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Sci Rep. 2016; 6: 37407.
Published online 2016 Nov 18. doi:  10.1038/srep37407
PMCID: PMC5114642
PMID: 27857227

How a High-Gradient Magnetic Field Could Affect Cell Life

Vitalii Zablotskii,a,1 Tatyana Polyakova,1 Oleg Lunov,1 and Alexandr Dejneka1
1Department of Optical and Biophysical Systems, Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, 18221, Czech Republic
azc.uzf@tolbaz
Author information ? Article notes ? Copyright and License information ? Disclaimer
Received 2016 Jun 27; Accepted 2016 Oct 28.

Abstract

The biological effects of high-gradient magnetic fields (HGMFs) have steadily gained the increased attention of researchers from different disciplines, such as cell biology, cell therapy, targeted stem cell delivery and nanomedicine. We present a theoretical framework towards a fundamental understanding of the effects of HGMFs on intracellular processes, highlighting new directions for the study of living cell machinery: changing the probability of ion-channel on/off switching events by membrane magneto-mechanical stress, suppression of cell growth by magnetic pressure, magnetically induced cell division and cell reprograming, and forced migration of membrane receptor proteins. By deriving a generalized form for the Nernst equation, we find that a relatively small magnetic field (approximately 1?T) with a large gradient (up to 1?GT/m) can significantly change the membrane potential of the cell and thus have a significant impact on not only the properties and biological functionality of cells but also cell fate.

In recent decades, the interaction of magnetic fields with living cells and organisms has captivated the interest of a broad scientific community drawn from a wide spectrum of disciplines, including biology, physics, chemistry, medicine and nanotechnologies. Extensive progress in experimental techniques and the design of new magnetic materials has resulted in the burgeoning development of new approaches to reveal the targets of magnetic fields on the intracellular and molecular levels,,.

The scientific literature is filled with thousands of works on the responses of living organisms to low, moderate and strong magnetic fields, for review see,,,,,,. However, the biological effects related to the gradient of the magnetic fields are poorly discussed. Relatively few studies have quantified magnetic gradient actions at the intracellular level. Nevertheless, namely spatially non-uniform magnetic fields with a large enough gradient are capable of significantly altering cell functions and even organisms. For example, a large-gradient magnetic field can affect FLG29.1 cell differentiation to form osteoclast-like cells. Under HGMFs, significant morphologic changes in osteoblast-like cells occurred, including expansion of the endoplasmic reticulum and mitochondria, an increased number of lysosomes, distorted microvilli, and aggregates of actin filaments. The early embryonic growth of the leopard frog (Rana pipiens) was strongly inhibited by a 1?T magnetic field with a high gradient of 84?Tm?1?.

When analyzing effects of magnetic fields on living cells, tissue and organisms, one should keep in mind that in most cases, the biological cells and tissue are diamagnetic with susceptibility very close to that of water. Therefore, the differences in the diamagnetic susceptibilities of cellular components are very low, which leads to tiny effects. In contrast, the exposure of cells and organisms to high-gradient magnetic fields (HGMFs) reveals many intriguing effects that might be directly related to the magnetic gradient force exerted on the whole cell and its organelles. Indeed, the magnetic force acting on a magnetic dipole moment is proportional to the field gradient, i.e., F????B (where B is magnetic induction). In the case of cells suspended in a weakly diamagnetic medium, the volumetric force is F????B2. Thus, after achieving a sufficient magnetic gradient, significant changes in cell functions, shape and spatial organization might be possible. In spite of the many interesting effects related to the application of spatially non-uniform magnetic fields, a key problem—how high-gradient magnetic fields change cell machinery—has never been carefully examined. Special interest exists in the case when the applied magnetic field dramatically changes in value and direction across the cell body. Here, the important question is: how will the cell respond and adapt itself to a high magnetic field gradient? From point of view of physics, the answer is the following. Considering the cell as a droplet of diamagnetic liquid placed in a non-uniform magnetic field, one can conclude that such a droplet will divide itself into several smaller drops to satisfy the minimum of the total system energy. A qualitatively similar effect—ferrofluid droplet division in a non-uniform magnetic field (B?=?68?mT) with gradient, dB/dz?=?6.6?Tm?1—was recently reported in. It is obvious that living cell mechanics is much more complex than that of a liquid droplet. Nevertheless, in spite of the small contribution of diamagnetic forces in the interplay between biological and physical factors in the cell machinery, the role of the magnetic gradient force can increase with increasing magnetic gradient. There are no principal physical limitations the increase of magnetic field gradients. For example, micro-magnet arrays can produce magnetic fields that are spatially modulated on the micron scale with a gradient up to 106?Tm?1 at micro-magnet edges,,,,. In the vicinity of a magnetic nanostructure, magnetic field gradients can be large enough (up to 107?Tm?1) for the field to vary appreciably over the separation between electrons in a radical pair thereby modulating the intracellular magnetocatalytic activity. Moreover, theoretical results show that an HGMF can lead to a significant enhancement of the performance of a chemical biocompass believed to exist in certain animals and birds. A non-uniform magnetic field up to 610?T with a gradient on the order of 106?Tm?1 on the millimeter scale was recently generated with a laser-driven capacitor-coil target by proton deflectometry.

To identify the intracellular targets and molecular effectors of magnetic fields and to reveal the underlying mechanisms, many complex multidisciplinary problems must be solved. As is often the case when multiple disciplines address a complex scientific problem, theoretical models and mathematical equations can provide a unifying platform to synergize the efforts. We present a theoretical framework for a fundamental understanding of the effects of magnetic gradient forces on intracellular processes, highlighting new directions of the study of living cell machinery affected by magneto-mechanical forces.

Results

Direct influence of a high-gradient magnetic field on the resting membrane potential of a cell

Membrane voltage is a key parameter regulating cell properties, machinery and communication. In general, electricity and the interaction of electric charges play major roles in the life of a cell. Indeed, a simple estimation (see Methods) of the electrostatic energy stored in the membrane of a spherical cell with radius 10??m and membrane voltage 70?mV is E???10?14–10?13?J, which is 6–7 orders of magnitude larger than thermal fluctuation energy and much larger than the energies of chemical bonds and membrane bending, which determine many membrane-mediated intracellular processes, such as shaping, rigidity, endocytosis, adhesion, crawling, division and apoptosis. Thus, the electrostatic contribution of the bending energy of charged cell membranes is large enough, and in a first approximation, the cell membrane rigidity is proportional to the square of the membrane voltage. Qualitative analysis presented in, shows that cells (able to proliferate rapidly, undifferentiated) with low values of membrane potential, which tend to depolarized, are highly plastic. In contrast, cells that are mature, terminally differentiated, and quiescent tend to be hyperpolarized. It should be stressed here that the membrane potential is not simply a reflection of the cell state but a parameter allowing the control of the cell fate, for example, artificial depolarization can prevent stem-cell differentiation, whereas artificial hyperpolarization can induce differentiation. Below, we analytically analyze the possibility of driving the membrane potential with externally applied, high-gradient magnetic fields.

When a high-gradient magnetic field is applied to a cell in medium, the magnetic gradient force acts on ions and can either assists or oppose ion movement through the membrane. The magnetic gradient force is given by An external file that holds a picture, illustration, etc. Object name is srep37407-m1.jpg, where p is the magnetic dipole moment of the ion, B is the magnetic induction, and the derivative is taken with respect to direction l, which is parallel to the magnetic dipole moment of an ion, l//p. Bearing in mind the former expression for the magnetic gradient force, in this case, when the ions diffuse in the presence of an HGMF, the Nernst equation reads as (see Methods)

An external file that holds a picture, illustration, etc. Object name is srep37407-m2.jpg

where e is the electron charge, z is the ion valence (z?=?+1 for a positive, univalent ion), F is the Faraday constant, R is the gas constant, T is the absolute temperature, Vm is the potential difference between the two membrane sides, and no and ni are the ion concentrations outside and inside a cell, L is the half-cell size. On the right side of Eq. 1, the second term describes the magnetic contribution to the resting potential. Thus, Eq. 1 represents a generalized form of the Nernst equation derived with regard to the influence of a high-gradient magnetic field. Depending on the direction of the magnetic gradient (“+” or “?” in Equation 1), an HGMF can cause either membrane potential depolarization or hyperpolarization, which regulates not only the entry of sodium, potassium, and calcium ions and biologically relevant molecules to the cell but many pivotal cell characteristics and functions. The key question is how large the gradient value should be to achieve a direct effect of the magnetic fields on the membrane potential. To address this question, we estimate the contribution of the magnetic term to the equilibrium membrane potential given by Eq. 1. For this estimation, the values of the magnetic moments of ions that create the membrane potential should be known. Typical ion-channel species (K+, Ca2+, Na+) and nearby water molecules are electron spin paired, so they have no spin electron magnetic moment and their magnetic moment is due to nuclear spin. It is interesting that 40Ca2+ ions have no nuclear magnetic moment. The magnetic moments of these ions are very small and are on the same order of magnitude as the nuclear magneton, ?n?=?5.05 10?27?J/T: pNa+?=?2.22?n (sodium-23), pK+?=?0.39?n (potassium-39), pCl??=?0.821?n (chloride-35), and pCa2+?=?0 (calcium-40). Among these ions, Na+ has the largest magnetic moment and Ca2+ has zero electronic and nuclear magnetic moments. For comparison, we list the magnetic moment values of relevant molecules: for H20 (para, antiparallel nuclear spins) p?=?0 and H20 (ortho, parallel nuclear spins) p?=??n and for hemoglobin Fe2+, the average magnetic moment measured for whole blood is equal to 5.46??B/Heme (where ?B is the Bohr magneton, ?B/?n???1836). Due to the nuclear spins of the hydrogen atoms, water consists of a mixture of spin zero (para) and spin one (ortho) molecules. The equilibrium ratio of ortho to paramolecules is 3?1, making 75% of water molecules magnetically active in sufficiently strong magnetic fields. HGMF, due to the relatively large magnetic moments of Na+ ions, can affect the formation of the action potential of a nerve cell. By estimation of the magnetic addition in Eq. 1 for the above values of magnetic moments of K+ and Na+ ions and biologically relevant molecules to the cell, we find that an externally applied magnetic field with a gradient value on the order of 108–109?Tm?1 can directly change the cell membrane potential by 1–10?mV. For example, in neuron cells, the opening of Na+ and K+ voltage-gated ion channels occurs with membrane potential depolarization as small as 7–12?mV. In this case, the direct effect of the application of HGMFs to the cell can manifest itself through the change of the probability of opening/closing the voltage-gated ion channels. However, as estimated above, to achieve membrane potential depolarization or hyperpolarization, one has to apply an HGMF with a gradient on the order of 109?Tm?1. The possibility of achieving such high values of magnetic gradient is described in the next section.

The currently reachable magnetic gradient (up to 106–107?Tm?1?,) has indirect effects related to the application of HGMGs to cells. First, the effects of magnetic fields with a gradient on the order of 106?Tm?1 can manifest itself through the change of the probability of opening/closing mechanosensitive ion channels. On the other hand, mechanical stress in the cell membrane can directly drive ion channel gating,,. Moreover, the membrane potential can be changed through agitation of the membrane ion channels. Recent studies have demonstrated the importance of the membrane potential value in the regulation of cell functions and signaling at the multicellular level, especially in relation to ion channel activity. For example, cancer cells tend to have low membrane potential (in absolute value), which has been connected to the overexpression of specific ion channels. Highly differentiated tumor cells (human hepatocellular carcinomas: Tong, HepG2, Hep3B, PLC/PRF/5, Mahlavu, and HA22T) have paradoxically small membrane potentials. The membrane potential controls the adipogenic and osteogenic differentiation of stem cells, which suggests the possibility to drive the differentiation pathway. The membrane potential plays a key role in the spatial organization of cytoskeletal and cell division-related proteins, mainly influencing bacterial cell division.

Static homogeneous magnetic fields can also affect the diffusion of biological particles through the Lorentz force and hypothetically change the membrane potential. However, the results presented in show that in solution, the Lorentz force can suppress the diffusion of univalent ions (e.g., Na+, K+, and Cl?), but the threshold magnetic field is extremely high, approximately 5.7?·?106?T (which is 2–4 orders of magnitude less than the magnetic field at a magnetar). On the other hand, the theoretically predicted threshold of gradient fields for producing a change in ion diffusion through the magnetic gradient stress is more than 105?T2m?1 for paramagnetic molecules FeCl3 and 02 and plasma proteins. Thus, in low and moderate magnetic fields, the biological effects should be rather dependent on the magnitude of the magnetic field gradient and not on the strength of the magnetic field, as was recently demonstrated in experiments with THP-1 cells. The magnetic systems capable of generating HGMFs and formulas allowing rapid estimation of the magnetic field gradient are described in Methods and Table 1. We now consider possible applications of these magnetic systems to control cell functions.

Table 1

Magnetic systems generating HGMFs.
System geometry Formula for estimation of the magnetic field gradient Notes Calculated field and gradient distributions (figures)
Spherical magnetic nanoparticle An external file that holds a picture, illustration, etc. Object name is srep37407-m22.jpg R is radius of MNP Fig. 3
Two pole to pole faced slabs An external file that holds a picture, illustration, etc. Object name is srep37407-m23.jpg x is the distance to the slab edge Fig. 4
Cylinder with a hole An external file that holds a picture, illustration, etc. Object name is srep37407-m24.jpg The limiting case, when r?0; z is the distance from the magnet top. Fig. 5
Array of micro-magnets No analytical expression ? Figs 1 and ?and22
Parabolic shaped magnetic pole An external file that holds a picture, illustration, etc. Object name is srep37407-m25.jpg Maximum attainable gradient for an optimal diameter.

To estimate a magnetic field gradient value, use the appropriate equation for a given distance (in meters), substitute the magnet characteristic ?0Mr (e.g. for a NdFeB magnet ?0Mr???1–1.2?T), and then calculate the field gradient.

Effects of an HGMF through intracellular mechanical stress

A possible alternative mechanism of cell response to HGMFs relies on the fact that magneto-mechanical stress can affect mechanosensitive membrane ion channels, for example, TREK-1 ion channels, which are stretch-activated potassium channels,. It is believed that a cell may have 102–104 ion channels, and the probability of any of them being open (at any given time) is typically in the range of a few to a few tens of percent,. Magnetic gradient forces exerted on cells impose mechanical stress on the plasma membrane and cell body. The cell senses this stress and elicits a mechanoelectric transduction cascade that initiates a response. In the cell membrane, mechanosensitive ion channels are responsible for transducing mechanical signals into electrical signals. Additional membrane tension, in our case induced by the high-gradient magnetic field, can increase the probability of mechanosensitive channel opening. Thus, plasma membrane mechanical stress activates transient receptor potential (TRP) channels. Below, we calculate the mechanical forces and stress in a cell placed in an HGMF.

The volume density of the magnetic gradient force (in Nm?3) acting on a cell is

An external file that holds a picture, illustration, etc. Object name is srep37407-m3.jpg

where ?m is the susceptibility of the medium, ?c is the susceptibility of the cell, and ?0 is the vacuum permeability. In Eq. 2, the difference of susceptibilities, ???=??m????c, defines the magnetic force direction: attraction or repulsion of a cell to/from the area with a high-gradient magnetic field. This force causes mechanical stress in the whole cell and cell membrane. Analysis of the possible biological effects of the action of magnetic gradient forces with volume density given by Eq. 2; one can compare these forces with the gravitational force density, fg?=??g?=?104?Nm?3 (where ? is the density of water and g is the acceleration of gravity). Assuming ?? to be 10–20% of the diamagnetic susceptibility of water (?w?=??9 ?10?6 in SI), B?=?1?T and |?B|?=?106?Tm?1, from Eq. 2, we obtain the magnetic force density f?=?(0.7–1.4)?·?106?Nm?3, which yields f???fg. Because the gravitation force (microgravity) or weightlessness (e.g., by magnetic levitation) affect cell development, growth and functions,, significant effects of the magnetic gradient forces would be expected. For example, the applied magnetic fields with gradient of approximately ?B2???103?T2m?1 were shown to change the subcellular morphology of osteoblast-like cells, and diamagnetic levitation plays a major role in the observed effects. Thus, significant effects on cell machinery caused by the magnetic gradient forces are expected. The magnetic forces that are exerted on the cell body are transmitted to the cell cytoskeleton and cell membrane. Even tiny mechanical forces that are slightly larger than the thermal fluctuation forces of less 1 pN (see Methods) can significantly affect cell functionality,,,.

The magnetic gradient forces given by Eq. 2 can directly drive paramagnetic cells and molecules. In general, cells are diamagnetic. However, recent research shows the existence of nonerythroid cell lines derived from human cell cancers that are sufficiently paramagnetic. Their paramagnetic behavior makes it possible to affect cell motion by application of an HGMF. Moreover, intracellular and intercellular free radicals, such as O3, NO, and NO2 and molecules FeCl3 and O2, are also paramagnetic and can be redistributed by both the Lorentz force and magnetic gradient force, as known from electrochemistry,.

