Hyperthermia is a medical heat-treatment, widely used in various medical fields and has a well-recognized effect in oncology. It is an ancient treatment. However, when making hyperthermia we are limited by numerous biological, physical/technical and physiological problems. The word hyperthermia means increased temperature by heating of tumors. This relatively simple, physical-physiological method has a phoenix-like history with some bright successes and many deep disappointments. Why is this enigma? What do we have in hand? Answers lie in the applied techniques.

Introduction

Cancer and its treatment have been one of the greatest challenges in the medical science for centuries. Nowadays, enormous economic and human resources are involved in this field, but according to the epidemic data the solution shall still be awaited for. Sure, the cancer is not the first and probably not the last one among the diseases which despite of the exceptional human efforts have not had any cure for a long time. The development of the medical knowledge in most of the cases follows some critical situations and crises, preparing the medical science to avoid the next crisis of the same nature.

The medieval medicine insisted basically on the ancient rule of “no cure”¹ for cancer, but the diagnostics and categorization had been further developed.² However, the treatment of patients suffering in cancer was put in practice only in the second half of the 19th century. Definitely, the main idea was always to concentrate on the drastic elimination of the tumor by surgical way, but they improved the therapies by drugs and diets as well.³ At the beginning of the 20th century the basis of the modern oncology had been established by a distinguished branch of scientists: Schleiden, Schwann, Virchow, Halstedt, Wertheim, Billroth and others.⁴ Nowadays, the oncology became one of the most interdisciplinary research fields: including the biology, biophysics, biochemistry, genetics, environmental sciences, epidemiology, immunology, microbiology, pathology, physiology, pharmacology, psychology, virology, etc. The modern oncology applies highly effective methods and treatments, but their side-effects and, in consequence, the impairment of the quality of life are also remarkable. In general, patients are treated with chemo- and radiotherapy to their toxicity limits in order to achieve maximal tumor destruction. However, these treatments are often not enough. In general, the tolerable toxic level limits the applications: the actually expected tumor destruction would request higher doses than it is tolerable as regards the accepted level of side effects (fig. 1A). The applied therapies might drastically reduce the actual demand of the further tumor destruction, but unfortunately the acceptable toxic tolerance is also reduced and the therapeutic gap is reestablished in most of the cases (fig. 1B). The gap between the toxic tolerance and the desirable destruction has to be bridged by a method, such as the hyperthermia: based on physical and physiological effects, its stress has no chemical origin or serious toxicity. Hyperthermia is an ideal combination therapy. It has low toxicity, mild side effects, and has been shown to provide synergies with many of the traditional treatment modalities.

Figure 1

A) There is a therapeutic gap between the toxic tolerance and the desired destruction. B) Treatments modify but do not eliminate the gap. Rationale of hyperthermia: surmount the therapeutic gap.

Besides the limited toxicity, the developed resistance against the actually applied treatments could also limit the efficacy of the methods. While the first treatment is able to suppress the tumor under its detectability, but it is not the sure outcome, as some malignant cells remained behind keep the possibility of relapse. The observed and hopeful complete remission in most of the cases makes only a temporary success. Parallel with this a more serious problem arises than this: some of the nonvanished malignant cells might become resistant to the actual treatment, so its next application could not be that successful as it was before, and in the successive steps we lose this treatment facility. Hyperthermia can be helpful in these cases as well because it may resensitize the malignant cells and enables them to be destructed.

Heat therapy (Hyperthermia) is an aboriginal, traditional healing method. Even the first known, more than 5000 years old, written medical report from the ancient Egypt mentions hyperthermia.⁵ The use of hyperthermia for cancer therapy was first documented by Hypocrites for the treatment of breast tumor.⁴ His approach of course was mainly supported by the Greek philosophy, where the fire (heat) had the highest level of abilities and freedom. Hyperthermia was also mentioned throughout the Middle Ages,⁶ but due to the strict Galenus' school and the inadequate heating techniques, the treatment has never became a standard in the oncology practice.

Among the first modern curative applications in oncology, Busch⁷ and Coley⁸ were successful at the end of the 19th century with artificial fever generated by infection and toxins, respectively. These systemic applications soon were followed by local and regional heating.^9-11 The leading German surgeon in that time, Bauer KH opinion in his monograph “Das Krebsproblem” about the oncologic hyperthermia is typical: ”All of these methods impress the patient very much, they do not impress their cancer at all.” However, very early, in 1912, a controlled Phase II clinical study was published on 100 patients showing the benefit of the thermo-radiation therapy.¹²

At the end of the last century, energy delivery by electromagnetic fields became possible; nevertheless, its use for hyperthermia only began about 30 years ago. The first symposium on oncological hyperthermia was held in Washington DC, USA in 1975; and the second one in Essen, Germany in 1977. Both conferences were supported by the local scientific communities. We may reckon with the born of the modern oncological hyperthermia from this time on as a strong candidate and a member of the acknowledged tumor therapies.

Hyperthermia today, like many early-stage therapies, lacks adequate treatment experience and long-range, comprehensive statistics that could help us optimize its use for all indications. Nowadays, the lack of acceptance of the oncological hyperthermia has not only statistical reasons; but the technical solutions are not adequate enough and the quality assurance, the control and standardization of the method itself have not been solved yet satisfactorily. Nevertheless, we will present a wealth of information about the mechanisms and effects of hyperthermia from the scientific literature and our own experience in the hope of proving hyperthermia's worth for further research.

