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Hyperthermia has been a modality to treat cancer for thousands of years. During this time, intensive efforts are concentrated on determining the dose of the proper treatment, but the dominantly
*in vitro* induced cellular death does not provide enough confidence for the clinical dosing. The cell-death by heat-monotherapy applications in laboratory experiments is difficult to apply in the complementary therapies in clinical applications. The newly developed nanotechnologies offer completely new possibilities in this field as well. Modulated electro-hyperthermia (mEHT, trade-name Oncothermia) is a nanoheating technology that has selective effects on membrane rafts and on the transmembrane proteins. This effect is thermal. The thermal action is in nanoscopic range which makes the phenomenon special. Our objective is to show the dose concept on this emerging method.

Hyperthermia, as a treatment in oncology, has a thousand-year tradition [

Oncologic hyperthermia massively uses external heat transfer from the outside towards the inside. The classical solution is based on heat-conduction from the skin. The heat-conduction is robustly increased by heat- convection of the induced intensive blood-flow in the skin.

The whole-body heating processes definitely follow this way, using the blood-flow in the subcutaneous capillary-bed, transferring the absorbed energy all over the body [

Another type of oncological hyperthermia is not systemic. Its volume ranges widely: from regional to local, from a part of the body to a nanoscopic targeting.

Their typical parameters are summarized in

Thermodynamically, the systemic and loco-regional treatments differ from their heat-flow direction between the tumor and its neighborhood. The blood-heating techniques pump heat-energy from blood to the tumor, while the blood works opposite in the loco-regional heating, cooling the anyway heated tumor because it remains in body temperature. The physiological limits are also different. While the systemic heating is limited at 42˚C, the local one has no limit in the tumor. The temperature limit of loco-regional treatment is only keeping the healthy vicinity of the tumor safe, as well as the skin, where the energy is pumped into the body.

Technically, the local deep-focusing is a great challenge. Most of the local treatments with deep focusing possibility use some kind of electromagnetic energy-absorption. Multiple new techniques are devoted to deliver the proper energy for heating [

One of the earliest non-invasive deep heating is the simple inductive way, which is typically achieved by the induction of eddy-currents in the body [

Interestingly, the trend of the modern hyperthermia is directed to the smaller targets. Their intensive locality is somehow similar in this character to the original galvanic methods. The typical high-energy focusing can be solved by microwaves [

Some modern laser ablative techniques work with ultrafast pulses with ultra large energy-density flow. Depending on the pulse-duration, it can be a few 100 W/cm^{2} and in nano-seconds can go to 10^{7} - 10^{8} W/cm^{2} [

The photodynamic therapy (PDT) [

Basic hyperthermia categories | Typical absorbed energy density (SAR) [W/kg] | Typical operating temperature [˚C] | Typical treated mass [kg] |
---|---|---|---|

Systemic (blood-heating) | 5 ÷ 10 | 38 ÷ 42 | 40 ÷ 100 |

Local/regional (tissue heating) | 10 ÷ 50 | 40 ÷ 45 | 1 ÷ 25 |

Ablation (tissue burning) | 5000 ÷ 25,000 | 60 ÷ 250 | 0.001 ÷ 0.02 |

drug-delivery, combined with the heat development. This could non-invasively treat shallow-seated tumors, only the light-source has to be introduced invasively (mostly with optical fibers) for heating in depth.

