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The physics of magnetic resonance imaging (MRI) concerns fundamental
physical Physical may refer to: * Physical examination, a regular overall check-up with a doctor * ''Physical'' (Olivia Newton-John album), 1981 ** "Physical" (Olivia Newton-John song) * ''Physical'' (Gabe Gurnsey album) * "Physical" (Alcazar song) (2004) * ...
considerations of MRI techniques and technological aspects of MRI devices. MRI is a
medical imaging Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to re ...
technique mostly used in
radiology Radiology ( ) is the medical discipline that uses medical imaging to diagnose diseases and guide their treatment, within the bodies of humans and other animals. It began with radiography (which is why its name has a root referring to radiat ...
and
nuclear medicine Nuclear medicine or nucleology is a medical specialty involving the application of radioactive substances in the diagnosis and treatment of disease. Nuclear imaging, in a sense, is " radiology done inside out" because it records radiation emi ...
in order to investigate the anatomy and physiology of the body, and to detect pathologies including tumors,
inflammation Inflammation (from la, inflammatio) is part of the complex biological response of body tissues to harmful stimuli, such as pathogens, damaged cells, or irritants, and is a protective response involving immune cells, blood vessels, and molec ...
, neurological conditions such as
stroke A stroke is a disease, medical condition in which poor cerebral circulation, blood flow to the brain causes cell death. There are two main types of stroke: brain ischemia, ischemic, due to lack of blood flow, and intracranial hemorrhage, hemorr ...
, disorders of muscles and joints, and abnormalities in the heart and blood vessels among others.
Contrast agents A contrast agent (or contrast medium) is a substance used to increase the contrast of structures or fluids within the body in medical imaging. Contrast agents absorb or alter external electromagnetism or ultrasound, which is different from radioph ...
may be injected
intravenously Intravenous therapy (abbreviated as IV therapy) is a medical technique that administers fluids, medications and nutrients directly into a person's vein. The intravenous route of administration is commonly used for rehydration or to provide nutrie ...
or into a joint to enhance the image and facilitate diagnosis. Unlike CT and
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10  nanometers, corresponding to frequencies in the range 30&nb ...
, MRI uses no
ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of subatomic particles or electromagnetic waves that have sufficient energy to ionize atoms or molecules by detaching electrons from them. Some particles can travel ...
and is, therefore, a safe procedure suitable for diagnosis in children and repeated runs. Patients with specific non-ferromagnetic metal implants,
cochlear implant A cochlear implant (CI) is a surgically implanted neuroprosthesis that provides a person who has moderate-to-profound sensorineural hearing loss with sound perception. With the help of therapy, cochlear implants may allow for improved speech unde ...
s, and cardiac pacemakers nowadays may also have an MRI in spite of effects of the strong magnetic fields. This does not apply on older devices, and details for medical professionals are provided by the device's manufacturer. Certain
atomic nuclei The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...
are able to absorb and emit
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
energy when placed in an external
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. In clinical and research MRI,
hydrogen atom A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen cons ...
s are most often used to generate a detectable radio-frequency signal that is received by antennas in close proximity to the anatomy being examined. Hydrogen atoms are naturally abundant in people and other biological organisms, particularly in
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
and fat. For this reason, most MRI scans essentially map the location of water and fat in the body. Pulses of radio waves excite the
nuclear spin In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe ...
energy transition, and magnetic field gradients localize the signal in space. By varying the parameters of the
pulse sequence In Fourier transform NMR spectroscopy and imaging, a pulse sequence describes a series of radio frequency pulses applied to the sample, such that the free induction decay is related to the characteristic frequencies of the desired signals. Afte ...
, different contrasts may be generated between tissues based on the relaxation properties of the hydrogen atoms therein. When inside the magnetic field (''B''0) of the scanner, the
magnetic moments In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagn ...
of the protons align to be either parallel or anti-parallel to the direction of the field. While each individual proton can only have one of two alignments, the collection of protons appear to behave as though they can have any alignment. Most protons align parallel to ''B''0 as this is a lower energy state. A
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
pulse is then applied, which can excite protons from parallel to anti-parallel alignment, only the latter are relevant to the rest of the discussion. In response to the force bringing them back to their equilibrium orientation, the protons undergo a rotating motion (
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...
), much like a spun wheel under the effect of gravity. The protons will return to the low energy state by the process of spin-lattice relaxation. This appears as a
magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ...
, which yields a changing voltage in receiver coils to give the signal. The frequency at which a proton or group of protons in a
voxel In 3D computer graphics, a voxel represents a value on a regular grid in three-dimensional space. As with pixels in a 2D bitmap, voxels themselves do not typically have their position (i.e. coordinates) explicitly encoded with their values. I ...
resonates depends on the strength of the local magnetic field around the proton or group of protons, a stronger field corresponds to a larger energy difference and higher frequency photons. By applying additional magnetic fields (gradients) that vary linearly over space, specific slices to be imaged can be selected, and an image is obtained by taking the 2-D
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed ...
of the spatial frequencies of the signal ( ''k''-space). Due to the magnetic
Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
from ''B''0 on the current flowing in the gradient coils, the gradient coils will try to move producing loud knocking sounds, for which patients require hearing protection.