Many of the researchers evaluating the capabilities of oncological hyperthermia share the opinion of the editorial comment of European Journal of Cancer in 2001: the biological effects are impressive, but physically the heat delivery is problematic. The hectic results are repulsive for the medical community. The opinion, to blame the “physics” (means technical insufficiency) for inadequate treatments is general in the field of oncological hyperthermia, formulating: “The biology is with us, the physics are against us”.¹³ In the latest oncological hyperthermia consensus meeting the physics was less problematic. However, in accordance with the many complex physiological effects a modification was proposed: “The biology and the physics are with us, but the physiology is against us”.¹⁴

The present situation apparently supports the above opinions. The opinion, to blame the “physics” (means technical insufficiency) for inadequate treatments is general in the field of oncological hyperthermia. Is the modern technique unable to meet the demands, indeed?

There is a definite group of physicians who submit that hyperthermia has a strong curative force in oncology; however, another group exists believing the opposite. Sure, both the positive and negative believers are not helpful to clarify the situation. We need interdisciplinary scientific analyses and hypotheses to go ahead with the topic.

The state of oncological hyperthermia today is similar to that of radiology at its infancy. When ionizing radiation was first discovered, many hypothesized its usefulness in oncology, yet its exact techniques, dose, contraindications, limits, and the conditions of optimal treatment were determined only several decades later. This is a natural process: every beginning shows these “symptoms”. However, the baby normally has to leave behind the teething-brash after a definite period. To remain a baby afterwards is abnormal. We think oncological hyperthermia has to get beyond the babyhood, it has to grow up in more definite manner; it has to cast off the infantile period!

Our present paper tries to explain the problem of the technical solutions. We would like to promote the harmony of the disciplines, and this interdisciplinary approach might be “with us” to win the war against the cancerous diseases.

Characterization Demand

Hyperthermia by its definition is the overheating of the selected tissues. Heat dosing and treatment standardization at hyperthermia are still significant problems. Technically, the dosing and control of the deep heat transfer is very difficult, requesting the same reproducible heat dose for each treatment within the target tissue. A “success parameter” has to take into account the efficiency of focusing, the heat conduction within the body and many other physiologic conditions before reliable protocols can be worked out.

Thermodynamical Approach

Heat put into a system (ΔQ) plus work done on a system (ΔW) is equal to the increase in internal energy of the system (ΔU), (first law of thermodynamics²⁹):

Sign Δ means a small change. During this small change the system does not alter (quasi-static approach). In a more rigorous description a differential calculus has to be used. Eq. (1) shows that the internal energy U is determined by the energy exchange. This exchange has various forms, all the available interactions (denote their number by n) have to be calculated. These terms can be easily defined by the pair products of intensive (Y_i) and extensive (X_i) parameters:

For example some of the terms are:

where T, S, p, V, Φ, e, E, P, H, M, α, s, f, l are the absolute temperature, entropy, pressure, volume, electric potential, electric charge, electric field, electric polarization, magnetic field, magnetization, surface tension, surface area, linear force, length, respectively; while N_j and μ_j are the number/mass and chemical potential of the various (k) particles (molecules, ions, clusters, etc.) in the system. Many other pair interactions (all the energetic terms) may be included in this energy balance. All the pairs have special biological meanings: TΔS is the absorbed heat, pΔV is the work of pressure (volume changes), ΦΔe is the work of the moving electric charges, (E·ΔP) and (H·ΔM) are the work of the electric and magnetic fields, μ_jΔN_j are the terms of the chemical reaction energies of various (j=1,2,3,…,k) species, aΔs can be the energy of the surface (membrane) changes, fΔ l could be the work of the muscle-fibers, etc. Only one of the terms, namely, the heat energy has temperature, all the other terms are other kinds of energy consumptions.

Definitely, if there are not any structural, chemical etc. interactions in the system, only the heat is absorbed, than (1) has no ΔL term:

or

where T_o is the original body temperature [C^o], c is the specific heat [J/kg/K] showing that how much energy is required to heat up 1 kg tissue by 1 K, ρ, V and m are the density [kg/m³], the mass [kg] and the volume [m³] of the heated tissue, respectively. ΔQ is the energy delivered [J] into the heated tissue. This picture could be the basic of the misleading interchange of the heat dose and temperature change; in (5) they are proportional. Do not forget that (5) is only valid if there is not any other interaction than the heat absorption. Of course, this is not the case at all in hyperthermia, where our definit goal is to change the structure and the biochemical constituents. In the study of (5) it is also important, that the time (dynamic effects) is not included in these static considerations. However, if the energy balance is time-dependent (the heat delivery and heat sink have power like relations, [J/s]), than the temperature becomes also time-dependent.

Have we any reason why hyperthermia uses intensive thermodynamic parameter (temperature) regarding the quasi-equilibrium of the treatment? No, of course, we have not. It is only the historical “bad habit”. This bad characterization is mostly responsible for the contradictory results, for the loss of comparability of the results, for the blame of physics/physiology!

Bio-Heat Equation

The thermodynamical energy balance defines the actual heat exchange: the energy change in time (∂U/∂t), its flow in space is: grad(I_U)= Σ(∂I_U/∂x_i), and its sources qU=q_e+q_m+q_b, where I_U is the energy current density, q_e, q_m and q_b are the energy source/sink from electric, metabolic and blood perfusion origins, respectively. The well known balance equation³⁰ is:

As it is well known from reference 31, the current density of the heat flow is proportional to the temperature gradient (heat diffusion):

By substituting (7) into (6) and by using (4) we obtain the so-called bio-heat (Pennes-) equation32 which serves for the description of tissue heating and internal energy transport. It has the form of

where T is the temperature of tissue; ρ and c are the mass density and the specific heat of tissue, respectively; λ is the coefficient of thermal conduction; ρ_bc_bv_b is the blood perfusion; T_b is the blood temperature (it is in fact a negative value at the locoregional treatment, cooling term, due to Tb < T; while in the whole body treatment it will be positive.).