One of the key functions of cells is ordering in space and time. High-precision cell positioning with micromagnets is a promising approach for tissue engineering. Indeed, the magnetic gradient force (Equation 2) is capable assisting cell migration to areas with the highest magnetic field gradient. It was recently demonstrated in ref.  that micromagnet arrays (with lateral size of 30–50??m and the same neighboring distances) coated with parylene produce high magnetic field gradients (up to 106?Tm?1) that affect cell behavior in two main ways: i) causing cell migration and adherence to a covered magnetic surface and ii) elongating the cells in the direction parallel to the edges of the micromagnet. The results of the calculations of the magnetic field and gradient distributions above four micromagnets are shown in Figs 1 and ?and2.2. The field and magnetic-gradient force distributions were calculated analytically using explicit expressions for the magnetic stray fields. As seen from Figs 1 and ?and2,2, there are several areas with the highest magnetic gradient. Thus, in the experiments, driven by magnetic gradient forces (Equation 2), cell migration was observed towards the areas with the strongest magnetic field gradient, thereby allowing the buildup of tunable, interconnected, stem cell networks.

An external file that holds a picture, illustration, etc. Object name is srep37407-f1.jpg

Spatial distribution of the scaled modulus of the magnetic field (B/?0Mr) calculated in the plane 5??m above four micromagnets (Mr is remanent magnetization).

Several cells are schematically drawn to demonstrate that the magnetic field varies in the same length scale as the cell mean size. The micromagnet sizes are 100?×?100??m, and the spacing is 100??m.

An external file that holds a picture, illustration, etc. Object name is srep37407-f2.jpg

Spatial distribution of the scaled planar component of the magnetic gradient (a) 5??m above the micromagnets shown in Fig. 1. (a) Vector field {?x(B/?0Mr)2,?y(B/?0Mr)2 } multiplied by the micro-magnet size. Arrows indicate the directions of the magnetic gradient forces. (b) Scaled modulus of the planar magnetic gradient (?x,y(B/?0Mr)2) multiplied by the micro-magnet size as a function of the x-coordinate. The gradient values were calculated along the OX-axis at distances from the magnet tops: 5??m, 7 and 10??m.

Recent studies indicate the crucial influence of external mechanical and magnetic forces on the cell shape, function and fate through physical interactions with the cytoskeleton network,,.

Local change of membrane potential and lateral migration of membrane receptor proteins in the vicinity of magnetic nanoparticles

A chain of magnetic nanoparticles (MNPs) placed on a cell membrane can create spatially modulated magnetic flux distributions with a sufficient gradient. The magnetic gradient forces localized near the MNPs affect cell functions in two main ways: i) changing the resting membrane potential, as predicted by Eq. 1, and ii) generating local magnetic pressure that can cause membrane deformation, resulting in cell membrane blebbing. The former can occur locally as a consequence of a very high field gradient, as given by Eq. 15 (Methods). For magnetite (Fe3O4) MNPs with Ms?=?510?kAm?1 and R?=?5?nm, estimation based on Eq. 15 gives |?Br|???2.6 108?Tm?1 at the membrane surface. This gradient magnitude is enough to change the resting potential by a few mV even though the ions driving the membrane potential have only nuclear values of magnetic moments. The second is related to the magnetic pressure due to the difference of the magnetic susceptibilities of the lipid membrane and cytosol. In the vicinity of an MNP, the magnetic pressure at the cell membrane is PMNP?=?fV/S?=?fh, where V and S are the volume and areas of a small part of the membrane and h is the membrane thickness. The analytical expression for this pressure is given in Methods. For chains of MNPs with parallel and perpendicular orientation of the magnetic moments with respect to the membrane surface, the magnetic pressure (PMNP) acts in directions perpendicular and parallel to the membrane, as it illustrated in Figs 3 (a–d) for two chains consisting of four MNPs. The magnetic pressure causes an imbalance in the osmotic and hydrostatic pressures, which in turn changes the flux of ions transported through the cell membrane. To estimate the magnetic pressure one should know the magnetic susceptibilities of the cellular contents, which can be found in ref.  and the references therein. In particular, the magnetic susceptibilities of proteins, lipids and water are ?p?=??9.726 10?6, ?lip?=??8.419 10?6 and ?w?=??9.035 10?6 (all in SI). Thus, proteins are more diamagnetic than water, i.e., ?p?<??w. Lipids are less diamagnetic than proteins and water (?lip?>??p and ?lip?>??w), resulting in their “quasi-paramagnetic” behavior with respect to lipids and the cytosol. Due to the difference of the magnetic susceptibilities of proteins and lipids, the membrane receptor proteins are attracted to the area with the highest magnetic field gradient generated by MNPs (see Fig. 3). Estimations of the lateral magnetic pressure (Equation18, Methods) acting on the membrane receptor protein at h?=?5?nm, r???R?=?5?nm, Ms?=?510?kAm?1 (magnetite MNPs) and ???=??p????lip?=?1.3 10?6 result in P?=?1.7?Pa. This pressure can force the lateral migration of membrane receptor protein towards the high-gradient field area. Moreover, cell membranes accommodate domains with heterogeneous sizes ranging from 10 to 200?nm, which are enriched in cholesterol and saturated lipids. Because the magnetic susceptibility of cholesterol is close to that of protein, ?ch?=??9.236 10?6?, these domains are subjected to the lateral magnetic pressure and forced diffusion occurs. This redistribution of the membrane domains can play a pivotal role in altering membrane functions.

An external file that holds a picture, illustration, etc. Object name is srep37407-f3.jpg

Vector fields of the magnetic induction (a and c) and magnetic gradient (b and d) in the vicinity of four magnetic nanoparticles magnetized parallel and perpendicular to the membrane surface. In (b and d) arrows indicate the directions of the magnetic gradient forces.

Magnetically assisted cell division

The first hint of the possibility of cell division by an HGMF was discussed above in relation to an experiment on the division of ferrofluid droplets in a moderate magnetic field with gradient dB/dz?=?6.6?Tm?1. The diamagnetic susceptibility of a cell is much smaller than that of a ferrofluid droplet. When discussing the effects of HGMFs on cells, we consider at least six orders of magnitude larger field gradients. Because the magnetic gradient force is proportional to the product of the magnetic susceptibility and the field gradient (Equation 2), in our case, one can expect a similar effect, i.e., stimulation of cell division by magnetic gradient forces. Magnetic gradient forces can be significantly increased by loading cells with magnetic nanoparticles. In experiments described in ref. , localized, nanoparticle-mediated magnetic forces were applied to HeLa cells through a magnetic field with a gradient from 2.5?103?Tm?1 to 7?104?Tm?1. Under the largest gradient, the cells loaded with magnetic nanoparticles exhibited ‘pull-in’ instability. However, under lower magnetic gradients and lower intracellular mechanical stress, biasing of the metaphase plate during mitosis was observed, which indicates that in HGMFs, magneto-mechanical stress is able to assist in the division of cells free of magnetic nanoparticles.

Therefore, we hypothesize that cell division can be either induced or assisted by a specifically, spatially modulated, magnetic gradient field. An example of such a magnetic field configuration and magnetic gradient force distribution is shown in Fig. 4, illustrating the field and its gradient (normalized ?B2) distributions generated in the gap between two uniformly magnetized magnets faced pole-to-pole. The field and gradient were calculated using the explicit analytical expressions for the magnetic field induction of rectangular, magnetized prisms,Figure 4b shows that between the magnetic poles, on the left and right parts of the central area, the magnetic gradient forces have opposite directions. If the mean size of this area is comparable to the cell size, a cell placed here will be subjected to two opposite forces, which can cause magnetic pressure that assists either cell division or cell compression. It is unknown how large this pressure should be to trigger cell division. In the literature, data on this subject are rather sparse. It was demonstrated that a pressure of 100?Pa can drive HeLa cell mitosis. This pressure is an achievable magnetic pressure, e.g., in one of the HGMF systems listed in Table 1.

An external file that holds a picture, illustration, etc. Object name is srep37407-f4.jpg

Vector fields of the magnetic induction (a) and magnetic gradient forces (b) between the two, pole-to-pole magnetic slabs and cell division. (c) Magnetic gradient forces (Equation 2) normalized to ??a?1?0Mr2 as a function of the x-coordinate. A hypothetical division of a cell in the highly non-uniform magnetic field (the central area) is illustrated.

Tumor arrest by magnetic pressure

Experiments suggested that mechanical stress can limit the growth of a spheroid of cancer cells by restricting cell division near the spheroid surface. Here, we show how magnetic pressure can arrest tumor growth. The idea is based on the fact that cancerous cells are enriched by Fe, and therefore they are more paramagnetic than healthy cells. In such a case, magnetic radial pressure can limit tumor growth due to the attractive magnetic gradient force acting on the “paramagnetic” cancerous cells. An example of magnetic field and gradient distributions above cylindrical magnets with a hole is shown in Fig. 5 (details of the calculations can be found in Methods). Magnetic pressure on tumor can be calculated as Ptum?=?fw, where f is the force density given by Eq. 2 and w is the width of the area corresponding to the maximum of the magnetic field gradient shown in Fig. 5. Estimations of the magnetic pressure on cancerous tissue with magnetic susceptibility ??=?6.3 10?6 (in SI units) for the calculated maximal value of the magnetic gradient, B|?B|/(R?1(?0Mr/4?))???160 (see Fig. 5 (b) and (c)) and magnet radius R?=?5?mm, hole radius 0.1?mm and w?=?1?mm, give pressure Ptum???1?Pa?=?1?pN ?m?2, which value seems to be not sufficient to affect cell functions. However, |?B| grows as the hole radius decreases or the distance z goes to zero (see Table 1 and Eq. 13 in Methods). Thus, adjusting the hole radius and distance, the magnetic gradient can be increased by hundreds of times to achieve pressures of hundreds of pascals, which can prevent cells from dividing. For example, it was shown in ref  that an external osmotic pressure as weak as 500?Pa slowed the growth rate of a tumor spheroid.

An external file that holds a picture, illustration, etc. Object name is srep37407-f5.jpg

Distributions of the scaled moduli of the magnetic induction (a) and magnetic gradient force (b) in the plane above a cylindrical magnet with an axial hole. (c) 2D-plot of the magnetic gradient force as a function of the radial coordinate. The magnetic induction modulus is normalized to (?0Mr/4?), whereas the modulus of magnetic gradient force is normalized to R?(?0Mr/4?)2. The calculations were performed for a magnet length 1?cm, magnet radius 0.5?cm, hole radius 0.1?cm, and distance between the magnet top and the plane of calculations of 0.1?cm.

Discussion

By summarizing the analyses of the above-considered phenomena, models and suggested mechanisms, one can identify the following intracellular effectors of applied HGMFs. We use the term “effector” to indicate a structural component of a cell that responds to an applied high-gradient, static magnetic field. Thus, the following are intracellular effectors of an HGMF: i) cytoskeleton remodeling, ii) changing the probability of ion channel on/off switching events, iii) causing the mechanical stress in the membrane, iv) membrane bending, v) migrating membrane receptor proteins, and vi) changing the ion flux balance and membrane potential due to magnetic gradient forces. A schematic illustration of the possible applications of HGMFs and intracellular effectors is shown in Fig. 6. Working alone, each of these effectors can significantly affect cell functions. However, they are not independent and can work in a certain pathway to alter the molecular machinery of a cell and synergize its response to an HGMF. For example, depending on cell type, state and edge, an externally applied HGMF can stimulate cell division, cause cell swelling followed by membrane blebbing and apoptosis, and change the differentiation pathway of stem cells and gene expression. For these and other effects of HGMFs, the magnetic gradient thresholds are shown in Table 2. The cell responses listed in Table 2 do not occur immediately upon application of the HGMF but can be delayed in time. After applying an HGMF, the cell response arises at timescales varying from a fraction of a second to days, which depends on cell type, magnetic gradient magnitude and time of exposure (see Methods).

An external file that holds a picture, illustration, etc. Object name is srep37407-f6.jpg

Schematic illustration of the possible applications of HGMFs and intracellular effectors.

Table 2

Thresholds for the effects of static HGMF.
Effects Threshold Cell type References
Diffusion of ions and biologically-relevant molecules in solutions ?B2???105?T2m?1 to affect the diffusion of paramagnetic molecules FeCl3, 02 and plasma proteins. n/a
Magnetically assisted cell migration and positioning (105–106)?Tm?1 mesenchymal stem cells
Change membrane potential (generalized Nernst equation, Eq. 1) (108–109)?Tm?1 all this work
Local change of membrane potential (108–109)?Tm?1 cells with MNPs on membrane this work
Changing probability of channel switch on/off events 103?Tm?1 cells with mechanosensitive ion channels
Tumor arrest (104–105)?Tm?1 cancer cells enriched by Fe this work
Magnetically assisted cell division (103–105)?Tm?1 HeLa cells, other cancerous cells with low membrane tension  and this work
Change differentiation pathway and gene expression 102?Tm?1 Mesenchymal stem cells
Magnetically assisted endocytosis (102–103)?Tm?1 PC-3 cells and fibroblasts
Cell swelling 103?Tm?1 THP-1 monocytic leukemia cells

Magnetic systems generating magnetic fields with gradients on the order of 109Tm?1 would allow for significant alteration of the membrane potential in accordance with predictions based on Eq. 1. Changes in membrane potential have proven to be pivotal not only in normal cell cycle progression but also in malignant transformation. Thus, driving the membrane potential with HGMFs opens new opportunities to study intercellular and intracellular processes and provides new routes to controlling cell fate. By understanding the ways in which HGMFs can be utilized to selectively generate the required cellular responses, we can begin to consider magnetic fields as tiny non-invasive tools that can remotely alter the cell machinery, promising broad application potential in cell therapy, neurobiology and nanomedicine. Ultimately, to address the most demanding challenges in medicine utilizing magnetic fields, it is necessary to answer the question: what are the parameters that can reliably allow us to define magnetic field effectors and cause-effect relationships between magnetic field application and cell response? To a large extent, by achieving experimental facilities that provide the highest values of magnetic field gradient, one can expect the discovery of new, exciting, biological effects of magnetic fields.

Methods

Generalized Nernst equation for membrane potential

Let us consider the Nernst equilibrium potential in the presence of a high-gradient magnetic field. In equilibrium, without a magnetic field, the free-energy change for the diffusion of an electrolyte into the cell is

An external file that holds a picture, illustration, etc. Object name is srep37407-m4.jpg

where z is the ion valence (z?=?+1 for a positive, univalent ion), F is the Faraday constant, R is the gas constant, T is the absolute temperature, Vm is the potential difference between the two membrane sides, and no and ni are the ion concentrations outside and inside a cell. By setting ?G to zero, which is the case when the movement of the ions is at equilibrium, one can arrive at the Nernst equation

An external file that holds a picture, illustration, etc. Object name is srep37407-m5.jpg

When a high-gradient magnetic field is applied to a cell in medium, the magnetic gradient force acts on ions and can either assists or oppose ion movement through the membrane. The magnetic gradient force is given by

An external file that holds a picture, illustration, etc. Object name is srep37407-m6.jpg

where p is the magnetic dipole moment of the ion, B is the magnetic induction, and the derivative is taken with respect to direction l, which is parallel to the magnetic dipole moment of an ion, l//p. Bearing in mind Eq. 5, in this case, when the ions diffuse in the presence of an HGMF, the free energy change is

An external file that holds a picture, illustration, etc. Object name is srep37407-m7.jpg

where L is the half-cell size and NA is the Avogadro constant. In Eq. 6, the last term represents the work of the magnetic gradient forces when a mole of magnetic ions diffuses across a membrane; the signs “plus” and “minus” correspond to the two limiting cases: the magnetic gradient force either assists or opposes the electric force exerted on ions moving across the membrane. In equilibrium ?G?=?0, and from Eq. 6, one can arrive at

An external file that holds a picture, illustration, etc. Object name is srep37407-m8.jpg

where e is the electron charge, which is Eq. 1 (see Results).

Thermal fluctuation forces

Cell works in a noisy environment created by thermal fluctuations. Therefore, the cellular cytoskeleton exhibits continual fluctuations due to thermal agitation. The thermal fluctuation forces of actin filaments are given by Fth?=?(kkBT)1/2, where k is the spring constant of a single F-actin filament and the thermal fluctuation energy is kBT?=?4.1?pN·nm at room temperature. In ref. , the effective spring constant for an F-actin network was keff?=?10?5?Nm?1. Thus, the estimated value of the thermal fluctuation force is Fth?=?0.2?pN. This value is slightly less than the measured minimal forces (0.3–0.5?pN) generated by actin filament polymerization.

