Theoretical evaluation of the distributed power dissipation in biological cells exposed to electric fields

The paper deals with the power dissipation caused by exposure of biological cells to electric fields of various frequencies. With DC and sub-MHz AC frequencies, power dissipation in the cell membrane is of the same order of magnitude as in the external medium. At MHz and GHz frequencies, dielectric relaxation leads to dielectric power dissipation gradually increasing with frequency, and total power dissipation within the membrane rises significantly. Since such local increase can lead to considerable biochemical and biophysical changes within the membrane, especially at higher frequencies, the bulk treatment does not provide a complete picture of effects of an exposure. In this paper, we theoretically analyze the distribution of power dissipation as a function of field frequency. We first discuss conductive power dissipation generated by DC exposures. Then, we focus on AC fields; starting with the established first-order model, which includes only conductive power dissipation and is valid at sub-MHz frequencies, we enhance it in two steps. We first introduce the capacitive properties of the cytoplasm and the external medium to obtain a second-order model, which still includes only conductive power dissipation. Then we enhance this model further by accounting for dielectric relaxation effects, thereby introducing dielectric power dissipation. The calculations show that due to the latter component, in the MHz range the power dissipation within the membrane significantly exceeds the value in the external medium, while in the lower GHz range this effect is even more pronounced. This implies that even in exposures that do not cause a significant temperature rise at the macroscopic, whole-system level, the locally increased power dissipation in cell membranes could lead to various effects at the microscopic, single-cell level.     

The state of water in biological systems as studied by proton and deuterium relaxation.

Careful experiments on the measurement of the intensity of the deuterium NMR signal for 2-H2 O in muscle and in its distillate were performed, and they showed that all 2-H2 O muscle is "NMR visible". The spin-lattice relaxation time (T1) of the water protons in the muscle and liver of mice and in egg white has been studied at six frequencies ranging from 4.5 to 6.0 MHz over the temperature range of +37 to --70 degrees C. T1 values of deuterons in 2H2 O of gastrocnemius muscle and liver of mice have been measured at three frequencies (4.5, 9.21 and 15.35 MHz) over the temperature range of +37 to --20 degrees C. Calculations on T1 for both proton and deuteron have been made and compared with the experimental data. It is suggested that the reduction of the T1 values compared to pure water and the frequency dependence of T1 are due to water molecules in the hydration layer of the macromolecules, and that the bulk of water molecules in the biological tissues and egg white undergoes relaxation like ordinary liquid water.     

Electrical Properties of Phospholipid Vesicles

The capacitance of the membrane of phospholipid vesicles and the electrical properties of the vesicle interior have been determined. To this end the electrical properties of phospholipid vesicles have been investigated over a frequency range extending from 1 kHz to 100 MHz. The dielectric behavior is characterized by two dispersions, one placed between 1 kHz and 1 MHz and the other between 1 and 100 MHz. The relaxational behavior at low frequencies is explained by counterion movement tangential to the vesicle surface and a reasonable value for the fixed charge of the vesicles is calculated from the dispersion magnitude. The relaxation at high frequencies is of the Maxwell-Wagner type and appears caused by the phospholipid bilayer bounding the interior phase of the vesicles. It is consistent with the existence of a closed bilayer with a capacitance of about 2 μF/cm² and an internal phase similar to the vesicle suspending medium. There is no indication of other than normally structured water inside the small vesicles.     

The high frequency properties of brain tissue

Computer modeling is becoming increasingly important in the realm of brain biomechanics and injury. New computer simulations range from modeling of brain surgery, a low frequency, high strain event, to predicting injury as a result of an impact to the head, a high frequency event with varying strain magnitudes. This range of modeling efforts requires characterization of the tissue over as wide a frequency and strain range as possible. Research done to date has concentrated on the low frequency properties of the tissue. Complex compression and complex shear moduli have been measured at frequencies up to 350 Hz. Impact modeling requires use of frequency data at significantly higher frequencies than these. The "wave-in-a-tube" ultrasonic method was applied to brain tissue to determine mechanical properties at frequencies between 100 kHz and 10 MHz. Of these properties, only complex bulk modulus |K*| is fairly invariant (2133 MPa) with respect to frequency. Complex shear and complex Young's moduli vary with frequency and approach an asymptotic upper limit. Some variation in complex Poisson's ratio was also observed.     

