Magnetic hyperthermia
Encyclopedia
Magnetic hyperthermia is the name given to an experimental cancer treatment
. It is based on the fact that magnetic nanoparticles
, when subjected to an alternating magnetic field, produce heat. As a consequence, if magnetic nanoparticles are put inside a tumor and the whole patient is placed in an alternating magnetic field of well-chosen amplitude and frequency, the tumor temperature would raise. This could kill the tumor cells by necrosis if the temperature is above 45 °C, or could improve the efficiency of chemotherapy if the temperature is raised around 42 °C. This treatment is tested on humans only in Germany, but research is done in several laboratories around the world to test and develop this technique.
, where A is the area of the hysteresis loop and f the frequency of the magnetic field. A is expressed in J/g and is also called "specific losses" of the material.
It should be noted that this expression is always true, whatever can be the complexity of determining A. Indeed, as will be more detailed below, A depends on a very complex manner on all the properties of the magnetic material. In the case of magnetic nanoparticles, it depends on their magnetocrystalline anisotropy
K, their volume V, the temperature T, the frequency of the magnetic field f, its amplitude
and on the volumic concentration of the nanoparticles which influences the magnetic interactions between them.
. Small sizes nanoparticles are composed of a single domain. Larger ones are composed of several domains minimizing the magnetostatic energy. At intermediate sizes, they display a beautiful magnetic structure called vortex
. A rough approximation to determine the size above which a magnetic nanoparticles is not single-domain any more is when its size is above the typical domain wall
dimension in the magnetic material, which ranges from a few to a few tens of nanometers. The nature of the domain structure have a profound influence of the hysteresis of the magnetic nanoparticles and, as a consequence of their hyperthermia properties.
nanoparticles. It is assumed in this part that the nanoparticle display a uniaxial anisotropy.
. They move and rotate randomly in the fluid, a phenomenon called Brownian motion
. When a magnetic field is applied to them, magnetic nanoparticles rotate and progressively align with the magnetic field due to the torque generated by the interaction of the magnetic field with the magnetization. This is similar to a compass
. The time taken for a magnetic nanoparticle to align with a small external magnetic field is given by the Brown relaxation time:
, where 
is the solvent viscosity. The delay between the magnetic field rotation and the magnetization rotation leads to an hysteresis.
. The magnetization oscillate between its two equilibrium positions. The typical time between two orientation changes is given by the Néel relaxation time
, where 
is an attempt time with a value around 10−9-10−10 seconds.
nanoparticle is inside a fluid at room temperature and that a sweeping magnetic field is suddenly applied with a direction opposite to the one of the nanoparticle magnetization. The nanoparticle will at the same time i) rotate in the fluid ii) the barrier between the two equilibrium positions of the magnetization will decrease iii) when the energy barrier becomes of the order of the thermal energy, the magnetization will switch (if the nanoparticle is not already align with the magnetic field due to its physical rotation). There is no simple analytical expression describing this reversal and the properties of the hysteresis loop in this very general case but numerical simulations and analytical expressions can be used in some cases .
, where 
is the complex susceptibility of the material. It is thus valid when the applied magnetic field is much smaller than the magnetic field needed to saturate the magnetization of the nanoparticle. It is able to take into account both the reversal by thermal activation and the reversal by Brownian motion.
The linear response theory uses an average relaxation time
, given by 
. The out of phase component of complex susceptibility is then given by 
. The hysteresis loop is then an ellipse with an area given by 
.
The Stoner–Wohlfarth model predicts that the coercive field at T=0 of an assembly of nanoparticles with randomly oriented axes is given by
. The area of the hysteresis is approximatively 
.
. Numerical simulations have shown that, in this case, the expression of the coercive field for randomly oriented nanoparticles is 
. One can see from this expression that the effect of the temperature is simply to reduce the coercive field of the nanoparticles.
s. Both mechanisms are strongly influenced by the structural defects at the surface or inside the nanoparticles and make difficult any quantitative prediction of the hysteresis loops shape and area from intrinsic parameters of the magnetic nanoparticles.
, where 
is the Rayleigh constant.
, which precisely used a high-frequency magnetic field to heat materials. It is however conceived to work at a single frequency and requires a water cooling system. It is also possible to build electromagnets or coils able to work at various frequencies at the condition to use variable capacitors. It is also possible to get rid of the cooling system in coils at the condition to build them with Litz wire
.
in a high-frequency magnetic field is self-heated and leads to erroneous temperature measurements. Temperature measurements in hyperthermia can be made using alcohol thermometer or optic fiber thermometers.