The q_m term is determined by the metabolic rate (M) and the mass density: q_m = ρM. The metabolic rate grows by the temperature gain ΔT: q_m∼1.1^ΔT;³³ therefore, in the case of 6°C increase the amount of growth will be 1.8-times. The metabolic heat production of tumor depends on the doubling time of its volume (ref. 34 and fig. 2), so it is determined by the speed of the development.

Figure 2

Metabolic heat production of breast cancer lesions (tumor size: 0.6-4.0 cm), shown as a function of the reciprocal value of volume doubling time. The rapid procedures (large 1/t values) are more intensive heat producers.

Defining q_e is more complicated, because it needs an approximation of the energy absorbed from the electromagnetic fields. In real situation the bio-electromagnetic interactions are more complex, and the measurement of the absorbed energy is necessary. The energy absorption is characterized by the specific absorption rate (SAR, [W/kg]), identifying the absorbed energy in unit mass:

The simplest case is the current flow through the given tissue, when the well-known Joule-heat is developed. This value (taking into account the well-known Ohm-law) is:

where E_local is the locally presented electric field in the tissue and s is the electric conductivity.

The solution of the partial differential equation (bio-heat equation) (8) should be reasonably given numerically because of the following arguments:

• The exact geometry of tissues is unknown;
• The equation parameters are not available in their exact form, the values change by tissues, tumors and individuals, as well as those are nonhomogenic in the tumor-tissue;
• A certain part of equation parameters—for example perfusion rate, metabolic thermal power, electric thermal power—can be expressed as a function of temperature, therefore the equation may be nonlinear as well;
• The treating electric field and for this reason the electric thermal power can be expressed as a function of position, and because of the skin effect it depends also on the temperature;
• The parameters of the transitional zone between the tumorus and healthy tissues are unknown; therefore the exact definition of boundary conditions is almost impossible.

The unanimity conditions of the bio-heat equation (8) are the initial data and boundary values. The initial data can be easily specified by the actual initial body temperature (T_o), assuming its homogeneity in the malignant area and its surrounding. (Note: sometimes it is not the case because of the higher tumor temperature due to its increased metabolic rate.) However, the boundary conditions (which are essential to solve (8) at least numerically) are more complicated to determine. Three types of boundary conditions may be considered:

• The boundary surface of the targeted area has a constant temperature. This assumption is supported by the observation that the functioning of tissue is normal outside the area, thus the increase in temperature augments the perfusion rate and—as a result—keeps the healthy tissue section on constant temperature.
• A boundary layer is formed on the surface of the targeted area. This could be physiologically constructed by a transient tissue between the malignant and healthy areas. The considerable increase of perfusion in the healthy tissue section close to the boundary surface presents an other problem, as the extent of this should be known as well.
• The transition of conductive heat-flux density and temperature is continuous on the boundary surface of target area. The consideration of this boundary condition means that the bio-heat equation (8) shall be solved both for the target area and for the area outside thereof, and the two solutions shall be matched at the boundary of the two areas in consideration. This is a very complicated task, mainly in the case where the surroundings can not be considered as infinitely large. Therefore, a newer boundary condition is needed.

These conditions—with the additional problem of knowing the SAR distribution in-situ—clearly show that the solution of bio-heat equation does not realistic for practical use. However, note the actual driving forces in the equation, which are always the temperature changes (gradients in space and time), and no assumption of the homogenic temperature could be valid. (In the case of homogenic temperature the bio-heat equation (8) does not exists.)

Control-Parameters

Technical Challenges

In the early days, simple heat diffusion was applied by using hot water or wax baths and heated objects.⁷⁵ Today, focused and unfocused energy delivery are applied by using electromagnetic fields.

To heat up the malignant tissues is a relatively simple demand but doing it selectively (focused on the malignancy only) up to the desired temperature (over 42°C) is not a simple technical task. This complication was the basis of the editorial: the physics are against us.¹³ The main technical problems:

• Deepness—achieving a deep energy delivery,
• Focusing—proper focusing (selection) on the malignant area,
• Reproducibility—conducting the treatment in the reproducible way,
• Control—having proper control of the process by keeping the parameters of the treatment,
• Personalization—making an in-situ tuning to fit to the actual situation to the best.

Regarding the technical and biophysical side of hyperthermia there are some problems. The most important ones are as follows:

1. The heat shock protein (HSP) concentration of tumorous tissues is high, as a matter of coarse, without any external influence and is further increased by the different inventions (apart form their modes).
2. The heat effect not suitably provided or focused may increase the oxygen supply of tumour, and therefore may intitiate its quick growth. The misfocused heat input involves the risk of necrocytosis of healthy tissues, and therefore may step up the formation of metastasis.
3. Technically, the reproduction and stability of heat input is difficult to control, therefore there is not any such technical “success parameter” the maintenance and monitoring of which can be considered as a reliable indicator of the success of treatment. The treatment of complex metamorphosis requires complex parameter ensemble, in this way, it is not to be expected that the succesful treatment process can be controlled by one or two parameters.
4. Technically, the main problem is the appropriate selection of the heat input, as well as, the selection of heat input technics and the formation of actual applicators are of vital importance. The applied eletromagnetic effect may cause in itself HSP increase and undesired tolerance formation without any heat input and temperature increase,⁷⁶ and may have some effect on the reactions of immune system as well.⁷⁷

Overview of the Existing Methods

Because of the huge difficulties in the proper technical realization, numerous and quite different technical solutions have been developed. Some categorizing points of the available techniques are collected in Table 1.

