn, Zn; B = Fe]) are more superior in terms of chemical stability, easy heat generation, easy processing for drug loading, targeting, imaging, etc.,,,,, Such magnetic particles dispersed in a carrier liquid medium are considered magnetic fluids.
|Figure 1: Two types of hyperthermia: (a) extracellular and (b) intracellular hyperthermia|
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There are two types of magnetic fluids assuming the uniform size of particles. The 1st type is smaller-sized particles, which are stable in the carrier liquid. Smaller particles can move with the Brownian motion More Details. In a liquid medium, smaller-sized particles are dispersible if the repulsive forces are more than the attractive forces and the gravitation force is much lower than the weight of the constituent particles. This can be brought by bringing like charges on the surface of smaller-sized particles. In addition, surfactant molecules can create steric hindrance among particles so that agglomeration among particles can be decreased. The 2nd type is larger-sized particles, which are not stable for longer duration in liquid medium. This type is not suitable for controlled heat generation, carrier for drug, as well as internalization in cancer cells.
As our body has 60–70 wt.% of water, stability of nanoparticles when injected through vein or transferred to muscle or bone or localized site is to be considered. When smaller-sized magnetic particles (e.g., 5 mg of Fe3O4) are added in a solvent (100 ml of water in a beaker) of viscosity ƞ and dielectric constant ɛ, the solvent medium will try to disperse particles (the attractive force [F] among particles is inversely proportional to the dielectric constant [ɛ]). In addition, the particles experience gravitational force, which tries to pull particles down to the bottom of a beaker. Such dispersed particles will go to different directions in a liquid (known as Brownian motion) and sometimes, they collide with each other [Figure 2]. In this process, heat is released in the surrounding. If the viscosity of the medium is too high, the Brownian motion can be stopped. However, the particles can still be dispersed in a medium. The Brownian relaxation is represented as:
|Figure 2: Brownian motion where small particles are suspended and moved in different directions: Small particles are (a) approaching, (b) collision, (c) after collision. (d) Schematic view of a particle having radius (rc) and hydrodynamic radius (rh)|
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where η is the dynamic viscosity of the carrier fluid, rh is the hydrodynamic radius, and T is the absolute temperature. The Brownian relaxation (τB) varies from ms to ms and even to hours depending on the particle size/hydrodynamic radius and temperature, assuming no effect from the gravitational force or external magnetic/electric force. In the presence of gravitational force or external magnetic/electric force, the equation (1) will vary.
Under sedimentation theory (no effect from external magnetic/electric force), apparent weight (W) of a spherical particle in a medium is given by Equation (2) as follows [Figure 3]:
|Figure 3: Dispersion of spherical particles in a liquid medium: (a) There is an apparent weight of particle = weight of particle (F) – Buoyancy (F/). A part of the particle is submerged into a liquid. (b) There is no almost apparent weight of the particle. F >> F/. The whole of a particle is inside the liquid. (c) Free body diagram of a submerge single particle, under external forces such as gravitational force (F2), lifting force (F1, which is equivalent to buoyancy), and frictional drag force (Fpl)|
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The weight of the spherical particle is 4/3 πr3ρg, where r is the radius of a particle with density (ρ) and g is acceleration due to gravity. The buoyancy can be defined by the product of the volume of the particle (because it occupies the same volume of liquid displaced by the particle) and the density of the medium (4/3 πr3ρ'g), where ρ' is the density of the liquid.
The frictional resistance R on the particle is given by R = where f is the coefficient of friction and is equal to the 6 πƞr, and is the velocity of the particle at a given moment. The R is defined by
Under the state of equilibrium, Equations (3) and (4) can be equated as follows:
where v is a settling velocity of a particle in liquid medium. If viscosity is high, the value of v is very small.
In case when the fluid dynamics behave as a turbulent, rotational, viscous, and incompressible fluid, then the sedimentation theory will be based on the Newton's second law (Equation 6). For solving the equation, the simplified way of representation is free body diagram (FBD) of the submerge single particle. The FBD of a single particle is shown in [Figure 3]c. This FBD of a single particle under external forces such as gravitational force (F 2), lifting force (F 1, which is equivalent to buoyancy), and frictional drag force (Fpl) is notified in [Figure 3]c.
