NationMaster - Encyclopedia: Relaxation (NMR)

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Encyclopedia > Relaxation (NMR)

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In the topic of Nuclear magnetic resonance (NMR) and Magnetic resonance imaging (MRI) any excited magnetic moment relaxes back to equilibrium, parallel to the magnetic field, conventionally referred to as the z axis. The term Relaxation describes this phenomenon, the evolution of magnetizations separately in two directions: Pacific Northwest National Laboratorys high magnetic field (800 MHz, 18. ... Magnetic Resonance Image showing a median sagittal cross section through a human head. ... Magnetization is a property of some materials (e. ...

longitudinal relaxation: The part of the magnetization vector M that is parallel to the main magnetic field B₀, designated as M_z. The process proceeds at a rate governed by a time constant T₁.

$M_z(t) = M_z(0) cdot left( 1 - e^{-t/T_1} right) ,$

transverse relaxation: The part of the magnetization vector M that is perpendicular to the main magnetic field B₀ designated as M_xy, M_T, or $M_{perp}$ . The process proceeds at a rate a governed by time constant T₂.

$M_{xy}(t) = M_{xy}(0) cdot e^{-t/T_2} ,$

1 T1
2 T2
3 T2*
4 The reason that T1 is slower than T2
5 Local magnetic field inhomogeneity
6 Common relaxation time constants in human tissues
7 Microscopic mechanism
8 References
9 See also

Fig. ...

T₁

See main article Spin-lattice relaxation time

In an ideal environment where strict conservation of angular momentum is true for the nuclei being observed, T₁ would not exist. When the magnetization of a nucleus in the experimental pulse is altered, it should maintain its precession. So the bulk magnetization which is set into a disequilibrium cannot equilibrate. However, in a real system, there is spin transfer between the observed nuclei and the environment. This allows for "forbidden" transitions to occur, and "relaxation" from "excited" state back to equilibrium. Spin-lattice relaxation time, known as T1, is a time constant in Nuclear Magnetic Resonance and Magnetic Resonance Imaging. ... In physics, angular momentum intuitively measures how much the linear momentum is directed around a certain point called the origin; the moment of momentum. ... Precession of a gyroscope Precession refers to a change in the direction of the axis of a rotating object. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

T₁ is by definition, the component of relaxation which occurs in the direction of the ambient magnetic field. This generally comes about by interactions between the nucleus of interest and unexcited nuclei in the environment, as well as electric fields in the environment (collectively known as the 'lattice'). Therefore, T₁ is known as "spin-lattice" relaxation.

T₁ is measured as the time required for the magnetization vector M to be restored to 63% of its original magnitude. It varies with the magnetic field B. Magnetization is a property of some materials (e. ... This template is misplaced. ...

T₂

See main article: Spin-spin relaxation time

In an idealized system, T₂ would also not exist. However, in real systems, there is spin transfer amongst excited nuclei which disperses magnetization that is out of equilibrium. Spin-spin relaxation time, known as T2, is a time constant in Nuclear Magnetic Resonance and Magnetic Resonance Imaging. ...

T₂, by definition, is the component of 'true' relaxation (see T₂*) to equilibrium that occurs perpendicular to the ambient magnetic field. Because of this, the relaxation is dominated by interactions between spinning nuclei which are already excited. For this reason, T₂ relaxation is called "transverse" or "spin-spin" relaxation.

Since T₂ processes follow an exponential decay, the quantity T₂ is defined as the time required for the transverse Magnetization vector to drop to 37% of its original magnitude after its initial excitation.

Unlike T₁, T₂ is much less susceptible to variations of field strength B.

T₂*

In an idealized system, all nuclei in a given chemical environment in a magnetic field spin with the same frequency. However, in real systems, there are minor differences in chemical environment which can lead to a distribution of resonance frequencies around the ideal. Over time, this distribution can lead to a dispersion of the tight distribution of magnetic spin vectors, and loss of signal (Free Induction Decay). In fact, for most magnetic resonance experiments, this "relaxation" dominates. A free induction decay (FID) curve is generated as excited nuclei relax in an NMR machine. ...

However, this is not a true "relaxation" process. For most molecules, the deviation from ideal relaxation is consistent over time, and the signal can be recovered by performing a spin echo experiment. Spin echo: Pulse sequence (above) and Signal (below) In nuclear magnetic resonance, spin echo refers to the refocusing of precessing nuclear spin magnetisation by a 180Â° pulse of resonant radiofrequency. ...

Unlike T₂, T₂* is influenced by magnetic field gradient irregularities. The T₂* relaxation time is always shorter than the T₂ relaxation time and lasts a few milliseconds.

The relationship between T₂, T₂*, and spin dephasing due to inhomogeneities (T₂_inhom) is given by 1/T₂* = 1/T₂ + 1/T₂_inhom.

The reason that T₁ is slower than T₂

As a general rule, the following always holds true: T₁ > T₂ > T₂*.

In order to get magnetization transfer, the energies and orientations of spins with magnetic entities in the lattice must be matched. In most setups, this is a relatively rare condition, compared to spin-spin interactions, which a priori are aligned with each other.