Table 1

Categorizing of hyperthermia methods.

The form of heat (energy) delivery has also considerable varieties (Tables 2, 3) applied in practice. Their invasivity and selectivity are categorized in Tables 4 and 5. Sure, the most modern heating technics are connected to the electromagnetic interactions. Their increasing number of applications could be observed in different categories of frequency (Table 6).

Table 2

Heat delivery methods for hyperthermia.

Table 3

Energy production categories for hyperthermia.

Table 4

Invasivity of hyperthermia methods.

Table 5

Selectivity of hyperthermia methods.

Table 6

Applied frequency ranges for hyperthermia.

Electromagnetic Heating Processes

Basic Effects

The electromagnetic fields (magnetic induction B and electric field strength E) interact with the material and change its state. The interacting electromagnetic field is described by the Maxwellian equations adapted in the actual medium:

where the notations rot and div are the derivatives by the space variables (field changes in the space), as well as ε_o and μ_o are the absolute permittivity and magnetic permeability, respectively. ρ_eff and j_eff are the material-dependent sources of fields, that is, the effective charge and current density, respectively. Their values depend on the free charge density (ρ) and their current densities (j), as well as the polarization (P) and magnetization (M) vectors of the material:

Assuming that the polarization depends only on the external electric field and the magnetization by the external magnetic field:

where α_e and α_m are the electric and magnetic susceptibilities, respectively, creating the relative electric permittivity and relative magnetic permeability ε_r = 1 + α_e and μ_r = 1 + am, respectively. The energy density (ρW) of the electromagnetic radiation⁷⁸ is:

In the case of radiofrequency currents the energy source (10) of bio-heat equation (8) mainly derives from the dielectric loss, so:

The temperature gain by the absorbed energy (if the physiologic modifications are neglected) is shown in Figure 3.

Figure 3

Result of a model calculation of the temperature gain in homogeneous media with stabilized surface temperature (constant environment).

The complex amplitude of the energy delivery (energy radiation, e.g., Poynting vector (S) expressed in W/m²) can be calculated as

The electromagnetic energy absorbed by the treated part and converted into heat equals to the surface (A) integral of the vector's average value calculated for the boundary surface of the treated part. Therefore,

The schematic structure of the complex conditions of the treated bio-matter is shown in Figure 4. The multilayered structure is the most common from the point of view of the chosen locoregional treatment. The layers represent the various tissues, e.g., skin epidermis, skin capillary bed, fatty tissue, muscle tissue, tumor tissue, etc. It may include nonlayered structures like blood-vessels, bone structures, lymph nodes, etc. The tissue (and the transmitter material, which is in most of the cases air or water) is characterized from electromagnetic point of view by the complex impedance function, which depends on the basic material constants, such as, on the dielectric permittivity (ε), the magnetic permeability (μ) and the conduction (σ) of the tissue. All the other parameters—like the attenuation constant (α), the phase-constant (β), the propagation constant (γ), the penetration depth (δ) and the actual wavelength in the tissue (λ), as well as the reflection ratio (ι)—can be calculated⁷⁹ from these basic material constants ε, μ and σ (f is the frequency of the applied treatment):

and the reflection and the impedances may be calculated^79,80 in the ith layer as:

Figure 4

Layered structure of the treated body part. The layers represent different tissues (e.g., skin and its structures, adipose tissues, muscle tissue, tumor tissue, etc., noted by numeration), characterized by their “d” thicknesses and “Z” (more...)

The interaction description is complicated enough, but it is definitely much more complex in the reality, where the perpendicularity, homogeneity, radiation condition, source geometry etc. might modify the results. This is the reason why at the calculation of real cases only numerical approximations can be considered. A minor possible simplification is that in the natural situation (without artificially added materials) the bio-material has no magnetic properties, as its relative magnetic permeability equals to one with high accuracy.

We have further complications when trying to keep in hand both the rather complex bioelectric interactions and the highly sophisticated mathematical apparatus: if our aim is to accomplish a deep heating condition we face many problems physically and physiologically as well. The main problematic points are:

1. The incident energy has a frequency-dependent exponential decay in the depth (fig. 5). The penetration is defined by the depth where the field intensity decreases by 1/e-part (about 36%) of the incident beam. (The absorbed energy is even less: about 14% of the incident energy.) The penetration of the field into the targeted material depends significantly on the applied antenna arrangement. The planar waves at the applied—relatively low—frequency generated by capacitive coupled antennas penetrate into the bio-systems by 14-20 cm^79,81 depending on the actual electric conductivity of the bio-tissue. The penetration depth for the planar waves is shown on Figure 6.
2. The incident energy beam reflects on the surfaces and internal boundaries as well. Generally, we must note that the reflection at the air-skin boundary is very high (it is more than 0.8 at 100 MHz and about 0.6 at 10 GHz⁸²).
3. The subcutaneous capillary bed tries to balance the local homeostasis, cools the skin by intensive blood perfusion. Also the deeper layers are blood-perfunded delivering rapidly the heat away from the targeted area.
4. The physical/electrodynamical parameters guide the heat absorption, which could prefer other selectivity than the desired one (e.g., the bone treatment could be problematic). Hot-spots/ layers/areas could be generated in unwanted locations involving risks for the healthy tissue. The hot-spot formation depends on many physical and physiological factors, such as:

• The local RF-current density increases by the decreased cross section of flow.
• The reflected waves at the internal tissue boundaries are summed.
• The tissues are nonhomogenic, their conduction and permitivity may change drastically by places.
• The body cavities could serve as hollow-space resonators caused by standing waves and their local field maxima.

