Paramagnetism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Paramagnetism 

 

When liquid oxygen is poured from a beaker into a strong magnet, the oxygen is temporarily contained between the magnetic poles owing to its paramagnetism.

 

 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, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer.

Paramagnetism is due to the presence of unpaired electrons in the material, so most atoms with incompletely filled atomic orbitals are paramagnetic, although exceptions such as copper exist. Due to their spin, unpaired electrons have a magnetic dipole moment and act like tiny magnets. An external magnetic field causes the electrons' spins to align parallel to the field, causing a net attraction. Paramagnetic materials include aluminium, oxygen, titanium, and iron oxide (FeO). Therefore, a simple rule of thumb is used in chemistry to determine whether a particle (atom, ion, or molecule) is paramagnetic or diamagnetic: if all electrons in the particle are paired, then the substance made of this particle is diamagnetic; if it has unpaired electrons, then the substance is paramagnetic.

Unlike ferromagnets, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field because thermal motion randomizes the spin orientations. (Some paramagnetic materials retain spin disorder even at absolute zero, meaning they are paramagnetic in the ground state, i.e. in the absence of thermal motion.) Thus the total magnetization drops to zero when the applied field is removed. Even in the presence of the field there is only a small induced magnetization because only a small fraction of the spins will be oriented by the field. This fraction is proportional to the field strength and this explains the linear dependency. The attraction experienced by ferromagnetic materials is non-linear and much stronger, so that it is easily observed, for instance, in the attraction between a refrigerator magnet and the iron of the refrigerator itself.

Relation to electron spins

Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments (dipoles), even in the absence of an applied field. The permanent moment generally is due to the spin of unpaired electrons in atomic or molecular electron orbitals. In pure paramagnetism, the dipoles do not interact with one another and are randomly oriented in the absence of an external field due to thermal agitation, resulting in zero net magnetic moment. When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field. In the classical description, this alignment can be understood to occur due to a torque being provided on the magnetic moments by an applied field, which tries to align the dipoles parallel to the applied field. However, the true origins of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum.

If there is sufficient energy exchange between neighbouring dipoles, they will interact, and may spontaneously align or anti-align and form magnetic domains, resulting in ferromagnetism (permanent magnets) or antiferromagnetism, respectively. Paramagnetic behavior can also be observed in ferromagnetic materials that are above their Curie temperature, and in antiferromagnets above their Néel temperature. At these temperatures, the available thermal energy simply overcomes the interaction energy between the spins.

In general, paramagnetic effects are quite small: the magnetic susceptibility is of the order of 10⁻³ to 10⁻⁵ for most paramagnets, but may be as high as 10⁻¹ for synthetic paramagnets such as ferrofluids.

Delocalization

Selected Pauli-paramagnetic metals

Material	Magnetic susceptibility, ${\displaystyle \chi _{v}}$ [10−5] (SI units)
Tungsten	6.8
Caesium	5.1
Aluminium	2.2
Lithium	1.4
Magnesium	1.2
Sodium	0.72

In conductive materials, the electrons are delocalized, that is, they travel through the solid more or less as free electrons. Conductivity can be understood in a band structure picture as arising from the incomplete filling of energy bands. In an ordinary nonmagnetic conductor the conduction band is identical for both spin-up and spin-down electrons. When a magnetic field is applied, the conduction band splits apart into a spin-up and a spin-down band due to the difference in magnetic potential energy for spin-up and spin-down electrons. Since the Fermi level must be identical for both bands, this means that there will be a small surplus of the type of spin in the band that moved downwards. This effect is a weak form of paramagnetism known as Pauli paramagnetism.

The effect always competes with a diamagnetic response of opposite sign due to all the core electrons of the atoms. Stronger forms of magnetism usually require localized rather than itinerant electrons. However, in some cases a band structure can result in which there are two delocalized sub-bands with states of opposite spins that have different energies. If one subband is preferentially filled over the other, one can have itinerant ferromagnetic order. This situation usually only occurs in relatively narrow (d-)bands, which are poorly delocalized.

s and p electrons

Generally, strong delocalization in a solid due to large overlap with neighboring wave functions means that there will be a large Fermi velocity; this means that the number of electrons in a band is less sensitive to shifts in that band's energy, implying a weak magnetism. This is why s- and p-type metals are typically either Pauli-paramagnetic or as in the case of gold even diamagnetic. In the latter case the diamagnetic contribution from the closed shell inner electrons simply wins over the weak paramagnetic term of the almost free electrons.

d and f electrons

Stronger magnetic effects are typically only observed when d or f electrons are involved. Particularly the latter are usually strongly localized. Moreover, the size of the magnetic moment on a lanthanide atom can be quite large as it can carry up to 7 unpaired electrons in the case of gadolinium(III) (hence its use in MRI). The high magnetic moments associated with lanthanides is one reason why superstrong magnets are typically based on elements like neodymium or samarium.

Molecular localization

The above picture is a generalization as it pertains to materials with an extended lattice rather than a molecular structure. Molecular structure can also lead to localization of electrons. Although there are usually energetic reasons why a molecular structure results such that it does not exhibit partly filled orbitals (i.e. unpaired spins), some non-closed shell moieties do occur in nature. Molecular oxygen is a good example. Even in the frozen solid it contains di-radical molecules resulting in paramagnetic behavior. The unpaired spins reside in orbitals derived from oxygen p wave functions, but the overlap is limited to the one neighbor in the O₂ molecules. The distances to other oxygen atoms in the lattice remain too large to lead to delocalization and the magnetic moments remain unpaired.

Theory

The Bohr–Van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. The paramagnetic response has then two possible quantum origins, either coming from permanent magnetic moments of the ions or from the spatial motion of the conduction electrons inside the material. Both description are given below.