Estimation of the electrostatic energy stored in the membrane

For a spherical cell, the electrostatic energy can be calculated as the energy of a charged capacitor

An external file that holds a picture, illustration, etc. Object name is srep37407-m9.jpg

where c is the electric capacitance and U is the voltage. For a spherical cell membrane with internal and external radii a and b, respectively, the electric capacitance is

An external file that holds a picture, illustration, etc. Object name is srep37407-m10.jpg

where ?0 is the permittivity of free space and ? is the dielectric constant of the lipid bilayer, which typically varies in the range 1–20. By inserting Eq. 9 into Eq. 8, we obtain the electrostatic cell energy as

An external file that holds a picture, illustration, etc. Object name is srep37407-m11.jpg

Finally, by inserting the following parameters into Eq. 10: ??=?5, U?=?70?mV, a???b?=?10??m and b???a?=?5?nm (which is the membrane thickness), one can obtain E???2.7 10?14 J.

Finding strength in the smallest magnets: magnetic systems generating HGMFs

Micro- and nano-magnets are extensively used for a wide spectrum of biomedical applications,. Here, we describe micro- and nano- magnets that can achieve extremely high field gradients. One way to achieve high values of magnetic gradient is to use small magnets and/or to operate near the magnet edges. This idea is based on the fact that the magnetic gradient forces benefits greatly from scale reduction; therefore, micro- and nanomagnets exhibit large magnetic gradient forces. Indeed, it can be easily demonstrated analytically that when all dimensions of a permanent magnet are reduced by the same factor k (with all of the magnetic characteristics preserved), the field gradient is multiplied by the reduction factor k.

Magnetized slabs

The magnetic stray field around a uniformly magnetized slab was calculated elsewhere,,,. Near the edge of a long, uniformly magnetized slab of width 2a, the magnetic field gradient obeys

An external file that holds a picture, illustration, etc. Object name is srep37407-m12.jpg

where x is the distance to the slab edge, n is an arbitrary unit vector directed from the slab edge to the point where the field gradient is calculated, and Mr is the remanent magnetization. Eq. 11 is valid for x«a, and the modulus of the magnetic field gradient does not depend on the direction of vector n. It follows from Eq. 11 that when approaching the slab edge (x???0), the magnetic field gradient grows and has a singularity. From Eq. 11, estimation with the value of the remanent magnetization of an NdFeB magnet and x?=?1??m gives a high value of magnetic field gradient of 5.4? 105?Tm?1. Similar values of magnetic gradient were measured close to the surface of micro-magnets in ref. .

Axially magnetized cylinder with a hole

We now consider a cylindrical magnet with an axial hole of radius r. The magnetic field and its gradient distributions can be calculated with the help of explicit formulas, Eqs 16 and 17 given below. In the limiting case, when r?0, directly above the hole, the axial component of the magnetic induction logarithmically depends on the distance, z, from the magnet top along the magnet axis

An external file that holds a picture, illustration, etc. Object name is srep37407-m13.jpg

The axial component of the field gradient is

An external file that holds a picture, illustration, etc. Object name is srep37407-m14.jpg

Similarly, for a single, uniformly magnetized, parabolic-shaped magnetic pole used in magnetic tweezers, the maximum magnetic field is given by

An external file that holds a picture, illustration, etc. Object name is srep37407-m15.jpg

where z is the distance from the magnet pole. Thus, in all of the considered cases, the value of the magnetic gradient increases dramatically when approaching the magnet edge. For example, for a single, parabolic-shaped magnetic pole of size 1??m, the gradient can reach 3?·?106?Tm?1 100?nm from the tip.

Magnetic nanoparticles

Let us consider a magnetic nanoparticle with a magnetic moment p?=?MsV (where Ms and V are the saturation magnetization and MNP volume). We can represent a nanoparticle as a small, spherical magnet with diameter equal to 2?R, that is, the single domain MNP acts as a dipole with magnetic moment p. Magnetic induction and its gradient at the axis parallel to the magnetic moment direction are given by

An external file that holds a picture, illustration, etc. Object name is srep37407-m16.jpg

Near the surface of the MNP, at r?=?R, the modulus of the radial magnetic gradient is An external file that holds a picture, illustration, etc. Object name is srep37407-m17.jpg, as follows from (15). The perpendicular component, B?, is two times smaller than B//. Thus, for the considered magnet geometry, close to the magnet surface (edge), the magnetic gradient is the same order of magnitude: An external file that holds a picture, illustration, etc. Object name is srep37407-m18.jpg, where r is the characteristic length scale of the task. We have analytically examined magnetic systems for producing high-gradient magnetic fields and calculated the magnetic flux and gradient distributions that might enable control of the cell shape and functions. The magnetic systems capable of generating HGMFs and formulas allowing rapid estimation of the magnetic field gradient are summarized in Table 1.

Magnetic field distribution near a cylindrical magnet with an axial hole

The magnetic field and force distributions were calculated with the help of the explicit analytical expressions for magnetic field induction generated by a cylindrical permanent magnet, magnetized along its symmetry axis. For homogeneously magnetized cylinder of the radius, a and length L, the axial (Bz) and radial (B?) components of the magnetic field induction can be calculated as:

An external file that holds a picture, illustration, etc. Object name is srep37407-m19.jpg

and

An external file that holds a picture, illustration, etc. Object name is srep37407-m20.jpg

where ? is the azimuthal angle, z is the coordinate along the symmetry axis of a cylinder, ? is the radial coordinate, Mr is the remanent magnetization and ?0 is the permeability of free space. To calculte the magnetic field of a magnet with the axial hole of raddius, r one should make the field superposition of two “up-” and “down-” magnetized cylinders: Bz?=?Bz1(a)???Bz2(r) and B??=?B?1(a)???B?2(r), where the subscripts 1 and 2 stand for up-magnetized and down-magnerized cylinders of the radii a and r, respectivelly.

Magnetic pressure in the vicinity of magnetic nanoparticles

From Eq. 2, with the help of Eq. 15, one can calculate magnetic pressure as

An external file that holds a picture, illustration, etc. Object name is srep37407-m21.jpg

where ?? is the difference of the magnetic susceptibilities of the lipid membrane and the cytosol.

Timescales of cell response to HGMFs

The HGMF-induced biological effects mediated by intracellular mechanical stress do not arise immediately upon applying the field. A time delay in cell response to switching on HGMF occurs. In low and moderate magnetic fields, the time delay of the cell response is dependent on the magnitude of the magnetic field gradient but not on the strength of the magnetic field. The following illustrates the hierarchy of the timescales of the observed cell responses to HGMFs for different magnetic gradients. In HGMFs with magnetic gradient of approximately |?B|???109?Tm?1, a cell response (change of the resting membrane) is expected within a second. Migration and adhesion of stem cells to the edges of micromagnets (at the edge |?B|???106?Tm?1) with subsequent cytoskeleton remodeling and changes of cell shape were observed during the first 4?hours after cell culture deposition on the magnetic system. During the following 3 days, the cells migrated and occupied the tops of the micromagnets, creating patterns that reflect the spatial distribution of magnetic gradient forces generated by micromagnet arrays. Exposure of the monocytic leukemia cells to a high-gradient magnetic field (up to |?B|???103?Tm?1) for 24?h induced cell swelling and triggered apoptosis. Changes in DNA organization, gene expression and the differentiation pathway of stem cells were detected after exposure to low-frequency (4?Hz) HGMF with |?B|???102?Tm?1 for 5 days.

Additional Information

How to cite this article: Zablotskii, V. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci. Rep6, 37407; doi: 10.1038/srep37407 (2016).

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Acknowledgments

The authors gratefully acknowledge Nora Dempsey and Dominique Givord for fruitful discussions. This work was supported by the J.E. Purkyne fellowship awarded by the Academy of Sciences of the Czech Republic.

Footnotes

Author Contributions V. Z., T. A., O. L. and A. D. contributed equally to this work.

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BioMed Central Biomed Central Web Site search submit a manuscript register this article Journal of NeuroEngineering and Rehabilitation Journal Front Page
J Neuroeng Rehabil. 2010; 7: 12.
Published online 2010 Feb 20. doi:  10.1186/1743-0003-7-12
PMCID: PMC2836366
PMID: 20170538

Transmembrane potential induced on the internal organelle by a time-varying magnetic field: a model study

Hui Ye,corresponding author1,2 Marija Cotic,3 Eunji E Kang,3 Michael G Fehlings,1,4 and Peter L Carlen1,2
1Toronto Western Research Institute, University Health Network, Toronto, Ontario, M5T 2S8, Canada
2Department of Physiology, University of Toronto, Toronto, Ontario, M5S 1A1, Canada
3Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ontario, M5S 1A1, Canada
4Department of Surgery, University of Toronto, Toronto, Ontario, M5S 1A1, Canada
corresponding authorCorresponding author.
Hui Ye: moc.liamg@pmet12yxh; Marija Cotic: moc.otnorotu@citoc.ajiram; Eunji E Kang: ac.otnorotu@gnak.nelle; Michael G Fehlings: ac.no.nhu@sgnilheF.leahciM; Peter L Carlen: ac.hcraesernhu@nelrac
Author information ? Article notes ? Copyright and License information ? Disclaimer

Abstract

Background

When a cell is exposed to a time-varying magnetic field, this leads to an induced voltage on the cytoplasmic membrane, as well as on the membranes of the internal organelles, such as mitochondria. These potential changes in the organelles could have a significant impact on their functionality. However, a quantitative analysis on the magnetically-induced membrane potential on the internal organelles has not been performed.

Methods

Using a two-shell model, we provided the first analytical solution for the transmembrane potential in the organelle membrane induced by a time-varying magnetic field. We then analyzed factors that impact on the polarization of the organelle, including the frequency of the magnetic field, the presence of the outer cytoplasmic membrane, and electrical and geometrical parameters of the cytoplasmic membrane and the organelle membrane.

Results

The amount of polarization in the organelle was less than its counterpart in the cytoplasmic membrane. This was largely due to the presence of the cell membrane, which “shielded” the internal organelle from excessive polarization by the field. Organelle polarization was largely dependent on the frequency of the magnetic field, and its polarization was not significant under the low frequency band used for transcranial magnetic stimulation (TMS). Both the properties of the cytoplasmic and the organelle membranes affect the polarization of the internal organelle in a frequency-dependent manner.

Conclusions

The work provided a theoretical framework and insights into factors affecting mitochondrial function under time-varying magnetic stimulation, and provided evidence that TMS does not affect normal mitochondrial functionality by altering its membrane potential

Background

Time-varying magnetic fields have been used to stimulate neural tissues since the start of 20th century []. Today, pulsed magnetic fields are used in stimulating the central nervous system, via a technique named transcranial magnetic stimulation (TMS). TMS is being explored in the treatment of depression [], seizures [,], Parkinson’s disease [], and Alzheimer’s disease [,]. It also facilitates long-lasting plastic changes induced by motor practice, leading to more remarkable and outlasting clinical gains during recovery from stroke or traumatic brain injury [].

When exposed to a time-varying magnetic field, the neural tissue is stimulated by an electric current via electromagnetic induction [], which induces an electrical potential that is superimposed on the resting membrane potential of the cell. The polarization could be controlled by appropriate geometrical positioning of the magnetic coil []. To investigate the effects of stimulation, theoretical studies have been performed to compute the magnetically induced electric field and potentials in the neuronal tissue, using models that represent nerve fibers [] or cell bodies [].

Mitochondria are involved in a large range of physiological processes such as supplying cellular energy, signaling, cellular differentiation, cell death, as well as the control of cell cycle and growth []. Their large negative membrane potential (-180 mV) in the mitochondrial inner membrane, which is generated by the electron-transport chain, is the main driving force in these regulatory processes []. Alteration of this large negative membrane potential has been associated with disruption in cellular homeostasis that leads to cell death in aging and many neurological disorders []. Thus, mitochondria can be a therapeutic target in many neurodegenerative diseases such as Alzheimer’s disease and Parkinson’s disease.

Two lines of evidences suggest that the physiology of mitochondria could be affected by the magnetic field via its induced transmembrane potential. First, magnetic fields can induce electric fields in the neural tissue, and it has been shown that exposure of a cell to an electrical field could introduce a voltage on the mitochondrial membrane []. This induced potential has led to many physiological/pathological changes, such as opening of the mitochondrial permeability transition pore complex []. Nanosecond pulsed electric fields (nsPEFs) can affect mitochondrial membrane [,], cause calcium release from internal stores [], and induce mitochondria-dependent apoptosis under severe stress [,]. Secondly, there is evidence that magnetic fields could alter several important physiological processes that are related to the mitochondrial membrane potential, including ATP synthesis [,], metabolic activities [,] and Ca2+handling [,]. An analysis of the mitochondrial membrane potential is of experimental significance in understanding its physiology/pathology under magnetic stimulation.

In this theoretical work, we have provided the first analytical solution for the transmembrane potential in an internal organelle (i.e., mitochondrion) that is induced by a time-varying magnetic field. The model was a two-shell cell structure, with the outer shell representing the cell membrane and the inner shell representing the membrane of an internal organelle. Factors that affect the amount of organelle polarization were investigated by parametric analysis, including field frequency, and properties of the cytoplasmic and organelle membranes. We also estimated to what degree magnetic fields used in TMS practice affect organelle polarization.

Methods

Spherical cell and internal organelle model in a time-varying magnetic field

Figure ?Figure11 shows the model representation of the cell membrane and the internal organelle, and their orientation to the coil that generates the magnetic field. Two coordinate systems were utilized to represent the cell and the coil, respectively.

An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-1.jpg

The model of a spherical cell with a concentric spherical internal organelle. A. Relative coil and the targeted cell location, and the direction of the magnetically-induced electrical field in the brain. The current flowing in the coil generated a sinusoidally alternating magnetic field, which in turn induced an electric current in the tissue, in the opposite direction. The small circle represented a single neuron in the brain. B. The cell and its internal organelle represented in a spherical coordinates (r??). The cell includes five homogenous, isotropic regions: the extracellular medium, the cytoplasmic membrane, the cytoplasm, the organelle membrane and the organelle interior The externally applied magnetic field was in cylindrical coordinates (r‘, ?‘, z‘). The axis of the magnetic field overlapped with the O‘ Z‘ axis. The distance between the center of the cell and the axis of the coil was C.

The co-centric spherical cell and the organelle were represented in a spherical coordinate system (r??) centered at point O. The cell membrane was represented as a very thin shell with inner radius R, outer radius Rand thickness D. The organelle membrane was represented as a very thin shell with inner radius r, outer radius rand thickness d. The two membrane shells divided the cellular environment into five homogenous, isotropic regions: extracellular medium (0#), cytoplasm membrane (1#), intracellular cytoplasm (2#), organelle membrane (3#) and the organelle internal (4#). The dielectric permittivities and the conductivities in the five regions were ?and ?i, respectively, where represents the region number.

The low-frequency magnetic field was represented in a cylindrical coordinate system (r‘, ?‘, z‘). The distance between the center of the cell (O) and the axis of the coil (O‘) was C. The externally applied, sinusoidally alternating magnetic field was symmetric about the O‘ Z‘ axis. The magnetic field was represented as An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i1.gif, where An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i2.gif was the unit vector in the direction of O‘ Z‘, was the angular frequency of the magnetic field, and An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i3.gif was the imaginary unit.

Model parameters

Table ?Table11 lists the parameters used for the model. To quantitatively investigate the amount of polarization on both the cytoplasmic and organelle membranes, we chose their geometrical and electrical parameters (standard values, the lower and upper limits) from the literature []. The frequency range of interest was determined to be between 2 – 200 kHz. The upper limit was determined by calculating the reciprocal value of the rising phase of a current pulse during peripheral nerve stimulation [,]. Most frequencies used in the experimental practices were lower than this value []. The intensity of the magnetic field was 2 Tesla from TMS practice. The standard frequency of the magnetic field was estimated to be 10 kHz, as the rising time of single pulses was ~100 ?s during TMS. This yielded the peak value of dB/dt = 2 × 104T/[].

Table 1

Model parameters.

Parameters Standard value Lower limit Upper limit
Extracellular conductivity (?0, S/m) 1.2

Cell membrane conductivity (?1, S/m) 3 × 10-7 1.0 × 10-8 1.0 × 10-6

Cytoplasmic conductivity (?2, S/m) 0.3 0.1 1.0

Mitochondrion membrane conductivity (?3, S/m) 3 × 10-7 1.0 × 10-8 1.0 × 10-5

Mitochondrion internal conductivity (?4, S/m) 0.3 0.1 1.0

Extracellular dielectric permittivity (?0, As/Vm) 6.4 × 10-10

Cell membrane dielectric permittivity (?1, As/Vm) 4.4 × 10-11 1.8 × 10-11 8.8 × 10-11

Cytoplasmic dielectric permittivity (?2, As/Vm) 6.4 × 10-10 3.5 × 10-10 7.0 × 10-10

Mitochondrion membrane permittivity (?3, As/Vm) 4.4 × 10-11 1.8 × 10-11 8.8 × 10-11

Mitochondrion internal permittivity (?4, As/Vm) 6.4 × 10-10 3.5 × 10-10 7.0 × 10-10

Cell radius (R, um) 10 5 100

Cell membrane thickness (Dnm) 5 3 7

Mitochondrion radius (r, um) 3 0.3 5

Mitochondrion membrane thickness (dnm) 5 1 8

Magnetic field intensity (B0, Tesla) 2

Magnetic field frequency (fkHz) 10 2 200

Governing equations for potentials and electric fields induced by the time-varying magnetic field

The electric field induced by the time varying magnetic field in the biological media was

equation image
(1)

where An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i5.gif is the magnetic vector potential induced by the current in the coil. The potential was the electric scalar potential due to charge accumulation that appears from the application of a time-varying magnetic field []. In spherical coordinates (r??), An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i6.gif. Using quasi-static approximations, in charge-free regions, was obtained by solving Laplace’s equation

equation image
(2)

Boundary conditions

Four boundary conditions were considered in the derivation of the potentials induced by the time-varying magnetic field.