History

The MRI scanner was developed from 1975 to 1977 at the
University of Nottingham , mottoeng = A city is built on wisdom , established = 1798 – teacher training college1881 – University College Nottingham1948 – university status , type = Public , chancellor ...
by Prof Raymond Andrew FRS FRSE following from his research into
nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
. The full body scanner was created in 1978.


Nuclear magnetism

Subatomic particles have the
quantum mechanical Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
property of
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally ...
. Certain nuclei such as 1 H (
protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron m ...
), 2H, 3 He, 23 Na or 31 P, have a non–zero spin and therefore a
magnetic moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electroma ...
. In the case of the so-called spin- nuclei, such as 1H, there are two spin states, sometimes referred to as ''up'' and ''down''. Nuclei such as 12 C have no unpaired
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
s or protons, and no net spin; however, the
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass num ...
13C does. When these spins are placed in a strong external
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
they
precess Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
around an axis along the direction of the field. Protons align in two energy eigenstates (the
Zeeman effect The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel pr ...
): one low-energy and one high-energy, which are separated by a very small splitting energy.


Resonance and relaxation

Quantum mechanics is required to accurately model the behaviour of a single proton. However,
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
can be used to describe the behaviour of an ensemble of protons adequately. As with other spin 1/2 particles, whenever the spin of a single proton is measured it can only have one of two results commonly called parallel and anti-parallel. When we discuss the state of a proton or protons we are referring to the
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
of that proton which is a linear combination of the parallel and anti-parallel states. In the presence of the magnetic field, B0, the protons will appear to precess at the Larmor frequency determined by the particle's gyro-magnetic ratio and the strength of the field. The static fields used most commonly in MRI cause precession which corresponds to a
radiofrequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upper ...
(RF)
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
. The net longitudinal magnetization in
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
is due to a tiny excess of protons in the lower energy state. This gives a net polarization that is parallel to the external field. Application of an RF pulse can tip this net polarization vector sideways (with, i.e., a so-called 90° pulse), or even reverse it (with a so-called 180° pulse). The protons will come into phase with the RF pulse and therefore each other. The recovery of longitudinal magnetization is called longitudinal or ''T''1 relaxation and occurs exponentially with a time constant ''T''1. The loss of phase coherence in the transverse plane is called transverse or ''T''2 relaxation. ''T''1 is thus associated with the
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
of the spin system, or the number of nuclei with parallel versus anti-parallel spin. ''T''2 on the other hand is associated with the
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
of the system, or the number of nuclei in phase. When the radio frequency pulse is turned off, the transverse vector component produces an oscillating magnetic field which induces a small current in the receiver coil. This signal is called the free induction decay (FID). In an idealized
nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
experiment, the FID decays approximately exponentially with a time constant ''T''2. However, in practical MRI there are small differences in the static magnetic field at different spatial locations ("inhomogeneities") that cause the Larmor frequency to vary across the body. This creates
destructive interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, which shortens the FID. The time constant for the observed decay of the FID is called the ''T'' relaxation time, and is always shorter than ''T''2. At the same time, the longitudinal magnetization starts to recover exponentially with a time constant ''T''1 which is much larger than ''T''2 (see below). In MRI, the static magnetic field is augmented by a field gradient coil to vary across the scanned region, so that different spatial locations become associated with different precession frequencies. Only those regions where the field is such that the precession frequencies match the RF frequency will experience excitation. Usually, these field gradients are modulated to sweep across the region to be scanned, and it is the almost
infinite Infinite may refer to: Mathematics * Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (group), a South Korean boy band *''Infinite'' (EP), debut EP of American m ...
variety of RF and gradient pulse sequences that gives MRI its versatility. Change of field gradient spreads the responding FID signal in the frequency domain, but this can be recovered and measured by a refocusing gradient (to create a so-called "gradient echo"), or by a radio frequency pulse (to create a so-called " spin-echo"), or in digital post-processing of the spread signal. The whole process can be repeated when some ''T''1-relaxation has occurred and the
thermal equilibrium Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
of the spins has been more or less restored. The repetition time (TR) is the time between two successive excitations of the same slice. Typically, in
soft tissue Soft tissue is all the tissue in the body that is not hardened by the processes of ossification or calcification such as bones and teeth. Soft tissue connects, surrounds or supports internal organs and bones, and includes muscle, tendons, ...
s ''T''1 is around one second while ''T''2 and ''T'' are a few tens of milliseconds. However, these values can vary widely between different tissues, as well as between different external magnetic fields. This behavior is one factor giving MRI its tremendous soft tissue contrast.
MRI contrast agent MRI contrast agents are contrast agents used to improve the visibility of internal body structures in magnetic resonance imaging (MRI). The most commonly used compounds for contrast enhancement are gadolinium-based. Such MRI contrast agents shorten ...
s, such as those containing
Gadolinium Gadolinium is a chemical element with the symbol Gd and atomic number 64. Gadolinium is a silvery-white metal when oxidation is removed. It is only slightly malleable and is a ductile rare-earth element. Gadolinium reacts with atmospheric oxygen ...
(III) work by altering (shortening) the relaxation parameters, especially ''T''1.