Curie's law

For low levels of magnetization, the magnetization of paramagnets follows what is known as Curie's law, at least approximately. This law indicates that the susceptibility, ${\displaystyle \scriptstyle \chi }$, of paramagnetic materials is inversely proportional to their temperature, i.e. that materials become more magnetic at lower temperatures. The mathematical expression is:

${\displaystyle \mathbf {M} =\chi \mathbf {H} ={\frac {C}{T}}\mathbf {H} }$

where:

${\displaystyle \mathbf {M} }$ is the resulting magnetization, measured in amperes/meter (A/m),

${\displaystyle \chi }$ is the volume magnetic susceptibility (dimensionless),

${\displaystyle H}$ is the auxiliary magnetic field (A/m),

${\displaystyle T}$ is absolute temperature, measured in kelvins (K),

${\displaystyle C}$ is a material-specific Curie constant (K).

Curie's law is valid under the commonly encountered conditions of low magnetization (μ_BH ≲ k_BT), but does not apply in the high-field/low-temperature regime where saturation of magnetization occurs (μ_BH ≳ k_BT) and magnetic dipoles are all aligned with the applied field. When the dipoles are aligned, increasing the external field will not increase the total magnetization since there can be no further alignment.

For a paramagnetic ion with noninteracting magnetic moments with angular momentum J, the Curie constant is related the individual ions' magnetic moments,

${\displaystyle C={\frac {n}{3k_{\mathrm {B} }}}\mu _{\mathrm {eff} }^{2}{\text{ where }}\mu _{\mathrm {eff} }=g_{J}\mu _{\mathrm {B} }{\sqrt {J(J+1)}}.}$

where n is the number of atoms per unit volume. The parameter μ_eff is interpreted as the effective magnetic moment per paramagnetic ion. If one uses a classical treatment with molecular magnetic moments represented as discrete magnetic dipoles, μ, a Curie Law expression of the same form will emerge with μ appearing in place of μ_eff.

When orbital angular momentum contributions to the magnetic moment are small, as occurs for most organic radicals or for octahedral transition metal complexes with d³ or high-spin d⁵ configurations, the effective magnetic moment takes the form ( with g-factor g_e = 2.0023... ≈ 2),

${\displaystyle \mu _{\mathrm {eff} }\simeq 2{\sqrt {S(S+1)}}\mu _{\mathrm {B} }={\sqrt {N_{\rm {u}}(N_{\rm {u}}+2)}}\mu _{\mathrm {B} },}$

where N_u is the number of unpaired electrons. In other transition metal complexes this yields a useful, if somewhat cruder, estimate.

When Curie constant is null, second order effects that couple the ground state with the excited states can also lead to a paramagnetic susceptibility independent of the temperature, known as Van Vleck susceptibility.

Pauli paramagnetism

For some alkali metals and noble metals, conduction electrons are weakly interacting and delocalized in space forming a Fermi gas. For these materials one contribution to the magnetic response comes from the interaction between the electron spins and the magnetic field known as Pauli paramagnetism. For a small magnetic field ${\displaystyle \mathbf {H} }$, the additional energy per electron from the interaction between an electron spin and the magnetic field is given by:

${\displaystyle \Delta E=-\mu _{0}\mathbf {H} \cdot {\boldsymbol {\mu }}_{e}=-\mu _{0}\mathbf {H} \cdot \left(-g_{e}{\frac {\mu _{\mathrm {B} }}{\hbar }}\mathbf {S} \right)=\pm \mu _{0}\mu _{\mathrm {B} }H,}$

where ${\displaystyle \mu _{0}}$ is the vacuum permeability, ${\displaystyle {\boldsymbol {\mu }}_{e}}$ is the electron magnetic moment, ${\displaystyle \mu _{\rm {B}}}$ is the Bohr magneton, ${\displaystyle \hbar }$ is the reduced Planck constant, and the g-factor cancels with the spin ${\displaystyle \mathbf {S} =\pm \hbar /2}$. The ${\displaystyle \pm }$ indicates that the sign is positive (negative) when the electron spin component in the direction of ${\displaystyle \mathbf {H} }$ is parallel (antiparallel) to the magnetic field.

In a metal, the application of an external magnetic field increases the density of electrons with spins antiparallel with the field and lowers the density of the electrons with opposite spin. Note: The arrows in this picture indicate spin direction, not magnetic moment.

For low temperatures with respect to the Fermi temperature ${\displaystyle T_{\rm {F}}}$ (around 10⁴ kelvins for metals), the number density of electrons ${\displaystyle n_{\uparrow }}$ (${\displaystyle n_{\downarrow }}$) pointing parallel (antiparallel) to the magnetic field can be written as:

${\displaystyle n_{\uparrow }\approx {\frac {n_{e}}{2}}-{\frac {\mu _{0}\mu _{\mathrm {B} }}{2}}g(E_{\mathrm {F} })H\quad ;\quad \left(n_{\downarrow }\approx {\frac {n_{e}}{2}}+{\frac {\mu _{0}\mu _{\mathrm {B} }}{2}}g(E_{\mathrm {F} })H\right),}$

with ${\displaystyle n_{e}}$ the total free-electrons density and ${\displaystyle g(E_{\mathrm {F} })}$ the electronic density of states (number of states per energy per volume) at the Fermi energy ${\displaystyle E_{\mathrm {F} }}$.