Dielectric properties of alginate beads and bound water relaxation studied by electrorotation

The electrical and dielectric properties of Ba²⁺ and Ca²⁺ cross‐linked alginate hydrogel beads were studied by means of single‐particle electrorotation. The use of microstructured electrodes allowed the measurements to be performed over a wide range of medium conductivity from about 5 mS/m to 1 S/m. Within a conductivity range, the beads exhibited measurable electrorotation response at frequencies above 0.2 MHz with two well‐resolved co‐ and antifield peaks. With increasing medium conductivity, both peaks shifted toward higher frequency and their magnitudes decreased greatly. The results were analyzed using various dielectric models that consider the beads as homogeneous spheres with conductive loss and allow the complex rotational behavior of beads to be explained in terms of conductivity and permittivity of the hydrogel. The rotation spectra could be fitted very accurately by assuming (a) a linear relationship between the internal hydrogel conductivity and the medium conductivity, and (b) a broad internal dispersion of the hydrogel centered between 20 and 40 MHz. We attribute this dispersion to the relaxation of water bound to the polysaccharide matrix of the beads. The dielectric characterization of alginate hydrogels is of enormous interest for biotechnology and medicine, where alginate beads are widely used for immobilization of cells and enzymes, for drug delivery, and as microcarriers for cell cultivation. © 1999 John Wiley & Sons, Inc. Biopoly 50: 227–237, 1999     

Theoretically proposed optimal frequency for ultrasound induced cartilage restoration

Background

Matching the frequency of the driving force to that of the system’s natural frequency of vibration results in greater amplitude response. Thus we hypothesize that applying ultrasound at the chondrocyte’s resonant frequency will result in greater deformation than applying similar ultrasound power at a frequency outside of the resonant bandwidth. Based on this resonant hypothesis, our group previously confirmed theoretically and experimentally that ultrasound stimulation of suspended chondrocytes at resonance (5 MHz) maximized gene expression of load inducible genes. However, this study was based on suspended chondrocytes. The resonant frequency of a chondrocyte does not only depend on the cell mass and intracellular stiffness, but also on the mechanical properties of the surrounding medium. An in vivo chondrocyte’s environment differs whether it be a blood clot (following microfracture), a hydrogel or the pericellular and extracellular matrices of the natural cartilage. All have distinct structures and compositions leading to different resonant frequencies. In this study, we present two theoretical models, the first model to understand the effects of the resonant frequency on the cellular deformation and the second to identify the optimal frequency range for clinical applications of ultrasound to enhance cartilage restoration.

Results

We showed that applying low-intensity ultrasound at the resonant frequency induced deformation equivalent to that experimentally calculated in previous studies at higher intensities and a 1 MHz frequency. Additionally, the resonant frequency of an in vivo chondrocyte in healthy conditions, osteoarthritic conditions, embedded in a blood clot and embedded in fibrin ranges from 3.5???4.8 MHz.

Conclusion

The main finding of this study is the theoretically proposed optimal frequency for clinical applications of therapeutic ultrasound induced cartilage restoration is 3.5???4.8 MHz (the resonant frequencies of in vivo chondrocytes). Application of ultrasound in this frequency range will maximize desired bioeffects.

     

Dielectric spectroscopy of single human erythrocytes at physiological ionic strength: dispersion of the cytoplasm.

Usually dielectrophoretic and electrorotation measurements are carried out at low ionic strength to reduce electrolysis and heat production. Such problems are minimized in microelectrode chambers. In a planar ultramicroelectrode chamber fabricated by semiconductor technology, we were able to measure the dielectric properties of human red blood cells in the frequency range from 2 kHz to 200 MHz up to physiological ion concentrations. At low ionic strength, red cells exhibit a typical electrorotation spectrum with an antifield rotation peak at low frequencies and a cofield rotation peak at higher ones. With increasing medium conductivity, both electrorotational peaks shift toward higher frequencies. The cofield peak becomes antifield for conductivities higher than 0.5 S/m. Because the polarizability of the external medium at these ionic strengths becomes similar to that of the cytoplasm, properties can be measured more sensitively. The critical dielectrophoretic frequencies were also determined. From our measurements, in the wide conductivity range from 2 mS/m to 1.5 S/m we propose a single-shell erythrocyte model. This pictures the cell as an oblate spheroid with a long semiaxis of 3.3 microns and an axial ratio of 1:2. Its membrane exhibits a capacitance of 0.997 x 10(-2) F/m2 and a specific conductance of 480 S/m2. The cytoplasmic parameters, a conductivity of 0.4 S/m at a dielectric constant of 212, disperse around 15 MHz to become 0.535 S/m and 50, respectively. We attribute this cytoplasmic dispersion to hemoglobin and cytoplasmic ion properties. In electrorotation measurements at about 60 MHz, an unexpectedly low rotation speed was observed. Around 180 MHz, the speed increased dramatically. By analysis of the electric chamber circuit properties, we were able to show that these effects are not due to cell polarization but are instead caused by a dramatic increase in the chamber field strength around 180 MHz. Although the chamber exhibits a resonance around 180 MHz, the harmonic content of the square-topped driving signals generates distortions of electrorotational spectra at far lower frequencies. Possible technological applications of chamber resonances are mentioned.     