A colloidal solution heated by an external magnetic field will be subject to convection
phenomena so the temperature inside the calorimeter is not homogeneous. Shaking of the colloidal solutions at the end of a measurement or average on several temperature probes can ensure a more accurate temperature measurement.
. They are in the context of MRI called "Superparamagnetic Iron Oxide Nanoparticles", or SPION. The main interest of these nanoparticles are their biocompatibility and their stability with respect to oxidation. The nanoparticles displaying the largest hysteresis area so far are the SPIONs synthesized by magnetotactic bacteria
, with A = 2.3 mJ/g although chemically synthesized nanoparticles reach values up to A = 1.5 mJ/g
experiments in hyperthermia require to make tumor cells absorb magnetic nanoparticles, to place them into an alternative magnetic field and to test their survival rate compared to tumor cells which would follow the same protocol but would not absorb magnetic nanoparticles.
Experimental cancer treatment
Experimental cancer treatments are medical therapies intended or claimed to treat cancer by improving on, supplementing or replacing conventional methods ....
. It is based on the fact that magnetic nanoparticles
Magnetic nanoparticles
Magnetic nanoparticles are a class of nanoparticle which can be manipulated using magnetic field. Such particles commonly consist of magnetic elements such as iron, nickel and cobalt and their chemical compounds. While nanoparticles are smaller than 1 micrometer in diameter , the larger microbeads...
, when subjected to an alternating magnetic field, produce heat. As a consequence, if magnetic nanoparticles are put inside a tumor and the whole patient is placed in an alternating magnetic field of well-chosen amplitude and frequency, the tumor temperature would raise. This could kill the tumor cells by necrosis if the temperature is above 45 °C, or could improve the efficiency of chemotherapy if the temperature is raised around 42 °C. This treatment is tested on humans only in Germany, but research is done in several laboratories around the world to test and develop this technique.
Generalities and definition
A general feature of many magnetic materials is to display a magnetic hysteresis when it is measured at a positive magnetic field, then negative, then positive again. The area of this hysteresis loop is dissipated in the environment under the form of thermal energy. This is the energy used in magnetic hyperthermia. The power dissipated by a magnetic material subjected to an alternative magnetic field is often called "Specific Absorption Rate" (SAR) in the community of magnetic hyperthermia; it is expressed in W/g of nanoparticles. The SAR of a given material is then simply given by:, where A is the area of the hysteresis loop and f the frequency of the magnetic field. A is expressed in J/g and is also called "specific losses" of the material.It should be noted that this expression is always true, whatever can be the complexity of determining A. Indeed, as will be more detailed below, A depends on a very complex manner on all the properties of the magnetic material. In the case of magnetic nanoparticles, it depends on their magnetocrystalline anisotropy
Magnetocrystalline anisotropy
Magnetocrystalline anisotropy is the dependence of the internal energy of a ferromagnet on the direction of its magnetization. As a result, certain crystallographic directions are preferred directions, or easy axes, for the magnetization. It is a special case of magnetic anisotropy...
K, their volume V, the temperature T, the frequency of the magnetic field f, its amplitude
and on the volumic concentration of the nanoparticles which influences the magnetic interactions between them.Influence of nanoparticle size on their domain structure
The size of nanoparticles have a great influence on their magnetic domainsMagnetic domains
A magnetic domain describes a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction...
. Small sizes nanoparticles are composed of a single domain. Larger ones are composed of several domains minimizing the magnetostatic energy. At intermediate sizes, they display a beautiful magnetic structure called vortex
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
. A rough approximation to determine the size above which a magnetic nanoparticles is not single-domain any more is when its size is above the typical domain wall
Domain wall
A domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...
dimension in the magnetic material, which ranges from a few to a few tens of nanometers. The nature of the domain structure have a profound influence of the hysteresis of the magnetic nanoparticles and, as a consequence of their hyperthermia properties.
Basic mechanisms involved in the magnetization reversal of magnetic single-domain nanoparticles
The goal of this part is to present the basic mechanisms which must be taken into account to describe the reversal of single domainSingle domain (magnetic)
Single domain, in magnetism, refers to the state of a ferromagnet in which the magnetization does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle . Such particles are very small...
nanoparticles. It is assumed in this part that the nanoparticle display a uniaxial anisotropy.