Imaging


Imaging schemes

A number of schemes have been devised for combining field gradients and radio frequency excitation to create an image: * 2D or 3D reconstruction from projections, such as in computed tomography. * Building the image point-by-point or line-by-line. * Gradients in the RF field rather than the static field. Although each of these schemes is occasionally used in specialist applications, the majority of MR Images today are created either by the two-dimensional
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed ...
(2DFT) technique with slice selection, or by the three-dimensional Fourier transform (3DFT) technique. Another name for 2DFT is spin-warp. What follows here is a description of the 2DFT technique with slice selection. The 3DFT technique is rather similar except that there is no slice selection and phase-encoding is performed in two separate directions.


Echo-planar imaging

Another scheme which is sometimes used, especially in
brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...
scanning or where images are needed very rapidly, is called echo-planar imaging (EPI): In this case, each RF excitation is followed by a train of gradient echoes with different spatial encoding. Multiplexed-EPI is even faster, e.g., for whole brain functional MRI (fMRI) or
diffusion MRI Diffusion-weighted magnetic resonance imaging (DWI or DW-MRI) is the use of specific MRI sequences as well as software that generates images from the resulting data that uses the diffusion of water molecules to generate contrast in MR images. It ...
.


Image contrast and contrast enhancement

Image contrast is created by differences in the strength of the NMR signal recovered from different locations within the sample. This depends upon the relative density of excited nuclei (usually
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
protons), on differences in relaxation times (''T''1, ''T''2, and ''T'') of those nuclei after the pulse sequence, and often on other parameters discussed under specialized MR scans. Contrast in most MR images is actually a mixture of all these effects, but careful design of the imaging pulse sequence allows one contrast mechanism to be emphasized while the others are minimized. The ability to choose different contrast mechanisms gives MRI tremendous flexibility. In the brain, ''T''1-weighting causes the nerve connections of
white matter White matter refers to areas of the central nervous system (CNS) that are mainly made up of myelinated axons, also called tracts. Long thought to be passive tissue, white matter affects learning and brain functions, modulating the distribu ...
to appear white, and the congregations of
neuron A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa ...
s of
gray matter Grey matter is a major component of the central nervous system, consisting of neuronal cell bodies, neuropil (dendrites and unmyelinated axons), glial cells (astrocytes and oligodendrocytes), synapses, and capillaries. Grey matter is distingui ...
to appear gray, while cerebrospinal fluid (CSF) appears dark. The contrast of white matter, gray matter and cerebrospinal fluid is reversed using ''T''2 or ''T'' imaging, whereas proton-density-weighted imaging provides little contrast in healthy subjects. Additionally, functional parameters such as cerebral blood flow (CBF), cerebral blood volume (CBV) or
blood oxygenation Pulse oximetry is a noninvasive method for monitoring a person's oxygen saturation. Peripheral oxygen saturation (SpO2) readings are typically within 2% accuracy (within 4% accuracy in 95% of cases) of the more accurate (and invasive) reading ...
can affect ''T''1, ''T''2, and ''T'' and so can be encoded with suitable pulse sequences. In some situations it is not possible to generate enough image contrast to adequately show the
anatomy Anatomy () is the branch of biology concerned with the study of the structure of organisms and their parts. Anatomy is a branch of natural science that deals with the structural organization of living things. It is an old science, having i ...
or
pathology Pathology is the study of the causes and effects of disease or injury. The word ''pathology'' also refers to the study of disease in general, incorporating a wide range of biology research fields and medical practices. However, when used in ...
of interest by adjusting the imaging parameters alone, in which case a
contrast agent A contrast agent (or contrast medium) is a substance used to increase the contrast of structures or fluids within the body in medical imaging. Contrast agents absorb or alter external electromagnetism or ultrasound, which is different from radiop ...
may be administered. This can be as simple as
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
, taken orally, for imaging the stomach and small bowel. However, most contrast agents used in MRI are selected for their specific magnetic properties. Most commonly, a
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, ...
contrast agent (usually a
gadolinium Gadolinium is a chemical element with the symbol Gd and atomic number 64. Gadolinium is a silvery-white metal when oxidation is removed. It is only slightly malleable and is a ductile rare-earth element. Gadolinium reacts with atmospheric oxygen ...
compound) is given. Gadolinium-enhanced tissues and fluids appear extremely bright on ''T''1-weighted images. This provides high sensitivity for detection of vascular tissues (e.g., tumors) and permits assessment of brain perfusion (e.g., in stroke). There have been concerns raised recently regarding the toxicity of gadolinium-based contrast agents and their impact on persons with impaired kidney function. (See ''Safety''/
Contrast agents A contrast agent (or contrast medium) is a substance used to increase the contrast of structures or fluids within the body in medical imaging. Contrast agents absorb or alter external electromagnetism or ultrasound, which is different from radioph ...
below.) More recently, superparamagnetic contrast agents, e.g.,
iron oxide Iron oxides are chemical compounds composed of iron and oxygen. Several iron oxides are recognized. All are black magnetic solids. Often they are non-stoichiometric. Oxyhydroxides are a related class of compounds, perhaps the best known of wh ...
nanoparticle A nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 10 ...
s, have become available. These agents appear very dark on ''T''-weighted images and may be used for liver imaging, as normal
liver The liver is a major organ only found in vertebrates which performs many essential biological functions such as detoxification of the organism, and the synthesis of proteins and biochemicals necessary for digestion and growth. In humans, it i ...
tissue retains the agent, but abnormal areas (e.g., scars, tumors) do not. They can also be taken orally, to improve visualization of the
gastrointestinal tract The gastrointestinal tract (GI tract, digestive tract, alimentary canal) is the tract or passageway of the digestive system that leads from the mouth to the anus. The GI tract contains all the major organs of the digestive system, in humans and ...
, and to prevent water in the gastrointestinal tract from obscuring other organs (e.g., the
pancreas The pancreas is an organ of the digestive system and endocrine system of vertebrates. In humans, it is located in the abdomen behind the stomach and functions as a gland. The pancreas is a mixed or heterocrine gland, i.e. it has both an ...
).
Diamagnetic Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted ...
agents such as
barium sulfate Barium sulfate (or sulphate) is the inorganic compound with the chemical formula Ba SO4. It is a white crystalline solid that is odorless and insoluble in water. It occurs as the mineral barite, which is the main commercial source of barium and ...
have also been studied for potential use in the
gastrointestinal tract The gastrointestinal tract (GI tract, digestive tract, alimentary canal) is the tract or passageway of the digestive system that leads from the mouth to the anus. The GI tract contains all the major organs of the digestive system, in humans and ...
, but are less frequently used.