The influence of the molecular structure of lipid membranes on the electric field distribution and energy absorption

We consider the influence of the molecular structure of phospholipid membranes on their dielectric properties in the radio frequency range. Membranes have a stratified dielectric structure on the submolecular level, with the lipid chains forming a central hydrophobic layer enclosed by the polar headgroups (HGs) and bound water layers. In our numerical model, isotropic permittivities of 2.2 and 48.8 were assigned to the lipid chain and bound water layers, respectively. The HG region was assumed to possess an anisotropic static permittivity with 142.2 and 30.2 in the tangential and normal directions, respectively. The permittivities of the HG and bound water regions have been assumed to disperse at frequencies around 51 and 345 MHz to become 2.2 and 1.8, respectively, in both the normal and tangential directions. Electric field distribution and absorption were calculated for phospholipid vesicles with 75 nm radius as an example. Significant absorption has been obtained in the HG and bound water regions. Averaging the membrane absorption over the layers resulted in a decreased absorption below 1 GHz but a more than 10-fold increase above 1 GHz, compared to a model with a homogeneous membrane of averaged properties. We propose single particle dielectric spectroscopy by AC electrokinetics at low-bulk medium conductivities for an experimental verification of our model.     

Impedance spectroscopy of alpha-beta tubulin heterodimer suspensions

Impedance spectroscopy is a technique that reveals information, such as macromolecular charges and related properties about protein suspensions and other materials. Here we report on impedance measurements over the frequency range of 1 Hz to 1 MHz of alpha-beta tubulin heterodimers suspended in a buffer. These and other polyelectrolyte suspensions show enormous dielectric responses at low frequencies, due both to the motion of charges suspended in the medium and to an electrical double layer that forms at each electrode-medium interface. We propose an equivalent circuit model to minimize electrode polarization effects and extract the intrinsic response of the bulk medium. At megaHertz frequencies, the conductivity increases with concentration below the critical concentration of approximately 1 mg/ml for microtubule polymerization, above which the conductivity decreases. This suggests that such measurements can be used to monitor the dynamics of microtubule polymerization. Finally, we obtain the net charge number per tubulin dimer of /Z/ = 306 in the saline buffer, which, if maintained as the dimers polymerized, would yield a linear charge density of 3.8 e/angstroms for the assembled microtubules. These results are potentially important for fundamental electrostatic processes in biomolecules and suggest the possibility of developing future bioelectronic applications.     

Microbubble detection following hyperbaric chamber dives using dual-frequency ultrasound

Venous gas emboli (VGE) can be readily detected in the bloodstream using existing ultrasound methods. No method currently exists to detect decompression-induced microbubbles in tissue. We hypothesized that dual-frequency ultrasound (DFU) could detect these microbubbles. With DFU, microbubbles are driven with two frequencies: a lower "pump" (set to the resonant frequency of the desired bubble size) and a higher "image" frequency. A bubble of the resonant size emits the sum and difference of the two transmitted frequencies. For this study we used a pump frequency of 2.25 MHz and an image frequency of 5.0 MHz, which detects bubbles of roughly 1-10 μm in diameter in a water tank. Four anesthetized swine were pressurized at 4.5 ATA for 2 h and decompressed over 5 min, inducing moderate to very severe VGE scores. Four sites on the thigh of each swine were monitored with DFU before and after the dives. A single mock dive was also performed. The number of sites returning signals consistent with microbubbles increased dramatically after the chamber dive (P < 0.01), but did not change with the mock dive. The increase in DFU signal after the chamber dive was sustained and present at multiple sites in multiple swine. This research shows for the first time that decompression-induced tissue microbubbles can be detected using DFU and that DFU could be used to monitor decompression-induced microbubbles at multiple sites on the body. Additionally, DFU could be used to track the time course of microbubble formation and growth during decompression stress.     

