Brief description of the principle of Magnetic Resonance being used for imaging purposes (MRI)


A sample is placed in magnetic field B0. The magnetic field will exert a torque on the spins, causing them to align themselves with the direction of the magnetic field B0. They will be adopting the lowest energy configuration which is termed "spin-up" or "parallel" to the magnetic field configuration. The progressive alignment of an increasing number of spins results in the growth of a net magnetization of the system, termed Mo (Mz), which represents the sum of the magnetic properties of the spins.


As a result, the energy of the spin system decreases and this is accompanied by a transfer of heat from the system. This procedure is termed "thermal relaxation" and is symbolized by T1. (Due to original studies performed in solids, which are characterized by a crystalline lattice, it is also termed "spin-lattice relaxation").


A radiofrequency field with a B1 oscillating magnetic field component is applied perpendicular to the main magnetic field Bo. The radiofrequency is chosen to be equal to the precession frequency of the spins. Initially, Mo is aligned with Bo but due to the torque by B1, it will be tipped out of alignment. Only when the frequency is identical to the precession can M and B1 remain "locked together in the appropriate relation for tipping and energy exchange". As a result the initial magnetisation Mo (Mz) is converted to a net transverse magnetization Mxy. In this state, there is phase coherence of the spins in the xy plane. It is the Mxy magnetization component that induces a current in the coil and thereby generates a magnetic resonance signal. Subsequently, after the end of the radiofrequency pulse is stopped, in the absence of the B1 torque, the net magnetisation will decay. The decay or dephasing of the transverse magnetization Mxy is termed T2 relaxation or "spin-spin relaxation".




Selected Questions from and some notes


Net Magnetization (M) - What is net magnetization and how does it apply to NMR?


How Magnetization Develops - Does the net magnetization (M) just instantly appear?


Following the placement of a subject in a magnetic field Bo, spins are aligned to the direction of this field resulting in the growth of a net magnetization M.


A radiofrequency field with a magnetic field component B1 is applied perpendicular to M. Its frequency is chosen near the precession frequency of the spins. This induces the rotation of M by 90 degrees.

“Like pushing a child on a swing, the B1 field must be applied near the Larmor frequency for this to occur.”

"If B1 rotates at any other frequency then it would be alternately in and out of phase with the spins which produce M. Only when the rotation rate of B1 closely matches the precession frequency can M and B1 remained locked together in the appropriate relation for tipping and energy exchange. The absorption and exchange of energy constitute a resonance phenomenon, sharply tuned to the natural nuclear precession frequency."




The Magnetic Resonance signal - FID


What signal does the precession of the magnetization M (vector) give?

The precession of the magnetization M (at the frequency termed "precession frequency") near a coil induces an alternating current in the coil with the same frequency. (Cf. relationship between rotation - vector approaching the coil - and current cycle).


This occurs in an MRI scanner with the transverse component Mxy and the scanner receiver coil.

The transverse component of the magnetization Mxy is created by the radiofrequency and is sustained by it.


If the radiofrequency is stopped, the spins will tend to become parallel to the z axis and the transverse magnetization component Mxy will gradually decrease or decay (or dephase). This procedure is known as T2 relaxation or transverse relaxation or spin-spin relaxation. As a result the current induced in the coil will also decay.


The generated signal is termed "free induction decay". (It was originally termed "nuclear induction decay" or "free induction" signal).


FID is a damped sine wave of the form:

[sin ω(o)t] e^-t/T2*)

where ω(o) is the Larmor frequency and T2* is a time constant


The FID is one of four basic types of NMR signals. The other three are: Gradient Echo (GRE), Spin echo (SE) and Stimulated echo.


Additional information:

Where does the MR signal come from?

What is a free induction decay (FID)?



Spin echo (SE) - Effect of two pulses in Magnetic Resonance

What NMR signal will we receive following an initial excitation pulse?

A damped sine wave termed FID.


What is defined as "echo" in Magnetic Resonance?

The reappearance or repetition of the NMR signal following its decay.


How is a NMR "echo" created?
An echo is created by the action of two successive pulses e.g. the standard 90° pulse followed by a 180° pulse.
(Following a small time interval from the end of the RF action, a signal appears.)


How is the NMR "echo" signal explained?
Following the stop of the 90° RF pulse excitation, which resulted in an FID signal, spins start to dephase while being on the xy plane (transverse plane). The application of a 180° RF pulse will exert a torque that will flip the spin system i.e. rotate it by 180°, an event followed by rephasing which will result in the growth of a macroscopic magnetization. The latter is made evident by the generation of a signal at the detection coil. This signal is called an "echo".