Figure 5

Schematic representation of the basic electromagnetic methods for an oscillating circuit. The three basic effects (electric field, magnetic field and electromagnetic radiation) are interconnected, their actual domination in one of the circuit elements (more...)

Figure 6

Penetration depth of planar waves into the tissue versus the frequency and the conductivity. The depth is approximated from simplified conditions of the imperfect conductor. (The shaded area represents the most common values for muscle tissue.)

The dangerous energy absorption and the consequent hot-spot on the surface are created not only by the maximal incident energy but by the low relative dielectric constant (large voltage drop) and the possible lateral currents (fig. 7).

Figure 7

The possible risk of surface burn originates from the perpendicular gradient of the field absorption, the low dielectric constant of the skin and subcutan fatty tissues, as well as from the possible lateral (surface) currents. All of these problems can (more...)

Technical Solutions

The electromagnetic, “deep-thermal” (not convective and not conductive) heating can be considered as significantly better than the convective and conductive methods. While the convective and conductive methods are limited by the thermodynamic heat conduction, the efficacy of the electromagnetic methods is mainly determined by the extensive interactions determined microscopically. The utilized energy can be uncoupled at any essential position of oscillatory circuit producing the given frequency. Therefore, this fact determines the radiation (Poynting's vector), the magnetic (inductive) and electric (capacitive) treatment techniques (fig. 8). The techniques are basically different in their dominating electromagnetic effects, and also differ in their actual technical solution (fig. 9).

Figure 8

Schematic representation of the basic electromagnetic methods for an oscillating circuit. The three basic effects (electric field, magnetic field and electromagnetic radiation) are interconnected, and their actual domination in one of the circuit elements (more...)

Figure 9

Basic arrangements of the electromagnetic methods: A) Capacitive coupling, using the electric field in a capacitor, B) Magnetic (inductive) coupling, using the magnetic field of a coil, C) Radiative coupling, using the radiated field of an antenna-array. (more...)

Main characteristics of the methods are collected in Figure 10.

Figure 10

Basic electromagnetic methods: A) inductive (magnetic), B) capacitive (electric), C) antenna-array (radiative).

Radiative Coupling

The radiative coupling by antenna array has two distinguishing categories in accordance with the relation of the wavelength (frequency) and the source-target distance (fig. 11). If the target distance measured from the source is smaller than the applied wavelength, then the wave can not be considered as radiaton, it acts by the change of the fields (E and B), and the Poynting vector (S) has no definite role. The two radiative methods are mainly different in their penetration depth (the far –field is more shallow) and the focusing ability (the interference can be modified by the phase-frequency characteristics, the attenuation only by the orientation of the beam). Basic disadvantage of the microwave treatments of higher frequency and shorter wavelength lies in its low penetration depth. (From this respect it slightly differs from the diffusion heating.) Other disadvantage is the possibility of destruction during the heating process, namely, similarly to the ionization radiation this method has harmful influence on the healthy tissues because of the high specific energy input and the selective energy absorption regarding the hydrogen oxide molecules. As the usage of kitchen microwave oven has also demonstrated, the open microwave source may entrain serious health problems.

Figure 11

The radiative coupling is well described by the radiation alone (Poynting vector) when the wavelength is small (frequency is high). In this case only the energy attenuation acts. If the wavelength is longer than the source-target distance, interference (more...)

A part of the near-field treatments uses significantly higher frequencies (up to the limit, which determines the wavelength and the target-distance), and uses interference focusing. The applied antennas (dipoles) work in the capacitive regime, however their optimal tuning is far away from the direct capacitive coupling; an array is harmonized to reach the interferences in the desired depth and place. Due to its higher frequency the penetration depth significantly decreases, which is partly compensated by the additional effects of the multi-antenna array.

The SAR values depend on the situation (far- or near-field), and are reduced considerably in near cases. The empirical ratio⁸³ observed:

where ζ_v and ζ_h are frequency-dependent parameters, while λ_v and λ_h are the wavelength in air at the target place; the indexes denote the vertical and horizontal wave-positions. The ζ_v and ζ_h parameters were measured⁸⁴ in the 10-915 MHz region. Using these data, the actual values of λ_SAR are always smaller than 1, measured also by others.⁸⁵ For 13.56 MHz and 135.6 MHz the values are 0.95 and 0.22, respectively; so the low frequencies in fact have no differences between the near- and far-field applications, while the SAR decreases in near fields at high frequency by more than 4-times. The inductive (magnetic) and capacitive (electric) couplings are always near field applications due to their low frequency and the field effects.

Radio-Frequency Waves in Near-Field Radiation

The radio-wave treatments belong to the lower frequency group of nonionizing radiations, covering the electromagnetic range approximately from 1 MHz to 30 MHz. With the reduction of frequency the risky and uncertain effects typical of microwave decrease, while the penetration depth significantly increases, and the specific delivered energy shows more homogenous distribution.