There is a selective tumor targeting applied by temperature sensitive liposome-jacketed drug-delivery [

The disadvantage of the weak coupling of magnetic fields in direct inductive heating turns to an advantage when artificial absorbers are applied. The energy absorption from the magnetic field is practically limited to these magnetic absorbing centers, orienting the SAR where the artificially inserted magnetic materials are. These materials will solely react with the electromagnetic fields, and their absorbed energy will be the source to heat up their surroundings. The energy absorption could be absolute, precisely guided by the place of these absorbers. In order to improve the magnetic energy absorption within the target tissue, magnetic materials, such as micro-particles [

Definite shifts of hyperthermia techniques have been made in the last decade, showing a trend to nanotechnology [

Based on nanotechnology, a new, emerging way is connected to various immune actions [

Evaluating the success of hyperthermia’s definitive dose is mandatory. Experts agree that the reliable dosing determines the future of oncologic hyperthermia [

The heating process is an energy transfer to the target. This energy could increase the temperature and could make many other accompanied effects [

When the energy-absorption and the energy-distribution is heterogenic, and has fluctuations in the volume, then the temperature measurement also has fluctuations, and we have to wait while the temperature is “equalized” to become a steady-state condition, where the temperature can be regarded as constant. This process emphasizes the time-parameter as important as the temperature itself in two ways: 1) Time duration and energy delivery are linearly proportional; 2) Longer time spreads the energy, approaches equilibrium mostly by non-linear way. Taking into consideration these parameters, complications grow with the heterogeneity of the absorbing target. For example, in case of the nanoheating an extremely huge energy density is absorbed in a very small volume, and the main heating effect is based on their heat-conductive environment.

For the proper dose definition, a well-defined goal (the expected effect) has to be described. The dose in this case must be derived from various model systems (in silico, in vitro and in vivo), while clinicians apply this method at the patient’s bed. Unfortunately, the two approaches (experimental and medical) do not meet organically. One of the multiple reasons of deviations is that the model systems are mostly treated by monotherapies, while medical practice predominantly uses the oncologic hyperthermia as a complementary method together with one or more “gold standards”. On the other hand, the biological variability is much more in the real treatment on humans than in the models. During experimental trials we can investigate the basic (mainly molecular) mechanisms of hyperthermia, while the clinical applications are sharply connected to the various physiological reactions, like the blood-flow, lymph-transports, and in consequence, the drug-delivery of chemotherapies, the oxygenation for radio-sensitizing, etc. Some special functional parameters of the treated organ are used for control of the in situ actions, but these methods are not at all standard enough to be used for dosing. The control of this type gives important safety information to avoid or minimize the adverse reactions, but not appropriate to use as dose. Some technical, mainly thermal parameters are also used to control the processes without proper dose. For example, the highest temperature achieved is used [

The concept of oncological doses is based on the maximal tolerable dose determined by dose escalation, measured in specific concentration of the drug (such as mg/m^{2}), or specific energy of the radiation (such as Gy = J/kg). The efficacy is measured mostly by the local control, the response rate, which is measured most frequently off-situ with imaging techniques. When the efficacy is measured on the survival or other long-time realization of the development of the disease (much longer than the treatment is active), it would be too complex to verify it as the dose, due to the fact that the interim control during the treatment process is mandatory.

The definition of the real dose must be based on the effect, which we expect by the application of the proper dose. The dose of an action is measured by the final effect, which is made by a “tool” (such as drug concentration, radiation, temperature, etc.). The effect in our case is the selective distortion of the cancer cells. The definition of the distortion is the cell-death of malignant cells without harm (or less harm) in their healthy counterpart. There are various possible ways of cell-killing in a wide range from necrosis to apoptosis, or autophagy, having many variations of their “mixture”, called necroptosis, aptonecrosis, etc. [

The inherent problem of dosing is that the quantity of the final result of the action of the tool is defined by the tool itself (concentration, intensity, etc.). The way from the action to the result considered standard is too rough―an oversimplified assumption in high complexity systems with high bio-variability.

