The malignant processes deviate from the healthy homeostatic control, and various “tricks” enable malignant cells to avoid the healthy regulation. Consequently, the malignant structures miss the apoptosis and proliferate without restriction, and without the formation of communication networks in the newly formed cells. The modulation supports the homeostatic control to rearrange the health regulation processes in various ways. The modulation acts with stochastic processes, using stochastic resonances for molecular excitations, supporting the regulative enzymatic processes. The number of stochastic resonant frequencies is as many as the number of enzymatic reactions. The malignant cells differ structurally and dynamically in their connections and interactions from their healthy host tissues. The radiofrequency carrier is modulated with an appropriate time-fractal (1/f) noise to select the autonomic cancer-cells, destroy them, or force the precancerous, semi-individual cells to participate in the networking connections. The modulation in this way limits the cellular autonomy of malignant cells and boosts the healthy control. The resonant energy triggers apoptotic processes and helps immunogenic actions deliver extracellular genetic information for antigen-presentation. The modulation is applied in clinical practice. The therapy (modulated electro-hyperthermia, mEHT) is intensively used in oncology in complementary applications and for palliative stages, and occasionally even as a monotherapy.
Healthy homeostasis controls the dynamic balance in the organism, ensuring the harmony of complex micro- and macro-interactions. Cancer destroys this harmony. The modulation goal is to find and force the malignant cells into apoptosis and to restore the healthy synchrony between cells and their communication.
The malignant processes are driven by the unicellular behavior and the individualism of the involved cells. The result is the breakdown of the integrity of the multicellular organization (which normally has a healthy networking structure). Cells with autonomy behavior have potential to better adapt to environmental changes. The transformation from the organized multicellular structure seen in healthy tissues to the structure seen in tumors is driven by the primitive transcriptional programs active in malignant cells [
Cancer is an organizing (networking) disease, where the cells abandon the cooperative advantages [
The concept of modulation applied in physiology is centered on the stochastic dynamics (time-dependent events) in the biosystems. The chosen frequency spectrum is devoted to promoting healthy controls and intended to suppress cancerous processes. The carrier frequency is in the radiofrequency (RF) range which delivers an audio range (<20 kHz) to the target. This method is well known and intensively applied by the various telecommunication networks (radio, TV, phone, GPS, etc.) to transfer information between the source and the distant targets.
The masking of the carrier can be achieved using different features of the RF wave, like its amplitude, frequency, or phase. The amplitude modulation was historically the first form of modulation, and it is the easiest to decode the delivered information (demodulation). The resulting shape of the signal follows the shape of modulation (
The question naturally arises: while the advantages of frequency modulation include better stability over distance, less vulnerability to interferences, better selectivity, why then do we not propose applying directly the modulation frequencies in order to transmit information in biological systems without carrier frequency?
The challenge is to deliver the low frequency to the body and the selected places. The low frequencies are blocked by the heterogenic isolating (capacitive) factors in the application. The adipose tissue in the layer at the skin, the various membranes, and isolation compartments block the low-frequency current because their electric impedance inversely depends on the frequency. This resistivity becomes too high in low frequencies, and no deep targeting of structures is possible. In order to overcome the adipose layer, invasive application could be introduced, but other isolations remain.
The proper solution for the direct effect would be the invasive application of low-frequency, electrodes in the tumor itself, where the low-frequency effect of isolators is negligible. However, the inserted electrodes develop a layer on the surface of electrodes in the tumor, which produces a complex impedance effect (Warburg impedance, ZW) [
Z W ( f ) = A ( 1 − i ) f (1)
where A is a constant and i = − 1 . To avoid the Warburg impedance, a high
frequency is necessary. This noise could limit the accuracy of the measurements. However, in low frequencies, the large Warburg resistance also produces large electric noise because the electric noise of the resistance is proportional to the value of the actual resistivity [
The other advantage of the high frequency carrier is its impedance selection, which focuses the effects on the malignant cells, with the dispersion relation to attack the membrane rafts for exciting extrinsic signal pathways to apoptosis.
The electromagnetic interactions with real biological systems are faced with a heterogeneous, non-linear, and complexly regulated target. The in vitro (cell lines), the ex-vivo (tissue samples), the in-vivo (animal experiments), and human applications differ from each other due to the heterogeneity and organization of the biological target. The active regulation processes in the targets, which are complex, could change the electrolytes in the tissue, varying the inhomogeneities, causing further complications in the evaluation of the interactions. The heterogeneity of the targets influences the results; however the structure and function of the cellular membranes have strong similarities, which allows for the use of some unified considerations.