Magnetic Field

A possibility of energy decoupling induced fundamentally by magnetic field may signify deep energy absorption. The penetration depth of magnetic field is extremely high in bio-systems, because of the very week interaction between the magnetic field and bio-material. For this reason, the energy absorbed by the tissues—from the energy transported by the magnetic field—manifests itself in the Eddy current or induced current part, namely, it is proportional to the conductivity of material. In this manner the decoupling with magnetic field is weak, its control is difficult and its selectivity can be assured only as a function of conductivity. The magnetic coupling can be enhanced significantly, if a magnetic material is placed into the targeted area. Generally, nano- or microparticle suspensions, seed, grain or rod magnetic pieces are inserted invasively. In more sophisticated cases the magnetic material's Curie-temperature (ferro-/paramagnetic phase transition) is set to a desired temperature in order to control the heat-delivery and fix the maximal temperature of the magnetic material (the ferromagnetic material absorbs, the paramagnetic does not absorb the magnetic field).

Electric Field

The energy depletion is effectuated dominantly by electric field anyway. Its advantage, namely, the strong interaction with the highly organized bio-matter (which is typically good dielectrics) also could be a disadvantage, though the penetration depth decreases as compared to the magnetic field. Consequently, the capacitive arrangement offers other advantages (the absorbed energy can be significantly increased and extra selectivity factors can be included in the system) and sets other problems (low penetration and possible surface or subcutaneous burn).

Next, we are going to discuss the case when the treated, layered part (for example a kernel and its pellicle and surface interface) is between the electrodes of the condenser supplied by radio-frequency power supply (fig. 12, a simplified model of fig. 4). Now, we are going to determine the electric power transformed into heat in the treated area with some simplifying assumptions.

Figure 12

Principle of dielectric heating (Layers represent the actual structure).

(1) The dielectric materials pursuant to (fig. 12) are homogenous, namely, the ε_r relative permeability and the σ electric conductivity are constant by layer (2). The problem is symmetric from geometric and electric point of view, namely, the thickness of the appropriate layers and their electric parameters are identical; the treated area is spherical and is to be found in the geometrical centre of the arrangement. (3). The extension of the area where the treated part can be found is large as compared to the extension of the treated part. This later assumption assures that a homogenous field is produced even in the tissue part including the treated area. Its advantage is that the field to be matched in accordance with the boundary condition can be determined by using an arrangement not including the treated area. It should be noted that this restriction is not too strong as the dipole field induced by the treated area is weak, and—as we will see—decreases in inverse ratio to the third power of the distance. The absorbed power which is transformed to heat in bio-matter can be calculated as follows:

where U_eff is the effective value of the generator voltage. The most important characteristic feature of the dielectric heating is that the order of magnitudes of the conducting and displacement (capacitive) currents is identical. At the same time this means that the magnitude order of dissipative (exothermal) process attached to the two types of current can be identical as well. The model of the one-layer dielectric heating can be seen in Figure 13. The field between the electrodes is excited by the high-frequency voltage impressed on the electrodes. The electromagnetic field can be expressed by using the Maxwell equation of electromagnetic field.

Figure 13

Physical model of dielectric heating.

As in the examined model the space charge equals to zero, and the living material is paramagnetic from magnetic point of view. We suppose that the living material between the electrodes can be considered homogenous—in the first approach—with linear behaviour at the given field strength. As the field strength is known, the electric thermal power can be calculated:

where we utilized that in the case of sinusoidal feeding U = Ũ exp(jωt) and J_o(pr) is the 0th order Bessel function.³² The SAR can then be approximately calculated in the form of

Comparison of the Methods

The typical characteristics of these methods are summarized in Table 7. Note that these values are only orienting, covering the mainstream of the electromagnetic heating; however, the actual applications could be rather different. In the followings, due to its dominant presence and practical importance, only the near-field applications are discussed.

Table 7

Basic electromagnetic methods: a) inductive (magnetic), b) capacitive (electric), c) antenna array (radiative).

A significant difference in application of the various methods lies in the focusing mechanisms. The artificial focusing (radiative and magnetic approaches) directs the energy absorption into the area where the malignancy is located, and tries to heat up the area homogeneously, which is in most of the cases not homogeneous at all. In the case of multi-centered liaisons the covered area includes both the healthy and malignant areas (fig. 14). In the capacitive case the actual differences in complex impedance and conductivity determine the area of the heat absorption irrespective of its size or multiplicity (fig. 15). The advantage is the self-supporting nature, and it has a positive feedback by the growing temperature⁴² when the selective differences between the malignant and healthy areas become even more pronounced.

Figure 14

Focusing arrangement by artificial focusing (radiative and magnetic approaches).

Figure 15

Focusing arrangement by capacitive arrangement (self-selective technics).

New Directions in Electromagnetic Oncologic Hyperthermia

Our main aim—namely to destroy selectively the malignant cells on microscopic level— needs a modification in our fixed ideas, because the applied hyperthermic effects are not selective enough, and their demand to the high temperatures introduces a new risk of toxicity: the deep burn. Recently, scientists have started to realize that the thermostatical thinking (the temperature has to be raised up as homogeneously as possible in the malignant area) has to be replaced by a more adequate thermodynamical one (the properly conducted temperature differences could be effective in destruction). Now we see that the hyperthermia-induced temperature gradients could have significant biological effects. A new branch of hyperthermia known as extracellular hyperthermia⁷⁴ or electro-hyperthermia²⁶ has been developed around this concept. Although this new technique recognizes the benefits of increased tissue temperature and its biological consequences, it also argues that nonequilibrium thermal effects are partially responsible for the observed clinical deviations from the purely temperature based treatment theory.