The majority of physicians who are using heating techniques have a common view about the cellular damage, stating its thermal behavior. However, the same forwarded energy exposition with identical energy-flow [W/m^{2}] can cause different energy-absorptions [

The simplest thermodynamical way is of course to measure the temperature, and by the higher kinetic energy that surmounts the energy barrier of the actual reactions. However, the heating differs in the target, even microscopically, and the same temperature acts differently for the large complex chemical machinery of the cell. If the temperature is high enough it acts for most of the possible reactions, irrespective of their state or actual needs. Due to the overall excitations the desired selection vanishes. Energizing by temperature does not take into account the individual energy barriers of the various reactions or reaction cascades; it is an overall driving force to react. It defines a certain probability of the effect of individual reactants. When the given reaction has the E_{a} barrier height (activation energy), the reaction rate k (probability of overpassing the barrier) is proportional to the exponential function of the ratio of the height of the barrier and the energy represented by the temperature that can be described by the Arrhenius law

where R_{G} is a universal gas-constant (R_{G} ≈ 8.3 [J/K/mol]). The excitation of the particles is temperature dependent. The actual pre-exponential factor (A) and the E_{a} activation energy have to be determined on an experimental basis. The general basis of the chemical reaction-kinetics with temperature is the Arrhenius law. The ATP synthesis is temperature dependent, also following the Arrhenius law [

The theoretical model of the criteria of the cell-death is described by the

simple reaction equation, which means the living cell N turns to (number of) dead one D by reaction rate χ. This could be modelled by autolysis, having the linear decay equation

where

The thermo-dynamical measurement of necrotic hyperthermia treatments in-vitro accurately fits the Arrhenius plot [

Introducing the damage function

It follows

Knowing the relevant parameters, the thermal dose is calculable from this equation [

When the chemical or structural properties change, the value of E_{c} changes, too. Due to the linearity of the Arrhenius plot and its reverse time dimension of χ, we introduce its reciprocal value as time constant [_{1} and T_{2} are close to each other, then

The thermal damage has a characteristic graph in dependence of 1/T as usually plotted by the Arrhenius conditions

In case of components of living materials (like proteins, cells, tissues) the ln(A) is approximated from the experiments by linear dependence

where ξ = 0.38 and ζ = −9.36 [

So the characteristic time is

Comparing the thermal cell damages to each other, we choose treatments made on T_{1} temperature by t_{1}, time and other one on T_{2} temperature by t_{2} duration. According to Equation (7) the thermal damage functions are

We consider two treatments thermally equal, when their thermal damages are equal. We can choose equivalent times using Equation (12), when we would like to compare the effects of

If the reference-time and corresponding temperatures are t_{r} and T_{r} respectively, then the iso-effective equivalent time, which is necessary at the T-temperature would be

When we choose

where

In consequence of this t_{r} reference choice, we can introduce a dose unit; when the heating is time-dependent, summarizing all the intervals regarded as constant temperature, using steady-state approximation. This cumulative value as “cumulative equivalent minutes” (CEM) is in steady-state

where t_{i} are the times when the corresponding T(t_{i}) regarded as constant. In a continuous change of the temperature, the sum is transformed to an integral

where the treatment time t is conventionally measured in minutes. The general equivalent time CEM in Equation (18) does not fix the reference for one definite cell-death, it is general for all the cases when the Arrhenius process is valid.

When the activation energy is constant, the Arrhenius plot is linear by the reciprocal of the temperature. However, when a drastic new reaction or phase transition happens the activation energy changes and the derivative of the Arrhenius curve is modified by the thermal load with increasing temperature. In this case, the anyway linear dependence of the logarithm of reaction-rate to 1/T breaks, the slope of the line changes, and a kink occurs on the Arrhenius plot [_{k} is the temperature (in Celsius units) T_{1}-where the kink (E_{a}_{1} ↔ E_{a}_{2} transition) occurs] relations are valid, we have

The step-function form of Ψ is consequence of the kink measured in the Arrhenius plot at temperature T_{k}, [K]. Classic hyperthermia had chosen for standardization this t_{43} point. Conventionally, the value of Ψ is noted R in this special necrosis-based standardization. By this choice, the reference point was definitely fixed as the necrotic threshold in the special in vitro experiments [_{k} = 316 K = 43˚C and Ψ_{1} = 0.5, Ψ_{2} = 0.25 [_{2} = 43˚C, made during a treatment-time t_{43}. The dose of the actual treatment refers on the equivalent time of the treatment on other T temperature (denoted by CEM43˚C) [

which implies E_{a}_{(<43˚C)} = 273 kcal/mol and E_{a}_{(≥43˚C)} = 138 kcal/mol. The kink temperature of the Arrhenius plot could vary by samples, and complementary or pre-treatments [