(A). The potential was continuous across the boundary of two different media. In this paper, this refers to the extracellular media/membrane interface (0#1#), the cell membrane/intracellular cytoplasm interface (1#2#), the intracellular cytoplasm/organelle membrane interface (2#3#), and the organelle membrane/organelle interior interface (3#4#).

(B). The normal component of the current density was continuous across two different media. For materials such as pure conductors, it was equal to the product of the electric field and the conductivity of the media. During time-varying field stimulation, the complex conductivity, defined as +j??, was used to account for the dielectric permittivity of the material []. Here, was the conductivity, was the dielectric permittivity of the tissue, was the angular frequency of the field. Therefore, on the extracellular media/membrane interface (0#1#),

equation image
(3)

On the cell membrane/intracellular cytoplasm interface (1#2#),

equation image
(4)

On the intracellular cytoplasm/organelle membrane interface (2#3#),

equation image
(5)

On the organelle membrane/organelle interior interface (3#4#),

equation image
(6)

where S?0+j??0S?1+j??1S?2+j??2S?3+j??and S?4+j??were the complex conductivities of the five media, respectively.

(C). The electric field at an infinite distance from the cell was not perturbed by the presence of the cell.

(D). The potential inside the organelle (= 0) was finite.

Magnetic vector potential An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i5.gif

When the center of the magnetic field was at point O’, An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i12.gif was in the direction of An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i2.gif since

equation image
(7)

where vector potential An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i5.gif was in the direction of An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i14.gif (Figure ?(Figure1).1). In cylindrical coordinates (r‘, ?‘, z‘), the magnetic vector potential was expressed as (Appendix A in []):

equation image
(8)

In order to calculate the potential distribution in the model cell, one needs to have an expression for An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i5.gif in spherical coordinates(r??). By coordinate transformation (Appendix B in []), we obtained the magnetic vector potential An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i5.gif in spherical coordinates (r??):

equation image
(9)

The vector potential components in the An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i17.gifAn external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i18.gifAn external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i19.gif directions were:

equation image
(10)

Software packages

Derivations of the equations were done with Mathematica 6.0 (Wolfram Research, Inc. Champaign, IL). Numerical simulations were done with Matlab 7.4.0 (The MathWorks, Inc. Natick, MA).

Results

Transmembrane potentials induced by a time-varying magnetic field

In spherical coordinates (r??), the solution for Laplace’s equation (2) can be written in the form

equation image
(13)

where CnDwere unknown coefficients (n = 0,1,2,3,4,5). We solved for those coefficients (Appendix) and substituted them into equation (13) to obtain the potential terms in the five model regions. Next, the transmembrane potential in a membrane can be obtained by subtracting the membrane potential at the inner surface from that at the outer surface.

In the cell membrane, the induced transmembrane potential was

equation image
(14)

Where, An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i25.gif.

equation image

In the organelle membrane, the induced transmembrane potential was

equation image
(15)

Where,

equation image

Similar regional polarization patterns were observed between the cell membrane and the organelle membrane, since they both depended on a sin?costerm. Since and were determined by the relative orientation of the coil to the cell, the patterns of polarization in the target cell and the organelle both depended on their orientations to the stimulation coil.

?cell and ?org at one instant moment were plotted for 10 KHz and 100 KHz, respectively (Figure ?(Figure2).2). The locations for the maximal polarization were on the equators of the cell and of the organelle membranes (= 90° or z = 0 plane). The two membranes were maximally depolarized at = 180° (deep red) and maximally hyperpolarized at = 0 (deep blue) on the equator, respectively. The cell and the organelle membranes were not polarized on the two poles corresponding to = 0° and = 180°, respectively. The full cycle of polarization by the time-varying magnetic field was also illustrated (see Additional file 1).

An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-2.jpg

Regional polarization of the cytoplasmic membrane and the organelle membrane by the time-varying magnetic field. The plot demonstrated an instant polarization pattern on both membranes. A cleft was made to illustrate the internal structure. The orientation of the cell to the coil was the same as that shown in Figure 1B. The color map represented the amount of polarization (in mV) calculated with the standard values listed in table 1. A. Field frequency was 10 KHz. B. Field frequency was 100 KHz.

Both ?cell and ?org depended on the geometrical parameters of the cell (R+RC) and the organelle (r+r), and the electrical properties of the five media considered in the model (S0S1S2S3S4). These parameters did not affect the polarization pattern. Therefore, we chose maximal polarizations (corresponding to the point that is defined by = 90°, = 270°) on the cell and organelle membranes (Figures ?(Figures11 and ?and2)2) for the further analysis of their dependency on the field frequency.

Frequency responses

Two factors contribute to the frequency-dependency of the polarizations (magnitude and phase) in the two membranes. First, the magnitude of the electrical field is proportional to the frequency of the externally applied magnetic field, as required by Faraday’s law. Second, the dielectric properties of the material considered in the model are frequency-dependent.

With the standard values, ?cell was always greater than and ?org (Figure ?(Figure3A).3A). At 10 kHz, the maximal polarization on the cell membrane was 9.397 mV, and the maximum polarization on the internal organelle was only 0.08 mV. Figure ?Figure3B3B plots the ratio of the two polarizations. As the frequency increased, ?orgbecame quantitatively comparable to ?cell. At extremely high frequency (~100 MHz), the ratio reached a plateau of 1 (not shown).

An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-3.jpg

The frequency dependency of ?cell and ?org. A. Maximal amplitudes of ?cell (large circle) and ?org plotted as a function of field frequency. B. Ratio of the two membrane polarizations as a function of the field frequency. C. Phases of ?cell (large circle) and ?org plotted as a function of field frequency. D. Phase difference between the two membrane polarizations.

The phase was defined as the phase difference between the externally applied magnetic field and membrane polarization, which was computed as the phase angle of the complex transmembrane potentials. Phase in the cell membrane was insensitive to the frequency change below 10 KHz. At 10 KHz, the phase in the cell membrane is -91.23°, which meant that an extra -1.23° was added to the membrane phase, due to frequency-dependent capacitive features of the tissue. On the other hand, phase response in the organelle membrane was more sensitive to the frequency change than the cell membrane, showing the dependence as low as 50 Hz. At 10 KHz, the phase in the organelle was -5.69°. Above 10 KHz, phases in both membranes increased with frequency. At 200 KHz, the phase in the cell membrane was -113.1°, and in the organelle membrane was -33.07°. Figure ?Figure3D3D plots the difference between the two phases as a function of frequency. At very low frequency (< 50 Hz), the two membranes demonstrated an in-phase polarization. At 10 KHz, their polarizations were nearly 90° out-of-phase.

“Interaction” between the cell membrane and the organelle membrane

Previous studies have shown that the cell membrane “shields” the internal cytoplasm and prevent the external field from penetrating inside the cell in electric stimulation [,]. Will similar phenomenon occur under magnetic stimulation? To estimate the impact of cell membrane on organelle polarization, we compared ?org with and without the presence of the cell membrane. The later was done by letting SS0and SSin equation (15), which removed the cell membrane,

Removal of the cell membrane allowed greater organelle polarization (Figure ?(Figure4A).4A). At 10 KHz, ?org was 2.82 mV in the absence of the cell membrane, which was considerably greater than 0.08 mV for the case with the cell membrane. This screening effect was more prominent at 200 KHz, where ?org was only 28.78 mV in the intact cell, and 55.87 mV without the cell membrane.

An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-4.jpg

“Shielding” effects of cytoplasmic membrane on the internal membrane. A. Amplitude of ?org with and without the presence of the cytoplasmic membrane. Presence of the cytoplasmic membrane reduced ?org. B. Phase of ?org with and without the presence of the cytoplasmic membrane.

The phase response for the isolated organelle was similar to a cell membrane that was directly exposed in the field (Figure ?(Figure4B).4B). Therefore, presence of the cell membrane not only” shielded” the internal mitochondria from excessive polarization by the external field, but also provides an extra phase term that reduce the phase delay between the field and the organelle response.

Alteration in the organelle polarization by removing the cell membrane suggested an “interactive” effect between the two membranes via electric fields. We next asked if the presence of the internal organelle might have the reciprocal effects on ?cell. To test this possibility, we removed the internal organelle and investigated its effect on ?cell. This was done by letting SSand SSin equation (14). Removal of the internal organelle did not introduce significant changes on ?cell (Figure ?(Figure5).5). Removal of the organelle led to a 0.001 mV increase in ?cell at 10 KHz, and a 1.3 mV increase at 200 KHz, respectively. The phase change caused by organelle removal was only 0.7 degrees at 200 KHz. These results suggest that the presence of the internal organelle only had trivial effects on the cytoplasmic membrane.

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Impact of the presence of internal organelle on ?cell. Amplitude (A) and phase (B) of ?cell with the presence of the internal organelle (cycle) or after the organelle was removed from the cell (line).

Dependency of ?org on the cell membrane parameters

To further investigate the shielding effects of the cell membrane on ?org, we systemically varied the cell membrane parameters within their physiological ranges, and studied their individual impacts on the organelle polarization. These parameters included the geometrical properties (radius and membrane thickness) and the electrical properties (cell membrane conductivity and dielectric permittivity) of the cell membrane. This was done by varying one parameter through its given range but maintaining the others at their standard values. Since the dielectric properties of the tissues were frequency dependent, the parameter sweep was done within a frequency range (2 – 200 KHz). This generated a set of data that could be depicted in a color plot of ?org (amplitude or phase) as a function of frequency and the studied parameters (Figures ?(Figures66).

An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-6.jpg

Dependency of ?org on the cytoplasmic membrane properties. Effects of cell diameter (A), cell membrane thickness (B), cell membrane conductivity (C) and cell membrane di-electricity (D) on the amplitude and phase of ?org.

At a low frequency band (< 10 KHz), ?org was trivial, since the magnitude of the induced electric field was small. ?org became considerably large beyond 10 KHz. Increase in the cell radius facilitates this polarization (Figure ?(Figure6A6A left). Increase in the cell radius did not significantly change the phase-frequency relation in the organelle. However, it increased the phase at relatively high frequency (~100 KHz, Figure ?Figure6A6A right). Increase in the cell membrane thickness compromised ?org, so that higher frequency was needed to induce considerable polarization in the organelle (Figure ?(Figure6B6B left). Variation in membrane thickness did not significantly alter the phase of the organelle polarization (Figure ?(Figure6B6B right). Since removal of the low-conductive cell membrane enhanced organelle polarization (Figure ?(Figure4A),4A), one might expect that an increase in the membrane conductivity could have a similar effect. However, within the physiological range considered in this paper, ?org was insensitive to the cell membrane conductivity (Figure ?(Figure6C6C left). The cell membrane conductivity did have a significant impact on the phase of mitochondria polarization. At extremely low values (<10-7S/m), ?org demonstrated a phase advance at frequency lower than 1 KHz (Figure ?(Figure6C6C right), rather than a phase delay, as was the case for the standard values (Figure ?(Figure3C).3C). The cell membrane dielectric permittivity represents the capacitive property of the membrane. Increase in this parameter facilitated ?org, so that ?org became noticeable at relatively lower frequency range (Figure ?(Figure6D6Dleft). An increase in this parameter also led to a decrease in the phase delay in the organelle polarization, which was most prominent at the frequency above 100 Hz (Figure ?(Figure6D6D right).

Dependency of ?org on its own biophysics

Previous studies have shown that polarization of a neuronal structure depends on its own membrane properties under both electrical [], and magnetic stimulations []. How do the membrane properties of the organelle membrane affect its own polarization?

An increase in the organelle radius led to a greater ?org (Figure ?(Figure7A,7A, left). The phase-frequency relationship differentiated at a radius value around 1.1 um. Above this value, the phase response followed a pattern depicted in Figure ?Figure3C,3C, i.e., the phase delay was -90 degree for low frequency and decreased to 0 at around 10 K Hz. Below this value, the phase showed a 90-degree advance instead of a lag in the low frequency range < 10 K Hz (Figure ?(Figure7A,7A, right). The membrane thickness has been generally agreed to be least significant to membrane polarization []. Varying membrane thickness in the organelle did not cause significant change in the magnitude (Figure ?(Figure7B,7B, left) nor the phase (Figure ?(Figure7B,7B, right) of ?org?org was also insensitive to its own electrical properties. Varying membrane conductivity (Figure ?(Figure7C)7C) or dielectricity (Figure ?(Figure7D)7D) in the organelle did not alter the frequency-dependent polarization in this structure.

An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-7.jpg

Dependency of ?org on its own membrane properties. Effects of organelle diameter (A), thickness (B), membrane conductivity (C) and membrane di-electricity (D) on the amplitude and phase of ?org.

Discussion

Similarities and differences to electrical stimulation

Analysis of ?org under magnetic stimulation reveals several commonalities and differences to that under electric stimulation. The build up of ?org requires the electric field to penetrate through the cytoplasmic membrane. In electric stimulation, this is achieved by directly applied electric current via electrodes. In magnetic stimulation, electric field is produced by electromagnetic induction.

Analysis on ?org under electric field has been performed in two recent publications. Vajrala et al. [] developed a three-membrane model that included the inner and our membranes of a mitochondrion, and have analytically solved ?cell and ?org under oscillatory electric fields. Another study [] has modeled the internal membrane response to the time-varying electric field, and has investigated the condition under which ?org can temporarily exceed ?cell under nanosecond duration pulsed electric fields.

Results obtained from this magnetic study share several commonalities with those from AC electric stimulation. Under both stimulation conditions, ?org can never exceed ?cell. The ratio between the (organelle/cell) increases with frequency, and this ratio can reach 1 at very high frequency (10Hz, data not shown). The phase responses of the organelle within a cell have not been analyzed previously under electric stimulation, which prevent direct comparison with this work. For an isolated mitochondrion, its response is similar to a single cell membrane under AC electric field stimulation [], except that an extra -90° phase is introduced by electromagnetic induction (Figure ?(Figure4B4B).

Stimulation on the internal organelle by time-varying magnetic field, though, has its own uniqueness. First, as a non-invasive method, magnetic stimulation is achieved by current induction inside the tissue, which prevents direct contact with the electrodes and introduces minimal discomfort. Second, the frequency responses of the internal organelle are different under the two stimulation protocols. In electric stimulation, magnitude of the field is independent of its frequency. In magnetic stimulation, however, the magnitude of the induced electric field is proportional to the frequency of the magnetic field (Faraday’s law). Consequently, alteration in the field frequency could also contribute to ?org. Low frequency field (< 1 KHz) is insufficient in building up noticeable ?org and ?cell (Figure ?(Figure3A).3A). Both ?org and ?cell increase with field frequency (Figure ?(Figure3A).3A). Therefore, it is unlikely possible to use high-frequency magnetic field to specifically target internal organelles, such as been done under AC electric stimulation with nanosecond pulses, for mitochondria electroporation and for the induction of mitochondria-dependent apoptosis [].

Cellular factors that influence ?cell

When a neuron is exposed to an electric field, a transmembrane potential is induced on its membrane. Attempts to analytically solve ?cell began as early as the 1950s [,]. Later works added more complexity to the modeled cell and provided insights into the factors affecting ?cell. These include electrical properties [,,,] of the cell, such as its membrane conductivity. Geometrical properties of the cell could also affect ?cell, such as its shape [,] and orientation to the field [,].

Presence of neighboring cells affect ?cell in a tissue with high-density cells, For example, isthmo-optic cells in pigeons can be excited by electrical field effect through ephaptic interaction produced by the nearby cells whose axons were activated by electric stimulation, suggesting that electrical field effect may play important roles in interneuronal communications []. In infinite cell suspensions, ?cell depended on cell volume fraction and cell arrangement []. Theoretical studies have proved that presence of a single cell affected ?cell in its neighboring cells, without direct physical contact between the two cells [].

This work investigates another important factor that might affect ?cell, i.e., presence of the internal organelle. We have previously solved ?cell for a spherical cell model under magnetic field stimulation, without considering the presence of the internal organelle []. This work extends the previous study by including an internal organelle in the cell model. Here, adding an organelle to the cell internal did not significantly change the magnitude and phase of ?cell (Figure ?(Figure55).