*"Free Induction Decay". Note that the term "nuclear induction" was used before the term "nuclear magnetic resonance"


Additional reference:



Figure: Spin echo. Image from Wikipedia (By Gavin W Morley - Own work, CC BY-SA 3.0 - slightly modified). Please refer to Wikipedia legend.




Stimulated Echo (STE) - Effect of three pulses in Magnetic Resonance


A spin echo (SE) is created by two RF pulses while a stimulated echo (STE) by three of more RF pulses. 


Following the stop of the first 90° RF pulse excitation, which resulted in a FID signal, spins start to dephase while being on the xy plane (transverse plane). The application of a second 90° RF pulse will exert a torque that will tip the spin system by 90°, i.e. towards the z axis, in the xz plane. In the z direction there is the Bo (main magnetic field of an MRI scanner). The Bo tends to make spins parallel to its magnetic field lines (cf. pointing to the same direction).


The spins will be both dephasing as well as receiving the influence of Bo. (The figure at link shows a four spin system and the different influence that a/b versus c/d spins receive).


A third 90° RF pulse will tip spins to the xy plane. The spins catch up with their partners, precess and rephase to generate a macroscopic magnetization. The latter is made evident by the generation of a signal at the detection coil. This signal is called a "stimulated echo". It is noted that not all components come into phase and also the relevant time is different between components. Therefore, the stimulated echo is of lower amplitude and is spread out more.




FB post




A pulse train in Magnetic Resonance generates a continuously present transverse magnetization signal (steady-state) "emitted from the subject"


One pulse generates an FID, two pulses a spin echo (SE) and three pulses a stimulated spin echo (STE). 

If the time between pulses (TR*) is long, the FID will have been completed before the SE/STE start. However, if the time between pulses in short, the FID will not have been completed but its tail will be merged with the beginning of the SE/STE.


Upon these condition, the transverse magnetization signal does not disappear but is continuously present. This results in the development of a steady-state transverse magnetization which is called a "Steady State Free Precession" (SSFP).




*Repetition Time (TR) is the cycle time between corresponding points on a repeating series of pulses and echoes


Gradient Echo (GRE) - What is a gradient echo, and how does it differ from an FID?

On the principle: A Gradient Echo consists of a dephasing gradient followed by a rephasing gradient. 


Use of these gradients is linked to four basic types of coherent gradient echo sequences: SSFP-FID, SSFP-Echo, SSFP-Double, SSFP-Balanced 


Spin Echo Variations - What is the difference between spin echo, multi-spin echo, and fast spin echo?


Please refer to this image as reference:




Human Brain Magnetic Resonance Current Density imaging (MRCDI)


Magnetic resonance current density imaging (MRCDI) is an emerging technique which combines the application of a weak time-varying current via surface electrodes with magnetic resonance imaging (MRI) to obtain information about current flow and conductivity of the head.


In MRI, the static magnetic field of the scanner (conventionally in the z axis) aligns the spins of the subject resulting in a net magnetization, represented by an Mz vector along the z axis. In MRICDI, an applied current induces a magnetic field in the head and the induced magnetic component in the z axis, termed ΔBc(z), slightly changes the precession frequency of the magnetization vector given that this frequency depends on the intensity of the magnetic field. This introduces either an acceleration or a deceleration (lag) of the precession, or in other words it changes the phase and specifically it modulates the phase of the measured MRI signal proportionally to ΔBc(z). The measurement of the current-induced phase changes can be used to determine the induced ΔBc(z) and to reconstruct the inner current flow and the conductivity distribution. The technique makes use of MRI sequences i.e. sets of pulses and gradients for optimal results such as multi-echo spin echo (MESE) and steady-state free precession free induction decay (SSFP-FID).


Göksu C, et al, Human in-vivo brain magnetic resonance current density imaging (MRCDI). Neuroimage. 2018;171:26-39.
Authors use a current flow reconstruction algorithm based on first order spatial derivatives of the measured current-induced magnetic field. Note: It is assumed that the x- and y-components can be neglected.
Background: Please refer to section about a "pulse train in Magnetic Resonance".




