Spreadsheet method for calculating the induced currents in bone-fracture healing by a low-frequency magnetic field

A commercially available spreadsheet program is used on a microcomputer to calculate the induced current density and electric field patterns produced in a nonhomogeneous, anisotropic model of tissue by a localized, low-frequency magnetic field source. Specific application is made to coils used to promote the healing of bone fractures in limbs. The variation of the conductivity of the fracture gap during healing causes the induced current density pattern to change correspondingly, whereas the induced electric field remains relatively unchanged. Use of more simplified, isotropic models for the bone and for the soft tissue leads to results that differ significantly from those obtained from the full model. The magnetic field beyond the region of the coils contributes little to the induced currents in the fracture gap if the gap is located near the center of the coils. © 1994 Wiley-Liss, Inc.     

Miniature-probe measurements of electric fields and currents induced by a 60-Hz magnetic field in rat and human models

A miniaturized probe was designed and built to provide detailed data on fields induced by a uniform 60-Hz magnetic field in homogeneous models of rat and human. The probe employed three silver wires twisted and potted in an 8-cm hypodermic needle. The exposed tips of the wires formed three sensing electrodes with a centered ground; highly sensitive voltage measurements were enabled by a lock-in amplifier. Tests were conducted in a 1-mT rms field that was uniform within +/- 5%. The models were made by casting 1.5% agar at 1-S/m conductivity into plastic-foam molds. The rat model was scaled 1:1 as an adult (22 cm length; mass about 640 g). The human model was scaled 1:4 as an adult (height = 46.5 cm; mass 1.4 kg). The probe was inserted into each model in several regions, and readings of induced fields were made under different exposure geometries. Maximal strengths of fields induced near the surface of the torso were as high as 120 microV/cm in the laterally exposed rat model. Data extrapolated from the quarter-scale human model revealed that an induced field as high as 700 microV/cm could occur at the torso of a frontally exposed human adult. An overall size-scale factor of about 5 appears to be appropriate for experimental exposures of rats that are intended to simulate currents induced in human beings by magnetic fields. The average strength of electric fields induced in the torso by a 1-mT magnetic field is comparable to that by a vertical electric-field at 60 kV/m and 28 kV/m, respectively, for the rat and human.     

Analysis of induced currents in a rat exposed to 50 Hz linearly and circularly polarized magnetic fields

This paper presents a numerical analysis of currents induced in a rat by linearly and circularly polarized magnetic fields of 50 Hz. Special focus was placed on pineal gland and retina of rats since these organs were often associated with the changes of melatonin synthesis and concentration. Induced currents in two MRI-based rat models with resolutions of up to 0.125 mm(3) were calculated by using the impedance method. We characterized the induced currents by amplitude and polarization. Calculated induced current densities were extremely small, i.e., < 30 microA/m(2) for both linearly and circularly polarized magnetic fields of 1.41 microT (peak). There were no significant differences in amplitude nor polarization of induced currents in the pineal gland between the linearly and the circularly polarized magnetic fields when the polarization was in a vertical plane. In contrast, the magnetic fields rotating in the horizontal plane produced most circularly polarized currents both in the pineal gland and in the retina.     

Effect of magnetic field exposure on calcium channel currents using patch clamp technique

Calcium influxes through the membrane of PC-12D cells were measured under exposure to DC biased AC magnetic fields in resonant conditions of the ion cyclotron and the ion parametric resonance hypotheses and compared with influxes in cells without exposure to the magnetic field. After cancellation of the geomagnetic field, the cells were exposed to the horizontal fields generated by a current sheet, a planar sheet of conductor which generated a satisfactorily homogeneous horizontal magnetic field on the stage of a microscope without hindering treatment of a cell under observation. At or near any resonant conditions, no change in calcium influx could be detected under standard patch clamp conditions.     

Magnetic field induced residual dipolar couplings of imino groups in nucleic acids from measurements at a single magnetic field

For base-paired nucleic acids, variations in ¹ J _NH and the imino ¹H chemical shift are both dominated by hydrogen bond length. In the absence of molecular alignment, the ¹ J _NH coupling for the imino proton then can be approximated by ¹ J _NH = (1.21Hz/ppm)δ_H − 103.5 ± 0.6 Hz, where δ_H represents the chemical shift of the imino proton in ppm. This relation permits imino residual dipolar couplings (RDCs) resulting from magnetic susceptibility anisotropy (MSA) to be extracted from measurement of (¹ J _NH + RDC) splittings at a single magnetic field strength. Magnetic field-induced RDCs were measured for tRNA^Val and the alignment tensor determined from magnetic-field alignment of tRNA^Val agrees well with the tensor calculated by summation of the MSA tensors of the individual nucleobases. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Jinfa Ying, Alexander Grishaev and Michael P. Latham contributed equally to this work.     