''k''-space

In 1983, Ljunggren and Twieg independently introduced the ''k''-space formalism, a technique that proved invaluable in unifying different MR imaging techniques. They showed that the demodulated MR signal ''S''(''t'') generated by the interaction between an ensemble of freely precessing nuclear spins in the presence of a linear magnetic field gradient ''G'' and a receiver-coil equals the Fourier transform of the effective spin density, \rho(\vec). Fundamentally, the signal is derived from
Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic in ...
: :S(t) = _\left( \vec(t) \right) \equiv \int_^\infty \mathrm\vec \ \rho( \vec ) \cdot e^ where: :\vec(t) \equiv \int_0^t \vec(\tau)\ \mathrm\tau In other words, as time progresses the signal traces out a trajectory in ''k''-space with the velocity vector of the trajectory proportional to the vector of the applied magnetic field gradient. By the term ''effective spin density'' we mean the true spin density \rho(\vec) corrected for the effects of ''T''1 preparation, ''T''2 decay, dephasing due to field inhomogeneity, flow, diffusion, etc. and any other phenomena that affect that amount of transverse magnetization available to induce signal in the RF probe or its phase with respect to the receiving coil' s electromagnetic field. From the basic ''k''-space formula, it follows immediately that we reconstruct an image I(\vec) by taking the
inverse Fourier transform In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information a ...
of the sampled data, viz. :I\left(\vec\right) = \int_^\infty \mathrm\vec \ S\left( \vec(t) \right) \cdot e^ Using the ''k''-space formalism, a number of seemingly complex ideas became simple. For example, it becomes very easy (for
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
s, in particular) to understand the role of phase encoding (the so-called spin-warp method). In a standard spin echo or gradient echo scan, where the readout (or view) gradient is constant (e.g., ''G''), a single line of ''k''-space is scanned per RF excitation. When the phase encoding gradient is zero, the line scanned is the ''k''x axis. When a non-zero phase-encoding pulse is added in between the RF excitation and the commencement of the readout gradient, this line moves up or down in ''k''-space, i.e., we scan the line ''k''y = constant. The ''k''-space formalism also makes it very easy to compare different scanning techniques. In single-shot EPI, all of ''k''-space is scanned in a single shot, following either a sinusoidal or zig-zag trajectory. Since alternating lines of ''k''-space are scanned in opposite directions, this must be taken into account in the reconstruction. Multi-shot EPI and fast spin echo techniques acquire only part of ''k''-space per excitation. In each shot, a different interleaved segment is acquired, and the shots are repeated until ''k''-space is sufficiently well-covered. Since the data at the center of ''k''-space represent lower spatial frequencies than the data at the edges of ''k''-space, the ''T''E value for the center of ''k''-space determines the image's ''T''2 contrast. The importance of the center of ''k''-space in determining image contrast can be exploited in more advanced imaging techniques. One such technique is spiral acquisition—a
rotating magnetic field A rotating magnetic field is the resultant magnetic field produced by a system of coils symmetrically placed and supplied with polyphase currents. A rotating magnetic field can be produced by a poly-phase (two or more phases) current or by a singl ...
gradient is applied, causing the trajectory in ''k''-space to spiral out from the center to the edge. Due to ''T''2 and ''T'' decay the signal is greatest at the start of the acquisition, hence acquiring the center of ''k''-space first improves contrast to noise ratio (CNR) when compared to conventional zig-zag acquisitions, especially in the presence of rapid movement. Since \vec x and \vec k are conjugate variables (with respect to the Fourier transform) we can use the
Nyquist theorem Nyquist may refer to: * Nyquist (surname) *Nyquist (horse), winner of the 2016 Kentucky Derby * Nyquist (programming language), computer programming language for sound synthesis and music composition See also *Johnson–Nyquist noise, thermal nois ...
to show that a step in ''k''-space determines the field of view of the image (maximum frequency that is correctly sampled) and the maximum value of k sampled determines the resolution; i.e., : \propto \frac \qquad \mathrm \propto , k_, \ . (These relationships apply to each axis independently.)