The average isolation of the various membranes in the tissues is enormous ≈1013 Ω/m [
The cellular membrane, regulating the ionic transport of selected ionic species in and out of the cells. The idea corresponds to the triode or transistor when the current that flows through the device is non-linearly regulated with an intermediate action (net of base), which could amplify the time-dependent signal. The membrane is also a non-linear element [
Measurement of the non-temperature dependent rectification (non-linearity) is not simple because it is not measurable through the living object when the integrity of the cells is intact. The current traveling through the cell meets twice with the transmitted signal, first from outside to inside the cell, and the second meeting is in the opposite direction. The two effects eliminate each other. The lipid bilayer, together with the ionic exchanges, completes the rectification phenomena [
We had shown [
The Fourier transformation of x ( t ) pink noise is:
F ( f ) = A i 2 π | f | (2)
where A is the amplitude. The noise power spectrum:
S ( f ) = F * ( f ) F ( f ) = − i A 2 π | f | i A 2 π | f | = ( A 2 π ) 2 1 | f | (3)
where the star is a sign of conjugation. Let be the signal function v ( t ) of the carrier signal
v ( t ) = U 0 cos 2 π f v t (4)
where f v = 13.56 MHz is the frequency of the carrier, U 0 is its amplitude (voltage in electric signal). The f v carrier frequency is in the overlapping range of β/δ-dispersions. The Fourier transform of the y ( t ) = x ( t ) cos 2 π f v t modulated signal:
Y ( f ) = 1 2 F ( f − f v ) + 1 2 F ( f + f v ) (5)
The Fourier transform of the pink noise modulated carrier is:
Y ( f ) = 1 2 A U 0 i 2 π 1 | f − f v | + 1 2 A U 0 i 2 π 1 | f + f v | (6)
Physically, only positive frequencies can be realized, so the power spectrum is:
S ( f ) = − i 1 2 A U 0 2 π 1 | f − f v | i 1 2 A U 0 2 π 1 | f − f v | = ( A U 0 4 π ) 2 1 | f − f v | (7)
The power spectra of pink noise and pink noise embedded in the carrier are shown in
Many chemical reactions have a coordinated subsequent chain, having a series of reactions in a definite order. This set is called the Markov process, a chain-like stochastic reaction-line. When the sequence of the realized states is such, each step depends solely on the state realized in the previous event
The biological processes have well-organized and controlled Markovian chain reactions, avoiding the sudden single-step liberation of energy during the catabolism. The series of effects in the time dynamics are Markovian. A two-state Markov process in which we assume that the coefficients can be influenced by an external electric field are described as follows:
d p 1 d t = − α p 1 + β p 2 d p 2 d t = α p 1 − β p 2 , p 1 + p 2 = 1 (8)
where p i ( i = 1 , 2 ) is the probability of the actual state, and α and β depend on the external electric field. This is the master equation of a Brownian particle bouncing back and forth in a potential well with two minima, excited by a force
of an external periodic field.
The cell works appropriately as long as the catalyst enzymes are not poisoned and, obviously, as long as the catalyst has something to catalyze. More specifically, although coenzymes provide a high degree of enzyme selectivity, there may be substances which have suppressor functions (enzyme poisons) that react in an opposite enzymatic way, or the coenzymes act to support the enzyme reaction (promoter function). On the other hand, when the cell actually does not have molecules to catalyze, the chemical reactions are terminated. We assume that the two states of the enzyme, A, and B, are stable but interchanging. The two states are the result of chemical reactions, with α forward, and β backward reaction rate:
A ⇄ β α B (9)
The concentration of the enzyme by [A] and [B] in confirmation states A and B. Then,
the kinetic equations of the reaction in (9):
d [ A ] d t = − α [ A ] + β [ B ] d [ B ] d t = α [ A ] − β [ B ] (10)
Enter the quantities in (10): [ T ] = [ A ] + [ B ] , p 1 = [ A ] [ T ] , p 2 = [ B ] [ T ] , the equation has the same form as the master Equation (8).
The study of a voltage-gated ion channel defines A ≡ O , and B ≡ C , where O is the open state and C is the closed state. In this way, the kinetic equation of the ion channel is again the master Equation (8).
To determine the mathematical form of transient probabilities, we examine the stationary state of (8). Then, d p i d t = 0 so
p 1 p 2 = β α (11)
The energy of the two states ±ΔE deviates from the reference level and assumes a Boltzmann distribution:
p 1 p 2 = β α = e − E 0 + Δ E k T e − E 0 − Δ E k T (12)
We obtain the Arrhenius law for reaction rates from (12):
α = C e − E 0 − Δ E k T , β = C e − E 0 + Δ E k T (13)
With this, from (8), we get a differential equation; e.g., for p 1
2 τ d p 1 d t = − ( e Δ E k T + e − Δ E k T ) p 1 + e − Δ E k T , 2 τ = ( C e − E 0 k T ) − 1 (14)
Apply Taylor series and stop at the first term, then
d p 1 d t = − 1 τ p 1 + 1 2 τ − 1 2 τ Δ E k T , 2 τ = ( C e − E 0 k T ) − 1 (15)
When the field strength is a harmonic function of time, the energy depends on it linearly:
Δ E = a sin ω t (16)
From (15) and (16), we get
d p 1 d t = − 1 τ p 1 + 1 2 τ − 1 2 τ a k T sin ω t (17)
To find the form of the excitation, the stationary solution of the following inhomogeneous differential equation has to be determined:
d p d t + 1 τ p = − 1 2 τ a k T sin ω t (18)
which is
p ^ ( k T ) = a 2 k T 1 τ 2 ω 2 + 1 = a 2 k T 1 1 + ( e E 0 k T 2 C ω ) 2 (19)
The solution shows that the probability associated with such an excitation varies according to a harmonic function with time, regarding the noise intensity of the thermal background kT. It follows a sharp maximum at a given f frequency as a function of kT noise intensity
Formulate this result oppositely: this also means that there is a frequency where the amplitude is maximum for a given noise level. The stochastic resonance rules also such microscopic molecular structural changes like the protein folding phenomenon [
The modulated carrier signal targets the selected malignant cells, and the cells rectify (demodulate) the received signal. The demodulation is basically a rectification process, which uses stochastic resonance [
2 τ d p 1 d t = − ( 2 + ( Δ E k T ) 2 ) p 1 + 1 − Δ E k T + 1 2 ( Δ E k T ) 2 , 2 τ = ( C e − E 0 k T ) − 1 (20)
Assume the field strength of the modulated signal is a harmonic function of time and let the energy depend linearly on it
Δ E = a ( 1 + m cos Ω t ) sin ω t (21)
where m < 1 , the modulation depth Ω is the modulator and the ω carrier frequency.