Vasoconstriction of the isolated communicating cerebral artery induced by field electrical stimulation

The vasoconstrictor effect elicited by field electrical stimulation of the posterior communicating cerebral artery of the goat was analyzed before and after treatment with pharmacological agents to find out if the adrenergic system was involved in this response. For this purpose, trains of 300 square wave pulses (1-32 Hz, 0.5 msec.) at supramaximal voltage were applies to these arteries producing a frequency-dependent increase in tension. The vasoconstrictor response was significantly reduced by tetrodotoxin (3 x 10(-6) M), phentolamine (10(-6) M) and bretylium (5 x 10(-4) M), but it was not modified by cocaine (10(-6) M). The contraction produced by electrical stimulation of arterial segments from goats pretreated with reserpine (0.02 mg/kg/day for three days) and from goats on which a bilateral superior cervical gangliectomy had been performed 12 days previously, was significantly reduced as compared with controls. These results show that a large part of the vasoconstrictor response of the goat cerebral vessels to field electrical stimulation is mediated by an adrenergic mechanism.     

Behavioural evidence that magnetic field effects in the land snail,Cepaea nemoralis,might not depend on magnetite or induced electric currents

Although extremely low frequency (ELF) magnetic fields (<300 Hz) appear to exert a variety of biological effects, the magnetic field sensing/transduction mechanism(s) remains to be established. Here, using the inhibitory effects of magnetic fields on endogenous opioid peptide-mediated “analgaesic” response of the land snail. Cepaea nemoralis, we addressed the mechanism(s) of action of ELF magnetic fields. Indirect mechanisms involving both induced electric fields and direct magnetic field detection mechanisms (e.g., magnetite, parametric resonance) were evaluated. Snails were exposed to a static magnetic field (B_DC=78±1 μT) and to a 60 Hz magnetic field (B_AC=299±1 μT peak) with the angle between the static and 60 Hz magnetic fields varied in eight steps between 0° and 90°. At 0° and 90°, the magnetic field reduced opioid-induced analgaesia by approximately 20%, and this inhibition was increased to a maximum of 50% when the angle was between 50° and 70°. Because B_AC was fixed in amplitude, direction, and frequency, any induced electric currents would be constant independent of the B_AC/B_DC angle. Also, an energy transduction mechanism involving magnetite should show greatest sensitivity at 90°. Therefore, the energy transduction mechanism probably does not involve induced electric currents or magnetite. Rather, our results suggest a direct magnetic field detection mechanism consistent with the parametric resonance model proposed by Lednev. © 1996 Wiley-Liss, Inc.     

Alternate indices of electric and magnetic field exposures among Ontario electrical utility workers

Epidemiologic studies examining the risk of cancer among occupational groups exposed to electric fields (EF) and or magnetic fields (MF) have relied on traditional summaries of exposure such as the time weighted arithmetic or geometric mean exposure. Findings from animal and cellular studies support the consideration of alternative measures of exposure capable of capturing threshold and intermittent measures of field strength. The main objective of this study was to identify a series of suitable exposure metrics for an ongoing cancer incidence study in a cohort of Ontario electric utility workers. Principal components analysis (PCA) and correlational analysis were used to explore the relationships within and between series of EF and MF exposure indices. Exposure data were collected using personal monitors worn by a sample of 820 workers which yielded 4247 worker days of measurement data. For both EF and MF, the first axis of the PCA identified a series of intercorrelated indices that included the geometric mean, median and arithmetic mean. A considerable portion of the variability in EF and MF exposures were accounted for by two other principal component axes. The second axes for EF and MF exposures were representative of the standard deviation (standard deviation) and thresholds of field measures. To a lesser extent, the variability in the exposure variable was explained by time dependent indices which consisted of autocorrelations at 5 min lags and average transitions in field strength. Our results suggest that the variability in exposure data can only be accounted for by using several exposure indices, and consequently, a series of metrics should be used when exploring the risk of cancer owing to MF and EF exposure in this cohort. Furthermore, the poor correlations observed between indices of MF and EF reinforce the need to be take both fields into account when assessing the risk of cancer in this occupational group. Bioelectromagnetics 19:140–151, 1998. © 1998 Wiley-Liss, Inc.     

Skin temperature changes induced by strong static magnetic field exposure

High intensity static magnetic fields, when applied to the whole body of the anesthetized rat, have previously been reported to decrease skin temperature. The hypothesis of the present study was that in diamagnetic water, molecules in the air play significant roles in the mechanism of skin temperature decrease. We used a horizontal cylindrical superconducting magnet. The magnet produced 8 T at its center. A thermistor probe was inserted in a subcutaneous pocket of the anesthetized rats to measure skin temperature. Animals (n=10) were placed in an open plastic holder in which the ambient air was free to move in any direction (group I). Animals (n=10) were placed in a closed holder in which the air circulation toward the direction of weak magnetic field was restricted (group II). Each holder was connected to a hydrometer to measure humidity around the animal in the holder. The data acquisition phase consisted of a 5 min baseline interval, followed by inserting the animal together with the holder into the center of the magnet bore for a 5 min exposure and a 5 min postexposure period outside the bore. In group I, skin temperature and humidity around the animal significantly decreased during exposure, followed by recovery after exposure. In group II, skin temperature and humidity did not decrease during the measurement. The skin temperature decrease was closely related to the decrease in humidity around the body of the animal in the holder, and the changes were completely blocked by restricting the air circulation in the direction of the bore entrance. Possible mechanisms responsible for the decrease in skin temperature may be associated with magnetically induced movement of water vapor at the skin surface, leading to skin temperature decrease.     

