Microtubules are extremely longitudinally conductive to alternating currents at frequencies close to the 27.12 MHz carrier wave of the LEAM RF EMF medical devices, in the range of approximately 12–50 MHz (57–61). Furthermore, the highly charged C-terminal tail domains of tubulin protrude from the microtubule surface and also oscillate at frequencies close to that of the carrier wave (14). Although induced oscillations at these frequencies may disrupt microtubule function and motor protein traffic, the carrier wave frequency is constant and cannot therefore be responsible for the personalized or tumour-specific effects of specific envelope wave frequencies. Furthermore, an entire microtubule with a length of only 20 nm would resonate at 27 MHz, but most microtubules are much longer, spanning the length of the cell and achieving lengths up to 50 µm (or even higher under laboratory conditions). We therefore speculate that the carrier wave has a potentiating effect on ion flows along microtubules that renders cells susceptible to the effects of the lower-frequency envelope wave.

Spontaneous electrical oscillation of microtubules at fundamental resonant frequencies of 29 and 39 Hz has been reported in patch-clamp electrophysiological experiments using purified microtubule sheets and bundles, and permeabilized neurites in vitro (62, 63). Under constant holding potentials of 1 mV, microtubule-associated charges spontaneously oscillated at these frequencies, with a more than sixfold concomitant increase in conductivity (62, 63). These observations are consistent with axial ion flows in and out of the nanopores between tubulin monomers in a microtubule, and the frequencies fall within the range of envelope wave frequencies produced by LEAM RF EMF devices. Resonant frequencies of microtubules in vivo may differ from those observed in the in vitro electrophysiological studies because of differences in factors such as ionic strength, pH, protein-protein interactions, and cellular architecture. We therefore speculate that the combination of carrier wave and envelope wave interactions with different microtubule ion flows may underlie the physiological and potential clinical effects of LEAM RF EMF exposure.

The subcellular positioning of mitochondria is tightly associated with their bioenergetic and cell-signalling functions. Mitochondria dynamically alter their subcellular localization by trafficking along microtubules using kinesin-1, and may also form a network enabling exchange of energy and signals between cells via membrane nanotubes (64–66). Perturbation of microtubules by EMF and resulting disruption of mitochondrial trafficking could therefore interfere with multiple mitochondrial functions. Consistent with this possibility, blocking mitochondrial anterograde trafficking by inhibiting integrin recycling led to detrimental amplification of reactive oxygen species in an in vitro study in breast cancer cell lines (67).

In a hypothesis-generating and exploratory experiment, we used transmission electron microscopy to evaluate mitochondrial ultrastructure in liver tumour biopsies taken from patients with HCC who had undergone LEAM RF EMF exposure (Figures 2, 3). Mitochondria appeared to congregate in cellular locations distant from microtubules, and to show morphological changes characterized by disorganized crista and swelling of the matrix. To our knowledge, these abnormalities have not been previously reported in the context of HCC. This finding needs replication in future studies, but is consistent with effects of LEAM RF EMF exposure on mitochondria.

Malignant cancer cells produce lactate by fermentation of glucose even in non-hypoxic conditions, in a phenomenon known as the Warburg effect (38, 39). This is far less energy-efficient than oxidative phosphorylation for ATP production, but provides the cell with glycolytic intermediates to support biosynthesis of nucleotides and amino acids for cell growth (11). Because the Warburg effect is a defining feature of malignancy, reversing it has been proposed as a route to new cancer therapies, for example using microRNAs (40, 68, 69).

We hypothesize that LEAM RF EMF exposure may shift cellular metabolism away from glycolysis in cancer cells and hence lead to the restoration of the normal phenotype.(70) Although the effects of low-power AM RF EMF exposure are non-thermal, the energy delivered is ultimately dissipated as molecular motion. In the following sections, we calculate the power delivered to the cell and the energy dissipation due to EMF induction of ionic flows in microtubules, and compare this with total cellular metabolic energy production. We conclude that this energy delivery may contribute significantly towards shifting the cellular energy balance.