Substituting this into our previous equation, we get that
2 τ d p 1 d t = − ( 2 + ( a k T ) 2 ( 1 + m cos Ω t ) 2 sin 2 ω t ) p 1 + 1 − a k T ( 1 + m cos Ω t ) sin ω t + 1 2 ( a k T ) 2 ( 1 + m cos Ω t ) 2 sin 2 ω t , 2 τ = ( C e − E 0 k T ) − 1 (22)
As a function of probability over time, there is a slow change and a rapid fluctuation. The first is from the modulation, and the second is from the carrier.
We are only interested in slow change now. To filter this out of the above equation, we average it over the time of the carrier period. In this case, the slow signal can be considered constant for the time functions, and the time average can be replaced by the fast one.
Under this rule, the slow change is
2 τ d p 1 d t = − ( 2 + ( a 2 k T ) 2 ( 1 + m cos Ω t ) 2 ) p 1 + 1 + 1 2 ( a 2 k T ) 2 ( 1 + m cos Ω t ) 2 , 2 τ = ( C e − E 0 k T ) − 1 (23)
equation describes.
Suppose the modulation depth is small. Then our above equation can be further simplified:
2 τ d p 1 d t = − ( 2 + ( a 2 k T ) 2 ( 1 + 2 m cos Ω t ) ) p 1 + 1 + 1 2 ( a 2 k T ) 2 ( 1 + 2 m cos Ω t ) (24)
This is now a linear differential equation with variable coefficients.
Although there is a general solution to this, we are not going anywhere with it, so we will apply the method of successive approximation to the solution.
Since we are looking for resonance, we only study the effect of the harmonic excitation function:
2 τ d p d t + [ 2 + ( a 2 k T ) 2 + ( a k T ) 2 m cos Ω t ] p = ( a 2 k T ) 2 m cos Ω t (25)
Introduce the
F ( p ) : = 2 τ d p d t + [ 2 + ( a 2 k T ) 2 ] p , f ( p ) : = p ( a k T ) 2 m cos Ω t (26)
expressions that are continuous functions of p.
Steps of successive approximation:
F ( p 1 ) = ( a 2 k T ) 2 m cos Ω t , F ( p 2 ) = f ( p 1 ) , F ( p i ) = f ( p i − 1 ) (27)
Now it’s true that
F ( p 1 ) + F ( p 2 ) + ⋯ + F ( p i ) = F ( p 1 + p 2 + ⋯ + p i ) = ( a 2 k T ) 2 m cos Ω t + f ( p 1 ) + f ( p 2 ) + ⋯ + f ( p i − 1 ) = ( a 2 k T ) 2 m cos Ω t + f ( p 1 + p 2 + ⋯ + p i − 1 ) (28)
If the procedure is convergent, then if i → ∞ , the line proceeds to the solution, and due to the required continuity the above expression reduces to the simple equation:
F ( p ) = ( a 2 k T ) 2 m cos Ω t + f ( p ) (29)
Now let’s look at the first approximation! This gives a solution of a smooth diff equation.
2 τ d p 1 d t + [ 2 + ( a 2 k T ) 2 ] p 1 = ( a m 2 k T ) 2 cos Ω t (30)
The amplitude of the variable probability according to the harmonic function with modulating frequency can now be determined as follows:
p ^ 1 ( R T ) = ( a m 2 k T ) 2 1 4 τ 2 Ω 2 + [ 2 + ( a 2 k T ) 2 ] 2 = ( a m 2 k T ) 2 1 [ 2 + ( a 2 k T ) 2 ] 2 + ( e E 0 k T C Ω ) 2 (31)
It is a resonance again
The expected actions mark out the following basic goals:
1) Supports the healthy network over the unhealthy network.
2) Selectively targets the cancer.
3) Supports the immune system, boosts the homeostatic harmony and chains of reactions.
4) Excites the selected molecules in selected cells for special molecular and immunogenic changes.
Due to the complex interconnection of the living objects, these effects are overlapping and are supporting each other.
In the following sections, we focus on emphasizing the features of modulation for fighting against cancer, which is a disease of the dynamic equilibrium breaking the multicellular cooperative network into unicellular individualism of the autonomic “selfish” cells. The task is twofold:
1) find and destroy the malignant cells. The intention is to act with the local treatment systemically, extend the task to the entire body;
2) force cellular homeostasis harmony with a homeostatic synchronization signal.
The role of each cell supports each other in the cellular network in a tissue, there must be an interaction between them to realize this. One such possibility is the cyclic interaction in which the thermal noise is eliminated and instead a noiseless mode of information exchange appears [
The social inclination is encoded by evolution into DNA. It is capable of creating a form of movement in which only noiseless modes are realized. As a result, two effects are realized, the noiseless communication, and harmony of physiochemical processes with stress and hormone dependent psychochemical ones. This later is a brain-controlled systemic process, fixing the well-being.