ΜRI quantification of magnetic field changes induced by tDCS* current in human brain

Jog MV, Smith RX, Jann K, et al. In-vivo Imaging of Magnetic Fields Induced by Transcranial Direct Current Stimulation (tDCS) in Human Brain using MRI. Sci Rep. 2016;6:34385.
"The proposed technique is based on Ampere’s law, which states that a direct current induces a linearly dependent magnetic field". "The induced magnetic field along the static field (Bz) of the MRI can be detected using field mapping."
"Τhe induced magnetic field is directly proportional to the applied tDCS current density". (cf. Equation 1)
"Magnetic resonance imaging (MRI) is able to map changes in magnetic field along the static magnetic field (Bz). Field disturbances perpendicular to Bz are generally invisible to MRI, as a consequence of the fact that (a) the Bz magnetic field is orders of magnitude larger than any typical disturbance and (b) magnetic fields add vectorially (Supplemental S2). Using MRI field mapping, field variations along Bz can be measured as phase angles according to
Φm = (γ *ΔBz * TE) mod(2π)
where Φm is the measured phase angle between 0 and 2π radians, γ is gyromagnetic ratio (a constant), ΔBz is the field deviation along Bz and TE is the echo time."
"The results show that the proposed technique is able to detect magnetic field changes as small as a nanotesla (nT) with a spatial resolution of a few millimeters."
*A common term for tDCS would be head mild electro-shock with direct current. This is an emerging promising therapy.

Measuring the magnetic field of the brain with MRI: the brain introduces a perturbation in the magnetic field of the scanner

The magnetic field of the brain perturbs the magnetic field of the scanner or in other words it introduces a perturbation in the magnetic field of the scanner. Any perturbation of the magnetic field ΔB (vector) can be written as the sum of two orthogonal components, one along Bz (parallel to Bz), and the other perpendicular to Bz.
The total magnetic field can be written as the vector sum of Bz and the perturbation, or equivalently, as a vector of length Bmag, at an angle θ to Bz.
For perturbations on the order of ppm, it is proven that θ is almost zero i.e. Btotal is along Bz.



ΜRI quantification of magnetic field changes induced by tACS current in human brain


"Magnetic resonance electrical impedance tomography (MREIT) techniques encode current flow in phase images."
"We used MREIT to measure magnetic flux density distributions caused by tACS currents, and then calculated current density distributions from these data."


Kasinadhuni AK et al, Brain Stimul. 2017;10(4):764-772.




Measurement of brain activity with NMR and ESR


"Feasibility of developing a method of imaging neuronal activity in the human brain: a theoretical review" by Holder D.S.


"It is proposed that, for the rapid changes related to the action potential, electron spin resonance using a potential-sensitive spin, label, impedance imaging and NMR are suitable in principle but that only ESR and impedance methods may have sufficient sensitivity and these merit further assessment."


"The Potential Use of Electron Spin Resonance Impedance Measurement to Image Neuronal Electrical Activity in the Human Brain" by Holder D.S. (1985)


Electrical and magnetic fields in medicine and biology - IEE Conference Publication No.257 (1985)

“Conference proceedings do not as a rule lead to exciting publications. This present volume, based on a conference held in London in December 1985 is perhaps one of the exceptions.”


Holder D.S is cited at U.S. Patent 4719425

"Holder investigated the possibility that neuronal firing can be detected by a form of electromagnetic radiation which can then be reconstructed to form three-dimensional images of this functional activity. Holder teaches the use of ESR and impedance imaging as giving the best results. Holder states that NMR, being well established for spectroscopy and imaging, could be employed to detect neuronal firing, but that current flux from ions moving across the neuronal membrane would be too small to be detectable by NMR."





Patent on measurement of brain activity with NMR and ESR


"The subject is placed in a spacially homogeneous main magnetic field and an RF pulse is applied to resonate a plurality of nuclear spins to produce an NMR signal." 


A plurality of NMR spectral lines are imaged.


The NMR spectral lines have a specific width. "It has been determined by the applicant, that the width of the spectral lines is broadened due to the electric activity in the brain. The discharge of a neuron in the brain introduces an inhomogeneity into the main magnetic field."


"A plurality of NMR spectral lines having a defined width are derived from the modulated NMR signal."


"The broadening is measured and the contribution of the spectral line width due to the electrical activity is then determined. This provides a measurement of the neuron discharge current flux in the brain" or in other words "the electrical activity of the brain".


"The physical factors broadening the NMR lines are many and discussions concerning their contributions to the overall spectral line width are available in the literature. The main factors are connected with relaxation processes: spin-lattice and spin-spin characterized by characteristic time constants T1 and T2 respectively. These time constants are indicative of the average time the nucleus retains its polarization and it can be shown that for tissues like grey matter of the brain T2 is much shorter than T1 and thus provides a major contribution to the line width Δf.