Dielectric spectroscopy study of myoglobin in glycerol-water mixtures

Due to the interest in protein dynamics, there are numerous dielectric relaxation studies of proteins in water and in glass-forming aqueous solvents such as glycerol-water mixtures. In the regime of low frequencies, the inevitable dc-conductivity of such systems limits the resolution of dynamics that are slow compared with the solvent relaxation. Solutions of myoglobin in glycerol/water mixtures of various compositions are measured by dielectric spectroscopy in the frequency range from 10 mHz to 10 MHz. The resolution of low frequency modes is improved by two approaches: electrical ‘cleaning’ and the analysis of the derivative of the real component of permittivity, which shows no direct signature of dc-conductivity. Effects of internal interfacial polarization are also addressed by measuring the same solvents in confinement as well as mixed with glass beads. We find two processes, the structural relaxation of the solvent and the slower rotational mode of the protein, with no indication at even lower frequencies of a dielectric signature of fluctuations associated with protein dynamics.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. I. Dielectric behavior of cell suspensions in 0.01-500 MHz and its simulation with a single-shell model

Frequency dependence of relative permittivity (dielectric constant) and conductivity, or the 'dielectric dispersion', of cultured cells (RBL-1 line) in suspension was measured using a fast impedance analyzer system capable of scanning 92 frequency points over a 10 kHz-500 MHz range within 80 s. Examination of the resulting dispersion curves of an improved reliability revealed that the dispersions consisted of at least two separate components. The low-frequency component (dispersion 1) had a permittivity increment (delta epsilon) of 10(3)-10(4) and a characteristic frequency (fc) at several hundred kHz; for the high-frequency component (dispersion 2), delta epsilon was smaller by a factor of 10(2) and fc = 10-30 MHz. Increments delta epsilon for both components increased with the volume fraction of cell suspension, while fc did not change appreciably as long as the conductivity of suspending medium was fixed. By fitting a model for shelled spheres (the 'single-shell' model) to the data of dispersion 1, the dielectric capacity of the plasma membrane phase (Cm) was estimated to be approx. 1.4 microF/cm2 for the cells in an isotonic medium. However, simulation by this particular shell model failed to reproduce the entire dispersion profile leaving a sizable discrepancy between theory and experiment especially at frequencies above 1 MHz where dispersion 2 took place. This discrepancy could not be filled up even by taking into consideration either the effect of cell size distribution actually determined or that of possible heterogeneity in the intracellular conductivity. The present data strongly indicate the need for a more penetrating model that effectively accounts for the behavior of dispersion 2.     

RF Exposure During Use of Electrosurgical Units

Electrosurgical units (ESUs) commonly used in operating suites employ radiofrequency (RF) energy for cutting and coagulation, and operate at different frequencies in the range 0.3–5 MHz. Around the electrode and cables, electric and magnetic fields at similar frequencies will be generated, and the surgeon using the ESU will therefore be exposed to these electromagnetic fields. In this study we have measured the levels of RF fields near the lead wires of two electrosurgical units, BARD 3000 operating at a fixed frequency of 0.5 MHz, and ERBE ICC 350 with a frequency range from 0.3 to 1 MHz. Electric fields were measured at distances from 5–30 cm from the lead wire. Measurements were done with the ESU both cutting and coagulating, and power levels ranging from 10–100 W. The magnetic field outside the lead wire was calculated from the measured current through the leads using standard theory. Using those measurements as a base, the calculated local exposure of the surgeon's hand was estimated to exceed 15 kV/m for the electric field and the corresponding value for the magnetic field was 16 µT. These calculations exceed the suggested international reference levels at 0.5 MHz (610 V/m and 4 µT, respectively).     

Spinning response of yeast cells to rotating electric fields

The frequency-dependent rotation or spinning motion of yeast cells subjected to a fourpole rotating electric field was examined over a very wide frequency range (500 Hz to 500 MHz). In the lower frequency range (500 Hz – 700 KHz) the yeast cells were observed to spin in a direction counter to the applied field, with a small peak at about 600 Hz and a more pronounced one at 20 KHz. For frequencies above 700 KHz the spinning of the cells switched direction from counter-field to co-field, with a maximum in the rotation rate at about 70 MHz and a subpeak at 20 MHz. The rate was also observed to exhibit a square dependence on the magnitude of the applied rotating field.     

Thermophysiological responses of human volunteers to whole body RF exposure at 220 MHz