1) One of the crucial steps to re-establish the cyclic symmetry is the synchrony between the cellular activities. The self-synchronization of the chemical processes was observed in the famous Belousov-Zhabotinsky (BZ) reaction [
2) The physiological state includes a dynamic chemically driven psychological state in the living organism corresponding to well-being. The relationship between physiological and conscious processes has puzzled many researchers, including Schrödinger [
The stored information passed down to the new cells through the individual DNA molecules regulates the organ’s function, but cannot be designated as controllers of the described self-organized communication. Despite their ability to store all the information about the body in the nucleic DNA, the cells, due to the organ collectivity, use only those pieces of information appropriate to their tasks in the organ. The intranuclear DNA is a blueprint for the production of the new cell. This condition provides amazingly high safety in the functioning of the organ. The “social” communication allows the organ to function even when a part of it is damaged. This is essentially Neumann’s concept of realizing a high-reliability system from low-reliability ones [
As the network becomes extensive, the communication signal goes over greater distances in an intensively noisy environment, so more and more information is being lost by distance. In the end, the cell cannot recover the received information. Beyond a limit, noise wins, no matter how good the noise-suppressing ability of the communication network of cells is. It can be assumed that the disintegration of the information network is a process similar to the phenomenon of stochastic resonance, i.e., the addition of a small amount of noise leads to the emergence of novel, primarily chaotic behavior. It is reasonable to assume that with stochastic resonance, that cell that lost its communication commits suicide, i.e., ends up with apoptosis.
The collective excitations comprise the non-local waves and activate the energy flow in the homeostatic networks. These excitations are mainly in the low-frequency range, and the expected frequency spectrum follows the natural 1/f fluctuations [
The self-similar self-organizing process is collective [
One of the fundamental ordering principles for healthy living subjects is a characteristic “democratic” energy supply in their organisms for optimal energy consumption. The “democratic” idea is more general than just the energy supply. It characterizes the information distribution, as well [
This “democracy” is regulated by general biophysical rules, governed by the competition for resources in micro- and macro-phenomena, having intensive interaction with their environment. The goal of the multicellular living object is forming cooperation, optimizing the energy intake. Due to its energetically openness, the individual living object needs internal cooperative distribution of the incoming energy. The survival of its parts determines the overall survival of the object, so the optimization of energy distribution is crucial.
In healthy multicellular systems, numerous mitochondria help the individual cellular functions. Even the otherwise similar cells may vary substantially in their mitochondrial content, together with their size and membrane potential [
The balancing of autocracy and democracy characterizes the evolution when the “selfish gene” [
Moreover, the complex homeostatic control shows the balancing of feedback mechanisms. The negative-feedback interaction tunes to keep the actual state as close to the accurate value, determined by the self-organizing system. Nevertheless, the system is energetically open, which is the mandatory condition for life, so the positive feedback mechanisms force some reactions, determining the metabolic processes in both directions (catabolism and anabolism). This obligatory constraint derives a certainly autocratic line when the probability of reactions drives the defined direction so the processes. Such necessary autocratic strategies can be beneficial for exerting control over asymmetric interactions [
Considering the complexity, the compulsory synchronization attempt by external modulated electric forces looks like a promising strategy in the cases when the collective harmony (the homeostatic regulation) is lost.
The biochemically masked, hidden tumor cells show biophysical peculiarities. This biophysical evidence is not enough to turn the immune attention on the tumors but could select them and force the selected cells to show their factual genetic errors.
The first recognizable feature is their enlarged metabolic rate. Due to the intensive proliferation, the energy demand of these cells exceeds the rate of their healthy hosts. The ion transports in their environment increase the conductivity as a result of the higher ionic concentrations. So the adequately chosen RF current has a higher current density in the tumor region, where the electric conductivity is higher than in the healthy host. The high current density in tumor allows for the use of the RF energy to act selectively on cancer and host tissues.
The impedance measurements on Erlich solid tumors [
The biophysical selectivity has another distinguishing phenomenon due to the cellular autonomy of cancer cells [
Nevertheless, one factor of this phenomenon offers a selection possibility, the weakening or complete loss of the networking connections of these cells to their neighbors. The loss of the cadherin intercellular links promotes tumor growth [
The third selective factor uses the modified structure of the tissue’s pattern, which is a usual experience of the pathologists to identify the stage and prognosis of the malignancy. The pattern changes the impedance for the RF-current, and also its reaction to the modulation of the carrier frequency fundamentally differs when it forces healthy harmony. The well-chosen modulation delivers such a time pattern, which corresponds with the homeostatic dynamism, and is synchronized with some basic phenomena. But, the cancer is out from this harmony, and the modulation drastically differs from their dynamic properties. There is a simple analogy to represent this process with the pushing of the swing in the playground. When the push is in harmony with the swing’s pendulum, it keeps moving with a small amount of energy; however, when the energizing push is out of harmony, considerable energy is lost, and the swing loses its kinetic energy. The applied modulation (synchronization) strategy has to be harmonized with the homeostatic regulation of individual systems.