Δf=1/(π T2)  

For a T2 value in the vicinity of 100 ms the line width is about 3 Hz." 



Combination of NMR and ESR in electron nuclear double resonance (ENDOR)


"A radio frequency (RF) pulse is applied via RF coils to excite to resonance a plurality of nuclear spins producing an NMR signal. A microwave (MW) pulse is applied via a high frequency resonator or radiator to excite to resonance a plurality of electron spins within the sample." (This produces an ESR signal). "The RF and MW pulses simultaneously resonate the nuclear and electron spins within the sample. The intensity of the MW signal is modulated, which translates into a modulation of the intensity of the NMR signal. The modulation is extracted from the NMR signal to produce an image representative of the local ESR (...)".


"There are two methods of establishing a very high frequency magnetic field which will satisfy conditions of ESR resonance in the principal field of the NMR imager. The ratio of ESR to NMR excitation frequencies which must be satisfied by the same principal field is in the range of 600 to 700. Preferably the ratio is equal to γe/γn =657." 


"An important factor is the choice of the ESR frequency. The sensitivity of the NMR readout increases with the intensity of the principal field. The imagers with the lowest magnetic field operate around B=0.03 T which corresponds to the NMR frequency for protons of 1.28 MHz and to the ESR frequency of 839 MHz. According to published data the (1/e) penetration depth at this frequency is 3.1 cm in the tissues with high water content and 20 cm in tissues with minimal water content (Radiofrequency Electromagnetic fields, NCRP Report 67, Wash., 1981). Thus, it may be possible to reach parts of the cerebral cortex and some other superficial structures, by means of surface coils. It may be possible to update the imager at a field lower than 0.03 T to remedy the penetration difficulties, however, sensitivity of the present method may be compromised. The unknown factor is the intensity of the very high frequency field that can be induced in the body in vivo. For this reason the ESR frequency source should operate with very narrow, high amplitude bursts of power, so that the average power level is tolerable."



Theoretical background


"Nuclei with a total magnetic moment μ placed in a magnetic field H(m) have an interaction energy described by the Hamiltonian:
Ĥ = μ H(m)

Assuming the field to be in the z-direction, the eigenvalues of energy are
E=γ(p)* ħ * H(z) * m       with  m = I,I-1,...,-I
where h=Planck's constant and m=angular momentum


For hydrogen I=1/2 and m =1/2 , a -1/2 transition between these two states has an energy of

ΔE= γ(p)* ħ * H(z)

or frequency associated with transition

ω = 2πf = γ(p) * H(z)


The factor γ(p) (note: gyromagnetic ratio) for hydrogen nucleus (proton) is equal to 2.6753 * 10^8 radian sec^-1 Tesla^-1. For a single electron in external magnetic field (spin S=1/2) the same formalism holds, but the gyromagnetic factor γ(e) is equal to 1.7576 * 10^8 radian sec^-1 Tesla^-1 or 657 times higher, owing to the much lesser mass of electron. 


In a hydrogen atom we have a nucleus with spin I=1/2 coupled to an electron with a spin of S=1/2." The Hamiltonian for such system is

H= γ(e)* ħ * H(z) * S(z) + AI.S - γ(n)* ħ * H(z) * I(z)

where A is a measure of coupling between the two spins. The expression is valid for the electron in the ground i.e. non-excited state.


In so called strong field approximation i.e. when  * S(z) + AI.S - γ(n)* h * H(z) * I(z) the Hamiltonian becomes 
H= γ(e)* ħ * H(z) * S(z) + AI.S - γ(n)* ħ * H(z) * I(z)(6) 

and the energy eigenvalues are then 

E=γ* ħ * H(z) * M + A m(I) m (S) -  γ(n)* ħ * H(z) m(I) m (S)= +-1/2 m(I) = +-1/2

There are four possible transitions in such a system, which are shown in FIG. 2. Symbol +- means ms =+1/2, mτ =-1/2 etc.


FIG. 2 is an energy level diagram showing the allowed transitions for an hydrogen atom in an external magnetic field H(z). 


The resonant frequencies for electronic and nuclear transitions are correspondingly:
We = γ(e)Hz + A/h MI
Wn = γ(n)Hz + A/h MS


There exists an Overhauser-Pound Family of Double Resonances (ref). In the nuclear Overhauser effect, one observes the change in the integrated intensity of the NMR absorption of a nuclear spin as a result of the concurrent saturation of another NMR resonance.