The starting point is the outcome of calculations is in vitro experiments with modulated radiofrequency using a previously published exposure system designed to replicate in vivo (human) conditions (16, 21). The sXcTEM027 exposure system apparatus (IT'IS Foundation, Zürich Switzerland) operating in the 27 MHz carrier wave region was used for in vitro experiments. The dosimetric assessments of 35 mm Petri dishes were performed for 2D culture cells in monolayer and suspension. The numerical dosimetry was verified by dosimetric temperature measurements. The non-uniformity of the specific absorption rate (SAR) distribution in the Petri dish filled with a small volume of cell culture media was determined and adjusted to represent SAR values determined in humans, as previously published (71). The heterogeneity of SAR with LEAM RF EMFs has not been evaluated in realistic tumour anatomies, to our knowledge, as has been performed for magnetic nanoparticle hyperthermia using micro computed tomography scans (72). Nevertheless, published dosimetry models for LEAM RF EMF provide an adequate starting point for estimating the power delivered to individual liver cells during exposure, as follows (16, 21, 71).

Dosimetric experiments with an RF EMF generator device were performed to estimate the specific absorption rate and distribution inside the human body. Numerical analysis based on the standardized anatomically based model of the human male (“Duke”) from the “Virtual Population” was performed and the simulation results were verified using SAR measurements in a simple rectangular phantom (73). Dosimetric experiments with radiofrequency in the MHz range exposure system for use during live cell imaging provided excellent exposure control and homogeneity.

Published dosimetry values for the P1 device calculate the average power delivered to a single human liver cell during exposure (9). Specific absorption rates were based on the “Duke” adult male model (weight 73 kg), one of ten models in the “Virtual Family” of whole-body anatomical models (73). The average power delivered by the EMF exposure device was 8.4 mW/kg for the liver (9). The average human liver weighs 1.3 kg and comprises 2.4 × 10¹¹ cells (74), so we can readily calculate that the average power delivered per cell is approximately 50 fW. Thermal modelling was performed with a 2 mm voxel size in tissues. The thermal results reached a steady state after approximately 20–25 min with a maximum increase of 0.24°C for nominal perfusion values (75).

The electrical current flowing through a single microtubule nanopore during oscillation at 29 Hz was estimated at 0.02–0.14 fA under an applied potential difference of 5 mV, in the electrophysiological study described above (62). From this, we can calculate the resistance of a single nanopore as 62.5 TΩ using Ohm's law (R = V/I). Ions flow in from one side of the microtubule wall and out from the other, so each pair of nanopores is a series resistor with a total resistance twice that of a single nanopore, equalling 125 TΩ. If a typical microtubule is 10 µm long and has 13 protofilaments each comprising 1,250 tubulin dimers, it contains 16,250 nanopores. Viewing this as a parallel arrangement of 8,125 nanopore pairs each with a resistance of 125 TΩ, the overall resistance of the microtubule can be estimated to be approximately 15 GΩ.

In a mitotic liver cancer cell, a microtubule plus-end is attached to a kinetochore and a minus-end interacts with a centrosome. If the potential difference across the microtubule in this setting is on the order of 1 mV, then we can calculate the current flowing as 0.07 pA from its resistance of 15 GΩ, again using Ohm's law. (47, 54–55) This translates into an ionic flow rate of 6 × 10⁵ unit charges per second per microtubule, which equates to 30 unit charges per second per nanopore for our typical microtubule with 16,250 nanopores. The frequency of charge transfer is therefore approximately 30 Hz. This is close to both the fundamental oscillation frequency in the electrophysiological study (62) and within the envelope wave frequency of the LEAM RF EMF devices. In this setting, one charge passes through each microtubule nanopore per cycle of the envelope wave, although the exact frequency would depend on cellular microtubule geometry and other factors. Nevertheless, the similarity in frequency between microtubule ion flows and the envelope wave provides a potential mechanism for transfer of electromagnetic energy into cancer cells.

We can also calculate the power dissipated by a single typical microtubule as 0.03 fW (using P = ½ V²/R since this represents the root mean square value of the power in an oscillating current situation described here, with the above values of 1 mV and 15 GΩ). Each kinetochore is attached to 30 microtubules and there are two copies of each of the 23 chromosomes, so we can estimate that there are 1,380 microtubules (excluding astral and polar microtubules) in a mitotic cell. The total power dissipated by microtubule ion flows in a single mitotic cell during oscillation at 29 Hz is therefore 46 fW, under the above assumptions. This value is very similar to the estimated power delivery of 50 fW per liver cell by the clinical EMF exposure device (see above).