Distinguishing the networked, and individual cells was studied in detail by the Nobel Laureate A. Szent-Gyorgyi. He applied an etiological approach: how does the cellular collectivity disappear [
The evolution on the cellular level is explained by an interplay of α- and β-stages [
Normal cellular division transforms locally the β-state to α-state, which is a normal process in the multicellular system, although it hurts the systemic collectivity in that local volume. Irregularity happens when the dividing cell remains in α-state, because the individual local conditions prefer autonomy, which ensures a high amount of energy intake to the cell. The long-time optimal collective demand overcame the individual interest of the cell. This state develops cancer which is regarded as “dismantling of multicellularity” [
The embryonic cellular organization could be a model of how the cancerous cluster can be stabilized. The “renegade” single-cell [
d b b = c d a a (32)
The (32) scaling is observed in the allometric comparison of the various living masses and their metabolic rates [
B c M ∝ M − 1 / 4 (33)
On the other the lifespan T of the tumor also has approximately the same dependence from the mass [
T ∝ M 1 / 4 (34)
Note that the universality of the values of exponents has intensive debates [
T tumor T healthy = ( M tumor M healthy ) α (35)
where α < 1 (most frequently it is α ≅ 1 / 4 ) and M tumor and M healthy are the mass of tumor and the healthy body part which is affected by the tumor, respectively. It is obvious, that M tumor < M healthy , so from (35)
T tumor T healthy < 1 (36)
We assume that the regulators of complete homeostatic control (proliferation, morphogenesis, physiology, immune system, etc.) have an intervention time varying according to (34). As a result of (36), the regulation time of the tumor is shorter than the healthy reaction. Hence, the tumor reacts quicker than the healthy regulation system, so its growth escapes from the standard supervision. The consequence of this is that the regulators in the body are unable to control an activated cancerous cellular cluster.
Since the embryonic cell must be connected to the food network of the adult body, it must develop and increase in its direction by a known mechanism of vascularization. But in the adult body, it is also slow as it has adapted to the adult body. The process goes through the genetic instability of cancer [
The special autonomy and high metabolic activity of the malignant cells allow recognition, and the selection and attack of them. The energy provided with the carefully chosen RF current targets the selected cells and excites a few chemical changes in the selected malignant cells.
Electromagnetic selection of the malignant cells guides the energy delivery. The living targets are inherently heterogenic in thermal and electric properties, so the structural selection at the cellular level needs additional selection to target the chosen heterogeneity of the malignant cells. For this, we have to choose the carrier frequency, acting on different parts of the tissue structure. The applied RF current triggers various processes, which are often grouped in dispersion regions by frequency, defined by the main character of the bio-electromagnetic exchanges.
The β-dispersion (~1 kHz - ~100 MHz broad spectrum) is linked to the cellular structure of biological materials [
The upper tail of the β-dispersion continues to the δ-dispersion (~1 MHz - ~1 GHz), which represents another mechanism. The δ-dispersion occurs at a distinguished frequency range above the main β-dispersion [
Other relaxation processes like those of molecular side chains, bound water molecules, diffusion of charged molecules, and near membrane bonds, could be added to the δ-dispersion.
In addition, the β/δ-dispersion of the chosen carrier frequency orients the attack on the membrane reaction of the impedance selected cells [
Homeostatic dynamic equilibrium is too complex for external constraints to be effective in repairing it. Tightly connected feedback mechanisms regulate the system, and the reaction of homeostatic control is against any simple constraints. An excellent example of this is the response to conventional hyperthermia, which aims to kill the tumor by the thermal effect of the absorbed energy. The heating is a valid objective, but unfortunately, homeostatic control mechanisms begin to correct this heating through various actions to maintain thermal balance. The most effective reaction is increased blood flow and perfusion, which aims to cool the heated lesion. However, this feedback carries a danger, as it increases the delivery of nutrients to the tumor and promotes metastasis by cell invasion into the bloodstream.
Consequently, any winning strategy to influence the dynamic equilibrium must work in conjunction with homeostatic controls, utilizing natural processes and supporting the immune system to recognize and destroy malignant cells throughout the body. The preparation of the immune system could be a perfect target for oncology treatments, instead of targeting cancer’s main strength, its proliferation. In this case, the lack of adaptive immunity to tumors can be revised, and the malignancy can be attacked by the host system itself.
The malignancy lacks the homeostatic complexity, turning the structural and dynamic conditions out of the healthy homeostatic network. Consequently, the challenging general tasks are fighting against cancer and the immune surveillance to support healthy homeostasis. The situation is complicated because the tumor cells hide their genetic information from the immune surveillance. They are well masked to avoid any systemic action against then, even the opposite: their demands are met as the system attempts to correct the irregularities. These “cheats” mislead the regulative actions and start to support the malignant cluster. Due to this falsely presented tumor status, the regular immune system does not act against it. The primary task is to present the signs of danger and stimulate the immune action to target and destroy the dangerous, highly proliferation cells.