On the basis of FBD of an undersubmerged single particle inside the liquid medium [Figure 3]c, the net effective rate of change of momentum by assuming no change in the mass (m) of a single particle is force that is given by Equation (6):
Whereas is the rate of change of vocity (acceleration).
The gravitational force (F 2) is given the following relation:
where ρp and Vp are the density and volume of the particle, respectively. The lifting force (F 1) from liquid is given by the following relation:
where ρl and Vp are the density of the liquid and volume of the liquid displaced by a single particle (which is equal to the volume of the particle), respectively.
The frictional drag force between single particle and liquid is given by the following relation:
where Cd and A1 are the drag coefficient and area of projection of particle perpendicular to the velocity (v), respectively.
Under steady state condition ,
the equation (6) becomes:
In case of Fe3O4 particles dispersed in water, the settling velocity (v) can be calculated using Equation 5. The density of Fe3O4 particles is ρ = 5.206 g/cm 3, density of water is ρ' = 1 g/cm 3, and viscosity of water is ƞ = 8.9 × 10−4 kg/s.m. In case of 10-nm particle size of Fe3O4, it can settle down to 1-cm distance in a period of 112 days. Here, it is assumed that there are no interactions among particles, and there is no external magnetic/electric force. It is suggested that monodispersed nanoparticles are very difficult to settle down if there is no interaction among particles as well as in the absence of an external magnetic/electric force.
Such smaller particles are useful in many applications such as used in magnetic-based hyperthermia for cancer treatment, as a magnetic resonance imaging contrast agent, for decreasing vibrations in ship and as a carrier for drug. These particles are considered superparamagnetic particles (SUPs). In SUPs, there is no magnetic attraction among monodispersed particles in liquid. An individual SUP has a spin relaxation of 10−9 s at room temperature (θ = 0°–180°). The net magnetization (Mnet) is 0. When a magnetic field is applied in such SUP, it can have net magnetization (Mnet≠ 0). When there is attraction among particles, there will be magnetic dipolar attraction. The energy of the system (E) is the total of anisotropic energy (EA), applied field energy (EH), and dipolar interaction energy (ED):
EA is anisotropy energy due to the shape or the crystalline structure of the particle. Assuming temperature-independent anisotropy, EA is defined as follows:
Here, every particle 'i' is considered as a single magnetic domain with . Single magnetic domains rotate coherently. K is the anisotropy constant. is the unit vector denoting the easy axis direction. Absolute value of magnetic moment = MsVi, where Ms is saturation magnetization and Vi is the volume of the i th particle.
Upon applying magnetic field, ED is defined as product of magnetic moment and applied field (H).
When distance (rij between magnetic single domains (or particles) in liquid decreases, there is ED, which is defined as
The magnetization of such smaller particles (SUPs) can be studied by direct current (DC) magnetization by dispersing different concentrations in carrier liquid (dilute to high concentrations). In this way, the contribution of dipolar interaction can also be determined. Increase of the concentration of SUP in liquid is likely to increase magnetization. At certain stage, magnetic fluid system can have magnetization in the absence of applied magnetic field due to agglomeration or high dipolar interaction. When there is dipolar interaction or broad size particle size distribution, a small value of coercivity (Hc) is observed. In addition, there will be a divergence in zero field cooled (FC) and FC curves of magnetization above the blocking temperature (known as superparamagnetic blocking temperature, TB). In general, water-dispersible SUPs have a large distribution of particle sizes because of hydrophilicity as compared to those dispersible in organic oil medium.
When AMF using induction coil is applied to smaller-sized particles, magnetic properties will be different from that when DC magnetic field is applied. In this review article, we will focus on the theoretical model for heat generation of SUPs under AC field.
| Theoretical Model for Heat Generation from Magnetic Fluids under Alternating Current Magnetic Field or Induction Coil|| |
The amount of induced magnetic field (Hind) in AMF or induction coil is dependent on the diameter of coil/ring (D in cm), current (i), and number of rings (n), and their relationship [Figure 4] is given by approximation.,
|Figure 4: Schematic diagram of induction heater where particles are inserted into a coil having diameter (D) and length (L)|
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Here, the diameter is almost same as the length of induction coil or solenoid. The AC frequency (f) can be varied using L-C-R circuit (L = inductor of coil, C = capacitor, and R = resistor).