In this approximation the magnetization is given as the magnetic moment of one electron times the difference in densities:

${\displaystyle M=\mu _{\mathrm {B} }(n_{\downarrow }-n_{\uparrow })=\mu _{0}\mu _{\mathrm {B} }^{2}g(E_{\mathrm {F} })H,}$

which yields a positive paramagnetic susceptibility independent of temperature:

${\displaystyle \chi _{\mathrm {P} }=\mu _{0}\mu _{\mathrm {B} }^{2}g(E_{\mathrm {F} }).}$

The Pauli paramagnetic susceptibility is a macroscopic effect and has to be contrasted with Landau diamagnetic susceptibility which is equal to minus one third of Pauli's and also comes from delocalized electrons. The Pauli susceptibility comes from the spin interaction with the magnetic field while the Landau susceptibility comes from the spatial motion of the electrons and it is independent of the spin. In doped semiconductors the ratio between Landau's and Pauli's susceptibilities changes as the effective mass of the charge carriers ${\displaystyle m^{*}}$ can differ from the electron mass ${\displaystyle m_{e}}$.

The magnetic response calculated for a gas of electrons is not the full picture as the magnetic susceptibility coming from the ions has to be included. Additionally, this formulas may break down for confined systems that differ from the bulk, like quantum dots, or for high fields, as demonstrated in the De Haas-Van Alphen effect.

Pauli paramagnetism is named after the physicist Wolfgang Pauli. Before Pauli's theory, the lack of a strong Curie paramagnetism in metals was an open problem as the leading model could not account for this contribution without the use of quantum statistics.

Examples of paramagnets

Materials that are called "paramagnets" are most often those that exhibit, at least over an appreciable temperature range, magnetic susceptibilities that adhere to the Curie or Curie–Weiss laws. In principle any system that contains atoms, ions, or molecules with unpaired spins can be called a paramagnet, but the interactions between them need to be carefully considered.

Systems with minimal interactions

The narrowest definition would be: a system with unpaired spins that do not interact with each other. In this narrowest sense, the only pure paramagnet is a dilute gas of monatomic hydrogen atoms. Each atom has one non-interacting unpaired electron.

A gas of lithium atoms already possess two paired core electrons that produce a diamagnetic response of opposite sign. Strictly speaking Li is a mixed system therefore, although admittedly the diamagnetic component is weak and often neglected. In the case of heavier elements the diamagnetic contribution becomes more important and in the case of metallic gold it dominates the properties. The element hydrogen is virtually never called 'paramagnetic' because the monatomic gas is stable only at extremely high temperature; H atoms combine to form molecular H₂ and in so doing, the magnetic moments are lost (quenched), because of the spins pair. Hydrogen is therefore diamagnetic and the same holds true for many other elements. Although the electronic configuration of the individual atoms (and ions) of most elements contain unpaired spins, they are not necessarily paramagnetic, because at ambient temperature quenching is very much the rule rather than the exception. The quenching tendency is weakest for f-electrons because f (especially 4f) orbitals are radially contracted and they overlap only weakly with orbitals on adjacent atoms. Consequently, the lanthanide elements with incompletely filled 4f-orbitals are paramagnetic or magnetically ordered.

μ_eff values for typical d³ and d⁵ transition metal complexes.

Material	μeff/μB
[Cr(NH3)6]Br3	3.77
K3[Cr(CN)6]	3.87
K3[MoCl6]	3.79
K4[V(CN)6]	3.78
[Mn(NH3)6]Cl2	5.92
(NH4)2[Mn(SO4)2]·6H2O	5.92
NH4[Fe(SO4)2]·12H2O	5.89

Thus, condensed phase paramagnets are only possible if the interactions of the spins that lead either to quenching or to ordering are kept at bay by structural isolation of the magnetic centers. There are two classes of materials for which this holds:

• Molecular materials with a (isolated) paramagnetic center.
  • Good examples are coordination complexes of d- or f-metals or proteins with such centers, e.g. myoglobin. In such materials the organic part of the molecule acts as an envelope shielding the spins from their neighbors.
  • Small molecules can be stable in radical form, oxygen O₂ is a good example. Such systems are quite rare because they tend to be rather reactive.
• Dilute systems.
  • Dissolving a paramagnetic species in a diamagnetic lattice at small concentrations, e.g. Nd³⁺ in CaCl₂ will separate the neodymium ions at large enough distances that they do not interact. Such systems are of prime importance for what can be considered the most sensitive method to study paramagnetic systems: EPR.

Systems with interactions

Idealized Curie–Weiss behavior; N.B. T_C=θ, but T_N is not θ. Paramagnetic regimes are denoted by solid lines. Close to T_N or T_C the behavior usually deviates from ideal.

As stated above, many materials that contain d- or f-elements do retain unquenched spins. Salts of such elements often show paramagnetic behavior but at low enough temperatures the magnetic moments may order. It is not uncommon to call such materials 'paramagnets', when referring to their paramagnetic behavior above their Curie or Néel-points, particularly if such temperatures are very low or have never been properly measured. Even for iron it is not uncommon to say that iron becomes a paramagnet above its relatively high Curie-point. In that case the Curie-point is seen as a phase transition between a ferromagnet and a 'paramagnet'. The word paramagnet now merely refers to the linear response of the system to an applied field, the temperature dependence of which requires an amended version of Curie's law, known as the Curie–Weiss law:

${\displaystyle \mathbf {M} ={\frac {C}{T-\theta }}\mathbf {H} }$

This amended law includes a term θ that describes the exchange interaction that is present albeit overcome by thermal motion. The sign of θ depends on whether ferro- or antiferromagnetic interactions dominate and it is seldom exactly zero, except in the dilute, isolated cases mentioned above.

Obviously, the paramagnetic Curie–Weiss description above T_N or T_C is a rather different interpretation of the word "paramagnet" as it does not imply the absence of interactions, but rather that the magnetic structure is random in the absence of an external field at these sufficiently high temperatures. Even if θ is close to zero this does not mean that there are no interactions, just that the aligning ferro- and the anti-aligning antiferromagnetic ones cancel. An additional complication is that the interactions are often different in different directions of the crystalline lattice (anisotropy), leading to complicated magnetic structures once ordered.