The critical point is the immunological recognition of the malignancy. The immune system needs recognizable signs to direct its actions. However, the highly adaptive hiding strategy of malignant cells protects them from being identified by immune cells. A practical possibility for cancer invasion is the innate antitumor immune action of NK cells [
As a standard in immune homeostatic regulation, all processes have promoters and suppressors, so in complexity, every effect maybe a friend or foe, which appears for NK cell activity as well [
The modulation also may effectively support the healthy additive immune effects with developing tumor-specific immune reactions. The challenge is how to present the genetic information of the malignancy in order to ignite the immune system. One of the possible solutions would be immunogenic cell death (ICD). The main point is the particular apoptosis starting with an external signal with the electric field, exciting the Trail R2 (DR5) death receptor with FADD-FAS complex, and the external signal through caspase (Cas) pathway goes to Cas8 and Cas3 finishing in apoptosis [
All of the above processes develop damage-associated molecular patterns (DAMP) [
The amplitude modulation (AM, <20 kHz) of the RF carrier frequency can
intensify the tumor-specific absorption as a part of the selection mechanism [
This phenomenon, however, has two connections to the temperature:
1) We know that 100% energy efficacy does not exist (entropy law), so the “lost” energy (which is kept as internal energy of the system) produces heat as well.
2) We know that the changing temperature changes the conditions of the “non-thermal” processes, which are in this way sharply dependent on the temperature. In other words, the reaction rate changes in the simplest case by the Arrhenius law. This complex process, which contains the thermal dependence of the “non-thermal” effect (transition effect), is described by Eyring transition state theory, which is proposed to describe the hyperthermia where this complexity appears. In Eyring’s description, the thermal part is the same as in the Arrhenius law. Still, it has a part, which is a structural dependent factor, which could change without any temperature change, describing the “non-thermal effect” in complex systems.
The DNA damage is non-thermal. It is a phase transition, which has to be fixed by oxygen or by blocking the repairing enzymes. It does not need a temperature change at all. However, we know that both the oxygen-related or enzymatic fixing reactions (which conserves the break as it is) are temperature-dependent. The oxygen and enzyme reactions rapidly change according to temperature, mostly with Arrhenius law. The radiotherapy result has two parts: a temperature-independent and a temperature-dependent part, in the same way as this model describes the modulated electro-hyperthermia (mEHT) effect. This is why the same dose (Gray) is proposed for both the radiation processes (radiotherapy: ionizing; and mEHT: non-ionizing radiation).
The dynamic structures, performing random stationary stochastic self-organizing processes, have practical applications in recognizing the diseases [
The pink-noise modulation applies the fractal knowledge to support the harmonization efforts of homeostatic regulation and induce stochastic resonance near the frequency of the carrier, to demodulate and excite the desired signal pathways. The intensive backing of the heathy influence on the cancer is mandatory because the tumors are out from the structural and dynamic coordination of the natural organizing control.
Technically a high frequency (RF) carrier delivers the well-chosen time pattern of the modulation, which transports the modulated signal to the body with a carefully fitted applicator [
The spectrum and the power density of the signal which drives the applicator are studied by decomposing the applicator voltage into a signal s ( t ) and a noise component n ( t ) :
u ( t ) = s ( t ) + n ( t ) , s ( t ) : = U 0 sin ω 0 t , n ( t ) : = m z ( t ) U 0 sin Ω t (37)
To calculate the power spectrum, we need to construct the autocorrelation
function u ( t ) :
u ( t ) ⊗ u ( t + τ ) : = lim T → ∞ 1 T ∫ − T T u ( t ) u ( t + τ ) d t (38)
where the sign ⊗ notes the necessary time integration of the signal with self in τ time-lag, and where we have taken into account a sufficiently sizeable averaging time. Considering the signal and noise components, we get:
u ( t ) ⊗ u ( t + τ ) : = s ( t ) ⊗ s ( t + τ ) + n ( t ) ⊗ n ( t + τ ) (39)
where the average of the function formed by the product of signal and noise approaches zero. First, the properties of the F { f ( t ) } Fourier transformation of the correlation function has to be calculated:
F { f ( t ) ⊗ g ( t + τ ) } = F ( ω ) G * ( ω ) , F { f ( t ) } = F ( ω ) , F { g ( t ) } = G ( ω ) (40)
where the ∗ star notation is a sign of conjugation. The Fourier transform is the pink noise in this approximation, so:
F { z ( t ) } = Z ( Ω ) = 1 i Ω (41)
thus the Fourier transform of noise:
F { n ( t ) } : = i 2 m U 0 [ Z ( | ω 0 − Ω | ) ] = i 2 m U 0 [ 1 i | ω 0 − Ω | ] (42)
consequently, the voltage power spectrum of the applicator:
Φ u u ( ω 0 ) : = F { u ( t ) ⊗ u ( t + τ ) } : = U 0 2 δ ( ω 0 − Ω ) + m 2 U 0 2 4 1 | ω 0 − Ω | (43)
According to the Wiener-Khinchin theorem [
Δ U 2 = ∫ ω ω + Δ Ω R u u ( Ω ) d Ω = ∫ ω + Δ Δ Ω ω + Δ Ω ( U 0 2 δ ( ω − Ω ) + m 2 U 0 2 4 1 | ω − Ω | ) d Ω = U 0 2 + m 2 U 0 2 4 ln Δ Ω Δ Δ Ω (44)
The second term of (44) shows that the square of the voltage amplitude can be extremely large near the carrier frequency, where the term tends to be infinite when Δ Δ Ω → 0 . It follows that the average potential:
Δ U e e : = Δ U 2 = U 0 2 + m 2 U 0 2 4 ln Δ Ω Δ Δ Ω (45)
And the field strength is represented as:
Δ E e f f = Δ U e f f d = 1 d U 0 2 + m 2 U 0 2 4 ln Δ Ω Δ Δ Ω (46)
where d is the distance between the electrodes. Of course, arbitrarily high performance cannot be physically realized. In practice, due to fast Fourier transformation, only a point spectrum is realized. Nevertheless, the field strength amplitude can be large enough, and so the modulation does not demand a high power for appropriate effect. In conclusion, the modulation effect transmits the low-frequency power spectrum of the pink noise near the 13.56 MHz carrier, highly efficiently, and forms two sidebands. The modulation results in very high amplitude field strength peaks near the carrier frequency.