Electro-hyperthermia is based on a capacitively coupled energy transfer applied at a frequency that is primarily absorbed in the extracellular matrix due to its inability to penetrate the cell membrane.⁸⁶ Although these temperature gradients typically relax within a few milliseconds, a constant energy delivery can maintain this gradient for extended periods of time, and may initiate special transports through the cellular membrane. The gradient-constructed heat flow might be significantly large and damage the first step of the membrane. This heat flow can produce extra ionic currents through the membrane, which depolarizes and therefore destabilizes the membrane. This requires ATP, resulting in further heat production at the membrane. The membrane permeability of water is much higher than in the case of ions, therefore, it is the main transported component in the thermodynamic coupling. Therefore, this thermal flux builds up an intracellular pressure, which is about 30% above the normal.⁷⁴ Since malignant cells typically have relatively rigid membranes due to increased phospholipids concentrations,⁸⁷ an increase in pressure will selectively destroy the malignant cells before it affects the healthy ones. These effects allow the application of hyperthermia not only in a more effective way, but also for the areas which have been mostly contraindicated for this method: the lung, liver, pancreas and brain treatments. Its preliminary clinical trials show the reality of the expectations: the malignancies of the liver,⁸⁸ brain⁸⁹ and pancreas⁹⁰ are exceptionally well respond to such type of treatment.

Cellular Effects

Some biophysical effects on cellular level might modify the technical applications. These microscopic effects mainly depend on the electric field, and in low frequency ranges may considerably influence the actual hyperthermia effects.⁷⁴

Absorption in Cellular Level

The effective electric field acts by the high polarization (large dielectric constant) of the bio-systems. From dielectric point of view, the simplest approach is to study the cellular structure in its three rather different parts (fig. 16),⁸⁶ as calculated, the frequency-dispersion energy absorption of the characteristic cellular structures (fig. 17).

Figure 16

Cellular structure by its dielectric properties.

Figure 17

Frequency-dependence of the absorbed energy for the cellular parts.

Changes of the Membrane Potential

The cell-membrane potential as a function of temperature may be calculated from the Goldman-Hodgkin-Katz (GHK) equation.⁹¹

where k is the Boltzmann-constant, e is the electron charge and C_i denotes the concentrations in different ions (Na, K, Cl subscripts) and different locations (extra- (e) and intracellular (i) superscript), ω_i denotes the membrane permeability for the ith ionic components. (The GHK equation was firstly proven on the nerve cells, but this describes the basic dynamical phenomena of the membrane stabilization for every eukaryote system. The static part of membrane stability is described by the Donan-approach.) The temperature dependence of the membrane potential is trivially linear. Substituting the real values of the membrane potential Umembr. = -70.2 mV, the slope of its temperaturedependence equals to -0.23 mV/K, which is definitely not a large effect, and we may conclude that the cellular membrane will not be effected by the temperature alone.

Consequently, the membrane potential increases, and the cell is hyperpolarized under increasing temperature.

Temperature Gradient on the Membrane

When the frequency is low enough to the selective energy-absorption (see fig. 17), then the temperature gradient has essential role in the membrane destruction. The actual energy balance is: ρ_ic_iV(dT/dt) = I_q + P_m, where ρ_ic_i is the specific heat capacity of the cell, V is the cell-volume, P_m is the metabolic heat-power. The I_q heat-current contains a metabolic and an electric term: I_q = I_qm + I_qe, where I_qm = -P_m ≈ const., so I_qe = ρ_ic_iV(dT/dt). Hence the heat-current density is j_qe = ρ_ic_i(V/A)(dT/dt), where A is the surface area of the cell. Its numerical value at 1K/s heating rate equals to j_qe = 140(W/m²), which is significant.⁷⁴ The temperature difference between the two sides of cell membrane can be calculated by the expression ΔT = (j_q/α) ≈ 0.007K. Consequently, the actual gradient on the 7 nm thick membrane amounts to 10⁶ K/m, which is a remarkable large value! It is well above the natural heat flow induced by metabolism, which is only j_qcell≅ 1.5·10^-3(W/m²), thus causes negligible (ΔT ≅ 7.5·10^-8K) temperature difference at the cell membrane.

Membrane Damage by Constrained Ion-Currents

According to the Onsager's nonequilibrium thermodynamic approach, all the various transport processes are tightly coupled, so in our present case, heat-transport is accompanied by electric current and mass transport. The Onsager-relation for heat and electric transport coupling takes the form of

where Φ is the electric potential, and the Lik values are the transport coefficients. The observed values are one order of magnitude larger than the coupled one,³¹ so we use the L_qe/L_qq ≈10^-1 approximation. Hence: j_e ≈ J_q (L_qe/L_qq) ≈ 1,510^-1 (A/m²). The usual data⁹² are j_Na = 1.26·10^-2A/m²) and j_K = 4.53·10^-2 (A/m²) for Na⁺ and K⁺ ions, respectively. In consequence, the forced current density is significantly larger than the natural one. This forced current is mainly Na⁺ influx. It depolarizes and therefore destabilizes the membrane, and stimulates the Na⁺/K⁺ pump activity which results in ATP transformations and further heating at the membrane.