Randomness of the structure also applies to the many metals that show a net paramagnetic response over a broad temperature range. They do not follow a Curie type law as function of temperature however, often they are more or less temperature independent. This type of behavior is of an itinerant nature and better called Pauli-paramagnetism, but it is not unusual to see, for example, the metal aluminium called a "paramagnet", even though interactions are strong enough to give this element very good electrical conductivity.

Superparamagnets

Some materials show induced magnetic behavior that follows a Curie type law but with exceptionally large values for the Curie constants. These materials are known as superparamagnets. They are characterized by a strong ferromagnetic or ferrimagnetic type of coupling into domains of a limited size that behave independently from one another. The bulk properties of such a system resembles that of a paramagnet, but on a microscopic level they are ordered. The materials do show an ordering temperature above which the behavior reverts to ordinary paramagnetism (with interaction). Ferrofluids are a good example, but the phenomenon can also occur inside solids, e.g., when dilute paramagnetic centers are introduced in a strong itinerant medium of ferromagnetic coupling such as when Fe is substituted in TlCu₂Se₂ or the alloy AuFe. Such systems contain ferromagnetically coupled clusters that freeze out at lower temperatures. They are also called mictomagnets.

Magnetic resonance imaging

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Magnetic_resonance_imaging

 

Magnetic resonance imaging
Play media Para-sagittal MRI of the head, with aliasing artifacts (nose and forehead appear at the back of the head)
Synonyms	nuclear magnetic resonance imaging (NMRI), magnetic resonance tomography (MRT)
ICD-9-CM	88.91
MeSH	D008279
MedlinePlus	003335

Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from CT and PET scans. MRI is a medical application of nuclear magnetic resonance (NMR) which can also be used for imaging in other NMR applications, such as NMR spectroscopy.

While the hazards of ionizing radiation are now well controlled in most medical contexts, an MRI may still be seen as a better choice than a CT scan. MRI is widely used in hospitals and clinics for medical diagnosis and staging and follow-up of disease without exposing the body to radiation. An MRI may yield different information compared with CT. Risks and discomfort may be associated with MRI scans. Compared with CT scans, MRI scans typically take longer and are louder, and they usually need the subject to enter a narrow, confining tube. In addition, people with some medical implants or other non-removable metal inside the body may be unable to undergo an MRI examination safely.

MRI was originally called NMRI (nuclear magnetic resonance imaging), but "nuclear" was dropped to avoid negative associations. Certain atomic nuclei are able to absorb radio frequency energy when placed in an external magnetic field; the resultant evolving spin polarization can induce a RF signal in a radio frequency coil and thereby be detected. In clinical and research MRI, hydrogen atoms are most often used to generate a macroscopic polarization that is detected by antennae close to the subject being examined. Hydrogen atoms are naturally abundant in humans and other biological organisms, particularly in water 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 energy transition, and magnetic field gradients localize the polarization in space. By varying the parameters of the pulse sequence, different contrasts may be generated between tissues based on the relaxation properties of the hydrogen atoms therein.

Since its development in the 1970s and 1980s, MRI has proven to be a versatile imaging technique. While MRI is most prominently used in diagnostic medicine and biomedical research, it also may be used to form images of non-living objects. Diffusion MRI and Functional MRI extends the utility of MRI to capture neuronal tracts and blood flow respectively in the nervous system, in addition to detailed spatial images. The sustained increase in demand for MRI within health systems has led to concerns about cost effectiveness and overdiagnosis.

Mechanism

Construction and physics

Schematic of construction of a cylindrical superconducting MR scanner

In most medical applications, hydrogen nuclei, which consist solely of a proton, that are in tissues create a signal that is processed to form an image of the body in terms of the density of those nuclei in a specific region. Given that the protons are affected by fields from other atoms to which they are bonded, it is possible to separate responses from hydrogen in specific compounds. To perform a study, the person is positioned within an MRI scanner that forms a strong magnetic field around the area to be imaged. First, energy from an oscillating magnetic field is temporarily applied to the patient at the appropriate resonance frequency. Scanning with X and Y gradient coils causes a selected region of the patient to experience the exact magnetic field required for the energy to be absorbed. The excited atoms emit a radio frequency (RF) signal, which is measured by a receiving coil. The RF signal may be processed to deduce position information by looking at the changes in RF level and phase caused by varying the local magnetic field using gradient coils. As these coils are rapidly switched during the excitation and response to perform a moving line scan, they create the characteristic repetitive noise of an MRI scan as the windings move slightly due to magnetostriction. The contrast between different tissues is determined by the rate at which excited atoms return to the equilibrium state. Exogenous contrast agents may be given to the person to make the image clearer.

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

A mobile MRI unit visiting Glebefields Health Centre, Tipton, England

MRI requires a magnetic field that is both strong and uniform to a few parts per million across the scan volume. The field strength of the magnet is measured in teslas – and while the majority of systems operate at 1.5 T, commercial systems are available between 0.2 and 7 T. Most clinical magnets are superconducting magnets, which require liquid helium to keep them very cold. Lower field strengths can be achieved with permanent magnets, which are often used in "open" MRI scanners for claustrophobic patients. Lower field strengths are also used in a portable MRI scanner approved by the FDA in 2020. Recently, MRI has been demonstrated also at ultra-low fields, i.e., in the microtesla-to-millitesla range, where sufficient signal quality is made possible by prepolarization (on the order of 10–100 mT) and by measuring the Larmor precession fields at about 100 microtesla with highly sensitive superconducting quantum interference devices (SQUIDs).