Factors that influence ?org during magnetic stimulation

Biological tissue is composed of many non-homogenous, anisotropic components, such as the cellular/axonal membrane, the internal organelles and the extracellular medium. The electrical properties (i.e., conductivities) of the tissue may vary with location in the tissue, even at a microscopic level. Under magnetic stimulation, several studies have provided insights into the impact of tissue properties on field distribution and tissue polarization [,].

This work further illustrates that the effects of magnetic stimulation are a function of tissue properties, by providing evidence that both the geometrical and electrical parameters of the cell/organelle membranes affect ?org. Both the radius of the cell and the organelle strongly affect ?org, which is in agree with previous studies [,]. Radius of the neuronal structure is important in determining the threshold for its own membrane polarization, as proved by in vitro studies on eukaryotic [] and bacterial cells []. This model prediction is potentially testable with voltage-sensitive dyes that can provide both high temporal and high spatial resolutions [,]. Another model prediction is that the amount of ?org is insensitive to the change in cell membrane conductivity. Evidence has shown that electric field can cause long-lasting increase in passive electrical conductance of the cell membrane, probably by opening of stable conductance pores []. The opening and closing of ion channels can also alter the membrane conductance. This model prediction can be tested by varying membrane conductivity, using ion-channel blockers applied to the cell membrane.

Implications for transcranial magnetic stimulation (TMS)

Another important finding in this study that within the frequency band used TMS, ?org is insignificant comparing with ?cell. At 10 KHz, a frequency that corresponds to the rising time of the electric pulses used in clinical TMS, the field causes considerable amount of change in ?cell, but only 0.08 mV change in ?org(Figure ?(Figure3A).3A). It is worth noting that even this value was probably a consequence of overestimation in the magnetic field intensity (B0). To simplify the calculation, B0 was a constant (2 Tesla) everywhere in the modeled region. In reality, the intensity of the magnetic field generated by a coil could decay quickly in the tissue far away from the coil [,]. The duration of the stimulation time was also likely overestimated. During TMS, neuronal responses are induced by pulses, as opposed to the mathematically more tractable sinusoidal stimulus used in this model. Under this scenario, the magnetically-induced electric field in the tissue (essentially the change in the transmembrane potential) is determined by An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i29.gif, which means the transmembrane potential can only be induced during the rise time (and decay time) during a step in the B field. Indeed, rise times of the field affect stimulation in clinic practice, and a faster rise time pulse is more efficient []. Therefore, ?org is unlikely significant enough in TMS to have physiological implications, and internal organelles such as mitochondria are not likely be the target in TMS practice. This conclusion is made after extensive analysis on model parameters with the values in broad physiological ranges (Table ?(Table1).1). To our knowledge and based on a Medline search, there have been no reports on mitochondria-related effects in TMS practice.

This paper provides two mechanisms to account for the ineffectiveness of magnetically-induced polarization in internal organelles under TMS parameters. First, the cell membrane, which is made up of lipids and proteins, provides a dominant “shielding effect” on the organelles and prevents certain amount of electric fields to penetrate into the cell membrane and polarize the organelle membrane (Figure ?(Figure4).4). Second, the radius of the organelle is always much smaller than that of the cell, which render them relatively insensitive to the magnetic field.

Future directions

Several simplifying assumptions were proposed in this model to facilitate the derivation of the analytical solutions. The model assumed that the cell was located in an electrically homogenous extracellular medium, which was an over-simplification of the true electrically anisotropic extracellular environment. Both the extracellular medium and cytoplasmic environment are not truly homogenous [,]. We found that neither parameter significantly affects the organelle or cytoplasmic membrane polarization (not shown).

Both the cell membrane and the mitochondria membranes were modeled as a single spherical shell. In reality, however, cellular structures have irregular shape, which may play an important role in the dynamics of membrane polarization [,]. The interior sphere was centered inside the cell to allow for mathematical simplicity of the model. However, as organelle locations vary spatially in a cell, we hypothesize that organelles located off-center of the cell or closer to the exterior cell membrane may be more sensitive to the applied field. Also, we believe the “shielding effect” of the cell membrane persists even when the separation distance between the two membranes is small (data not shown). The membrane of the organelle was modeled as a single internal shell as in a previous study [], rather than a two-shell structure, representative of the inner and our membranes of a mitochondrion, respectively []. The highly curved projections of the cell body and the organelle membrane may provide focal points for even greater changes in the induced transmembrane potential []. Future study will use numerical methods with multi-compartment modeling or finite element meshes to represent these structure complexities.

All the dielectric permittivities in the model were assumed to be frequency-independent, which was valid for the low frequencies considered (10-200 kHz). When field frequency exceeds several hundreds of megahertz, the finite mobility of molecular dipoles starts to weaken the polarization processes []. This phenomenon, known as dielectric relaxation, is characterized with decrease in the permittivities and increase in the conductivity. When this happens, the complex conductivity should be defined as (?) + j?? (?), where (?) and (?) are frequency-dependent conductivity and permittivity, respectively. By implementing this term in equations (14) and (15), one can estimate the transmembrane potentials in the cell and in the organelle when dielectric relaxation occurs.

Conclusions

This work provides the first analytical solution for the transmembrane potentials in an internal organelle (?org) in response to time-varying magnetic stimulation. The frequency response of the membrane under magnetic stimulation is different from that under electric field stimulation. This work provides evidence that the presence of the internal organelle does not significantly affect polarization of the cell membrane (?cell). Moreover, ?org is always smaller than ?cell under low frequency range (< 200 KHz), largely due to the “shielding effect” imposed by the presence of the cell membrane. Both the geometrical and electrical properties of the cell membrane affect ?org in a frequency-dependent manner. The properties of the organelle membrane also affect ?org in a frequency-dependent manner. Finally, the present study provides evidence that normal mitochondrial functionality is not likely affected by transcranial magnetic stimulation, via altering its membrane potential.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

HY was involved with model equation derivation, data analysis, and drafting of the manuscript. MC was involved in generating figures. MGF and PLC supervised and coordinated the study. In addition, MC, EEK, MGF and PLC helped in drafting of the manuscript. All authors read and approved the final manuscript.

Appendix

Determining unknown coefficients Cn, Din equation (13) using boundary conditions

Since was bounded at = 0 and ? ?, from equation (13) we had

equation image

Therefore, expressions for the potential distribution in the extracellular media, the cell membrane, the cytoplasm, the organelle membrane, and organelle interior are:

equation image
(A-1)

We substituted A0(equation 10) and the An external file that holds a picture, illustration, etc. Object name is 1743-0003-7-12-i17.gif components of ?in the five regions into (1) to yield the expressions of the normal components of the electric fields in the five regions:

equation image
(A-6)

Following boundary condition (A), was continuous at the extracellular media/membrane (R+), the membrane/intracellular cytoplasm interfaces (R), the cytoplasm/organelle interface and the organelle membrane/organelle interior interface.

equation image
(A-11)

We then used the boundary condition (B), that the normal components of the current densities were continuous between two different media (equations 3-6), to obtain the following equations:

equation image
(A-15)

We solved (A-11) to (A-18) the last eight unknown coefficients D0-D3, C1-C4. (see Additional file 2).

 

Supplementary Material

Additional file 1:

Dynamic membrane potential changes in the cell and in the internal organelle. A movie that shows the membrane potentials in the cell and in the organelle, induced by a 100 KHz magnetic field.

Additional file 2:

Membrane potentials in the cell and in the internal organelle. Mathematic derivations of the membrane potentials.

Acknowledgements

This work was supported by CIHR and a Canadian Heart and Stroke Foundation postdoctoral fellowship to Hui Ye. The authors thank Joe Hayek for valuable comments to the paper.

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Biomed Sci Instrum. 2004;40:469-74.

Noninvasive treatment of inflammation using electromagnetic fields: current and emergin therapeutic potential.

Johnson MT, Waite LR, Nindl G.

Center for Medical Education, Indiana University School of Medicine, Terre Haute, IN 47809, USA.

Magnets, electric current and time varying magnetic fields always have played a role in human medicine. Natural magnetic stones were used in ancient cultures to induce a therapeutic effect and modern clinical practice would be far less effective without nuclear magnetic resonance imaging, cardiac pacemakers, and bone growth stimulators. This paper presents a summary of natural and artificial electromagnetic field (EMF) characteristics that are currently in use or under investigation for other therapeutic applications. This background understanding provides a basis for discussion on the success and possible risks of emerging and novel EMF therapies. Although interest in energy medicine has existed for centuries in some parts of the world, in recent years this is an area of heightened interest for western healthcare practitioners. This awareness has been triggered by the growing body of knowledge on how EMFs interact with cellular systems. EMF therapy for the treatment of pain, cancer, epilepsy, and inflammatory diseases like psoriasis, tendinitis and rheumatoid arthritis is currently being explored. The long-term success of this new area of medicine is still unknown. On the one hand, it remains to be seen whether positive human outcomes with EMF therapy could be explained by enhancement of the placebo effect. Optimistically, EMF therapy has the potential to revolutionize medicine, which is currently dominated by pharmaceutical and surgical interventions. In this case, new therapeutic tools may be developed for future clinicians to provide noninvasive treatments with low risk of side effects and no problem with drug interactions.

Possible therapeutic applications of pulsed magnetic fields

Navratil, L. et.al.  Czech Republic

Magnetotherapy is a relatively new, nowadays however, relatively widespread method in several medical disciplines. The mechanism proper of the favorable action of the pulsed magnetic field on the living organism is not quite clear so far, clinical investigations revealed, however, a favorable anti-inflammatory, angioedematous and analgesic therapeutic effect. The authors sought an optimal frequency of the pulsed magnetic field with regard to the character of the disease. They focused attention above all on treatment of acute and chronic inflammatory conditions of the locomotor apparatus, ischaemia of the blood vessels of the lower extremities, dyspeptic syndrome, lactation mastitis and other diseases. One therapeutic cycle lasted 20 minutes, the mean number of cycles varied between 5.8 and 7.7. A regression of complaints was recorded as a rule after 2-3 sessions. The optimal frequency of the pulsed magnetic field seems to be a value between 10.0 and 25.0 Hz. It is useful in particular in severe conditions to repeat the therapeutic cycle after 2-3 months. The advantage of this therapeutic method is the minimal number of contraindications.

Kosm Biol Aviakosm Med. 1990 May-Jun;24(3):3-11.

Effect of low-frequency electromagnetic fields on the individual functional systems of the body.

[Article in Russian]

Zagorskaia EA, Klimovitskii VIa, Mel’nichenko VP, Rodina GP, Semenov SN.

This paper is a review of recent publications about the effects of low frequency electromagnetic fields (EMF) (constant and pulsed) on the cardiovascular, neuroendocrine, and blood systems of experimental animals and industrial workers exposed to them. It is reported that the regulatory systems (nervous and endocrine) are highly sensitive to EMF. It is obvious that investigations of hormone-receptor interactions can help better understand EMF effects on the endocrine system and the body as a whole. Published data about EMF effects on the cardiovascular system and blood are often contradictory, probably, because of different estimates of allowable limits recognized in various countries. It is hypothesized that circulatory changes are largely dependent on the central regulatory structures, particularly hypothalamus. White blood responses to the exposure, being most significant among hematological reactions, are also induced, to a certain extent, by regulatory mechanisms. The EMF effects may depend on the initial state and individual properties of the biological organism. It is postulated that the EMF effects on regulatory mechanisms may be related to primary disorders in cellular and mitochondrial membranes.

Beneficial effects of electromagnetic fields.

Bassett C. Bioelectric Research Center, Columbia University New York

Selective control of cell function by applying specifically configured, weak, time-varying magnetic fields has added a new, exciting dimension to biology and medicine. Field parameters for therapeutic, pulsed electromagnetic field (PEMFs) were designed to induce voltages similar to those produced, normally, during dynamic mechanical deformation of connective tissues. As a result, a wide variety of challenging musculoskeletal disorders have been treated successfully over the past two decades. More than a quarter million patients with chronically ununited fractures have benefitted, worldwide, from this surgically non-invasive method, without risk, discomfort, or the high costs of operative repair. Many of the athermal bioresponses, at the cellular and subcellular levels, have been identified and found appropriate to correct or modify the pathologic processes for which PEMFs have been used. Not only is efficacy supported by these basic studies but by a number of double-blind trials. As understanding of mechanisms expands, specific requirements for field energetics are being defined and the range of treatable ills broadened. These include nerve regeneration, wound healing, graft behavior, diabetes, and myocardial and cerebral ischemia (heartattack and stroke), among other conditions. Preliminary data even suggest possible benefits in controlling malignancy.

Bioelectromagnetics Applications in Medicine

PANEL MEMBERS AND CONTRIBUTING AUTHORS

Beverly Rubik, Ph.D.–Chair

Robert O. Becker, M.D.

Robert G. Flower, M.S.

Carlton F. Hazlewood, Ph.D.

Abraham R. Liboff, Ph.D.

Jan Walleczek, Ph.D.

Overview

Bioelectromagnetics (BEM) is the emerging science that studies how living organisms interact with electromagnetic (EM) fields. Electrical phenomena are found in all living organisms. Moreover, electrical currents exist in the body that are capable of producing magnetic fields that extend outside the body. Consequently, they can be influenced by external magnetic and EM fields as well. Changes in the body’s natural fields may produce physical and behavioral changes. To understand how these field effects may occur, it is first useful to discuss some basic phenomena associated with EM fields.

In its simplest form, a magnetic field is a field of magnetic force extending out from a permanent magnet. Magnetic fields are produced by moving electrical currents. For example, when an electrical current flows in a wire, the movement of the electrons through the wire produces a magnetic field in the space around the wire (fig. 1). If the current is a direct current (DC), it flows in one direction and the magnetic field is steady. If the electrical current in the wire is pulsing, or fluctuating–such as in alternating current (AC), which means the current flow is switching directions–the magnetic field also fluctuates. The strength of the magnetic field depends on the amount of current flowing in the wire; the more current, the stronger the magnetic field. An EM field contains both an electrical field and a magnetic field. In the case of a fluctuating magnetic or EM field, the field is characterized by its rate, or frequency, of fluctuation (e.g., one fluctuation per second is equal to 1 hertz [Hz], the unit of frequency).

A field fluctuating in this fashion theoretically extends out in space to infinity, decreasing in strength with distance and ultimately becoming lost in the jumble of other EM and magnetic fields that fill space. Since it is fluctuating at a certain frequency, it also has a wave motion (fig. 2). The wave moves outward at the speed of light (roughly 186,000 miles per second). As a result, it has a wavelength (i.e., the distance between crests of the wave) that is inversely related to its frequency. For example, a 1-Hz frequency has a wavelength of millions of miles, whereas a 1-million-Hz, or 1-megahertz (MHz), frequency has a wavelength of several hundred feet, and a 100-MHz frequency has a wavelength of about 6 feet.

All of the known frequencies of EM waves or fields are represented in the EM spectrum, ranging from DC (zero frequency) to the highest frequencies, such as gamma and cosmic rays. The EM spectrum includes x rays, visible light, microwaves, and television and radio frequencies, among many others. Moreover, all EM fields are force fields that carry energy through space and are capable of producing an effect at a distance. These fields have characteristics of both waves and particles. Depending on what types of experiments one does to investigate light, radio waves, or any other part of the EM spectrum, one will find either waves or particles called photons.

A photon is a tiny packet of energy that has no measurable mass. The greater the energy of the photon, the greater the frequency associated with its waveform. The human eye detects only a narrow band of frequencies within the EM spectrum, that of light. One photon gives up its energy to the retina in the back of the eye, which converts it into an electrical signal in the nervous system that produces the sensation of light.

Table 1 shows the usual classification of EM fields in terms of their frequency of oscillation, ranging from DC through extremely low frequency (ELF), low frequency, radio frequency (RF), microwave and radar, infrared, visible light, ultraviolet, x rays, and gamma rays. For oscillating fields, the higher the frequency, the greater the energy.

Endogenous fields (those produced within the body) are to be distinguished from exogenous fields (those produced by sources outside the body). Exogenous EM fields can be classified as either natural, such as the earth’s geomagnetic field, or artificial (e.g., power lines, transformers, appliances, radio transmitters, and medical devices). The term electropollution refers to artificial EM fields that may be associated with health risks.

In radiation biophysics, an EM field is classified as ionizing if its energy is high enough to dislodge electrons from an atom or molecule. High-energy, high-frequency forms of EM radiation, such as gamma rays and x rays, are strongly ionizing in biological matter. For this reason, prolonged exposure to such rays is harmful. Radiation in the middle portion of the frequency and energy spectrum–such as visible, especially ultraviolet, light–is weakly ionizing (i.e., it can be ionizing or not, depending on the target molecules).

Although it has long been known that exposure to strongly ionizing EM radiation can cause extreme damage in biological tissues, only recently have epidemiological studies and other evidence implicated long-term exposure to nonionizing, exogenous EM fields, such as those emitted by power lines, in increased health hazards. These hazards may include an increased risk in children of developing leukemia (Bierbaum and Peters, 1991; Nair et al., 1989; Wilson et al., 1990a).