Dispersed SUP undergoes two types of relaxations namely Brownian and Nèel's relaxation. The Brownian relaxation is applicable to all particles, which results due to particle rotation or collision, whereas Nèel's relaxation is applicable only on superparamagnetic nanoparticles due to magnetic moment rotation. The Brownian relaxation is represented in Equation (1).
On the other hand, Nèel relaxation [Figure 5] is given as:
|Figure 5: (a) Orientation of magnetic moment of magnetic particles of different sizes under thermal energy (kT). Energy versus θ (°) for (b) big and (c) small magnetic nanoparticles under thermal energy (kT)|
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where of the order of 10−9 s and △E the anisotropic energy barrier which is the product of anisotropic energy constant (K) and volume (V), kBi is the Boltzmann's constant, and T is the absolute temperature. Nèel's relaxation is fast for smaller nanoparticles. When nanoparticles are dispersed, the spin relaxation of the nanoparticles gets accelerated.
It is worthwhile to mention that on the application of DC magnetic field, we could not observe significant heating for SUP (where no coercivity Hc= 0 Oe) because of one direction of the applied magnetic field. SUPs at room temperature have spin relaxation of the order of 10−9 s. As the measured time is 0.1–1 s in DC magnetic measurement, it cannot determine the spin relaxation. Moreover, in AMF, the direction of current is changing over time. In case of hyperthermia experiment, 100–300 kHz frequency along with a field of 100–400 Oe is applied. Beyond this frequency limit, electric polarization effect will arise. The permittivity is dependent on field frequency and/or permeability is dependent on the magnetic field. Hence, at this frequency range, the experimental window time is of ~10−6 s, which is closer to superparamagnetic spin relaxation. Thus, magnetic moments can be observed through AC magnetization [Figure 6]. At low temperature (below the superparamagnetic blocking temperature), the hysteresis loop can be observed due to transition from superparamagnetic to ferromagnetic particles [Figure 7]. The term “Superparamagnetic” means that a high moment of 102–104 mB per particle is associated, but paramagnetic in nature (almost zero moment) due to fast relaxation of spins (at, T >>Tb). This is different from paramagnetic substance where it has an atomic moment [Figure 8]. At low temperature (say 5 K), the paramagnetic substance can have constant moment per atom and the moment decreases with temperature. At room temperature (say 300 K, where thermal energy is high), the moment increases almost linearly with the magnetic field.
|Figure 6: Spin relaxation: Magnetic single domains are dispersed in a fluid medium at different times and with or without a magnetic field (H): (a) H = 0 Oe, t = 0 s, M = 0; (b) H = 0 Oe, t = 10-9 s, M = 0; and (c) H = 0 Oe, t = 10-5 s, M ? 0. (d) Nèel's relaxation, where single domain superparamagnetic particle rotates from 0° to 180°. Here, thermal energy (kT) overcomes the particle' energy (KV)|
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|Figure 7: (a) Superparamagnetic particles at 300 K (M vs. H curve) and (b) ferromagnetic particles at 5 K, where superparamagnetic becomes ferromagnetic at 5 K, which is much below the blocking temperature (Tb) (M vs. H curve)|
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|Figure 8: Behavior of paramagnetic substance at 5 K and 300 K or higher temperature|
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Hysteresis loss in AMF is given as follows:
where f is the frequency of AMF, and it is represented as f = ω/2π, M is magnetization, and H is the applied magnetic field (H). Magnetic susceptibility χ is defined as the ratio of magnetization M to the applied magneticfield. In the AMF, χ is represented as follows:
where χ/ is the real part of susceptibility and χ// is represented as follows:
where τ is the total relaxation contributed by Brownian (τB) and Nèel's relaxations τN Heat loss from particles with m (the permeability of a material), d (the diameter of the particle), and ρ (resistivity of the material) due to eddy current (i.e., a result of the interaction of a conductive material with an oscillating magnetic field according to the Faraday's and Lenz's laws) is given by
Thus, total heat/power dissipation from particles is provided by:
where m0 is the permeability of free space.