Membrane Damage by Increasing Pressure

According to the Onsager's theorem, the heat flow is coupled to the volume (mass) transport as well. (The entire complex phenomenon is simplified on the intensive pairs only.) The relevant Onsager-relations are:

The membrane permeability is much higher for water than for ions, so the main transported component in this coupling is water. The dynamic equilibrium hydrostatic pressure can be determined by the pressure equality on both sides of the membrane,³⁰ so:

where Q^* is the transport heat and V is the molecular volume of the water. The transport-heat value for 1 liter water at normal conditions (room temperature, normal pressure) equals⁹³ to Q^*H₂O = 71,2kJ, consequently:

This means that the ΔT = 0.01K temperature difference generates Δp = 1.32 bar = 1.32·10⁵ Pa pressure, which is a large value. Consequently, the lateral tensile stress rises due to the lateral dilatation generated by the radial mechanical pressure from the electric field, and the hydrostatic pressure difference tries to balance it. The lateral tensile stress calculated from the above nonequilibrium transports using D = 10 μm cell-diameter and ξ = 10nm membrane thickness results in σ_ny = (DΔp/4x) = 1.32(10 μm/410 nm) ≈ 3·10⁷ Pa = 30 MPa, which is a huge value! Comparing this value to the regular conditions: the induced scalar pressure (from the Maxwell stress-tensor⁷⁸) is σ_r = εE² ≈ 3·10³ Pa, which is too small to be relevant and negligible in relation to the transport pressure. The maximal tolerable lateral tensile stress amounts to σ_max = (2 - 20)·10⁵ Pa,⁹⁴ which is smaller by two order of magnitudes than the temperature induced stress. The increase of the osmotic pressure also contributes as an additional factor to the damage of cellular membrane. The increase of the ECM temperature boosts the electro-chemical potentials in the ECM electrolyte. The chemical potentials are: μ = μ_i0 + V _ip + RTlnγc_i + Z_iFU, where V_i is the molar-volume, μ_i0 is the initial chemical potential, p is the pressure, γ is the activity coefficient, c_i is the concentration and Z_i is the ionizing state of the i-th component. F is the Faraday number and U is the membrane potential. With the increasing j_Na, both j_K and j_Cl decrease, therefore, in stationary membrane state the intracellular concentrations C_k⁽ⁱ⁾ (k = Na⁺, K⁺, Cl^-) also grow. This process increases the osmotic pressure in the intracellular liquid, while decreases it in ECM.

The above theoretical considerations can be used in many applications. Unfortunately, the complications in the analytical way force us to use different numerical calculations. The numerically calculated results for kernels are in good correspondence with the observations, and allow explaining some seed stimulation effects. Also the nondirected effect of the power lines in the plough-lands could be studied in this frame.

Summary

In our opinion, the hyperthermia (definitely, it is a heat-dose treatment) is a temperature-dependent but not temperaturedetermined process. The temperature concept is not bad as long as the physiological factors (blood flow/vascularization, metabolism, chaperone-protein production, dissemination, apoptotic action, etc.) are included, and the tissue can be regarded as homogenic, semi-isolated from the surroundings. Unfortunately, these conditions are not common, so sometimes the temperature gives statistically significant, sometimes random results. This is the reason why some trials check the patients before, and divide them on the “heatable” and “not-heatable” groups,⁹⁵ and randomize for trial only the previous group. For this group the anyway scientifically incorrect and assumed equivalence of the heat dose to the temperature is an acceptable approach. On the other hand, this preselection excludes a large number of patients receiving hyperthermia; however, this treatment could be a help for them as well. The exclusion was made on an insufficient characterization of the method.

A relevant characterization of oncological hyperthermia for quality guidelines has to be started from the aims: it is to destroy the malignant cells! This demand contains some more precise requests: selectivity and blockage of further proliferation and dissemination. Distortion could be promptly direct (the cells become necrotic during the treatment) or indirect (tune killing conditions; the cells become necrotic or apoptotic after the treatment). The demands actually do not contain any temperature request.

Hyperthermia is an emerging effective treatment method in oncology. It has shown significant improvements in tumor response rates and patient morbidity in combination with other treatment methods, such as surgery, chemotherapy, radiation therapy and gene therapy or applied as a monotherapy. Nevertheless, hyperthermia is still in its infancy. The thermal dose quantification is likely to remain of practical importance. We have to characterize the hyperthermia by thermal dose and not by temperature. Thermal dose changes many energetic processes in the tissue, and in their physiology. Most of the changes (structural and chemical changes) are out of modification of the temperature, only the entropy changes. The nonequilibrium thermodynamics describes how the absorbed heat could excite various (e.g., diffusional, electric, chemical, etc.) processes. The dynamism of the absorption determines the dynamism of the processes (e.g., reaction rates, diffusion dynamism, etc.) and, by these, drives the efficacy of the processes as well. These phenomena (which are anyway in the focus of the tumor destruction) are completely out of the possibility of temperature characterization. Hyperthermia suffers from a lack of standards and a lack of scientific consensus about its effects on malignant and healthy tissues. In order that hyperthermia shall gain widespread approval and clinical use, the technique requires extensive further research and standardization. For this we need an open mind and have to outgrow the dogmatic habits.

The hyperthermia is an interdisciplinary approach. We have to use the historic roots, the scientific achievements on other areas. The hyperthermic oncology is in the wave of the demands: nontoxic, excellent in any combinations with other treatments, with minor contraindications.

Hyperthermia has been considered a remarkably developing form of tumorous tissue overheating and tumour treatment. This method is based on the higher heat sensitivity of tumorous tissues and the totality of physiological processes resulting from the effect of heat.

Conclusions and Perspectives

What/who is against the oncologic hyperthermia? Nothing/nobody from outside. We are against ourselves by constraining the temperature concept over all. The physics, biology and physiology are with us if we make a correct approach. We are convinced that the perspectives of hyperthermia in oncology are very bright and promising. What we have in hand is a practically nontoxic effect with huge potential and advantages. However, we have to clarify the technical issues to make this capable method technically comparable, and provide for a control which is safe enough in terms of modern medical demands.

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