However, it also has been discovered that oscillating nonionizing EM fields in the ELF range can have vigorous biological effects that may be beneficial and thus nonharmful (Becker and Marino, 1982; Brighton and Pollack, 1991). This discovery is a cornerstone in the foundation of BEM research and application.

Specific changes in the field configuration and exposure pattern of low-level EM fields can produce highly specific biological responses. More intriguing, some specific frequencies have highly specific effects on tissues in the body, just as drugs have their specific effects on target tissues. The actual mechanism by which EM fields produce biological effects is under intense study. Evidence suggests that the cell membrane may be one of the primary locations where applied EM fields act on the cell. EM forces at the membrane’s outer surface could modify ligand-receptor interactions (e.g., the binding of messenger chemicals such as hormones and growth factors to specialized cell membrane molecules called receptors), which in turn would alter the state of large membrane molecules that play a role in controlling the cell’s internal processes (Tenforde and Kaune, 1987). Experiments to establish the full details of a mechanistic chain of events such as this, however, are just beginning.

Another line of study focuses on the endogenous EM fields. At the level of body tissues and organs, electrical activity is known to exhibit macroscopic patterns that contain medically useful information. For example, the diagnostic procedures of electroencephalography (EEG) and electrocardiography are based on detection of endogenous EM fields produced in the central nervous system and heart muscle, respectively. Taking the observations in these two systems a step further, current BEM research is exploring the possibility that weak EM fields associated with nerve activity in other tissues and organs might also carry information of diagnostic value. New technologies for constructing extremely sensitive EM transducers (e.g., magnetometers and electrometers) and for signal processing recently have made this line of research feasible.

Recent BEM research has uncovered a form of endogenous EM radiation in the visible region of the spectrum that is emitted by most living organisms, ranging from plant seeds to humans (Chwirot et al., 1987, Mathew and Rumar, in press, Popp et al., 1984, 1988, 1992). Some evidence indicates that this extremely low-level light, known as biophoton emission, may be important in bioregulation, membrane transport, and gene expression. It is possible that the effects (both beneficial and harmful) of exogenous fields may be mediated by alterations in endogenous fields. Thus, externally applied EM fields from medical devices may act to correct abnormalities in endogenous EM fields characteristic of disease states. Furthermore, the energy of the biophotons and processes involving their emission as well as other endogenous fields of the body may prove to be involved in energetic therapies, such as healer interactions.

At the cutting edge of BEM research lies the question of how endogenous body EM fields may change as a result of changes in consciousness. The recent formation and rapid growth of a new society, the International Society for the Study of Subtle Energies and Energy Medicine, is indicative of the growing interest in this field._

Figure 3 illustrates several types of EM fields of interest in BEM research.

Medical Applications of Bioelectromagnetics

Medical research applications of BEM began almost simultaneously with Michael Faraday’s discovery of electromagnetic induction in the late 1700s. Immediately thereafter came the famous experiments of the 18th-century physician and physicist Luigi Galvani, who showed with frog legs that there was a connection between electricity and muscle contraction. This was followed by the work of Alessandro Volta, the Italian physicist whose investigation into electricity led him to correctly interpret Galvani’s experiments with muscle, showing that the metal electrodes and not the tissue generated the current. From this early work came a plethora of devices for the diagnosis and treatment of disease, using first static electricity, then electrical currents, and, later, frequencies from different regions of the EM spectrum. Like other treatment methods, certain devices were seen as unconventional at first, only to become widely accepted later. For example, many of the medical devices that make up the core of modern, scientifically based medicine, such as x-ray devices, at one time were considered highly experimental.

Most of today’s medical EM devices use relatively large levels of electrical, magnetic, or EM energy. The main topic of this chapter, however, is the use of the nonionizing portion of the EM spectrum, particularly at low levels, which is the focus of BEM research.

Nonionizing BEM medical applications may be classified according to whether they are thermal (heat producing in biologic tissue) or nonthermal. Thermal applications of nonionizing radiation (i.e., application of heat) include RF hyperthermia, laser and RF surgery, and RF diathermy.

The most important BEM modalities in alternative medicine are the nonthermal applications of nonionizing radiation. The term nonthermal is used with two different meanings in the medical and scientific literature. Biologically (or medically) nonthermal means that it “causes no significant gross tissue heating”; this is the most common usage. Physically (or scientifically) nonthermal means “below the thermal noise limit at physiological temperatures.” The energy level of thermal noise is much lower than that required to cause heating of tissue; thus, any physically nonthermal application is automatically biologically nonthermal.

All of the nonthermal applications of nonionizing radiation are nonthermal in the biological sense. That is, they cause no significant heating of tissue. Some of the newer, unconventional BEM applications are also physically nonthermal. A variety of alternative medical practices developed outside the United States employ nonionizing EM fields at nonthermal intensities. For instance, microwave resonance therapy, which is used primarily in Russia, employs low-intensity (either continuous or pulse-modulated), sinusoidal microwave radiation to treat a variety of conditions, including arthritis, ulcers, esophagitis, hypertension, chronic pain, cerebral palsy, neurological disorders, and side effects of cancer chemotherapy (Devyatkov et al., 1991). Thousands of people in Russia also have been treated by specific frequencies of extremely low-level microwaves applied at certain acupuncture points.

The mechanism of action of microwave resonance therapy is thought to involve modifications in cell membrane transport or production of chemical mediators or both. Although a sizable body of Russian-language literature on this technique already exists, no independent validation studies have been conducted in the West. However, if such treatments prove to be effective, current views on the role of information and thermal noise (i.e., order and disorder) in living systems, which hold that biological information is stored in molecular structures, may need revision. It may be that such information is stored at the level of the whole organism in the endogenous EM field, which may be used informationally in biological regulation and cellular communication (i.e., not due to energy content or power intensity). If exogenous, extremely low-level nonionizing fields with energy contents well below the thermal noise limit produce biological effects, they may be acting on the body in such a way that they alter the body’s own field. That is to say, biological information would be altered by the exogenous EM fields.

The eight major new (or “unconventional”) applications of nonthermal, nonionizing EM fields are as follows:

1. Bone repair.

2. Nerve stimulation.

3. Wound healing.

4. Treatment of osteoarthritis.

5. Electroacupuncture.

6. Tissue regeneration.

7. Immune system stimulation.

8. Neuroendocrine modulations.

These applications of BEM and the evidence for their efficacy are discussed in the following section.

Research Base

Applications 1 through 5 above have been clinically tested and are in limited clinical use. On the basis of existing animal and cellular studies, applications 6 through 8 offer the potential for developing new clinical treatments, but clinical trials have not yet been conducted.

Bone Repair

Three types of applied EM fields are known to promote healing of nonunion bone fractures (i.e., those that fail to heal spontaneously):

* Pulsed EM fields (PEMFs) and sinusoidal EM fields (AC fields).

* DC fields.

* Combined AC-DC magnetic fields tuned to ion-resonant frequencies (these are extremely low-intensity, physically nonthermal fields) (Weinstein et al., 1990).

Approval of the U.S. Food and Drug Administration (FDA) has been obtained on PEMF and DC applications and is pending for the AC-DC application. In PEMF and AC applications, the repetition frequencies used are in the ELF range (Bassett, 1989). In DC applications, magnetic field intensities range from 100 microgauss to 100 gauss (G), and electric currents range from less than 0.1 microampere to milliamperes (Baranowski and Black, 1987)._ FDA approval of these therapies covers only their use to promote healing of nonunion bone fractures, not to accelerate routine healing of uncomplicated fractures.

Efficacy of EM bone repair treatment has been confirmed in double-blind clinical trials (Barker et al., 1984; Sharrard, 1990). A conservative estimate is that as of 1985 more than 100,000 people had been treated with such devices (Bassett et al., 1974, 1982; Brighton et al., 1979, 1981; Goldenberg and Hansen, 1972; Hinsenkamp et al., 1985).

Stimulation and Measurement of Nerve Activity

These applications fall into the following seven categories:

1. Transcutaneous electrical nerve stimulation (TENS). In this medical application, two electrodes are applied to the skin via wires attached to a portable electrical generating device, which may be clipped to the patient’s belt (Hagfors and Hyme, 1975). Perhaps more than 100 types of FDA-approved devices in this category are currently available and used in physical therapy for pain relief. All of them operate on the same basis.

2. Transcranial electrostimulation (TCES). These devices are similar to the TENS units. They apply extremely low currents (below the nerve excitation threshold) to the brain via two electrodes applied to the head and are used for behavioral/psychological modification (e.g., to reduce symptoms of depression, anxiety, and insomnia) (Shealy et al., 1992). A recent meta-analysis covering at least 12 clinical trials selected from more than 100 published reports found that TCES can alleviate anxiety disorders (Klawansky et al., 1992). With support from the National Institutes of Health (NIH), TCES is under evaluation for alleviation of drug dependence.

3. Neuromagnetic stimulation. In this application, which has both diagnostic and therapeutic uses, a magnetic pulse is applied noninvasively to a part of the patient’s body to stimulate nerve activity. In diagnostic use, a pulse is applied to the cerebral cortex, and the patient’s physiological responses are monitored to obtain a dynamic picture of the brain-body interface (Hallett and Cohen, 1989). As a treatment modality, it is being used in lieu of electroshock therapy to treat certain types of affective disorder (e.g., major depression) and seizures (Anninos and Tsagas, 1991). Neuromagnetic stimulation also is used in nerve conduction studies for conditions such as carpal tunnel syndrome.

4. Electromyography. This diagnostic application detects electrical potentials associated with muscle contraction. Specific electrical patterns have been associated with certain abnormal states (e.g., denervated muscle). This method, along with electromyographic biofeedback, is being used to treat carpal tunnel syndrome and other movement disorders.

5. Electroencephalography. This neurodiagnostic application detects brainwaves. Coupled with EEG biofeedback it is used to treat a variety of conditions, such as learning disabilities, attention deficit and hyperactivity disorders, chronic alcoholism, and stroke.

6. Electroretinography. This diagnostic application monitors electrical potentials across the retina to assess eye movements. This is one of the few methods available for noninvasive monitoring of rapid eye movement sleep.

7. Low-energy emission therapy. This application uses an antenna positioned in the patient’s mouth to administer amplitude-modulated EM fields. It has been shown to affect the central nervous system, and pilot clinical studies show efficacy in treating insomnia (Hajdukovic et al., 1992) and hypertension (Pasche et al., 1989).

Soft-tissue Wound Healing

The following studies have demonstrated accelerated healing of soft-tissue wounds using DC, PEMF, and electrochemical modalities:

* When wound healing is abnormal (retarded or arrested), electric or magnetic field applications may trigger healing to occur. A review of several reports indicates that fields may be useful in this regard (Lee et al., 1993; Vodovnik and Karba, 1992).

* PEMFs have been used clinically to treat venous skin ulcers. Results of several double-blind studies showed that PEMF stimulation promotes cell activation and cell proliferation through an effect on the cell membrane, particularly on endothelial cells (Ieran et al., 1990; Stiller et al., 1992).

* ELF and RF fields are applied to accelerate wound healing. Since skin wounds have unique electrical potentials and currents, stimulation of these electrical factors by a variety of exogenous EM fields can aid in the healing process by causing dedifferentiation (i.e., conversion to a more primitive form) of the nearby cells followed by accelerated cell proliferation (O’Connor et al., 1990).

* An electrochemical treatment that provides scarless regenerative wound healing uses electricity solely to introduce active metallic ions, such as silver, into the tissue. The electric field plays no role itself (Becker, 1987, 1990, 1992).

* PEMF increases the rate of formation of epithelial (skin) cells in partially healed wounds (Mertz et al., 1988).

* AC EM fields promote the repair of injured vascular networks (Herbst et al., 1988).

* EM devices have been patented for treating atherosclerotic lesions (i.e., small blood clots that build up on the walls of arteries and cause cardiovascular disease) and to control tissue growth (Gordon, 1986; Liboff et al., 1992b).

Osteoarthritis

In a recent clinical trial using a double-blind, randomized protocol with placebo control, osteoarthritis (primarily of the knee) treated noninvasively by pulsed 30-Hz, 60-G PEMFs showed the treatment group improved substantially more than the placebo group (Trock et al., 1993). It is believed that applied magnetic fields act to suppress inflammatory responses at the cell membrane level (O’Connor et al., 1990).

Electroacupuncture

Electrical stimulation via acupuncture needles is often used as an enhancement or replacement for manual needling. Clinical benefits have been demonstrated for the use of electrical stimulation (electrostimulation) in combination with acupuncture as well as for electrostimulation applied directly to acupuncture points.

As an enhancement of acupuncture, a small-scale study showed electrostimulation with acupuncture to be beneficial in the treatment of post-operative pain (Christensen and Noreng, 1989). Other controlled studies have shown good success in using electrostimulation with acupuncture in the treatment of chemotherapy-induced sickness in cancer patients (Dundee and Ghaly, 1989). In addition, electrical stimulation with acupuncture was recently shown to be beneficial in the treatment of renal colic (Lee et al., 1992).

As a replacement for acupuncture, electrostimulation applied in a controlled study to acupuncture points by a TENS unit was effective in inducing uterine contractions in postterm pregnant women (Dunn and Rogers, 1989). Further, research with rats has shown that electrostimulation at such points can enhance peripheral motor nerve regeneration (McDevitt et al., 1987) and sensory nerve sprouting (Pomeranz et al., 1984).

Regeneration

Animal research in this area indicates that the body’s endogenous EM fields are involved in growth processes and that modifications of these fields can lead to modest regeneration of severed limbs (Becker, 1987; Becker and Spadero, 1972; Smith, 1967). Russian research and clinical applications, along with studies now under way in the United States, indicate that low-intensity microwaves apparently stimulate bone marrow stem cell division and may be useful in enhancing the effects of chemotherapy by maintaining the formation and development, or hematopoiesis, of various types of blood cells (Devyatkov et al., 1991).

The following studies are also relevant to the use of BEM for regeneration:

* PEMF applications to promote peripheral nerve regeneration (Orgel et al., 1992; Sisken, 1992).

* The “diapulse” method of using pulsed, high-frequency EM fields for human wrist nerve regeneration (Wilson et al., 1974).

* DC applications to promote rat spinal cord regeneration (Fehlings et al., 1992; Hurlbert and Tator, 1992).

* Swedish work showing that BEM promotes rat sciatic nerve regeneration (Kanje and Rusovan, 1992; Rusovan and Kanje, 1991, 1992; Rusovan et al., 1992).

Immune System

During the past two decades, the effects of EM exposure on the immune system and its components have been extensively studied. While early studies indicated that long-term exposure to EM fields might negatively affect the immune system, there is promising new research showing that applied EM fields may be able to beneficially modulate immune responses. For example, studies with human lymphocytes show that exogenous EM or magnetic fields can produce changes in calcium transport (Walleczek, 1992) and cause mediation of the mitogenic response (i.e., the stimulation of the division of cellular nuclei; certain types of immune cells begin to divide and reproduce rapidly in response to certain stimuli, or mitogens). This finding has led to research investigating the possible augmentation by applied EM fields of a type of immune cell population called natural killer cells, which are important in helping the body fight against cancer and viruses (Cadossi et al., 1988a, 1988b; Cossarizza et al., 1989a, 1989b, 1989c).

Potential Neuroendocrine Modulations

Low-level PEMFs have typically been shown to suppress levels of melatonin, which is secreted by the pineal gland and is believed to regulate the body’s inner clock (Lerchl et al., 1990; Wilson et al., 1990b). Melatonin, as a hormone, is oncostatic (i.e., it stops cancer growth). Thus, if melatonin can be suppressed by certain magnetic fields, it also may be possible to employ magnetic fields with different characteristics to stimulate melatonin secretion for the treatment of cancer. Other applications may include use of EM fields to affect melatonin secretion to normalize circadian rhythms in people with jet lag and sleep cycle disturbances.

Table 2 provides an overview of selected citations to the refereed literature for these applications.

Future Research Opportunities

Although to date there is an extensive base of literature on the use of BEM for medical applications, the overall research strategy into this phenomenon has been quite fragmented. Because of BEM’s potential for the treatment of a wide range of conditions, an integrated research program is needed that includes both basic and clinical research in BEM. These two approaches should be pursued vigorously and simultaneously along parallel tracks.

Basic research is needed to refine or develop new BEM technologies with the aim of establishing the fundamental knowledge about the body’s endogenous EM fields and how they interact with clinically applied EM fields. A basic understanding of the BEM of the human body might provide insight into the scientific bioenergetic or bioinformational principles by which other areas of alternative medicine, such as homeopathy, acupuncture, and energetic therapies, may function. Furthermore, fundamental knowledge of BEM principles in the human body, in conjunction with psychophysiological states, might help facilitate understanding of mind-body regulation.

Clinical research, including preclinical assessments, is also essential, with the aim of bringing the most promising BEM treatments and diagnostics from limited use into widespread use as quickly as possible. Although a number of BEM devices show promise as new diagnostics or therapeutics, they must be tested on humans to show exactly when they are effective and when they are not. Moreover, measures of clinical effectiveness and safety are required for FDA approval of BEM medical devices. Ultimately, knowledge about the safety of new BEM medical devices can be ascertained only from the appropriate clinical trials.