Reversal by Brownian motion
In hyperthermia application, the nanoparticles are in a fluid, the blood. During in vitro hyperthermia measurements they are generally dispersed in a liquid and form a ferrofluidFerrofluid
A ferrofluid is a liquid which becomes strongly magnetized in the presence of a magnetic field.Ferrofluids are colloidal liquids made of nanoscale ferromagnetic, or ferrimagnetic, particles suspended in a carrier fluid . Each tiny particle is thoroughly coated with a surfactant to inhibit clumping...
. They move and rotate randomly in the fluid, a phenomenon called Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
. When a magnetic field is applied to them, magnetic nanoparticles rotate and progressively align with the magnetic field due to the torque generated by the interaction of the magnetic field with the magnetization. This is similar to a compass
Compass
A compass is a navigational instrument that shows directions in a frame of reference that is stationary relative to the surface of the earth. The frame of reference defines the four cardinal directions – north, south, east, and west. Intermediate directions are also defined...
. The time taken for a magnetic nanoparticle to align with a small external magnetic field is given by the Brown relaxation time:
, where is the solvent viscosity. The delay between the magnetic field rotation and the magnetization rotation leads to an hysteresis.Reversal by thermal activation
The magnetization of the nanoparticle can spontaneously change of orientation under the influence of thermal energy, a phenomenon called superparamagnetismSuperparamagnetism
Superparamagnetism is a form of magnetism, which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time...
. The magnetization oscillate between its two equilibrium positions. The typical time between two orientation changes is given by the Néel relaxation time
, where is an attempt time with a value around 10−9-10−10 seconds.Reversal by the suppression of the anisotropy barrier by a magnetic field
The magnetization of the nanoparticle is also reversed when an applied magnetic field is large enough to suppress the energy barrier between the two equilibrium positions, a phenomenon which is known as the Stoner–Wohlfarth model of magnetization reversal.Combination of the three mechanisms
In the most general case, the reversal of the magnetization is due to a combination of the three mechanisms described above. For instance, let us imagine that a single domainSingle domain (magnetic)
Single domain, in magnetism, refers to the state of a ferromagnet in which the magnetization does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle . Such particles are very small...
nanoparticle is inside a fluid at room temperature and that a sweeping magnetic field is suddenly applied with a direction opposite to the one of the nanoparticle magnetization. The nanoparticle will at the same time i) rotate in the fluid ii) the barrier between the two equilibrium positions of the magnetization will decrease iii) when the energy barrier becomes of the order of the thermal energy, the magnetization will switch (if the nanoparticle is not already align with the magnetic field due to its physical rotation). There is no simple analytical expression describing this reversal and the properties of the hysteresis loop in this very general case but numerical simulations and analytical expressions can be used in some cases .
The linear response theory
The linear response theory is only valid when the response of the magnetic material is linear with the applied magnetic field and can be thus written under the form, where is the complex susceptibility of the material. It is thus valid when the applied magnetic field is much smaller than the magnetic field needed to saturate the magnetization of the nanoparticle. It is able to take into account both the reversal by thermal activation and the reversal by Brownian motion.The linear response theory uses an average relaxation time
, given by . The out of phase component of complex susceptibility is then given by . The hysteresis loop is then an ellipse with an area given by .The Stoner–Wohlfarth model and the maximum area
The Stoner–Wohlfarth model allows one to calculate the hysteresis loop of magnetic nanoparticles at T=0 with the assumption that the nanoparticles are fixed in the magnetic field (the Brownian motion is neglected) and magnetically independent. Its main interest is to predict the maximum hysteresis area for independent nanoparticles with given properties. Indeed, the addition of thermal energy or Brownian motion only leads to a decrease of the hysteresis loop area (see below).The Stoner–Wohlfarth model predicts that the coercive field at T=0 of an assembly of nanoparticles with randomly oriented axes is given by
. The area of the hysteresis is approximatively .Extension of the Stoner–Wohlfarth model to include temperature and frequency
Extensions of the Stoner–Wohlfarth model have been done to include the influence of the temperature and frequency on the hysteresis loop. These extensions are only valid is the effect of the temperature or of the frequency are small, i.e. if. Numerical simulations have shown that, in this case, the expression of the coercive field for randomly oriented nanoparticles is . One can see from this expression that the effect of the temperature is simply to reduce the coercive field of the nanoparticles.Basic mechanisms involved in the magnetization of magnetic multi-domain nanoparticles
In multi-domain nanoparticles the basic ingredients to describe the magnetization reversal are the nucleation of new domains and the propagation of domain wallDomain wall
A domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...
s. Both mechanisms are strongly influenced by the structural defects at the surface or inside the nanoparticles and make difficult any quantitative prediction of the hysteresis loops shape and area from intrinsic parameters of the magnetic nanoparticles.
