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. Following this, the radiofrequency pulse is stopped. In the absence of the B1 torque, the net magnetisation will decay towards the z direction and electromagnetic energy will be released/emitted. The emitted electromagnetic energy will be captured by a coil, thereby providing a magnetic resonance signal. The decay or dephasing of the transverse magnetization Mxy is termed T2 relaxation or "spin-spin relaxation".
Net Magnetization (M) - What is net magnetization and how does it apply to NMR? http://mriquestions.com/net-magnetization-m.html
How Magnetization Develops - Does the net magnetization (M) just instantly appear? http://mriquestions.com/does-m-instantly-appear.html
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."
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.
Where does the MR signal come from? http://mriquestions.com/origin-of-mr-signal.html
What is a free induction decay (FID)? http://mriquestions.com/free-induction-decay.html
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"
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 http://mriquestions.com/stimulated-echoes.html 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.
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 http://mriquestions.com/tr-and-te.html
Gradient Echo (GRE) - What is a gradient echo, and how does it differ from an FID? http://mriquestions.com/gradient-echo.html
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? http://mriquestions.com/se-vs-multi-se-vs-fse.html
Please refer to this image as reference:
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.
"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.
"Feasibility of developing a method of imaging neuronal activity in the human brain: a theoretical review" by Holder D.S. https://link.springer.com/article/10.1007/BF02442813
"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) https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5187897
“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 https://www.google.com/patents/US4719425
"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."
"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.
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."
"Nuclei with a total magnetic moment μ placed in a magnetic field H(m) have an interaction energy described by the Hamiltonian:
H = μ H(m)
Assuming the field to be in the z-direction, the eigenvalues of energy are
E=γ(p)* h * H(z) * m m = I,I-1,...,-I
where h=Planck's constant and m=angular momentum
For hydrogen I=1/2 and m =1/2 , -1/2 transition between these two states has an energy of
ΔE= γ(p)* h * 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)* h * H(z) * S(z) + AI.S - γ(n)* h * 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)* h * H(z) * S(z) + AI.S - γ(n)* h * H(z) * I(z)(6)
and the energy eigenvalues are then
E=γ* h * H(z) * M + A m(I) m (S) - γ(n)* h * 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.
Google spreasheet link: http://bit.ly/2S3mMWA
Combination of the following sources:
1. NMR Frequency Tables Bruker http://kodu.ut.ee/~laurit/AK2/NMR_tables_Bruker2012.pdf (page 8)
2. Wikipedia https://en.wikipedia.org/wiki/Gyromagnetic_ratio
3. Hyperphysics http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/nmr.html
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 http://bit.ly/2EbnnC7
(image is from Excel spreadsheet)
Figure: Measurements of permittivity in suspensions of yeast cells for different ions. Table for calculation of resonant frequencies.
CONDUCTOR: A conductor is an object or material that allows the flow of electrical current. https://en.wikipedia.org/wiki/Electrical_conductor
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. https://en.wikipedia.org/wiki/Dielectric
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." https://en.wikipedia.org/wiki/Relative_permittivity
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." https://en.wikipedia.org/wiki/Permittivity
The vacuum permittivity ε0 (also called permittivity of free space or the electric constant) appears in the Coulomb force constant.
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  discovered that this resonance signature appeared only when certain specific values of the vertical DC magnetic field were superposed on the system".
 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. https://www.ncbi.nlm.nih.gov/pubmed/3836676
The term "Ion Cyclotron Resonance" (ICR) "was originally invoked  to explain an extraordinary set of observations by Blackman's group  indicating a strong dependence on the orientation of the magnetostatic field when studying the Ca-efflux model system [13*]."
 Liboff. A.R., Geomagnetic Cyclotron Resonance in Living Cells https://www.researchgate.net/publication/329881265_Geomagnetic_Cyclotron_Resonance_in_Living_Cells
"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 . This, coupled to the focus on the potential hazards attached to 50/60 Hz electromagnetic power delivery sources , 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  against the occurrence in living tissue of any classical ICR mechanism  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 , 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)