T1 and T2

Effects of TR and TE on MR signal

 

Examples of T1-weighted, T2-weighted and PD-weighted MRI scans

Each tissue returns to its equilibrium state after excitation by the independent relaxation processes of T1 (spin-lattice; that is, magnetization in the same direction as the static magnetic field) and T2 (spin-spin; transverse to the static magnetic field). To create a T1-weighted image, magnetization is allowed to recover before measuring the MR signal by changing the repetition time (TR). This image weighting is useful for assessing the cerebral cortex, identifying fatty tissue, characterizing focal liver lesions, and in general, obtaining morphological information, as well as for post-contrast imaging. To create a T2-weighted image, magnetization is allowed to decay before measuring the MR signal by changing the echo time (TE). This image weighting is useful for detecting edema and inflammation, revealing white matter lesions, and assessing zonal anatomy in the prostate and uterus.

The standard display of MRI images is to represent fluid characteristics in black and white images, where different tissues turn out as follows:

Signal	T1-weighted	T2-weighted
High	Fat Subacute hemorrhage Melanin Protein-rich fluid Slowly flowing blood Paramagnetic or diamagnetic substances, such as gadolinium, manganese, copper Cortical pseudolaminar necrosis Anatomy	More water content, as in edema, tumor, infarction, inflammation and infection Extracellularly located methemoglobin in subacute hemorrhage Fat Pathology
Inter- mediate	Gray matter darker than white matter	White matter darker than grey matter
Low	Bone Urine CSF Air More water content, as in edema, tumor, infarction, inflammation, infection, hyperacute or chronic hemorrhage Low proton density as in calcification	Bone Air Low proton density, as in calcification and fibrosis Paramagnetic material, such as deoxyhemoglobin, intracelullar methemoglobin, iron, ferritin, hemosiderin, melanin Protein-rich fluid

Diagnostics

Usage by organ or system

Patient being positioned for MR study of the head and abdomen

MRI has a wide range of applications in medical diagnosis and more than 25,000 scanners are estimated to be in use worldwide. MRI affects diagnosis and treatment in many specialties although the effect on improved health outcomes is disputed in certain cases.

MRI is the investigation of choice in the preoperative staging of rectal and prostate cancer and has a role in the diagnosis, staging, and follow-up of other tumors, as well as for determining areas of tissue for sampling in biobanking.

Neuroimaging

MRI diffusion tensor imaging of white matter tracts

MRI is the investigative tool of choice for neurological cancers over CT, as it offers better visualization of the posterior cranial fossa, containing the brainstem and the cerebellum. The contrast provided between grey and white matter makes MRI the best choice for many conditions of the central nervous system, including demyelinating diseases, dementia, cerebrovascular disease, infectious diseases, Alzheimer's disease and epilepsy. Since many images are taken milliseconds apart, it shows how the brain responds to different stimuli, enabling researchers to study both the functional and structural brain abnormalities in psychological disorders. MRI also is used in guided stereotactic surgery and radiosurgery for treatment of intracranial tumors, arteriovenous malformations, and other surgically treatable conditions using a device known as the N-localizer.

Cardiovascular

MR angiogram in congenital heart disease

Cardiac MRI is complementary to other imaging techniques, such as echocardiography, cardiac CT, and nuclear medicine. It can be used to assess the structure and the function of the heart. Its applications include assessment of myocardial ischemia and viability, cardiomyopathies, myocarditis, iron overload, vascular diseases, and congenital heart disease.

Musculoskeletal

Applications in the musculoskeletal system include spinal imaging, assessment of joint disease, and soft tissue tumors. Also, MRI techniques can be used for diagnostic imaging of systemic muscle diseases.

Liver and gastrointestinal

Hepatobiliary MR is used to detect and characterize lesions of the liver, pancreas, and bile ducts. Focal or diffuse disorders of the liver may be evaluated using diffusion-weighted, opposed-phase imaging and dynamic contrast enhancement sequences. Extracellular contrast agents are used widely in liver MRI, and newer hepatobiliary contrast agents also provide the opportunity to perform functional biliary imaging. Anatomical imaging of the bile ducts is achieved by using a heavily T2-weighted sequence in magnetic resonance cholangiopancreatography (MRCP). Functional imaging of the pancreas is performed following administration of secretin. MR enterography provides non-invasive assessment of inflammatory bowel disease and small bowel tumors. MR-colonography may play a role in the detection of large polyps in patients at increased risk of colorectal cancer.

Angiography

Magnetic resonance angiography

Magnetic resonance angiography (MRA) generates pictures of the arteries to evaluate them for stenosis (abnormal narrowing) or aneurysms (vessel wall dilatations, at risk of rupture). MRA is often used to evaluate the arteries of the neck and brain, the thoracic and abdominal aorta, the renal arteries, and the legs (called a "run-off"). A variety of techniques can be used to generate the pictures, such as administration of a paramagnetic contrast agent (gadolinium) or using a technique known as "flow-related enhancement" (e.g., 2D and 3D time-of-flight sequences), where most of the signal on an image is due to blood that recently moved into that plane (see also FLASH MRI).

Techniques involving phase accumulation (known as phase contrast angiography) can also be used to generate flow velocity maps easily and accurately. Magnetic resonance venography (MRV) is a similar procedure that is used to image veins. In this method, the tissue is now excited inferiorly, while the signal is gathered in the plane immediately superior to the excitation plane—thus imaging the venous blood that recently moved from the excited plane.

Contrast agents

MRI for imaging anatomical structures or blood flow do not require contrast agents since the varying properties of the tissues or blood provide natural contrasts. However, for more specific types of imaging, exogenous contrast agents may be given intravenously, orally, or intra-articularly. The most commonly used intravenous contrast agents are based on chelates of gadolinium. In general, these agents have proved safer than the iodinated contrast agents used in X-ray radiography or CT. Anaphylactoid reactions are rare, occurring in approx. 0.03–0.1%. Of particular interest is the lower incidence of nephrotoxicity, compared with iodinated agents, when given at usual doses—this has made contrast-enhanced MRI scanning an option for patients with renal impairment, who would otherwise not be able to undergo contrast-enhanced CT.