Basic

The current status of basic research in BEM may be summarized as follows:

* Nonionizing, nonthermal exogenous EM fields exert measurable bioeffects in living organisms. In general, the organism’s response to applied EM fields is highly frequency specific and the dose-response curve is nonlinear (i.e., application of an additional amount of the EM field does not elicit a response of equal magnitude; the response eventually diminishes no matter how additional EM stimuli are applied). Extremely weak EM fields may, at the proper frequency and site of application, produce large effects that are either clinically beneficial or harmful.

* The cell membrane has been proposed as the primary site of transduction of EM field bioeffects. Relevant mechanisms may include changes in cell-membrane binding and transport processes, displacement or deformation of polarized molecules, modifications in the conformation of biological water (i.e., water that comprises organisms), and others.

* The physical mechanisms by which EM fields may act on biomolecules are far too complex to discuss here. However, the following references propose such physical mechanisms: Grundler et al., in press; Liboff, 1985, 1991; and Liboff et al., 1991.

* Endogenous nonthermal EM fields ranging from DC to the visible spectral region may be intimately involved in regulating physiological and biochemical processes.

Consequently, the following pressing needs should be addressed in developing a basic BEM research program:

* Standardized protocols for measuring dosages for therapeutically applied EM fields should be established and followed uniformly in BEM research. Protocols are needed for characterizing (i.e., defining and measuring) EM field sources (both exogenous and endogenous) and EM parameters of biological subjects. Such variables must be characterized in greater detail than is commonly practiced in clinical research. Artifacts caused by ambient EM fields in the laboratory environment (e.g., from power lines and laboratory equipment) must be avoided.

* In general, a balanced, strategic approach to basic research–including studies in humans, animals, and cells along with theoretical modeling and close collaboration with other investigators in alternative medicine–will produce the most valuable results in the long run.

* Many independent parameters characterize nonthermal nonionizing EM fields, including pulsed vs. nonpulsed and sinusoidal vs. other waveforms; frequency; phase; intensity (as a function of spatial position); voltage; and current. If multiple fields are combined, these parameters must be specified for each component. Additional parameters necessary for characterizing the medical application of EM fields include the site of application and the time course of exposure. All of these can be experimentally varied, producing an enormous range of possibilities. To date, there has been little systematic research to explore the potential biological effects of this vast array of applied field parameter characteristics.

Clinical

Clinical trials of BEM-based treatments for the following conditions may yield useful results relatively soon: arthritis, psychophysiological states (including drug dependence and epilepsy), wound healing and regeneration, intractable pain, Parkinson’s disease, spinal cord injury, closed head injury, cerebral palsy (spasticity reduction), learning disabilities, headache, degenerative conditions associated with aging, cancer, and acquired immunodeficiency syndrome (AIDS).

EM fields may be applied clinically as the primary therapy or as adjuvant therapy along with other treatments in the conditions listed above. Effectiveness can be measured via the following clinical markers:

* In arthritis, the usual clinical criteria, including decrease of pain, less swelling, and thus a greater potential for mobility.

* In psychophysiological problems, relief from symptoms of drug withdrawal and alleviation of depressive anxiety and its symptoms.

* In epilepsy, return to greater normality in EEG, more normal sleep patterns, and reduction in required drug dosages.

* In wound healing and regeneration, repair of soft tissue and reduction of collagenous tissue in scar formation; regrowth via blastemal (primitive cell) formation and increase in tensile strength of surgical wounds; alleviation of decubitus chronic ulcers (bedsores); increased angiogenesis (regrowth of vascular tissue such as blood vessels); and healing of recalcitrant (i.e., unresponsive to treatment) chronic venous ulcers.

For instance, a short-term, double-blind clinical trial of magnetic field therapy could be based on the protocol of Trock et al. (1993) for osteoarthritis of the knee or elbow. This protocol is as follows:

* A suitable patient population is divided into treatment and control groups. Individual assignments are coded and remain unknown to patients, clinicians, and operators until treatment and assessment are complete.

* Pretreatment clinical markers are assessed by clinicians or by patients themselves or both.

* Treatments consist of 3 to 5 half-hour sessions each week for a total of 18 treatments over 5-6 weeks.

* During treatment, each patient inserts the affected limb into the opening of a Helmholtz coil (a solenoid about 12 inches in diameter and 6 inches long) and rests while appropriate currents are applied to the coil via a preset program.

* The treatment is noninvasive and painless; the patient feels nothing; there is no measurable transfer of heat to the patient.

* The control group follows the same procedure except that, unknown to operator and patient, a “dummy” apparatus (altered internally so that no current flows in the coil) is used.

* Patients’ posttreatment clinical markers are assessed.

* Appropriate data reduction (scoring of assessments, decoding of the treatment and control groups, and statistical analysis) is performed.

Clinical trials of BEM-based treatments for a variety of other conditions could follow a similar general outline.

Key Issues

Certain key issues or controversies surrounding BEM have inhibited progress in this field. These issues fall into several distinct areas: medical controversy, scientific controversy, barriers, and other issues.

Medical Controversy

A number of uncharacterized “black box” medical treatment and diagnostic devices–some legal and some illegal–have been associated with EM medical treatment. Whether they operate on the basis of BEM principles is unknown. Among these devices are the following: radionics devices, Lakhovsky multiple-wave oscillator, Priore’s machine, Rife’s inert gas discharge tubes, violet ray tubes, Reich’s orgone energy devices, EAV machines, and biocircuit devices. There are at least six alternative explanations for how these and other such devices operate: (1) They are ineffectual and are based on erroneous application of physical principles. (2) They may be operating on BEM principles, but they are uncharacterized. (3) They may operate on acoustic principles (sound or ultrasound waves) rather than BEM. (4) In the case of diagnostic devices, they may work by focusing the intuitive capacity of the practitioner. (5) In the case of long-distance applications, they may operate by means of nonlocal properties of consciousness of patient and practitioner. (6) They may be operating on the energy of some domain that is uncharacterized at present.

A recent survey (Eisenberg et al., 1993) showed that about 1 percent of the U.S. population used energy healing techniques that included a variety of EM devices. Indeed, more of the respondents in this 1990 survey used energy healing techniques than used homeopathy and acupuncture in the treatment of either serious or chronic disease. In addition to the use of devices by practitioners, a plethora of consumer medical products that use magnetic energy are purported to promote relaxation or to treat a variety of illnesses. For example, for the bed there are mattress pads impregnated with magnets; there are magnets to attach to the site of an athletic injury; and there are small pelletlike magnets to place over specific points on the body. Most of these so-called therapeutic magnets, also called biomagnets, come from Japan. However, no known published journal articles demonstrating effectiveness via clinical trials exist.

Some of the medical modalities discussed in this report, although presently accepted medically or legally in the United States, have not necessarily passed the most recent requirements of safety or effectiveness. FDA approval of a significant number of BEM-based devices, primarily those used in bone repair and neurostimulation, was “grandfathered.” That is, medical devices sold in the United States prior to the Medical Device Law of the late 1970s automatically received FDA approval for use in the same manner and for the same medical conditions for which they were used prior to the law’s enactment. Grandfathering by the FDA applies not only to BEM devices but to all devices covered by the Medical Device Law. However, neither the safety nor the effectiveness of grandfathered devices is established (i.e., they are approved on the basis of a “presumption” by the FDA, but they usually remain incompletely studied). Reexamination of devices in use, whether grandfathered or not, may be warranted.

There are three possible ways of resolving controversies associated with BEM and its application: (1) elucidating the fundamental principles underlying the device, or at least the historical basis for the development of the device; (2) conducting properly designed case control studies and clinical trials to validate effects that have been reported or claimed for BEM-based treatments; and (3) increasing the medical community’s awareness of well-documented, controlled clinical trials that indicate the effectiveness of specific BEM applications (see table 2).

Scientific Controversy

Some physicists claim that low-intensity, nonionizing EM fields have no bioeffects other than resistive (joule) heating of tissue. One such argument is based on a physical model in which the only EM field parameter considered relevant to biological systems is power density (Adair, 1991). The argument asserts that measurable nonthermal bioeffects of EM fields are “impossible” because they contradict known physical laws or would require a “new physics” to explain them.

However, numerous independent experiments reported in the refereed-journal research literature conclusively establish that nonthermal bioeffects of low-intensity EM fields do indeed exist. Moreover, the experimental results lend support to certain new approaches in theoretical modeling of the interactions between EM fields and biological matter. Most researchers now feel that BEM bioeffects will become comprehensible not by forsaking physics but rather by developing more sophisticated, detailed models based on known physical laws, in which additional parameters (e.g., frequency, intensity, waveform, and field directionality) are taken into account.

Barriers

The following barriers to BEM research exist:

* Members of NIH review panels in medical applications might not be adequately knowledgeable about alternative medical practices or BEM. This is the most serious barrier.

* Funding in BEM research is weighted heavily toward the study of hazards of EM fields; there is little funding for potential beneficial medical applications or the study of basic mechanisms of EM interactions with life processes. Also, the bulk of EM field research is administered by the Department of Defense and the Department of Energy, agencies with missions unrelated to medical research. The small amount of BEM work funded by NIH thus far has addressed mostly the hazards of EM fields. In late 1993 the National Institute of Environmental Health Sciences issued requests for grant application in the areas of (1) cellular effects of low-frequency EM fields and (2) effects of 60-Hz EM fields in vivo. The latter project is concerned solely with safety in power line and appliance exposures. However, the former apparently does not rule out the investigation of possible beneficial effects from low-frequency fields, although the focus is clearly on assessing previously reported effects of 60-Hz EM fields on cellular processes.

* Regulatory barriers to making new BEM devices available to practitioners are formidable. The approval process is slow and exorbitantly expensive even for conventional medical devices.

* Barriers in education include the following: (1) basic education in biological science is weak in physics, (2) undergraduate-and graduate-level programs in BEM are virtually nonexistent, and (3) multidisciplinary training is lacking in medicine and biology.

* The mainstream scientific and medical communities are basically conservative and respond to emerging disciplines, such as BEM, with reactions ranging from ignorance and apathy to open hostility. Consequently, accomplished senior researchers may not be aware of the opportunities for fruitful work in (or in collaboration with others in) BEM, while junior researchers may be reluctant to enter a field perceived by some as detrimental to career advancement.

Other Issues

Other key issues that need to be considered in developing a comprehensive research and development agenda for BEM include the following:

* Separate studies prepared for the Office of Technology Assessment, the National Institute of Occupational Safety and Health, and the Environmental Protection Agency have recommended independently that research on fundamental mechanisms of EM field interactions in humans receive high priority (Bierbaum and Peters, 1991; Nair et al., 1989; U.S. EPA, 1991). Moreover, a 1985 report prepared by scientists at the Centers for Devices and Radiological Health recommended that future research on EM field interactions with living systems “be directed at exploring beneficial medical applications of EMR (electromagnetic radiation) modulation of immune responses” (Budd and Czerski, 1985).

* Elucidation of the physical mechanisms of BEM medical modalities is the single most powerful key to developing efficient and optimal clinical intervention. Even a relatively small advance beyond present knowledge of fundamental mechanisms would be of considerable practical value. In addition, progress in the development of a mechanistic explanation of the effects of alternative medicine could increase its acceptability in the eyes of mainstream medicine and science.

* BEM potentially offers a powerful new approach to understanding the neuroendocrine and immunological bases of certain major medical problems (e.g., wound healing, cancer, and AIDS). However, substantial funding and time are required to perform the basic research needed in developing this approach.

* BEM may provide a comprehensive biophysical framework grounded in fundamental science, through which many alternative medical practices can be studied. BEM offers a promising starting point for scientifically exploring various traditional alternative medical systems (Becker and Marino, 1982).

Basic Research Priorities

The most fruitful topics for future basic research investigations of BEM may include the following:

* Developing assay methods based on EM field interactions in cells (e.g., for potassium transport, calcium transport, and cytotoxicity). These assays could then be applied to existing studies of such phenomena in cellular systems.

* Developing BEM-based treatments for osteoporosis, on basis of the large body of existing work on EM bone repair and other research (e.g., Brighton et al., 1985; Cruess and Bassett, 1983; Liboff et al., 1992a; MadroZero, 1990; Magee et al., 1991; Skerry et al., 1991). NASA researchers have already expressed interest in collaborative work to develop BEM treatments for weightlessness-induced osteoporosis.

* Measuring neurobiochemical changes in the blood in response to microcurrent skin stimulation in animals or humans with different frequencies, waveforms, and carrier waves. Such measurements should be made for preclinical evaluation of neurostimulation devices.

* Furthering studies of mechanisms of EM field interactions in cells and tissues with emphasis on coherent or cooperative states and resonant phenomena in biomolecules; and on coherent brainwave states and other long-range interactions in biological systems.

* Studying the role of water as a mediator in biological interactions with emphasis on the quantum EM aspects of its conformation (i.e., “structure,” as implied in some forms of homeopathy). The response of biologic water to EM fields should be studied experimentally. A novel informational capacity of water in relation to EM bioeffects may provide insights into homeopathy and healer interactions (i.e., “laying on of hands”).

* Studying in detail the role of the body’s internally generated (endogenous) EM fields and the body’s other natural electromagnetic parameters (see the “Manual Healing Methods” chapter). Knowledge of such processes should be applied to develop novel diagnostic methods and to understand alternative medical treatments such as acupuncture, electroacupuncture, and biofield therapies. Furthermore, exploratory research on the role of the body’s energy fields in relation to the role of states of consciousness in health and healing should be launched.

* Establishing a knowledge base (an intelligent database) to provide convenient access to all significant BEM work in both basic and clinical research.

* Performing systematic reviews as well as meta-analytic reviews of existing BEM studies to identify the frequency and quality of research concerning BEM as well as most promising clinical end points for BEM treatments in humans.

Summary

Just as exposure to high-energy radiation has unquestioned hazards, radiation has long been a key weapon in the fight against many types of cancers. Likewise, although there are indications that some EM fields may be hazardous, there is now increasing evidence that there are beneficial bioeffects of certain low-intensity nonthermal EM fields.

In clinical practice, BEM applications offer the possibility of more economical and more effective diagnostics and new noninvasive therapies for medical problems, including those considered intractable or recalcitrant to conventional treatments. The sizable body of recent work cited in this chapter has established the feasibility of treatments based on BEM, although the mainstream medical community is largely unaware of this work.

In biomedical research, BEM can provide a better understanding of fundamental mechanisms of communication and regulation at levels ranging from intracellular to organismic. Improved knowledge of fundamental mechanisms of EM field interactions could lead directly to major advances in diagnostic and treatment methods.

In the study of other alternative medical modalities, BEM offers a unified conceptual framework that may help explain how certain diagnostic and therapeutic techniques (e.g., acupuncture, homeopathy, certain types of ethnomedicine, and healer effects) may produce results that are difficult to understand from a more conventional viewpoint. These areas of alternative medicine are currently based entirely on empirical (i.e., experimentation and observation rather than theory) and phenomenological (i.e., the classification and description of any fact, circumstance, or experience without any attempt at explanation) approaches. Thus, their future development could be accelerated as a scientific understanding if their mechanisms of action are ascertained.

References

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Table 1. Electromagnetic Spectrum

Frequency range (Hz)* Classification Biological effect

0 Direct current Nonionizing

0 – 300 Extremely low frequency Nonionizing

300 – 104 Low frequency Nonionizing

104 – 109 Radio frequency Nonionizing

109 – 1012 Microwave and radar bands Nonionizing

1012 – 4 x 1014 Infrared band Nonionizing

4 x 1014 – 7 x 1014 Visible light Weakly ionizing

7 x 1014 – 1018 Ultraviolet band Weakly ionizing

1018 – 1020 X rays Strongly ionizing

Over 1020 Gamma rays Strongly ionizing

* Division of the EM spectrum into frequency bands is based on conventional but arbitrary usage in various disciplines.