We next consider what proportion of the normal cellular energy budget corresponds to the approximately 50 fW delivered by LEAM RF EMFs and dissipated by microtubule ion flows. We start by estimating the metabolic power of normal cells as 3 pW per cell using two separate methods. First, the human body uses about 100 W of metabolic power at rest and comprises 3.7 × 10¹³ cells on average, meaning that each cell uses 3 pW (76). Secondly, each cell contains about 2,000 mitochondria, which each produce about 30,000 ATP molecules per second by oxidative phosphorylation (74). ATP releases 30 kJ/mol of free energy upon hydrolysis or 5 × 10^–20 J per molecule (76). Multiplying these values together also gives a metabolic power of 3 pW per cell. The estimates of approximately 50 fW for EMF power delivered and dissipated per cell therefore correspond to approximately 1.5% of metabolic power in normal cells.

In liver cancer cells, mitochondrial oxidative phosphorylation can be reduced by as much as 50%, depending on the disease stage, as cancer cells undergo the Warburg effect and shift to rely increasingly on glycolytic ATP production (77, 78). The human liver normally produces 30 mmol of ATP per minute by oxidative phosphorylation, or 3 × 10²⁰ molecules of ATP per second, each releasing 5 × 10^–20 J upon hydrolysis (35), which corresponds to a metabolic power of 15 W (or 15% of whole-body metabolic power).

Glycolysis is nine times less efficient than oxidative phosphorylation, so to maintain the same energy output, cells need to increase glucose consumption by an equivalent factor (77, 78). Consequently, 50 fW per cell may correspond to as much as 13.5% of glucose consumption in cells using glycolysis, compared with 1.5% in those using oxidative phosphorylation. Two-thirds of resting metabolic rate is devoted to heat production (76), so the energy delivered by EMFs may contribute meaningfully to the cellular energy budget. This may hence represent a significant shift in energy production away from glycolysis, which could counteract the Warburg effect and deprive cells of energy-rich metabolites produced from glycolysis (70) with a potential reduction in tumour growth and an overall decrease of the energetic burden the tumour imposes on the rest of the patient's body, consistently with the reported quality of life amelioration of the treated patients.

We have shown that the frequency of charge transfer across isolated microtubules in vitro (approximately 30 Hz) falls within the envelope wave frequency range of therapeutic LEAM RF EMF devices. This frequency is likely to vary depending on cell morphology, physiology, and other factors. It may therefore fall within the same range as haemodynamically active and potentially therapeutic envelope wave frequencies (approximately 10–1,000 Hz). This provides a potential mechanism for transfer of EMF energy into cells, and dissipation of power via the ionic flows across microtubules. The power level is far too low to cause detectable heating of tissues, at about 8 mW for the whole liver and 50 fW per liver cell, but may nevertheless result in a significant shift of up to 13.5% in metabolic energy balance away from glycolysis. This could lead to suppression of the Warburg effect and promotion of a normal cellular metabolic phenotype. We hypothesize that this may be one of the mechanisms underlying the long-term disease control observed in patients with HCC in clinical trials. Direct effects of LEAM RF EMFs most likely involve subcellular electrically charged structures such as microtubules and possibly ionic flows around them, with predominant influence on mitosis. Hence, given a typically low mitotic fraction of cells within a tumour relative to the overall cell population and the much higher proportion of time cells reside within other phases of the cell cycle, a more complete explanation of long-lasting effects of EMFs on the tumour most likely requires metabolic effects which can endure long enough to affect cell fate/survival including a change of the phenotype mentioned above.

The structure of the cytoskeleton may underlie the potentially beneficial clinical effects of exposure to LEAM RM EMF using devices producing a 27.12 MHz carrier wave and envelope waves at specific frequencies in the range of approximately 10 Hz to 20 kHz. In particular, oscillating ionic flows may form in the condensed ions surrounding and within microtubules by resonant coupling with envelope waves of specific frequencies. These ionic flows may then lead to interference with ion channels, cell division, motor proteins, mitochondrial trafficking and morphology, and cellular energy balance. These putative mechanisms of action are potentially overlapping and not mutually exclusive, and all require further investigation by specifically designed assays. The efficacy of LEAM RF EMF in patients with HCC will be tested in randomized controlled studies. Nevertheless, we conclude that systemic exposure to LEAM RF EMFs of specific frequencies is a potential route to modifying the behaviour of cancer cells in patients with advanced disease.