Gadolinium-based contrast reagents are typically octadentate complexes of gadolinium(III). The complex is very stable (log K > 20) so that that, in use, the concentration of the un-complexed Gd³⁺ ions should be below the toxicity limit. The 9th place in the metal ion's coordination sphere is occupied by a water molecule which exchanges rapidly with water molecules in the reagent molecule's immediate environment, affecting the magnetic resonance relaxation time.

In December 2017, the Food and Drug Administration (FDA) in the United States announced in a drug safety communication that new warnings were to be included on all gadolinium-based contrast agents (GBCAs). The FDA also called for increased patient education and requiring gadolinium contrast vendors to conduct additional animal and clinical studies to assess the safety of these agents. Although gadolinium agents have proved useful for patients with kidney impairment, in patients with severe kidney failure requiring dialysis there is a risk of a rare but serious illness, nephrogenic systemic fibrosis, which may be linked to the use of certain gadolinium-containing agents. The most frequently linked is gadodiamide, but other agents have been linked too. Although a causal link has not been definitively established, current guidelines in the United States are that dialysis patients should only receive gadolinium agents where essential and that dialysis should be performed as soon as possible after the scan to remove the agent from the body promptly.

In Europe, where more gadolinium-containing agents are available, a classification of agents according to potential risks has been released. In 2008, a new contrast agent named gadoxetate, brand name Eovist (US) or Primovist (EU), was approved for diagnostic use: This has the theoretical benefit of a dual excretion path.

Sequences

An MRI sequence is a particular setting of radiofrequency pulses and gradients, resulting in a particular image appearance. The T1 and T2 weighting can also be described as MRI sequences.

Overview table

This table does not include uncommon and experimental sequences.

Group	Sequence	Abbr.	Physics	Main clinical distinctions	Example
Spin echo	T1 weighted	T1	Measuring spin–lattice relaxation by using a short repetition time (TR) and echo time (TE).	Lower signal for more water content, as in edema, tumor, infarction, inflammation, infection, hyperacute or chronic hemorrhage. High signal for fat High signal for paramagnetic substances, such as MRI contrast agents Standard foundation and comparison for other sequences
	T2 weighted	T2	Measuring spin–spin relaxation by using long TR and TE times	Higher signal for more water content Low signal for fat − Note that this only applies to standard Spin Echo (SE) sequences and not the more modern Fast Spin Echo (FSE) sequence (also referred to as Turbo Spin Echo, TSE), which is the most commonly used technique today. In FSE/TSE, fat will have a high signal. Low signal for paramagnetic substances Standard foundation and comparison for other sequences
	Proton density weighted	PD	Long TR (to reduce T1) and short TE (to minimize T2).	Joint disease and injury. High signal from meniscus tears. (pictured)
Gradient echo (GRE)	Steady-state free precession	SSFP	Maintenance of a steady, residual transverse magnetisation over successive cycles.	Creation of cardiac MRI videos (pictured).
	Effective T2 or "T2-star"	T2*	Spoiled gradient recalled echo (GRE) with a long echo time and small flip angle	Low signal from hemosiderin deposits (pictured) and hemorrhages.
	Susceptibility-weighted	SWI	Spoiled gradient recalled echo (GRE), fully flow compensated, long echo time, combines phase image with magnitude image	Detecting small amounts of hemorrhage (diffuse axonal injury pictured) or calcium.
Inversion recovery	Short tau inversion recovery	STIR	Fat suppression by setting an inversion time where the signal of fat is zero.	High signal in edema, such as in more severe stress fracture. Shin splints pictured:
	Fluid-attenuated inversion recovery	FLAIR	Fluid suppression by setting an inversion time that nulls fluids	High signal in lacunar infarction, multiple sclerosis (MS) plaques, subarachnoid haemorrhage and meningitis (pictured).
	Double inversion recovery	DIR	Simultaneous suppression of cerebrospinal fluid and white matter by two inversion times.	High signal of multiple sclerosis plaques (pictured).
Diffusion weighted (DWI)	Conventional	DWI	Measure of Brownian motion of water molecules.	High signal within minutes of cerebral infarction (pictured).
	Apparent diffusion coefficient	ADC	Reduced T2 weighting by taking multiple conventional DWI images with different DWI weighting, and the change corresponds to diffusion.	Low signal minutes after cerebral infarction (pictured).
	Diffusion tensor	DTI	Mainly tractography (pictured) by an overall greater Brownian motion of water molecules in the directions of nerve fibers.	Evaluating white matter deformation by tumors Reduced fractional anisotropy may indicate dementia.
Perfusion weighted (PWI)	Dynamic susceptibility contrast	DSC	Measures changes over time in susceptibility-induced signal loss due to gadolinium contrast injection.	Provides measurements of blood flow In cerebral infarction, the infarcted core and the penumbra have decreased perfusion and delayed contrast arrival (pictured).
	Arterial spin labelling	ASL	Magnetic labeling of arterial blood below the imaging slab, which subsequently enters the region of interest. It does not need gadolinium contrast.
	Dynamic contrast enhanced	DCE	Measures changes over time in the shortening of the spin–lattice relaxation (T1) induced by a gadolinium contrast bolus.	Faster Gd contrast uptake along with other features is suggestive of malignancy (pictured).
Functional MRI (fMRI)	Blood-oxygen-level dependent imaging	BOLD	Changes in oxygen saturation-dependent magnetism of hemoglobin reflects tissue activity.	Localizing brain activity from performing an assigned task (e.g. talking, moving fingers) before surgery, also used in research of cognition.
Magnetic resonance angiography (MRA) and venography	Time-of-flight	TOF	Blood entering the imaged area is not yet magnetically saturated, giving it a much higher signal when using short echo time and flow compensation.	Detection of aneurysm, stenosis, or dissection
	Phase-contrast magnetic resonance imaging	PC-MRA	Two gradients with equal magnitude, but opposite direction, are used to encode a phase shift, which is proportional to the velocity of spins.	Detection of aneurysm, stenosis, or dissection (pictured).	(VIPR)

Other specialized configurations

Magnetic resonance spectroscopy

Magnetic resonance spectroscopy (MRS) is used to measure the levels of different metabolites in body tissues, which can be achieved through a variety of single voxel or imaging-based techniques. The MR signal produces a spectrum of resonances that corresponds to different molecular arrangements of the isotope being "excited". This signature is used to diagnose certain metabolic disorders, especially those affecting the brain, and to provide information on tumor metabolism.