The E-cadherin-β-catenin complex plays a crucial role in cellular adhesion [
Together with the collective and individual states, a third entity exists too: the pluripotent embryonic resting state (δ), stem cells that adapt themselves to their actual micro-environment [
The collective activity of cells emits pink noise, which is the noise of self-organization, and so it is the noise originated from the function of homeostasis. The essence of the pink noise of homeostasis is that the function of the organ-specific networked cells is regulated actively in their energy exchange in the harmony of the complex surveillance. Consequently, the variance of physiological signals remains constant over time.
The glycocalyx shell and cell membrane of a cancer cell are also different from those of a healthy cell. Because of this, the movement of proteins in the cell membrane by lateral diffusion is also more limited. Adherents are particular protein formulas that can move in the cell membrane by lateral diffusion. Contact between two cells can occur when two such proteins meet and chemically bond with each other by lateral diffusion
The glycocalyx shell of cancer cells is known to be charged highly negatively. This results in repulsion, so the attraction, which is one of the preconditions for cell recognition and the start of the adhesion process, cannot prevail. Consequently, the bond-formation is hampered by the strong negative charge of the cancer cell glycocalyx shell, so the formation of intercellular bonds and networking in malignancy is unlikely.
The condition for the formation of cellular collectivity is that the cell must be fixed with adherent bonds and junctions, which is largely missing in malignant tumors. The modulation/demodulation stochastic resonance of noise contains signals of very high amplitude, forcing the cell clusters to intercellular bonding, manifested in communication between cells, forming functional collectivity. The self-organizing signal transformed around a carrier produces large fields. The formed gradient promotes the adhesion bonding of neighboring cells. The pink-noise modulated electric field with a very high field strength which the amplitude is transformed near 13.56 MHz, helps build the bonds of adherent proteins
The pink noise modulation transformed around 13.56 MHz creates a field strength gradient towards the cell contact site. Attraction by a gradient of field strength towards the point of contact occurs between the cells. Proteins are normally dipolar with polarization vector p . Therefore, a cataphoretic force F = ( p ∇ ) E acts to move the proteins toward the point of contact. The gradient
generates a high cataphoretic force
Due to the increased temperature in the contact point, the barrier between the protein electronic states could be easier overcome, so the moderate temperature helps the bonding. So it is expected that the thermal effect of mEHT helps the process. However, when the temperature is high, the break of bonds is more likely.
The heat-shock proteins (HSPs) are chaperons to help in stabilizing the dynamic equilibrium of the cells. They are named according to their molecular weight. The first observations have connected these proteins to the heat-stress [
We elaborate on a theory that pink noise mEHT is suitable for enhanced HSP expression in the membrane and extracellular electrolyte. There are two important arguments for triggering the effect:
1. The carrier frequency is chosen in the range of the β/δ-dispersion, acting on lipid/protein bonds in the cell membrane.
2. The existence of high power amplitudes produced by the pink noise shifted to the carrier-frequency location.
The selection ensures that we excite the intended targeted cells with the high power pink-noise fluctuation near the carrier frequency. The RF-current density is increased at the cell membrane due to the β/δ-dispersion. The carrier would shift the pink noise into the β/δ-dispersion range, and there we expose the membrane to the pink noise. Streamlines pass from one cell to another at the points of contact of the cells. Electric fields with very high field strengths and gradients are generated in these places
The connection points have high local SAR. However, due to the high field strength gradient enhanced by pink noise, a dielectrophoretic force also occurs, which moves half of this high SAR location to the micro-domains of the membrane thermo-sensor. The micro-domains are exposed to increased stress due to high power amplitudes. On the one hand, the stress effect is heat stress due to the high SAR and, on the other hand, mechanical deformation stress due to the high field strength gradient.
The β/δ-dispersion is used to produce HSP, and the selected target triggers the production of HSP70 for immune stimuli [
The biological transformation of normal (β) to cancerous (α) is a communication phase transition which is explained on the level of individual cells [
The division naturally needs higher energy income than the regular life of the cells. The cytoskeleton polymerization during the cell division breaks the networking connections, allowing the free formation of the new cytoskeleton and intensifying support of the microenvironment of the dividing cells by higher diffusion in the free electrolyte. After finishing the division, the cells are reconnected, the network control activates again. The internal energy resources promote the appropriate, satisfactory amount of energy. Together with the environmental sources, the cells build up the daughter cells with the healthy cellular division [
The strategy to eliminate the cancerous processes focuses on the weakest point of the tumor: individualism. The missing overall network makes them vulnerable, as they are alone in fighting the stress.