Example of a pulse sequence

In the timing diagram, the horizontal axis represents time. The vertical axis represents: (top row) amplitude of radio frequency pulses; (middle rows) amplitudes of the three orthogonal magnetic field gradient pulses; and (bottom row) receiver analog-to-digital converter (ADC). Radio frequencies are transmitted at the Larmor frequency of the nuclide to be imaged. For example, for 1H in a magnetic field of 1  T, a frequency of 42.5781  MHz would be employed. The three field gradients are labeled ''G''X (typically corresponding to a patient's left-to-right direction and colored red in diagram), ''G''Y (typically corresponding to a patient's front-to-back direction and colored green in diagram), and ''G''Z (typically corresponding to a patient's head-to-toe direction and colored blue in diagram). Where negative-going gradient pulses are shown, they represent reversal of the gradient direction, i.e., right-to-left, back-to-front or toe-to-head. For human scanning, gradient strengths of 1–100 mT/m are employed: Higher gradient strengths permit better resolution and faster imaging. The pulse sequence shown here would produce a transverse (axial) image. The first part of the pulse sequence, SS, achieves "slice selection". A shaped pulse (shown here with a sinc modulation) causes a 90°
nutation Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame ...
of longitudinal nuclear magnetization within a slab, or slice, creating transverse magnetization. The second part of the pulse sequence, PE, imparts a phase shift upon the slice-selected nuclear magnetization, varying with its location in the Y direction. The third part of the pulse sequence, another slice selection (of the same slice) uses another shaped pulse to cause a 180° rotation of transverse nuclear magnetization within the slice. This transverse magnetisation refocuses to form a spin echo at a time ''T''E. During the spin echo, a frequency-encoding (FE) or readout gradient is applied, making the resonant frequency of the nuclear magnetization vary with its location in the X direction. The signal is sampled ''n''FE times by the ADC during this period, as represented by the vertical lines. Typically ''n''FE of between 128 and 512 samples are taken. The longitudinal magnetisation is then allowed to recover somewhat and after a time ''T''R the whole sequence is repeated ''n''PE times, but with the phase-encoding gradient incremented (indicated by the horizontal hatching in the green gradient block). Typically ''n''PE of between 128 and 512 repetitions are made. The negative-going lobes in ''G''X and ''G''Z are imposed to ensure that, at time ''T''E (the spin echo maximum), phase only encodes spatial location in the Y direction. Typically ''T''E is between 5 ms and 100 ms, while ''T''R is between 100 ms and 2000 ms. After the two-dimensional matrix (typical dimension between 128 × 128 and 512 × 512) has been acquired, producing the so-called ''k''-space data, a two-dimensional inverse Fourier transform is performed to provide the familiar MR image. Either the magnitude or phase of the Fourier transform can be taken, the former being far more common.


Overview of main sequences


MRI scanner


Construction and operation

The major components of an MRI scanner are: the main magnet, which polarizes the sample, the shim coils for correcting inhomogeneities in the main magnetic field, the gradient system which is used to localize the MR signal and the RF system, which excites the sample and detects the resulting NMR signal. The whole system is controlled by one or more computers.


Magnet

The magnet is the largest and most expensive component of the scanner, and the remainder of the scanner is built around it. The strength of the magnet is measured in teslas (T). Clinical magnets generally have a field strength in the range 0.1–3.0 T, with research systems available up to 9.4 T for human use and 21 T for animal systems. In the United States, field strengths up to 4 T have been approved by the FDA for clinical use. Just as important as the strength of the main magnet is its precision. The straightness of the magnetic lines within the center (or, as it is technically known, the iso-center) of the magnet needs to be near-perfect. This is known as homogeneity. Fluctuations (inhomogeneities in the field strength) within the scan region should be less than three parts per million (3 ppm). Three types of magnets have been used: * Permanent magnet: Conventional magnets made from ferromagnetic materials (e.g., steel alloys containing
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s such as