However, according to the various experiments below and above the breakpoint temperature, the activation energies do not fit to the fixed R values. One well-accepted result [_{a}_{1} = 365 kcal/mol ≈ 1527 kJ/mol below this point, while above E_{a}_{2 }= 148 kcal/mol ≈ 620 kJ/mol. These values implicate R_{(<43˚C)} = 0.159; R_{(≥43˚C)} = 0.474, instead of R_{(<43˚C)} = 0.25; R_{(≥43˚C)} = 0.5, respectively. The error is significantly robust (~36%), below the breakpoint, showing that the non-necrotic damage cannot be described accurately with the classic CEM43˚C dose.

The Arrhenius picture is useful for various heating induced changes in tissues and in physiological phenomena [

The cell-death could be performed by various parallel ways. Keeping the standard Arrhenius-based Henrique-Moritz model [

There are various kinds of the cell-deaths, having a huge variation of the activation energy, so the linear Arrhenius plot with one single straight line and one breakpoint on it is too idealistic [

However, the definite phase-transition temperature (Arrhenius kink) changes by the chemotherapies [

The above described dose idea does not cover all cell-damage processes. E_{a} could vary by the actual effects, having not only a simple, immediate necrosis. In a simple case when the electromagnetic heating is applied, we may suppose a deviation of the effects on at least two different groups; the dominant thermal changes, which depend only on the absorbed energy (SAR) irrespective the source of the energy delivery. Another part of the effect could depend on the mode of how the energy was delivered, that is, the actual electro-magnetic field, which is the source of the interactive forces, could make special effects on the ionic charges and dipoles which are the constructive elements of the biomatter. These effects are thermally induced, but not necessarily thermal. They are behaving at least as phase-transition of first order, having so called “latent heat”. This means that after reaching the transition temperature that value does not change until the transition process is completed. In this interval the temperature will be independent from the pumped in SAR value. In this simplest case, when we divide the cause of the cell-death on the purely thermal and non-thermal but thermally induced components, the parallel reactions could be described as follows

where A is the cell treated complexly, and

Note the “non-thermal” component is only apparently not thermal. It well depend on the heat-energy which is needed for the chemical changes. This “latent heat” is energy associated with the energy of phase-change of the substance and it occurs in case of every first-order phase-transition. In case of pure water the latent-heat at melting of ice is 334 kJ/kg, while at the evaporation it is 2260 kJ/kg at 0˚C and 100˚C respectively. During of the absorbing of the “latent heat” the temperature does not change, so it is better to use the statement of “actually non-temperature dependent” [

Here, the dynamism of the processes is not included, and the time of staying in the actual state has no role. What is probable, however, is that the electric excitation process definitely has a longer time than the thermal one. The cross-effects are also not counted. The processes when one kind of excitation promotes the other one are calculated only by their final death independently from the history of the process itself. We consider that the thermal effects are dominantly necrotic, while the electrical one is dominantly necrotic, and note again that no strict border exists between the processes, or between the thermal and electric excitation. There is a massive appearance of thermally induced electric and electrically induced thermal effects, making the complete process complex. Applying a model of first order parallel reactions, the reaction-kinetic equations are

Supposing the likely conditions of

From this, the concentration of the cells in activated state is

With this, we get the following simple reaction-kinetic equation

Following this method, the second reaction of Equation (21) will be such a simple decay reaction equation