Since 1994, our research has demonstrated how thermophysiological responses are mobilized in human volunteers exposed to three radio frequencies, 100, 450, and 2450 MHz. A significant gap in this frequency range is now filled by the present study, conducted at 220 MHz. Thermoregulatory responses of heat loss and heat production were measured in six adult volunteers (five males, one female, aged 24-63 years) during 45 min whole body dorsal exposures to 220 MHz radio frequency (RF) energy. Three power densities (PD = 9, 12, and 15 mW/cm(2) [1 mW/cm(2) = 10 W/m(2)], whole body average normalized specific absorption rate [SAR] = 0.045 [W/kg]/[mW/cm(2)] = 0.0045 [W/kg]/[W/m(2)]) were tested at each of three ambient temperatures (T(a) = 24, 28, and 31 degrees C) plus T(a) controls (no RF). Measured responses included esophageal (T(esoph)) and seven skin temperatures (T(sk)), metabolic rate (M), local sweat rate, and local skin blood flow (SkBF). Derived measures included heart rate (HR), respiration rate, and total evaporative water loss (EWL). Finite difference-time domain (FDTD) modeling of a seated 70 kg human exposed to 220 MHz predicted six localized "hot spots" at which local temperatures were also measured. No changes in M occurred under any test condition, while T(esoph) showed small changes (< or =0.35 degrees C) but never exceeded 37.3 degrees C. As with similar exposures at 100 MHz, local T(sk) changed little and modest increases in SkBF were recorded. At 220 MHz, vigorous sweating occurred at PD = 12 and 15 mW/cm(2), with sweating levels higher than those observed for equivalent PD at 100 MHz. Predicted "hot spots" were confirmed by local temperature measurements. The FDTD model showed the local SAR in deep neural tissues that harbor temperature-sensitive neurons (e.g., brainstem, spinal cord) to be greater at 220 than at 100 MHz. Human exposure at both 220 and 100 MHz results in far less skin heating than occurs during exposure at 450 MHz. However, the exposed subjects thermoregulate efficiently because of increased heat loss responses, particularly sweating. It is clear that these responses are controlled by neural signals from thermosensors deep in the brainstem and spinal cord, rather than those in the skin.     

Dielectric properties of mouse MCA1 fibrosarcoma at different stages of development

The in vitro bulk electrical properties of MCA1 fibrosarcoma induced in C57B1/6 male mice were measured at frequencies of 10 kHz to 100 MHz, with some tissues measured to 2 GHz. The properties of normal surrounding tissue also were measured. A comparison of the dielectric properties between three different stages of tumor development as well as that between various locations within the tumor is reported. Statistical analysis of the experimental results revealed statistically significant differences in the dielectric constant and conductivity of the tumor tissues at various stages of development as measured at frequencies below 10 MHz. Conductivity values at different stages also differ at a frequency of 100 MHz. At other frequencies these differences were found to be statistically insignificant.     

Dielectric spectroscopy of mammalian cells

The capacitance of suspensions of CHO and HeLa cells (0.5–3×10⁶ cells/ml) has been measured between 0.2 and 10 MHz. As frequencies decrease, there is a continuous increase in capacitance of both the cell suspension and the spent growth medium free of cells, a phenomenon which is partially attributed to an increased polarisation of the electrodes. At a given frequency, subtraction of the capacitance of the spent medium from that of the cell suspension allows one to determine the capacitance of the cells only. The intensity of this signal varies linearly with the biomass and cell size.At low frequencies such as those used in this study (0.25 MHz), where sensitivity is the highest, concentrations as low as 0.5×10⁶ cells/ml can be accurately measured.Suggestions are made how to make these measures on-line, non-invasive and in real time.     

The peculiarities of the microwave in the frequency range of 51-52 GHz spectrum effects on E. coli cells

The effects of microwaves on conformation of nucleoids in E. coli cells were studied by the method of anomalous viscosity time dependence (AVTD) at various frequencies in the range of 51-52 GHz and the power flux density of 100 microW/cm(2) . Linearly polarized microwaves resulted in significant effects within specific frequency windows of resonance type. The distances between frequency windows were in the range of 55-180 MHz. Only one of two possible circular polarizations, left-handed or right-handed, was shown to be effective at each frequency window. The sign of effective circular polarization alternated between frequency windows. We show that the effects of microwaves on E. coli cells as measured by the AVTD technique are not caused by adhesion of cells. The half-width of the 51.575 GHz resonance was measured to be 120+/-20 MHz. This value is very close to the half-width of the 51.755 GHz resonance as it has previously been determined at the same power flux density. The obtained data suggest similar targets for effects of microwaves at these two resonance frequencies and provide evidence for non-thermal nature of observed microwave effects.     

Manipulation of herpes simplex virus type 1 by dielectrophoresis

The frequency-dependent dielectrophoretic behaviour of an enveloped mammalian virus, herpes simplex virus type 1 is described. It is demonstrated that over the range 10 kHz–20 MHz, these viral particles, when suspended in an aqueous medium of conductivity 5 mS m^?1, can be manipulated by both positive and negative dielectrophoresis using microfabricated electrode arrays. The observed transition from positive to negative dielectrophoresis at frequencies around 4.5 MHz is in qualitative agreement with a simple model of the virus as a conducting particle surrounded by an insulating membrane.