neodymium Neodymium is a chemical element with the symbol Nd and atomic number 60. It is the fourth member of the lanthanide series and is considered to be one of the rare-earth metals. It is a hard, slightly malleable, silvery metal that quickly tarn ...
) can be used to provide the static magnetic field. A permanent magnet that is powerful enough to be used in an MRI will be extremely large and bulky; they can weigh over 100 tonnes. Permanent magnet MRIs are very inexpensive to maintain; this cannot be said of the other types of MRI magnets, but there are significant drawbacks to using permanent magnets. They are only capable of achieving weak field strengths compared to other MRI magnets (usually less than 0.4 T) and they are of limited precision and stability. Permanent magnets also present special safety issues; since their magnetic fields cannot be "turned off," ferromagnetic objects are virtually impossible to remove from them once they come into direct contact. Permanent magnets also require special care when they are being brought to their site of installation. * Resistive electromagnet: A
solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose ...
wound from copper wire is an alternative to a permanent magnet. An advantage is low initial cost, but field strength and stability are limited. The electromagnet requires considerable electrical energy during operation which can make it expensive to operate. This design is essentially obsolete. * Superconducting electromagnet: When a niobium-titanium or niobium-tin alloy is cooled by
liquid helium Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity. At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temp ...
to 4 K (−269 °C, −452 °F) it becomes a superconductor, losing resistance to flow of electric current. An electromagnet constructed with superconductors can have extremely high field strengths, with very high stability. The construction of such magnets is extremely costly, and the cryogenic helium is expensive and difficult to handle. However, despite their cost, helium cooled superconducting magnets are the most common type found in MRI scanners today. Most superconducting magnets have their coils of superconductive wire immersed in liquid helium, inside a vessel called a
cryostat A cryostat (from ''cryo'' meaning cold and ''stat'' meaning stable) is a device used to maintain low cryogenic temperatures of samples or devices mounted within the cryostat. Low temperatures may be maintained within a cryostat by using various r ...
. Despite thermal insulation, sometimes including a second cryostat containing
liquid nitrogen Liquid nitrogen—LN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about . It is produced industrially by fractional distillation of liquid air. It is a colorless, low viscosity liquid that is wid ...
, ambient heat causes the helium to slowly boil off. Such magnets, therefore, require regular topping-up with liquid helium. Generally a
cryocooler A refrigerator designed to reach cryogenic temperatures (below ) is often called a cryocooler. The term is most often used for smaller systems, typically table-top size, with input powers less than about 20 kW. Some can have input powers as lo ...
, also known as a coldhead, is used to recondense some helium vapor back into the liquid helium bath. Several manufacturers now offer 'cryogenless' scanners, where instead of being immersed in liquid helium the magnet wire is cooled directly by a cryocooler. Alternatively, the magnet may be cooled by carefully placing liquid helium in strategic spots, dramatically reducing the amount of liquid helium used, or,
high temperature superconductor High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previo ...
s may be used instead. Magnets are available in a variety of shapes. However, permanent magnets are most frequently 'C' shaped, and superconducting magnets most frequently cylindrical. C-shaped superconducting magnets and box-shaped permanent magnets have also been used. Magnetic field strength is an important factor in determining image quality. Higher magnetic fields increase
signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in de ...
, permitting higher resolution or faster scanning. However, higher field strengths require more costly magnets with higher maintenance costs, and have increased safety concerns. A field strength of 1.0–1.5 T is a good compromise between cost and performance for general medical use. However, for certain specialist uses (e.g., brain imaging) higher field strengths are desirable, with some hospitals now using 3.0 T scanners.