Models to be used for multi-domain nanoparticles
At low magnetic field, the hysteresis loop is expected to be a Rayleigh loop. In this case, the hysteresis area is, where is the Rayleigh constant.Producing a high frequency magnetic field
Two basic means to produce the high frequency field necessary to study hyperthermia can be used: the coil and the electromagnet. For the "coil" way, a very simple method to get the high frequency magnetic field is to use an induction furnaceInduction furnace
An induction furnace is an electrical furnace in which the heat is applied by induction heating of metal. The advantage of the induction furnace is a clean, energy-efficient and well-controllable melting process compared to most other means of metal melting...
, which precisely used a high-frequency magnetic field to heat materials. It is however conceived to work at a single frequency and requires a water cooling system. It is also possible to build electromagnets or coils able to work at various frequencies at the condition to use variable capacitors. It is also possible to get rid of the cooling system in coils at the condition to build them with Litz wire
Litz wire
Litz wire is a type of cable used in electronics to carry alternating current. The wire is designed to reduce the skin effect and proximity effect losses in conductors used at frequencies up to about 1 MHz...
.
Measuring the temperature and artefacts
A platinum or semi-conductor resistance thermometerResistance thermometer
Resistance thermometers, also called resistance temperature detectors or resistive thermal devices , are sensors used to measure temperature by correlating the resistance of the RTD element with temperature. Most RTD elements consist of a length of fine coiled wire wrapped around a ceramic or glass...
in a high-frequency magnetic field is self-heated and leads to erroneous temperature measurements. Temperature measurements in hyperthermia can be made using alcohol thermometer or optic fiber thermometers.
A colloidal solution heated by an external magnetic field will be subject to convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
phenomena so the temperature inside the calorimeter is not homogeneous. Shaking of the colloidal solutions at the end of a measurement or average on several temperature probes can ensure a more accurate temperature measurement.
Iron oxide nanoparticles
The most widely used magnetic nanoparticles for hyperthermia consists in iron oxide nanoparticles. Similar nanoparticles are used as MRI contrast agentMRI contrast agent
MRI contrast agents are a group of contrast media used to improve the visibility of internal body structures in magnetic resonance imaging . The most commonly used compounds for contrast enhancement are gadolinium-based. MRI contrast agents alter the relaxation times of tissues and body cavities...
. They are in the context of MRI called "Superparamagnetic Iron Oxide Nanoparticles", or SPION. The main interest of these nanoparticles are their biocompatibility and their stability with respect to oxidation. The nanoparticles displaying the largest hysteresis area so far are the SPIONs synthesized by magnetotactic bacteria
Magnetotactic bacteria
Magnetotactic bacteria are a polyphyletic group of bacteria discovered by Richard P. Blakemore in 1975, that orient along the magnetic field lines of Earth's magnetic field. To perform this task, these bacteria have organelles called magnetosomes that contain magnetic crystals...
, with A = 2.3 mJ/g although chemically synthesized nanoparticles reach values up to A = 1.5 mJ/g
Metallic nanoparticles
The higher magnetization of metallic nanoparticles of Co, Fe or FeCo compared to iron oxide increases the maximum SAR values which can be reached using them in hyperthermia applications. A = 1.5 mJ/g has been reported for FeCo nanoparticles, A = 3.25 mJ/g for Co nanoparticles and A=5.6 mJ/g for Fe nanoparticles. The main issue with respect to metallic nanoparticles concerns their protection against oxidation and their eventual toxicity.Ex vivo experiments
Ex vivoEx vivo
Ex vivo means that which takes place outside an organism. In science, ex vivo refers to experimentation or measurements done in or on tissue in an artificial environment outside the organism with the minimum alteration of natural conditions...
experiments in hyperthermia require to make tumor cells absorb magnetic nanoparticles, to place them into an alternative magnetic field and to test their survival rate compared to tumor cells which would follow the same protocol but would not absorb magnetic nanoparticles.
Clinical trials
The only hyperthermia setup suitable to treat humans has been developed at the Charité Medical School, Clinic of Radiation Therapy in Berlin. Andreas Jordan's team in this hospital has performed clinical trials on patients with prostate cancers.External links
- Hyperthermia - Cancer therapy hots up article on physics.org