Magnetic resonance spectroscopic imaging (MRSI) combines both spectroscopic and imaging methods to produce spatially localized spectra from within the sample or patient. The spatial resolution is much lower (limited by the available SNR), but the spectra in each voxel contains information about many metabolites. Because the available signal is used to encode spatial and spectral information, MRSI requires high SNR achievable only at higher field strengths (3 T and above). The high procurement and maintenance costs of MRI with extremely high field strengths inhibit their popularity. However, recent compressed sensing-based software algorithms (e.g., SAMV) have been proposed to achieve super-resolution without requiring such high field strengths.

Real-time MRI

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Real-time MRI of a human heart at a resolution of 50 ms

Real-time MRI refers to the continuous imaging of moving objects (such as the heart) in real time. One of the many different strategies developed since the early 2000s is based on radial FLASH MRI, and iterative reconstruction. This gives a temporal resolution of 20–30 ms for images with an in-plane resolution of 1.5–2.0 mm. Balanced steady-state free precession (bSSFP) imaging has a better image contrast between the blood pool and myocardium than the FLASH MRI, yet it will produce severe banding artifact when the B0 inhomogeneity is strong. Real-time MRI is likely to add important information on diseases of the heart and the joints, and in many cases may make MRI examinations easier and more comfortable for patients, especially for the patients who cannot hold their breathings or who have arrhythmia.

Interventional MRI

The lack of harmful effects on the patient and the operator make MRI well-suited for interventional radiology, where the images produced by an MRI scanner guide minimally invasive procedures. Such procedures use no ferromagnetic instruments.

A specialized growing subset of interventional MRI is intraoperative MRI, in which an MRI is used in surgery. Some specialized MRI systems allow imaging concurrent with the surgical procedure. More typically, the surgical procedure is temporarily interrupted so that MRI can assess the success of the procedure or guide subsequent surgical work.

Magnetic resonance guided focused ultrasound

In guided therapy, high-intensity focused ultrasound (HIFU) beams are focused on a tissue, that are controlled using MR thermal imaging. Due to the high energy at the focus, the temperature rises to above 65 °C (150 °F) which completely destroys the tissue. This technology can achieve precise ablation of diseased tissue. MR imaging provides a three-dimensional view of the target tissue, allowing for the precise focusing of ultrasound energy. The MR imaging provides quantitative, real-time, thermal images of the treated area. This allows the physician to ensure that the temperature generated during each cycle of ultrasound energy is sufficient to cause thermal ablation within the desired tissue and if not, to adapt the parameters to ensure effective treatment.

Multinuclear imaging

Hydrogen has the most frequently imaged nucleus in MRI because it is present in biological tissues in great abundance, and because its high gyromagnetic ratio gives a strong signal. However, any nucleus with a net nuclear spin could potentially be imaged with MRI. Such nuclei include helium-3, lithium-7, carbon-13, fluorine-19, oxygen-17, sodium-23, phosphorus-31 and xenon-129. ²³Na and ³¹P are naturally abundant in the body, so they can be imaged directly. Gaseous isotopes such as ³He or ¹²⁹Xe must be hyperpolarized and then inhaled as their nuclear density is too low to yield a useful signal under normal conditions. ¹⁷O and ¹⁹F can be administered in sufficient quantities in liquid form (e.g. ¹⁷O-water) that hyperpolarization is not a necessity. Using helium or xenon has the advantage of reduced background noise, and therefore increased contrast for the image itself, because these elements are not normally present in biological tissues.

Moreover, the nucleus of any atom that has a net nuclear spin and that is bonded to a hydrogen atom could potentially be imaged via heteronuclear magnetization transfer MRI that would image the high-gyromagnetic-ratio hydrogen nucleus instead of the low-gyromagnetic-ratio nucleus that is bonded to the hydrogen atom. In principle, hetereonuclear magnetization transfer MRI could be used to detect the presence or absence of specific chemical bonds.

Multinuclear imaging is primarily a research technique at present. However, potential applications include functional imaging and imaging of organs poorly seen on ¹H MRI (e.g., lungs and bones) or as alternative contrast agents. Inhaled hyperpolarized ³He can be used to image the distribution of air spaces within the lungs. Injectable solutions containing ¹³C or stabilized bubbles of hyperpolarized ¹²⁹Xe have been studied as contrast agents for angiography and perfusion imaging. ³¹P can potentially provide information on bone density and structure, as well as functional imaging of the brain. Multinuclear imaging holds the potential to chart the distribution of lithium in the human brain, this element finding use as an important drug for those with conditions such as bipolar disorder.

Molecular imaging by MRI

MRI has the advantages of having very high spatial resolution and is very adept at morphological imaging and functional imaging. MRI does have several disadvantages though. First, MRI has a sensitivity of around 10⁻³ mol/L to 10⁻⁵ mol/L, which, compared to other types of imaging, can be very limiting. This problem stems from the fact that the population difference between the nuclear spin states is very small at room temperature. For example, at 1.5 teslas, a typical field strength for clinical MRI, the difference between high and low energy states is approximately 9 molecules per 2 million. Improvements to increase MR sensitivity include increasing magnetic field strength and hyperpolarization via optical pumping or dynamic nuclear polarization. There are also a variety of signal amplification schemes based on chemical exchange that increase sensitivity.