The malignant development misses the healthy homeostatic regulation. The systemic controls do not work. Their extreme energy demand drives their systemic effect. The cancerous process concentrates on intensive proliferation and uses healthy hosts to support it. This complex process misleads the healthy host, presenting their actions as normal energy-demand for healing the lesion like a wound (as was described shown 25 years ago [
The permanent reparation demand depletes the available stem cells, [
Ignoring the healthy regulations and the collectivity of the host tissue has some structural and temporal signs to recognize it. The structure of the individual cells is more disordered than the networked healthy tissue, and the intensive individual metabolic demand changes the structure of extracellular electrolyte. The permanent cellular division periodically collapses the cell’s actual cytoskeleton and builds up new ones again, decomposed by the subsequent fission and repolymerization. This changes the cellular form individually, and the active dynamism, which differs from the healthy regulated one, is expressed in the noise of the tumor processes. The noisy difference is measurable by electric impedance [
The practice of modulated electromagnetic applications connects the knowledge of hyperthermia with electromagnetic effects. The modulated electro-hyperthermia (mEHT, trade name oncothermia®) has used this method for years in a broad application for various tumors. Below we summarize the most crucial information-set about its processes and results, showing publications.
Numerous practical applications proved the feasibility of the mEHT treatments. Based on some principal considerations, the method uses the thermal and non-thermal effects [
The temperature development is a complex process [
The extracellular action complexly interconnects the electric field with the thermal effects [
The RF energy is predominantly absorbed on the clustered transmembrane proteins (rafts) [
A recent review summarizes the molecular biology background of the tumor damage mechanisms revealed in cancer models [
In the clinical application, the safety of the method was investigated in one of the most sensitive organs, the brain. The prospective safety study involved the dose-expansion for non-invasive transcranial therapy in 3rd and 4th line, advanced; relapsed high-grade gliomas and proved the safety even in the daily applications [
Recently a review had summarized the clinical evidence of mEHT for the practicing oncologists [
Notably, most studies have single-arm protocols, which have inherent complications in evaluating the mEHT method. The patients involved in these studies are in relapsed advanced stages when the conventional therapies are limited or have failed. Collecting a cohort for reference at this stage is exceptionally challenging and, in most cases, impossible [
Other analysis of single-arm results uses the self-similarity of living processes [
The modulation of radiofrequency carriers causes stochastic resonances, which act mainly on enzymatic processes. The demodulation is also effectively performed by stochastic resonance, which allows the low-frequency modulation information to be delivered selectively to the cancerous cells. There are as many resonant frequencies as there are enzymatic reactions that exist.
The modulation intensively changes the paradigm of cancer treatment. It boosts the healthy network and selectively destroys the malignant cells. The cell-killing process is immunogenic, allowing for the release of genetic information
in a molecular pattern (DAMP), which could form antigen presenting cells and develop tumor-specific immune reactions. The modulated signal is a complex mixture of non-thermal electron excitation for chemical reactions, and thermal boosting of the enzymatic reactions.
The complex homeostatic network has a cyclic symmetry which controls the balance and the apoptotic processes. The living cellular structures are open to the effects of energy, requiring energy input, followed by the output of waste. This organized transport system is not possible without direct cellular communication (no “social signal”). The cyclic topological order makes the noiseless inter- and intra-cellular communications possible despite the thermal noise background.
The malignant transformation breaks the organized transport system and seeks to build up new structures for the new demands. However, there are fundamental differences: the healthy construction is driven by the collective signal and seeks to optimize the energy-use for highest efficacy, while the malignant construction is only driven by the topology and physics of the mass number of individual, competing cells, irrespective of the efficacy of the energy conversion. The new structure modifies the cell-cell communications and arranges the malignant cellular microenvironment suitable for the autonomic actions. The topology in this meaning has significant diagnostic (pathologic) meaning: the more the pattern of tumor (networking “mesh” and form of the cells) resembles the healthy cells, the less malignant the tumor is.
The modulation affects the malignant construction in various ways:
1) boosts the healthy network;
2) limits the autonomy of the cells;
3) selects the malignant cells and targets them with resonance energy-absorption;
4) excites selected molecules, influencing and promoting the enzymatic processes;
5) supports the immune system and triggers selective antitumor effects;
6) regenerates the lost intercellular adherent bonds, and with this limits the invasion of the malignant cells;
7) frees the HSP70 extracellularly to carry genetic information about the malignant cell to antigen-presenting cells;
8) supports the cellular communications and the synchrony of the cells.
The modulation signal is a time-fractal representing the systemic homeostatic fluctuations. It is self-similar, having 1/f noise of the power density. It might promote the-establishing the lost cellular communications or stimulate apoptosis of the cells which remain individual.
The modulation principles to support the healthy processes have broad feasibility to treat the patients. The therapy is a complex, multi-component clinical process, where one of the factors is the modulated electro-hyperthermia (mEHT). The mEHT has proved its exceptional capability to treat late-stage, relapsed cancerous tumors, complementary to any other conventional therapies. In instances where there are no further treatment options available, mEHT could be applied as monotherapy, or in some cases, could desensitize tumors to the previously ineffective conventional treatment.
This work was supported by the Hungarian National Research Development and Innovation Office PIACI KFI grant: 2019-1.1.1-PIACI-KFI-2019-00011.
The author declares no conflicts of interest regarding the publication of this paper.
Szasz, A. (2022) Time-Fractal Modulation—Possible Modulation Effects in Human Therapy. Open Journal of Biophysics, 12, 38-87. https://doi.org/10.4236/ojbiphy.2022.121003