More simply, if T₂ were to be slower than T₁, then the magnetizations perpendicular to the initial direction would have not dephased by the time the sample had returned to equilibrium. This is physically impossible, as once the sample has returned to equilibrium, there is no magnetization perpendicular to the original direction. Hence, T₁ must be greater than or equal to T₂.

Local magnetic field inhomogeneity

Besides, due to the inhomogeneity in main field, there occurs intra-voxel dephasing resulting in a far faster decay of the signal from transverse magnetization than that predicted by T₂ decay, which can be written as: A voxel (a portmanteau of the words volumetric and pixel) is a volume element, representing a value on a regular grid in three dimensional space. ... Dephasing is a process in which coherence in a substance caused by perturbation decays over time, and the system returns to the state before perturbation. ...

$M_{xy}(t) = e^{-t/T_2^*}cdot M_{xy}(t=0) ; ,$

$T_2^*<<T_2 ,$

The corresponding transverse relaxation time constant is thus T₂^*, which is much smaller than T₂. The relation between them is:

$frac{1}{T_2^*}=frac{1}{T_2}+gamma Delta B_0$

where γ represents gyromagnetic ratio, and ΔB₀ the difference in strength of the locally varying field. In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic dipole moment to its angular momentum. ...

Common relaxation time constants in human tissues

Following is a table of the approximate values of the two relaxation time constants for nonpathological human tissues, just for simple reference.

**At a main field of 1.5 T**
Tissue Type	Approximate T₁ value in ms	Approximate T₂ value in ms
Adipose tissues	240-250	60-80
Whole blood (deoxygenated)	1350	50
Whole blood (oxygenated)	1350	200
Cerebrospinal fluid (similar to pure water)	2200-2400	500-1400
Gray matter of cerebrum	920	100
White matter of cerebrum	780	90
Liver	490	40
Kidneys	650	60-75
Muscles	860-900	50

Following is a table of the approximate values of the two relaxation time constants for chemicals that commonly show up in human brain magnetic resonance spectroscopy (MRS) studies, physiologically or pathologically. SI unit. ... One millisecond is one-thousandth of a second. ... It has been suggested that Subcutaneous fat be merged into this article or section. ... Red blood cells (erythrocytes) are present in the blood and help carry oxygen to the rest of the cells in the body Blood is a circulating tissue composed of fluid plasma and cells (red blood cells, white blood cells, platelets). ... Red blood cells (erythrocytes) are present in the blood and help carry oxygen to the rest of the cells in the body Blood is a circulating tissue composed of fluid plasma and cells (red blood cells, white blood cells, platelets). ... Human blood smear: a - erythrocytes; b - neutrophil; c - eosinophil; d - lymphocyte. ... Cerebrospinal fluid (CSF), Liquor cerebrospinalis, is a clear bodily fluid that occupies the subarachnoid space in the brain (the space between the skull and the cerebral cortexâ€”more specifically, between the arachnoid and pia layers of the meninges). ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... Grey matter (or gray matter) is a major component of the central nervous system, consisting of nerve cell bodies, glial cells (astroglia and oligodendrocytes), capillaries, and short nerve cell extensions/processes (axons and dendrites). ... For other articles about other subjects named brain see brain (disambiguation). ... White matter is one of the two main solid components of the central nervous system. ... For other articles about other subjects named brain see brain (disambiguation). ... The liver is an organ present in vertebrates and some other animals. ... Kidneys viewed from behind with spine removed The kidneys are bean-shaped excretory organs in vertebrates. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... Italic text // ahh addiing sum spiice iin hurr`` For other uses, see Brain (disambiguation). ... For the scientific journal entitled Magnetic Resonance Imaging, see Magnetic Resonance Imaging (journal). ... This article or section does not cite any references or sources. ... Pathology (from Greek pathos, feeling, pain, suffering; and logos, study of; see also -ology) is the study of the processes underlying disease and other forms of illness, harmful abnormality, or dysfunction. ...

**At a main field of 1.5 T**
Creatine (Cr) and Phosphocreatine (PCr) ^[1]	3.0 ppm	gray matter: 1150-1340, white matter: 1050-1360	gray matter: 198-207, white matter: 194-218
Signals of Chemical Groups	Relative resonance frequency	Approximate T₁ value (ms)	Approximate T₂ value (ms)
N-Acetyl group (NA), mainly from N-Acetylaspartate (NAA) ^[2]	2.0 ppm	gray matter: 1170-1370, white matter: 1220-1410	gray matter: 388-426, white matter: 436-519
—CH₃ group of Lactate ^[3]	1.33 ppm (doublet: 1.27 & 1.39 ppm)	(To be listed)	1040

Creatine is a nitrogenous organic acid that naturally occurs in vertebrates and helps to supply energy to muscle cells. ... Phosphocreatine, also known as creatine phosphate or PCr, is a phosphorylated creatine molecule that is an important energy store in skeletal muscle. ... N-Acetyl aspartate (NAA) is a derivative of aspartic acid with a formula of C6H9NO5 and a molecular weight of 175. ... Lactic acid is a chemical compound that plays a role in several biochemical processes. ...