To achieve molecular imaging of disease biomarkers using MRI, targeted MRI contrast agents with high specificity and high relaxivity (sensitivity) are required. To date, many studies have been devoted to developing targeted-MRI contrast agents to achieve molecular imaging by MRI. Commonly, peptides, antibodies, or small ligands, and small protein domains, such as HER-2 affibodies, have been applied to achieve targeting. To enhance the sensitivity of the contrast agents, these targeting moieties are usually linked to high payload MRI contrast agents or MRI contrast agents with high relaxivities. A new class of gene targeting MR contrast agents has been introduced to show gene action of unique mRNA and gene transcription factor proteins. These new contrast agents can trace cells with unique mRNA, microRNA and virus; tissue response to inflammation in living brains. The MR reports change in gene expression with positive correlation to TaqMan analysis, optical and electron microscopy.

Parallel MRI

It takes time to gather MRI data using sequential applications of magnetic field gradients. Even for the most streamlined of MRI sequences, there are physical and physiologic limits to the rate of gradient switching. Parallel MRI circumvents these limits by gathering some portion of the data simultaneously, rather than in a traditional sequential fashion. This is accomplished using arrays of radiofrequency (RF) detector coils, each with a different ‘view’ of the body. A reduced set of gradient steps is applied, and the remaining spatial information is filled in by combining signals from various coils, based on their known spatial sensitivity patterns. The resulting acceleration is limited by the number of coils and by the signal to noise ratio (which decreases with increasing acceleration), but two- to four-fold accelerations may commonly be achieved with suitable coil array configurations, and substantially higher accelerations have been demonstrated with specialized coil arrays. Parallel MRI may be used with most MRI sequences.

After a number of early suggestions for using arrays of detectors to accelerate imaging went largely unremarked in the MRI field, parallel imaging saw widespread development and application following the introduction of the SiMultaneous Acquisition of Spatial Harmonics (SMASH) technique in 1996-7. The SENSitivity Encoding (SENSE) and Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) techniques are the parallel imaging methods in most common use today. The advent of parallel MRI resulted in extensive research and development in image reconstruction and RF coil design, as well as in a rapid expansion of the number of receiver channels available on commercial MR systems. Parallel MRI is now used routinely for MRI examinations in a wide range of body areas and clinical or research applications.

Safety

MRI is in general a safe technique, although injuries may occur as a result of failed safety procedures or human error. Contraindications to MRI include most cochlear implants and cardiac pacemakers, shrapnel, and metallic foreign bodies in the eyes. Magnetic resonance imaging in pregnancy appears to be safe at least during the second and third trimesters if done without contrast agents. Since MRI does not use any ionizing radiation, its use is generally favored in preference to CT when either modality could yield the same information. Some patients experience claustrophobia and may require sedation. Amplitude and rapid switching of gradient coils during image acquisition may cause peripheral nerve stimulation.

MRI uses powerful magnets and can therefore cause magnetic materials to move at great speeds posing a projectile risk, and may cause fatal accidents. However, as millions of MRIs are performed globally each year, fatalities are extremely rare.

Overuse

Medical societies issue guidelines for when physicians should use MRI on patients and recommend against overuse. MRI can detect health problems or confirm a diagnosis, but medical societies often recommend that MRI not be the first procedure for creating a plan to diagnose or manage a patient's complaint. A common case is to use MRI to seek a cause of low back pain; the American College of Physicians, for example, recommends against this procedure as unlikely to result in a positive outcome for the patient.

Artifacts

Motion artifact (T1 coronal study of cervical vertebrae)

An MRI artifact is a visual artifact, that is, an anomaly during visual representation. Many different artifacts can occur during magnetic resonance imaging (MRI), some affecting the diagnostic quality, while others may be confused with pathology. Artifacts can be classified as patient-related, signal processing-dependent and hardware (machine)-related.

Non-medical use

MRI is used industrially mainly for routine analysis of chemicals. The nuclear magnetic resonance technique is also used, for example, to measure the ratio between water and fat in foods, monitoring of flow of corrosive fluids in pipes, or to study molecular structures such as catalysts.

Being non-invasive and non-damaging, MRI can be used to study the anatomy of plants, their water transportation processes and water balance. It is also applied to veterinary radiology for diagnostic purposes. Outside this, its use in zoology is limited due to the high cost; but it can be used on many species.

In palaeontology it is used to examine the structure of fossils.

Forensic imaging provides graphic documentation of an autopsy, which manual autopsy does not. CT scanning provides quick whole-body imaging of skeletal and parenchymal alterations, whereas MRI imaging gives better representation of soft tissue pathology. But MRI is more expensive, and more time-consuming to utilize. Moreover, the quality of MR imaging deteriorates below 10 °C.

History

In 1971 at Stony Brook University, Paul Lauterbur applied magnetic field gradients in all three dimensions and a back-projection technique to create NMR images. He published the first images of two tubes of water in 1973 in the journal Nature, followed by the picture of a living animal, a clam, and in 1974 by the image of the thoracic cavity of a mouse. Lauterbur called his imaging method zeugmatography, a term which was replaced by (N)MR imaging. In the late 1970s, physicists Peter Mansfield and Paul Lauterbur developed MRI-related techniques, like the echo-planar imaging (EPI) technique.

Advances in semiconductor technology were crucial to the development of practical MRI, which requires a large amount of computational power. This was made possible by the rapidly increasing number of transistors on a single integrated circuit chip. Mansfield and Lauterbur were awarded the 2003 Nobel Prize in Physiology or Medicine for their "discoveries concerning magnetic resonance imaging".