FIG. 3 shows an energy level diagram for S=1/2 and I=1/2 showing the transitions being `pumped` or excited and observed transitions. We and Wn are nuclear and electronic relaxations. 


In Electron Nuclear Double Resonance (ENDOR) transitions 1-2 or 4-3 are pumped. In Electron Electron Double Resonance (ELDOR) transition 2-3 is pumped. The observed transition is 4-1. In the simple NMR the same transition is excited and its relaxation observed (4-3) or (1-2). If in addition another transition (e.g. 2-3 or 1-4) is excited, than the intensity of levels will be changed and change in intensity and apparent change in the relaxation rate will manifest itself in the monitored NMR transition, so if the ESR `pumping` generator is amplitude modulated including pulsing on and off, this modulation will be transferred to the NMR signal. The limiting case of amplitude modulation is on-off pulsing. It may be expected that if the ESR pumping generator is frequency modulated instead of amplitude modulated, and if the frequency deviation is sufficiently high, it will have the same effect on the NMR signal."



Figure: Please refer to legends mentioned on the image.

Line width of NMR signal


Excerpts from | - Link posted by Dr. Robert Duncan

"NMR lines are extraordinarily sharp, and extraordinarily close together (in energetic terms) compared to higher energy spectroscopic methods. So much so that Heisenberg uncertainty broadening (which is a function of lifetime of a given energy state, and hence relaxation rates) is a dominant feature of many NMR spectra, and can limit our ability to measure and interpret spectra. When relaxation is very fast, NMR lines are broad, J-coupling may not be resolved or the signal may even be difficult or impossible to detect."
"We distinguish two types of relaxation, Spin-Lattice (T1, also known as longitudinal relaxation, or relaxation in the z-direction) and Spin-Spin (T2, also known as transverse relaxation, or relaxation in the x-y plane)."
"The line width of an NMR signal is determined by T2 - short T2 means broader lines (ν1/2 = 1/πT2, ν1/2 = width at half height)."
T1 Relaxation (Spin-Lattice Relaxation): gain and loss of magnetization in the z-direction. NMR lines are at least as wide as specified by the Heisenberg Uncertainty Principle broadening due to inherent lifetime of spin states (the actual width is governed by T2).
ΔE Δt = h/2π
hδν δt = h/2π
ν½/2 >= 1/2πT1 (Half-width at half height)
ν½ >= 1/πT1 (Width at half height)
T2 Relaxation (Spin-Spin Relaxation): Heisenberg Uncertainty Principle broadening due to lifetime of spin coherence - gain and loss of magnetization in the x,y-direction.
ν½ = 1/π T2 T2 < = T1
For protons, T2 is usually between 1 and 10 seconds
T2 = 1 sec, ν½ = 1/π = 0.3 Hz
T2 = 10 sec, ν½ = 1/10 π = 0.03 Hz



As mentioned in Wikipedia, "an atomic transition is associated with a specific amount of energy, E. However, when this energy is measured by means of some spectroscopic technique, the line is not infinitely sharp, but has a particular shape. Numerous factors can contribute to the broadening of spectral lines. A principal source of broadening is lifetime broadening. According to the uncertainty principle the uncertainty in energy, ΔE and the lifetime, Δt, of the excited state are related by:

ΔE Δt ≦ ћ

This determines the minimum possible line width. As the excited state decays exponentially in time this effect produces a line with Lorentzian shape in terms of frequency (or wavenumber) (Figure 11).


A Lorentzian line shape function can be represented as


where L signifies a Lorentzian function standardized, for spectroscopic purposes, to a maximum value of 1; x is a subsidiary variable defined as


where p0 is the position of the maximum (corresponding to the transition energy E), p is a position, and w is the full width at half maximum (FWHM), the width of the curve when the intensity is half the maximum intensity (this occurs at the points p = p0±w/2). The unit of p0, p and w is typically wavenumber or frequency. The variable x is dimensionless and is zero at p=p0.


Figure 11: Comparison of Gaussian (red) and Lorentzian (blue) standardized line shapes. The HWHM (w/2) is 1. From Wikipedia.


The shape of lines in a nuclear magnetic resonance (NMR) spectrum is determined by the process of free induction decay. This decay is approximately exponential, so the line shape is Lorentzian.[10] This follows because the Fourier transform of an exponential function in the time domain is a Lorentzian in the frequency domain. In NMR spectroscopy the lifetime of the excited states is relatively long, so the lines are very sharp, producing high-resolution spectra.