Table 2. Selected Literature Citations on Biomedical Effects of Nonthermal EM Fields

Frequency range of EM fields

Location or type of bioeffect_

DC_ELF, including sinusoidal, pulsed, and mixed_

RF and microwave_

IR, visible, and UV light_

Review articles and monographs___

Bone and cartilage, including treatments for bone repair and osteoporosis_Brighton et al., 1981;

Baranowsi & Black, 1987;

Papatheofanis, 1989_Bassett et al., 1982;

Barker et al., 1984;

Brighton et al., 1985;

Hinsenkamp et al., 1985;

Huraki et al., 1987;

Bassett, 1989;

MadroZero, 1990;

Sharrard, 1990;

Grande et al., 1991;

Magee et al., 1991;

Pollack et al., 1991;

Skerry et al., 1991;

Ryaby et al., 1992___Brighton et al., 1979__

Soft tissue, including wound healing, regeneratrion, and vascular­tissue effects_Becker, 1987;

Becker, 1990;

Becker, 1992;

Vodovnik & Karba, 1992_Gordon, 1986;

Herbst et al., 1988;

Mertz et al., 1988;

Yen­Patton et al., 1988;

Albertini et al., 1990;

Ieran et al., 1990;

Im & Hoopes, 1991;

Kraus, 1992;

Liboff et al., 1992b;

Stiller et al., 1992;

Vodovnik & Karba, 1992_Devyatkov et al., 1991__Vodovnik & Karba, 1992__

Neural tissue, including nerve growth and regeneration__Wilson et al., 1974;

Rusovan & Kanje, 1991;

Subramanian et al., 1991;

Horton et al., 1992;

Rusovan & Kanje, 1992;

Rusovan et al., 1992_____

Neural stimulation effects, including TENS and TCES__Hagfors & Hyme, 1975;

Hallett & Cohen, 1989;

Anninos & Tsagas, 1991;

Klawansky et al., 1992_____

Psychophysiological and behavioral effects___Pasche et al., 1989;

Devyatkov et al., 1991;

Hajdukovic et al., 1992_Thomas et al., 1986_O’Connor & Lovely, 1988__

Electroacupuncture_McDevitt et al., 1987_Pomeranz et al., 1984;

Christensen & Noreng, 1989;

Dundee & Ghaly, 1989;

Lee et al., 1992_____

Neuroendocrine effects, including melatonin modifications_Feinendegen & Muhlensiepen, 1987_Lerchl et al., 1990;

Wilson et al., 1990a, 1990b___O’Connor & Lovely, 1988__

Immune system effects__Cadossi et al., 1988a;

Cadossi et al., 1988b;

Cossarizza et al., 1989a;

Cossarizza et al., 1989b;

Rosenthal & Obe, 1989;

Phillips & McChesney, 1991;

Walleczek, 1992_____

Arthritis treatments__Grande et al., 1991;

Trock et al., 1993_Devyatkov et al., 1991____

Cellular and subcellular effects, including effects on cell membrane, genetic system, and tumors_Easterly, 1982;

Liburdy & Tenforde, 1986;

Foxall et al., 1991;

Miklavcic et al., 1991;

Short et al., 1992_Cohen et al., 1986;

Takahashi et al., 1987;

Adey, 1992;

Marron et al., 1988;

Onuma & Hui, 1988;

Brayman & Miller, 1989;

Cossarizza et al., 1989a, 1989b;

De Loecker et al., 1989;

Goodman et al., 1989;

Rodemann et al., 1989;

Brayman & Miller, 1990;

Lerchl et al., 1990;

Omote et al., 1990;

Greene et al., 1991;

Liboff et al., 1991_Guy, 1987;

Chen & Ghandi, 1989;

Brown & Chattpadhyay, 1991;

Devyatkov et al., 1991__Adey & Lawrence, 1984;

Marino, 1988;

Blank & Findl, 1987;

Ramel & Norden, 1991;

Grundler et al., in press__

Endogenous EM fields, including biophotons__Mathew & Rumar, in press_Mathew & Rumar, in press_Popp et al., 1984;

Chwirot et al., 1987;

Chwirot, 1988;

Popp et al., 1988_Wijk & Schamhart, 1988;

Popp et al., 1992__

Note: Reports listed in table 2 are selected from refereed medical and scientific journals, multiauthor monographs, conference proceedings, and patents. See References for identification of sources. This is a representative selection from a large body of relevant sources and is not meant to be exhaustive or definitive.

A more detailed introduction to the field of BEM and an overview of research progress is available in the following monographs and conference proceedings: Adey, 1992; Adey and Lawrence, 1984; Becker and Marino, 1982; Blank, 1993; Blank and Findl, 1987; Brighton and Pollack, 1991; Brighton et al., 1979; Liboff and Rinaldi, 1974; Marino, 1988; O’Connor et al., 1990; O’Connor and Lovely, 1988; Popp et al., 1992; and Ramel and Norden, 1991.

Gauss is a unit of magnetic flux density. For comparison, a typical magnet used to hold papers vertically on a refrigerator is 200 G.

Pulsed Electromagnetic Field Therapy, PEMT.  How does it work?

Lecture abstract Dr. D. Laycock, Ph.D. Med. Eng. MBES, MIPEM, B.Ed.

All living cells within the body possess potentials between the inner and outer membrane of the cell, which, under normal healthy circumstances, are fixed. Different cells, e.g. Muscle cells and Nerve cells, have different potentials of about -70 mV respectively. When cells are damaged, these potentials change such that the balance across the membrane changes, causing the attraction of positive sodium ions into the cell and negative trace elements and proteins out of the cell. The net result is that liquid is attracted into the interstitial area and swelling or oedema ensues. The application of pulsed magnetic fields has, through research findings, been shown to help the body to restore normal potentials at an accelerated rate, thus aiding the healing of most wounds and reducing swelling faster. The most effective frequencies found by researchers so far, are very low frequency pulses of a 50Hz base. These, if gradually increased to 25 pulses per second for time periods of 600 seconds (10 minutes), condition the damaged tissue to aid the natural healing process.

Pain reduction is another area in which pulsed electromagnetic therapy has been shown to be very effective. Pain signals are transmitted along nerve cells to pre-synaptic terminals. At these terminals, channels in the cell alter due to a movement of ions. The membrane potential changes, causing the release of a chemical transmitter from a synaptic vesicle contained within the membrane. The pain signal is chemically transferred across the synaptic gap to chemical receptors on the post-synaptic nerve cell. This all happens in about 1/2000th of a second, as the synaptic gap is only 20 to 50 nm wide. As the pain signal, in chemical form, approaches the post-synaptic cell, the membrane changes and the signal is transferred. If we look at the voltages across the synaptic membrane then, under no pain conditions, the level is about -70 mV. When the pain signal approaches, the membrane potential increases to approximately +30 mV, allowing a sodium flow. This in turn triggers the synaptic vesicle to release the chemical transmitter and so transfer the pain signal across the synaptic gap or cleft. After the transmission, the voltage reduces back to its normal quiescent level until the next pain signal arrives.

The application of pulsed magnetism to painful sites causes the membrane to be lowered to a hyper-polarization level of about -90 mV. When a pain signal is detected, the voltage must now be raised to a relatively higher level in order to fire the synaptic vesicles. Since the average change of potential required to reach the trigger voltage of nearly +30 mV is +100 mV, the required change is too great and only +10 mV is attained. This voltage is generally too low to cause the synaptic vesicle to release the chemical transmitter and hence the pain signal is blocked. The most effective frequencies that have been observed from research in order to cause the above changes to membrane potentials, are a base frequency of around 100Hz and pulse rate settings of between 5 and 25Hz.

Pulsed magnetic field therapy and the physiotherapist

Dr. D. C. Laycock, Ph.D. Med. Eng. Westville Consultants

The therapeutic effect of the application of pulsed magnetic field therapy (PMFT) has at last received world-wide recognition, although for a long time many practitioners saw it only as an aid to fracture union. Research has now shown that it has the potential to improve a wide range of conditions, although few understood just how it achieved its effectiveness. Extensive research has since been carried out to determine the mechanism by which this occurs. For the physiotherapist, presented with a wide range of clinical problems, PMFT is an invaluable aid to the clinic.

Resolution of soft tissue injuries:

Over the past few years, research has shown that its effectiveness is not through heat production – as is the case with some modern treatments – but is at the cellular level. One significant outcome of this is the effect it has on soft tissue injuries. As early as 1940 it was suggested that magnetic fields might influence membrane permeability. It has since been established that magnetic fields can influence ATP (Adenosine Tri-phosphate) production; increase the supply of oxygen and nutrients via the vascular system; improve the removal of waste via the lymphatic system; and help to re-balance the distribution of ions across the cell membrane. Healthy cells in tissue have a membrane potential difference between the inner and outer membrane. This causes a steady flow of ions through its pores. In a damaged cell the potential is raised and an increased and an increased sodium inflow occurs. As a result, interstitial fluid is attracted to the area, resulting in swelling and oedema.
The application of PMFT to damaged cells accelerates the re-establishment of normal potentials (Sansaverino) increasing the rate of healing and reducing swelling. This can help to disperse bruising also. A magnetic field pulsed at 5Hz with a base frequency of 50Hz can have the same effect as an ice pack in that in that it causes vasoconstriction.

Effects on fracture repair:

Acceptance of magnetic fields in medicine came about foremost in the field of orthopedics. Low frequency and low intensity fields have been used extensively for the treatment of non-union fractures. By 1979 this method was approved in the USA as a safe and effective treatment for non-union fractures; for failed arthroses; and for congenital pseudo-arthroses. According to Bassett this method has been used by more than 6,000 surgeons. The success rate was over 80% for tibial lesions. No patient suffered complications and biological side-effects included improved healing and increased neural function. In-depth research carried out to investigate this, shows that magnetic fields influence the process of bone formation in the intercellular medium. Madronero showed that bone healing was promoted by means of the influence of the magnetic field on the crystal formation of calcium salts.

Pain reduction:

Pulsed magnetic field therapy has been shown to bring about a reduction of pain, which again is due to action at the cellular level. Pain is transmitted as an electric signal, which encounters gaps at intervals along its path. The signal is transferred in the form of a chemical signal across the synaptic gap and this is detected by receptors on the post-synaptic membrane. A charge of about -70mV exists across the inner and outer membranes, but when a pain signal arrives it raises this to +30mV. This action causes channels to open in the membrane, triggering the release of a chemical transmitter and allowing ions to flow into the synaptic gap. The cell then re-polarizes to its previous resting level. Research by Warnke suggests that PMFT affects the quiescent potential of the membrane, lowering it to a hyper-polarized level of -90mV. Transmission is effectively blocked since the pain signal is unable to raise the potential to the level required to trigger the release of the chemical transmitter. Again, the frequency of the applied magnetic field is important, as the most effective frequency to produce this effect was found to be a base frequency of 100Hz pulsed at between 5 and 25 pulses per second.

Clinical applications:

The value of pulsed magnetic field therapy has been shown to cover a wide range of conditions, with well documented trials carried out by hospitals, rheumatologists and physiotherapists. For example, the department of rheumatology at Addenbrookes Hospital carried out investigations into the use of PMFT for the treatment of persistent rotator cuff tendinitis. The treatment was applied to patients who had symptoms refractory to steroid injection and other conventional treatments. At the end of the trial, 65% of these were symptom free, with 18% of the remainder being greatly improved.

Lau (School of Medicine, Loma University, USA) reported on the application of PMFT to the problems of diabetic retinopathy. Patients were treated over a 6-week period, 76% of the patients had a reduction in the level of numbness and tingling. All patients had a reduction of pain, with 66% reporting that they were totally pain-free. Many research studies, including Lau, reported on the application of PMFT for conditions such as sports injuries and for patients with joint and spinal problems. Although these are too numerous to mention individually, in almost every instance there was a reduction, if not complete resolution of symptoms. Soft tissue injuries and joint pains tended to be resolved within 5 days of treatment. Patients with cervical problems and low back pain were also successfully treated, whereas previous treatment with ice, traction and other therapies had been unsuccessful. In yet another trial, the effect of applying PMFT to sufferers of Multiple Sclerosis was investigated (Geseo) 70% of sufferers had a reduction of weakness, pain and spasticity, with 50% reporting improvement of their bladder incontinence. Through the evaluation of hundreds of research papers, a number of points have been established regarding PMFT: The field must be pulsed, with low frequency to achieve the best effect.

Different conditions require different frequencies. For example, 5Hz causes vasoconstriction whilst 10Hz and above causes vasodilatation. Biological effectiveness is achieved in just 10 minutes for most injuries, so that long treatment sessions are not required. When used at the correct level there are no recorded side effects. Although PMFT is not yet recommended for use during pregnancy or in the presence of tumors, there are papers to suggest that magnetic fields can inhibit the growth of tumors.

Modification of biological behavior of cells by Pulsing Electromagnetic fields, (PMFT)

Ben Philipson, Curatronic Ltd.

On the major part of the calcified mass of adult bone there are no changes in bone mass, however there is a part on which bone is being formed and a part on which bone is being resorbed. Decalcification occurs when bone resorption is greater than bone formation. Bone formation comprises two steps, the laying down of the extra-cellular matrix and the deposition therein of bone salts. The dynamic processes of formation and destruction of bone are under cellular control. Bone formation is controlled by single nuclear cells called Osteoblasts, and bone resorption by multinuclear giant cells are called Osteoclasts. Bone is a specialized connective tissue, in which a matrix consisting of collagen fibers and a large variety of other proteins and ground substance are impregnated with a solid mineral. The bone matrix is responsible for the resistance of bone to tractional and torsional forces. The collagen forms more than 25 % of the bones and is synthesized by osteoblasts. On the bone surface collagen fibers are normally arranged in concentric rings of hard calcified matrix.

The bone minerals provide to the bone compressive strength and rigidity. It contains the mineral salts hydroxyapatite and calcium. In addition there are small amounts of magnesium hydroxide, fluoride and sulphate. As these salts are deposited in the framework formed by the collagen fibers of the matrix, crystallization occurs and the tissue hardens. This process is called calcification or mineralisation. Both the concentrations of ions of calcium and phosphate in the extracellular fluid maintain crystallization. If the concentration is not adequate the tissue will not be hard enough resulting in increased bone fracture risk.
There are two types of bone structure. Cortical (compact) bone and trabecular (spongy) bone. Cortical bone is more dense and constitutes of 80 % of the skeletal mass and forms the external layer of all bones in the human body. Trabecular bone consists of lamellae arranged in an irregular latticework of thin plates of bone and helps long bones to resist the stress of weight placed on them.

The process by which bone forms is called ossification. Bone forms either by the mineralisation of cartilage or directly by osteoblasts in a collagenous matrix. During the first two decades of life bone grows, followed by consolidation and reaching its peak value around thirty five years. After this peak, bone loss starts. Nutritional factors, especially calcium intake, the level of physical activity and generic factors are important in determining the peak bone mass.
When a bone is fractured, it heals with bone. Bone is the only solid tissue in the body that can replace itself. Bone healing is simple when it occurs smoothly, complicated when it does not. The process is being initiated by stimuli from the bone itself. Fractures through bone with a good blood supply, surrounded by muscle and without soft tissue trauma, have an excellent chance of healing, but fractures at the middle of long bones, particularly with extensive soft tissue damage, have a high incidence of non-union.

Selected low-energy time-varying electromagnetic fields have been used during the past 15 years to treat un-united fractures (non-unions). More than 100,000 patients, mainly in the USA, have been treated. Retrospective studies have substantiated their biological effectiveness in large numbers. Bone is responsive to the mechanical demands placed on it. When loading diminishes, as it does during bed rest, immobilization and weightlessness, bone mass is lost. On the other hand when loading is increased correctly, bone mass increases.

Results of bio-mechanical and histologic investigations prove that electromagnetic fields not only prevent bone loss, but also restores bone mass, once lost. A program was set up at McGill University of Montreal, where was found that electromagnetic fields damp bone resorption activity. Furthermore prove was found that selected electromagnetic fields increase bone formation.

The resorption of bone is lowest and formation of new bone greatest, when energy of the imposed fields is concentrated in the lower frequency components. These results are consistent with other studies showing, that cells respond to a broad spectrum of frequencies. They appear to be most sensitive to frequencies in the range of those produced endogenously, that is in the range of 100 Hz or less.

Tissue dosimetry studies show that the frequency response of cortical bone over a range of 100 Hz to 20 kHz show a steep roll off between 100 and 200 Hz.
Electromagnetic fields at specific frequencies have shown to produce osteogenic effects in a turkey ulna model. Furthermore low-amplitude signals decrease bone resorption in a canine fibular model. Lifestyle factors like malnutrition, smoking, excessive use of alcohol and a sedentary lifestyle contribute to, and worsen, osteoporosis. It is not known whether this response derives from decreased osteoblastic activity, increased osteoclastic resorption, or both. Elderly persons can heal fractures in normal intervals, showing that osteoblasts can be activated by appropriate stimuli.

A study at the University of Hawaii School of Medicine was designed to provide concrete data on the restoration of bone mass in post-menopausal females. A total of 20 subjects between 57 and 75 years, all with decreased bone mineral density as defined by a bone densitometer, were treated during a period of 12 weeks. After a period of 6 weeks the bone density rose in those patients with an average of 5.6%.

Electromagnetic fields do modify biological behavior by inducing electrical changes around and within the cell. The key to rational use of electromagnetic fields lies in the ability to define the specific treatment parameters (amplitude, frequency, orientation and timing). Properly applied pulsed electromagnetic fields, if scaled for whole body use, has clear clinical benefits in the treatment of bone diseases and related pain, often caused by micro-fractures in vertebrae. In addition, joint pain caused by worn out cartilage layers can be treated successfully, through electromagnetic stimulation, increasing the partial oxygen pressure and resulting in increased calcium transport. Repair and growth of cartilage is thus stimulated, preventing grinding of the bones.