Microscopic mechanism

In 1948, Nicolaas Bloembergen, Edward Mills Purcell, and R.V. Pound proposed the so-called Bloembergen-Purcell-Pound theory (BPP theory) to explain the relaxation constant of a pure substance in correspondence with its state, taking into account the effect of tumbling motion of molecules on the local magnetic field disturbance ^[4]. The theory was in good agreement with the experiments for pure substance, but not for complicated environment such as human body. 1948 (MCMXLVIII) was a leap year starting on Thursday (the link is to a full 1948 calendar). ... Nicolaas Bloembergen (born Dordrecht, March 11, 1920) is a Dutch physicist. ... Edward Mills Purcell (August 30, 1912 â€“ March 7, 1997) was an American physicist who shared the 1952 Nobel Prize for Physics for his independent discovery (published 1946) of nuclear magnetic resonance in liquids and in solids. ... In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ...

From this theory, one can get T₁、T₂:

$frac{1}{T_1}=K[frac{tau_c}{1+omega_0^2tau_c^2}+frac{4tau_c}{1+4omega_0^2tau_c^2}]$

$frac{1}{T_2}=frac{K}{2}[3tau_c+frac{5tau_c}{1+omega_0^2tau_c^2}+frac{2tau_c}{1+4omega_0^2tau_c^2}]$ ,

where $ω 0$ is the Larmor frequency in correspondence with the strength of the main magnetic field $B 0$ . $τ c$ is the correlation time of the molecular tumbling motion. $K=frac{3mu^2}{160pi^2}frac{hbar^2gamma^4}{r^6}$ is a constant with μ being the magnetic dipole moment of the spin-1/2 nuclei, $hbar=frac{h}{2pi}$ the reduced Planck constant, γ the gyromagnetic ratio of such species of nuclei, and r the distance between the two nuclei carrying magnetic dipole moment. In physics, Larmor precession, named after Joseph Larmor refers to the precession of the magnetic moments of electrons, atomic nuclei, and atoms around the direction of an external magnetic field. ... Tumbling can have several meanings: Tumbling is floor gymnastics, similar to somersault, backhandsprings, and cartwheels. ... In physics, the magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. ... In quantum mechanics, spin is an intrinsic property of all elementary particles. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic dipole moment to its angular momentum. ...

Taking for example the H₂O molecules in liquid phase without the contamination of oxygen 17, the value of K is 1.02×10¹⁰ sec^-2 and the correlation time $τ c$ is on the order of ps = $10 - 12$ sec, while hydrogen nuclei ¹H (protons) at 1.5 tesla carry an Larmor frequency of approximately 64 MHz. We can then estimate using τ_c = 5×10^-12 sec: A liquid will usually assume the shape of its container. ... Oxygen (O) Standard atomic mass: 15. ... A picosecond is an SI unit of time equal to 10-12 of a second. ... Look up second in Wiktionary, the free dictionary. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Tesla may refer to: Nikola Tesla, a Serbian-American physicist, inventor, and electrical engineer. ... A megahertz (MHz) is one million (106) hertz, a measure of frequency. ...

$omega_0tau_c = 3.2times 10^{-5}$ (dimensionless)

$T_1=(1.02times 10^{10}[frac{ 5times 10^{-12} }{1 + (3.2times 10^{-5} )^2} + frac{ 4cdot 5times 10^{-12} }{1 + 4cdot (3.2times 10^{-5} )^2}])^{-1}$ = 3.92 sec

$T_2=(frac{1.02times 10^{10}}{2}[3cdot 5times 10^{-12} + frac{5cdot 5times 10^{-12} }{1 + (3.2times 10^{-5} )^2} + frac{ 2cdot 5times 10^{-12} }{1 + 4cdot (3.2times 10^{-5} )^2}])^{-1}$ = 3.92 sec,

which is close to the experimental value, 3.6 sec. Meanwhile, we can see that at this extreme case, T₁ equals T₂.

References

^ Chemicals of brain relaxation time at 1.5T. Kreis R, Ernst T, and Ross BD "Absolute Quantification of Water and Metabolites in the Human Brain. II. Metabolite Concentrations" Journal of Magnetic Resonance, Series B 102 (1993): 9-19
^ Lactate rexalation time at 1.5 T. Isobe T, Matsumura A, Anno I, Kawamura H, Muraishi H, Umeda T, Nose T. "Effect of J coupling and T2 Relaxation in Assessing of Methyl Lactate Signal using PRESS Sequence MR Spectroscopy." Igaku Butsuri (2005) v25. 2:68-74.
^ BPP theory. Bloembergen, E.M. Purcell, R.V. Pound "Relaxation Effects in Nuclear Magnetic Resonance Absorption" Physical Review (1948) v73. 7:679-746

Contents

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T2

T2*

The reason that T1 is slower than T2

Local magnetic field inhomogeneity

Common relaxation time constants in human tissues

Microscopic mechanism

References

See also

T₁

T₂

T₂*

The reason that T₁ is slower than T₂