After these calculations the cell damage could be described by the following irreversible parallel reaction scheme

which could be described by the following reaction-kinetic equations

where

From where the so-called “branching ratio” is

This means that the concentration ratio of the death-cells depends only on the ratio of the apparent reaction

rates. When the

branches is constant, which means in our case that the ration of necrotic (caused by global SAR) and apoptotic cell damage (caused by local SAR) is independent of the temperature. We suppose that the apparent reaction rate also fulfils the Arrhenius law, then

where C_{i} is a constant, E_{ai} is the cellular activation energy of i-th components, and R is the universal gas-con- stant (R = 8.314 J/K/mole). Then the consequence is a fixed ratio

Consequently, the global cell damage described by the first equation of Equation (28) has the following kinetic equation

where we used the branching ratio from Equation (30). Introducing the damage function as

where t_{0} is the starting time of the process (t_{0} = 0) and the a consequence of Equation (33) we get

With this, the damage function is calculable

where

On the above basis we introduce the generalized iso-effect of the thermal dose. Treatments could be compared by their efficacy, which has not only thermal, but “non-thermal” components, too. In this case

where the situation corresponds to the pure thermal case described in Equations (12) and (13) if the points of 1 and 2 are close to each other, and the coefficients of the exponential function are nearly equal. Consequently, the isodose principle is identical with thermal despite of the additional (synergistic) effect of thermally induced, but not directly temperature dependent factors.

According to Equation (38) and using the condition of the equivalence described above, the functions of thermal damage at

In a cumulative approach, we get, similarly to Equation (18)

where Ψ is a function determined by the Arrhenius law

When E_{a} and A_{n} are constants and the

where, Q_{gen} is a generalized pre-factor

The general equivalent time CEM_{gen} in Equation (40) does not fix the reference for one definite cell-death or for definite duration of the process. The A_{n}/A_{r} ratio could be very high in special processes (like electroporation [_{n}/A_{r} ≈ 77). The cell-destroying process could be guided by very little temperature change with extra huge thermal gradient on the plasma-membrane [

Modulated electro-hyperthermia (oncothermia, OTM) is devoted to solve the currentproblems [^{2+} influx into the cytoplasm.

The apoptotic damage usually takes a longer time to be performed. Its usual visibility takes at least 24 h, and could not be globally considered as simple Arrhenius plot, because this process is much more complex by its chemical changes. The multiple processes that are needed for apoptosis [

In case of oncothermia the physical character of the action is the electric field. This applied field increases the temperature by:

・ global absorption (general SAR), which is the overall absorbed energy of the target divided by its mass, which is selected by impedance differences between the target and the normal tissue [^{2+} influx and thermolysis [

This is because the thermal activation of transient receptor potentials (TRPs) has a crucial role in the apoptotic cell-death, caused by modulated electric field [

In cases of the modulated electrohyperthermia studies, the concentrations of the dead cells by thermal damage is [A_{t}], and the concentration of the dead cells made by electric damage is [A_{e}], then the branching ratio by the experiments [

Using the Equations (37) and (44) we get

The combined thermal and electric effects have three times more cell distortion than the thermal has alone.

The selective and effective cell destruction makes a new kind of hyperthermia in oncology possible. This new treatment could use the definite electric and thermal in homogeneities of the tumor to kill effectively the cancer-cells without hurting their healthy vicinity. This selective SAR process causes the strong synergy between the direct thermal and indirect thermal (special electric field absorption) processes [

Generalized dose has been introduced for the non-homogeneous temperature distribution including the electric field absorption as a component of SAR. The generalization is discussed in the frame of thermal effects applied in the Arrhenius thermal law. The dosing and efficacy of modulated electro-hyperthermia (oncothermia) are described, and due to the non-homogeneous heating and selective targeting it is about three times higher than that of the homogeneous classical mass-heating.

GyulaVincze,OliverSzasz,AndrasSzasz, (2015) Generalization of the Thermal Dose of Hyperthermia in Oncology. Open Journal of Biophysics,05,97-114. doi: 10.4236/ojbiphy.2015.54009