Spatial Encoding and Frequency Encoding in Magnetic Resonance


Spatial encoding
1. Differences in frequency. (Magnetic field gradients)
2. Differences in phase.
3. Differences in signal timing.
4. Distance from receiver coils
Frequency Encoding

Nuclear Magnetic Resonance can by performed in high-field, low-field including Earth's-field and zero-field


Low field NMR: | Earth's-field NMR (EFNMR):

"The earth's magnetic field is very small (~50 μT) and so the resonance frequencies are likewise very low (just a little over 2000 Hz for hydrogen). MRI and MRS have both been performed using only the earth's magnetic field."

Zero-field NMR:

One implementation of zero-field NMR is the use of atomic magnetometers or optically pumped magnetometers with rubidium vapor cells. Recently an MRI portable helmet was announced which was also cited in the NIH director's blog.

Note: Cf. Nuclear quadrupole resonance
(currently investigated for the detection of explosives)



Low-field MRI uses hyperpolarization


A main factor determining signal quality in MRI is the signal-to-noise ratio (SNR) which is proportional to nuclear spin alignment or polarization.


High-field MRI uses increased magnetic field strength to this purpose, while low-field MRI uses different "hyperpolarization schemes" which increase polarization by orders of magnitude. 
(Note that equilibrium nuclear spin polarization is only 10^-6 (1 in a million spins) to 10^-5 at conditions of human body temperature and B0 of several Tesla.)


For hyperpolarization please refer to One hyperpolarization technique is "spin-exchange optical pumping" where optical pumping of an alkali (e.g. rubidium) is mediated by circularly polarized light and the excited electrons transfer angular momentum to a noble gas like He and Xe.


Another hyperpolarization technique is "dynamic nuclear polarization" which consists of the transfer of spin polarization from an electron to a nucleus, thereby aligning the nucleus spin to the measure that the electron spin is aligned. Polarization transfer necessitates continuous microwave irradiation at a frequency close to the electron paramagnetic resonance (EPR) frequency. Mechanisms for the microwave-driven DNP processes are: the Overhauser effect (OE), the solid-effect (SE), the cross-effect (CE) and thermal-mixing (TM).




Zero-Field Magnetometer

"Light from a precisely tuned semiconductor laser (1) passes through a glass vapor cell containing rubidium atoms (2) and is captured by a photodetector (3). When the background magnetic field is equal to zero, the rubidium atoms become largely transparent. A magnetic field in a direction perpendicular to the light path causes the atoms absorb more light. The photodetector senses this change in transparency and produces an electric current proportional to the light transmitted through the vapor cell."
Excitation/Absorption === Less Transmittance/transparency

Brain MRI in Ultra-Low Field (ULF) of 6.5 mT using balanced Steady-State-Free-Precession" (b-SSFP)* sequences


Facebook link


NMR/ESR magnetogyric ratios and calculation of NMR/ESR frequencies for magnetic field of central France (0.000047 Tesla)

Google spreasheet link:


Combination of the following sources:

1. NMR Frequency Tables Bruker (page 8)
2. Wikipedia
3. Hyperphysics


It is suggested for convenience to hide the columns with the mention "Gyromagnetic ratio" referring to Wikipedia and Hyperphysics after having taken notice of them.


Note: The correct term according to IUPAC is "Magnetogyric ratio" as this refers to the ratio of the magnetic moment to the angular momentum

(image is from Excel spreadsheet)


Figure: NMR/ESR Magnetogyric ratios and frequencies

Biological systems reacting to electromagnetic field combinations which satisfy magnetic resonance conditions

First indications that a biological system might be sensitive to NMR conditions wereprovided by results of dielectrophoresis measurements.
Measurements of permittivity in suspensions of yeast cells demonstrate sharp peaks upon NMR conditions for ions H, P, Na, Cl, and K and also upon ESR (Electron Spin Resonance) conditions
Examples presented at paper of this link
a. dielectrophoresis; b. dielectric permittivity c. generation time (cell growth); d. reduced cell size, increased cell number, no change in total cell mass; e. enzyme-substrate reaction.
Please refer to a similar scientific report freely available at this link
Note the you can use the spreadsheet that was posted previously to calculate the resonance frequencies for 0,00005 Tesla as shown in picture.
Related reference:
Excerpt: "The proton NMR condition represents a very sharply defined resonance condition whereby energy can be inserted into a living system in a very specific manner".