Transmembrane electrical currents of spin-labeled hydrophobic ions.

When spin-labeled phosphonium ions are rapidly mixed with phospholipid vesicles, time-dependent changes in the electron paramagnetic resonance spectrum of the spin label are observed. These changes are interpreted in terms of transmembrane transport of the hydrophobic ion, and simple analysis of the data at different membrane potentials is shown to give the binding constant of the ion to both membrane surfaces, the permeability, and current-voltage relationship for the vesicle membrane in the presence of the hydrophobic ion. These results establish the time resolution for methods using the phosphonium ion as a probe of time-dependent potentials across vesicle membranes, as well as provide fundamental information regarding the binding and transport of hydrophobic cations across bilayers. This latter point is significant in view of the fact that hydrophobic cations have not been well characterized in planar bilayers due to their weak binding and low conductance.     

Osmotically induced electrical signals from actin filaments.

Actin filaments, F-actin, a major component of the cortical cytoskeleton, play an important role in a variety of cell functions. In this report we have assessed the role of osmotic stress on the electrochemical properties of F-actin. The spontaneous Donnan potential of a polymerized actin solution (5 mg/ml) was -3.93 +/- 1.84 mV, which was linearly reduced by osmotic stress on the order of 1-20 mOsm (0.28 +/- 0.06 mV/mM). Calculated surface charge density was reduced and eventually reversed by increasing the osmotic stress as expected for a phase transition behavior. The electro-osmotic behavior of F-actin disappeared at pH 5.5 and was dependent on its filamentous nature. Furthermore, osmotically stressed F-actin displayed a nonlinear electric response upon application of electric fields on the order of 500-2,000 V/cm. These data indicate that F-actin in solution may display nonideal electro-osmotic properties consistent with ionic "cable" behavior which may be of biological significance in the processing and conduction of electrical signals within the cellular compartment.     

Influence of human model resolution on computed currents induced in organs by 60-Hz magnetic fields

The effects of human body model resolution on computed electric fields induced by 60 Hz uniform magnetic fields are investigated. A recently-developed scalar potential finite difference code for low-frequency electromagnetic computations is used to model induction in two anatomically realistic human body models. The first model consists of 204 290 cubic voxels with 7.2-mm edges, while the second comprises 1 639 146 cubic voxels with 3.6-mm edges. Calculations on the lower-resolution model using, for example, the finite difference time domain or impedance methods, push the capabilities of workstations. The scalar method, in contrast, can handle the higher-resolution model using comparable resources. The results are given in terms of average and maximum electric field intensities and current density magnitudes in selected tissues and organs. Although the lower-resolution model provides generally acceptable results, there are important differences that make the added computational burden of the higher-resolution calculations worthwhile. In particular, the higher-resolution modelling generally predicts peak electric fields intensities and current density magnitudes that are slightly higher than those computed using the lower-resolution modelling. The differences can be quite large for small organs such as glands. Bioelectromagnetics 18:478–490, 1997. © 1997 Wiley-Liss, Inc.     

Neurobiological effects of pulsed magnetic field on diabetes‐induced neuropathy

In the clinic, although several pharmacological agents or surgical procedures are used to treat diabetes and diabetes‐induced neuropathic pain, their success has been limited. Therefore, development of different alternatives in treatments is very important. The purpose of this study was to determine the efficacy of pulsed magnetic field (PMF) in improving signs and symptoms of diabetic neuropathy. In this study, the effects of PMF treatment were investigated in Streptozotocin (STZ)‐induced acute and chronic diabetic rats by measuring the thermal latencies, mechanical thresholds, whole blood glucose levels and body weights. After STZ administration to rats, blood glucose level elevated and body weight decreased. Although PMF treatment did not affect changes in body weight, the blood glucose levels of PMF‐treated diabetic rats exhibited a decrease during the treatments. Diabetic animals displayed marked decrease in mechanical thresholds and thermal latencies. While treatment of PMF partially restored the mechanical thresholds and thermal latency in acute diabetic rats, PMF caused a corrective effect on only mechanical threshold of chronic diabetic rats. These results suggested that treatment of PMF can potentially ameliorate the painful symptoms of diabetes, such as hyperalgesia and allodynia, by partially preventing the hyperglycemia. Bioelectromagnetics 31:39–47, 2010. © 2009 Wiley‐Liss, Inc.