Shims

When the MR scanner is placed in the hospital or clinic, its main magnetic field is far from being homogeneous enough to be used for scanning. That is why before doing fine tuning of the field using a sample, the magnetic field of the magnet must be measured and shimmed. After a sample is placed into the scanner, the main magnetic field is distorted by susceptibility boundaries within that sample, causing signal dropout (regions showing no signal) and spatial distortions in acquired images. For humans or animals the effect is particularly pronounced at air-tissue boundaries such as the
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(due to
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, ...
oxygen in air) making, for example, the frontal lobes of the brain difficult to image. To restore field homogeneity a set of shim coils is included in the scanner. These are resistive coils, usually at room temperature, capable of producing field corrections distributed as several orders of
spherical harmonics In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form ...
. After placing the sample in the scanner, the ''B''0 field is 'shimmed' by adjusting currents in the shim coils. Field homogeneity is measured by examining an FID signal in the absence of field gradients. The FID from a poorly shimmed sample will show a complex decay envelope, often with many humps. Shim currents are then adjusted to produce a large amplitude exponentially decaying FID, indicating a homogeneous ''B''0 field. The process is usually automated.


Gradients

Gradient coils are used to spatially encode the positions of protons by varying the magnetic field linearly across the imaging volume. The Larmor frequency will then vary as a function of position in the ''x'', ''y'' and ''z''-axes. Gradient coils are usually resistive electromagnets powered by sophisticated
amplifiers An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost th ...
which permit rapid and precise adjustments to their field strength and direction. Typical gradient systems are capable of producing gradients from 20 to 100 mT/m (i.e., in a 1.5 T magnet, when a maximal ''z''-axis gradient is applied, the field strength may be 1.45 T at one end of a 1 m long bore and 1.55 T at the other). It is the magnetic gradients that determine the plane of imaging—because the orthogonal gradients can be combined freely, any plane can be selected for imaging. Scan speed is dependent on performance of the gradient system. Stronger gradients allow for faster imaging, or for higher resolution; similarly, gradient systems capable of faster switching can also permit faster scanning. However, gradient performance is limited by safety concerns over nerve stimulation. Some important characteristics of gradient amplifiers and gradient coils are slew rate and gradient strength. As mentioned earlier, a gradient coil will create an additional, linearly varying magnetic field that adds or subtracts from the main magnetic field. This additional magnetic field will have components in all 3 directions, viz. ''x'', ''y'' and ''z''; however, only the component along the magnetic field (usually called the ''z''-axis, hence denoted ''G''''z'') is useful for imaging. Along any given axis, the gradient will add to the magnetic field on one side of the zero position and subtract from it on the other side. Since the additional field is a gradient, it has units of
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per centimeter or millitesla per meter (mT/m). High performance gradient coils used in MRI are typically capable of producing a gradient magnetic field of approximate 30 mT/m or higher for a 1.5 T MRI. The slew rate of a gradient system is a measure of how quickly the gradients can be ramped on or off. Typical higher performance gradients have a slew rate of up to 100–200 T·m−1·s−1. The slew rate depends both on the gradient coil (it takes more time to ramp up or down a large coil than a small coil) and on the performance of the gradient amplifier (it takes a lot of voltage to overcome the inductance of the coil) and has significant influence on image quality.