Figure: Measurements of permittivity in suspensions of yeast cells for different ions. Table for calculation of resonant frequencies.



Some definitions:


CONDUCTOR: A conductor is an object or material that allows the flow of electrical current.



INSULATOR: An electrical insulator is a material that does not allow the flow of electric current. Its internal electric charges do not flow freely under the influence of an electric field. The property that distinguishes an insulator is resistivity.



DIELECTRIC: A dielectric is an electrical insulator which does not allow flow of electric charges but only a slight shift from their average equilibrium positions (displacement current) causing dielectric polarization.


ELECTRIC SUSCEPTIBIITY: "The electric susceptibility χ(e) of a dielectric material is a measure of how easily it polarizes in response to an electric field. This, in turn, determines the electric permittivity of the material."


PERMITTIVITY & RELATIVE PERMITTIVITY: "Permittivity is a material property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum."

Dielectric constant is the historical term for relative permittivity.


"Permittivity ε "is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium."


The vacuum permittivity ε0 (also called permittivity of free space or the electric constant) appears in the Coulomb force constant.




Ion magnetic resonance in biological systems due to power lines

From the book "The Body Electric" by Robert Becker (Author), Gary Selden (Contributor) p.297: "In simplified terms, nuclear magnetic resonance is present when the magnetic fields around atomic nuclei are induced to vibrate in unison. The phenomenon requires two external magnetic fields, one steady and one pulsating. For every chemical element, the oscillating field at a specific frequency will induce resonance within the steady-state field at a certain strength."
"In 1983 a research team under A. H. Jafary-Asl showed that the earth's magnetic background could serve as the steady field, while the harmonics of power line frequencies could produce a time-varying field that would induce nuclear magnetic resonance in at least two common atoms of living tissue—potassium and chlorine. Other elements might also be susceptible to the effect. Bacteria and yeast cells exposed to these NMR conditions doubled their rate of DNA synthesis and proliferation, but daughter cells were half size."
p.296 "The Navy has found stronger fields near its 76-H3 ELF antenna and reradiated at that frequency from a power line a mile away."
p.326 "Satellite measurements have proven that artificial energies from power lines are similarly amplified high above the earth, a phenomenon known as power-line harmonic resonance (PLHR)."

"Ion Forced-Oscillation Mechanism": EMF-induced forced-oscillation of ions can influence channel gating

"A review of the whole EMF-bioeffects literature reveals that the most bioactive EMFs are the lower frequency ones, especially the ELF fields (Goodman et al. 1995). Moreover its is shown that pulsed EMFs are more bioactive than continuous fields of the same rest characteristics (...). The pulse repetition frequency is always a low frequency, most usually ELF. We argue that the reason for the intense bioactivity of modern low-intensity microwave fields is most likely the ELF pulsing and modulation frequencies they include and not the RF carrier wave itself."
"Polarized man-made EMFs/EMR will induce a coherent and parallel forced-oscillation on every charged/polar molecule withing biological tissue."
"A forced-oscillation of mobile ions, induced by an external polarized EMF can result in irregular gating of electrosensitive ion channels on the cell membranes. That was described in detail in Panagopoulos et al (2000a, 2002). According to this theory - the plausibility of which in actual biological conditions was verified by numerical test (Halgamuge and Abeyrathne 2011) - the forced-oscillation of ions in the vicinity of the voltage-sensors of voltage-gated ion channels can exert forces on these sensors equal to or greater than the forces known to physiologically gate these channels."
"Irregular gating of these channels can potentially disrupt any cell's electrochemical balance and function (Alberts et al. 1994), leading to a variety of biological/health effects including the most detrimental ones, such as DNA damage, cell death or cancer (Pall 2013, 2015).
"Most cation channels (Ca+2, K+, Na+, etc) on the membranes of all animal cells, are voltage-gated, or as they are usually called, "electrosensitive" (Alberts et al. 1994)".
"Microwave Effects on DNA and Proteins" - edited by C.D. Geddes
Excerpt from Chapter 1 authored by D.J. Panagopoulos







The discovery of the Calcium-Efflux effect


Extremely weak VHF fields (147 MHz, 1-2 mW/cm^2) amplitude modulated at 6 Hz, 9 Hz, 11 Hz and 16 Hz lead to progressive increase in 45Ca2+ efflux from brains. These effects gradually decline at higher frequencies. (Attached figure)


Bawin SM, Kaczmarek LK, Adey WR. Effects of modulated VHF fields on the central nervous system. Ann N Y Acad Sci. 1975;247:74-81.|



Previously, it had been shown that extremely weak VHF fields (147 MHz, 1 mW/cm^2) amplitude modulated at low frequencies (cf. "brain wave frequencies") strongly influenced spontaneous and conditioned EEG patterns in the cat (Bawin S thesis, 1972, Bawin S et al 1973).