The loss power density P (Wm −3) is related to the specific loss power or commonly specific absorption rate (SAR) expressed in W g−1. The SAR is calculated using the following relation:
where △T/△t is the slope of the time-dependent temperature curve at the initial time [Figure 9]. C is the specific heat capacity of combined SUP and solvent. The value of mmagn is considered as the amount of MNPs or Fe per total amount of MNPs or Fe and solvent.
|Figure 9: Way of calculation of specific absorption rate: Slope of temperature versus time|
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| How to Employ Particles in Clinical Studies|| |
Usually, AC fields with a few kHz frequency (f = 100–250 kHz) and a low magnetic field (H = 100–400 Oe) are safe for clinical studies. Depending on the heat required at a particular site, the values of f and H can be varied. SUPs should have magnetization of 40–60 emu/g at 1–3 Tesla magnetic field; otherwise, a higher amount of particles is required, which might not be suitable for clinical studies. The SUP should be highly biocompatible. For up to 1–5 mg of SUPs in 1 million cells, it should have 90% cell viability. If SUPs have high SAR, it can generate a temperature of 42°C within a few minutes (3–5 min). The temperature should be maintained by varying magnetic field at a fixed frequency. This will be a better option instead of varying the frequency. Another option to control the temperature of hyperthermia is the use of a sample having a low Curie temperature at 60°C –80°C (e.g., LaSrMnO3) or substitution of Fe in Fe3-xO4 by Zn or other compounds having electric and magnetic dipoles or hybrids, etc. In some cases, by changing the magnetic field and frequency for a particular concentration of magnetic fluids, hyperthermia temperature can be maintained for a few minutes to hours.[,,,,,,,,,
The combination of hyperthermia with anticancer drug and/or irradiation (gamma rays) will be advantageous for the treatment of cancer. In addition, if the surface of SUP is tagged with antibody molecules, it will help in the diagnosis of cancer cells. In combination with luminescent nanoparticles, it can provide imaging of cells that whether particles are internalized into cells.,,, The type of heat dissipation at different parts of the living body is different. For clinical studies, bio-heat transfer equation for convection, conduction, radiation, circulation of blood, dielectric constant of material (skin, muscle, liver, heart, bone, etc.), and temperature profile need to be studied. The modeling and simulation in terms of engineering aspects will help in getting a proper heat transfer mechanism. A minimum of three temperature sensors should be employed for clinical studies. One is to be monitored at tumor site, where hyperthermia temperature has to be provided. Other two are monitored at the nearby tumor site and at the normal body, which is away from the tumor site.
In order to investigate the heating efficacy of magnetic nanoparticles by taking Fe3O4 SUP, these nanoparticles are dispersed in a suitable medium to form a stable colloidal suspension (also known as magnetic fluid or ferrofluid). This ferrofluid is then placed inside an induction coil (with diameter 6 cm with six turns). The AC is applied (f = 200 kHz) along with the magnetic field (H = 100–400 Oe). The latter can be adjusted by changing the input power to the coil. A temperature probe is inserted inside the fluid, and temperature is monitored as a function of time. Typically, a solution of 3 mg/mL of Fe3O4 nanoparticles in water is taken, and the temperature generation from particles with time at different powers is plotted [Figure 10]. The SAR value of 47.61 W/g is obtained at 4 kW power.
|Figure 10: Temperature generation from Fe3O4 superparamagnetic particle with time at different powers|
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| Summary|| |
In this review article, we have summarized the possible sources of heat generation for hyperthermia treatment. Extracellular heat treatment has many disadvantages over intracellular heat treatment of cancer. The theory behind heat generation from SUPs under AMF is presented. Precautions to be taken care of in this approach are also mentioned.
This work is a part of Ph. D. Thesis of Rashmi Joshi. Bheeshma Pratap Singh acknowledges the award through Inspire Faculty (IFA17-MS-109) provided by DST, Government of India. Authors thank Dr. A. K. Tyagi, Chemistry Group, BARC and Dr. P. A. Hassan, Chemistry Division, BARC for their support and encouragement during this work.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10]