Radio frequency system

The
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
(RF)
transmission Transmission may refer to: Medicine, science and technology * Power transmission ** Electric power transmission ** Propulsion transmission, technology allowing controlled application of power *** Automatic transmission *** Manual transmission ** ...
system consists of an RF synthesizer,
power amplifier An audio power amplifier (or power amp) is an electronic amplifier that amplifies low-power electronic audio signals, such as the signal from a radio receiver or an electric guitar pickup, to a level that is high enough for driving louds ...
and transmitting coil. That coil is usually built into the body of the scanner. The power of the transmitter is variable, but high-end whole-body scanners may have a peak output power of up to 35 kW, and be capable of sustaining average power of 1 kW. Although these
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
s are in the RF range of tens of
megahertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one ...
(often in the
shortwave radio Shortwave radio is radio transmission using shortwave (SW) radio frequencies. There is no official definition of the band, but the range always includes all of the high frequency band (HF), which extends from 3 to 30 MHz (100 to 10 m ...
portion of the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging fro ...
) at powers usually exceeding the highest powers used by
amateur radio Amateur radio, also known as ham radio, is the use of the radio frequency spectrum for purposes of non-commercial exchange of messages, wireless experimentation, self-training, private recreation, radiosport, contesting, and emergency commu ...
, there is very little RF interference produced by the MRI machine. The reason for this, is that the MRI is not a radio transmitter. The RF frequency
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
produced in the "transmitting coil" is a magnetic near-field with very little associated changing
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
component (such as all conventional radio wave transmissions have). Thus, the high-powered electromagnetic field produced in the MRI transmitter coil does not produce much
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
at its RF frequency, and the power is confined to the coil space and not radiated as "radio waves." Thus, the transmitting coil is a good EM ''field'' transmitter at radio frequency, but a poor EM ''radiation'' transmitter at radio frequency. The receiver consists of the coil, pre-amplifier and signal processing system. The RF
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
produced by nuclear relaxation inside the subject is true EM radiation (radio waves), and these leave the subject as RF radiation, but they are of such low power as to also not cause appreciable RF interference that can be picked up by nearby radio tuners (in addition, MRI scanners are generally situated in metal mesh lined rooms which act as
Faraday cage A Faraday cage or Faraday shield is an enclosure used to block electromagnetic fields. A Faraday shield may be formed by a continuous covering of conductive material, or in the case of a Faraday cage, by a mesh of such materials. Faraday cages ...
s.) While it is possible to scan using the integrated coil for RF transmission and MR signal reception, if a small region is being imaged, then better image quality (i.e., higher signal-to-noise ratio) is obtained by using a close-fitting smaller coil. A variety of coils are available which fit closely around parts of the body such as the head, knee, wrist, breast, or internally, e.g., the rectum. A recent development in MRI technology has been the development of sophisticated multi-element phased array coils which are capable of acquiring multiple channels of data in parallel. This 'parallel imaging' technique uses unique acquisition schemes that allow for accelerated imaging, by replacing some of the spatial coding originating from the magnetic gradients with the spatial sensitivity of the different coil elements. However, the increased acceleration also reduces the signal-to-noise ratio and can create residual artifacts in the image reconstruction. Two frequently used parallel acquisition and reconstruction schemes are known as SENSE and GRAPPA. A detailed review of parallel imaging techniques can be found here:


References


Further reading

* * * * * * * * * * * * {{refend Magnetic resonance imaging