Notes and following excerpts of post from the book "Biological and Medical Aspects of Electromagnetic Fields" edited by Greenebaum B. and Barnes F.

Chapter 9 "The Ion Cyclotron Resonance Hypothesis" authored by Liboff. A.R. (p.298)


The observed calcium-efflux signature, "at first referred to as a "window", has the appearance of a resonance curve."


"The Blackman experiment [12] discovered that this resonance signature appeared only when certain specific values of the vertical DC magnetic field were superposed on the system".


[12] Blackman CF, Benane SG, Rabinowitz JR, House DE, Joines WT. A role for the magnetic field in the radiation-induced efflux of calcium ions from brain tissue in vitro. Bioelectromagnetics. 1985;6(4):327-37.


The term "Ion Cyclotron Resonance" (ICR) "was originally invoked [4] to explain an extraordinary set of observations by Blackman's group [12] indicating a strong dependence on the orientation of the magnetostatic field when studying the Ca-efflux model system [13*]."


[4] Liboff. A.R., Geomagnetic Cyclotron Resonance in Living Cells


*first reference



Excerpt from:;jsessionid=304AFAE8518463164762EA2FC8065402?doi=


"More detailed testing of ELF frequencies between 1 and 510 Hz have shown a series of frequency windows of effects, separated by no-effect frequencies (Figure 3). It was subsequently shown that both the intensity (Figure 4) and the orientation of the earth's magnetic field during exposure can alter effects at specific frequencies. These results led to the development of ion resonance models and tests of their predictions (Blackman, 1985; Liboff, 1985)."




"Science: How magnetic fields could upset your ions"




The Ion Cyclotron Resonance (ICR) hypothesis for biological systems


"The ICR hypothesis holds that the physiological activity of those ions implicated in cell signaling processes, including, among others, Ca2+, Mg2+, and K+, can be altered when the ratio of applied signal frequency to the static magnetic field is equal to the ionic charge-to-mass ratio. This is expressed as 

ω/B = q/m (Equation 9.1)

where the radial frequency ω = 2πf, as measured in radians per second, is used instead of f, the frequency measured in hertz."


"The ICR hypothesis has especial significance attached to magnetostatic fields whose intensity is of the order of the GMF (geomagnetic field) (20-60 μT). This becomes apparent when the charge-to-mass ratios of key biological ions are substituted into Equation 9.1. These ratios range from about 2 to 8 x 10^6 C/Kg, implying that a static magnetic field of 50 μT corresponds to resonance frequencies in the order of 10-100 Hz (Figure 9.1)." 


"Such frequencies could conceivably have physiological significance since they correspond to approximately to the frequency range generated in the central nervous system [1]. This, coupled to the focus on the potential hazards attached to 50/60 Hz electromagnetic power delivery sources [2], has sparked study of the ICR hypothesis, in terms of both experiments specifically designed to test this hypothesis as well as theoretical models seeking an explanatory basis at the molecular level."


"Because of constraints mainly arising form unfavorable damping conditions, there are strong arguments [4] against the occurrence in living tissue of any classical ICR mechanism [5] as occurs, say, for energetic charged particles moving in a vacuum under the influence of a parallel static and AC magnetic fields. The circular and helical paths associated with such undamped motion are invariably the result of the Lorentz force, which imparts an acceleration a to a charged particle of mass m moving at velocity v in a magnetic field B:


a=(q/m) (v x B)


Nevertheless, arguments have been raised [6-11] that although the biological response may not correspond to the effects resulting from ICR-specific helical pathways of charged particles [4], the coupling is nevertheless a function of the ICR frequency as predicted by Equation 9.1."



Excerpts from the book "Biological and Medical Aspects of Electromagnetic Fields" edited by Greenebaum B. and Barnes F.
Chapter 9 "The Ion Cyclotron Resonance Hypothesis" authored by Liboff. A.R. (p.298)





Additional reference on "Nuclear magnetic and cyclotronic resonances" at this link.


Effects of electromagnetic radiation - Effects of cell phones at this link.