In physics, the spin–spin relaxation is the mechanism by which Mxy, the transverse component of the magnetization vector, exponentially decays towards its equilibrium value in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). It is characterized by the spin–spin relaxation time, known as T2, a time constant characterizing the signal decay.[1] [2] [3] It is named in contrast to T1, the spin–lattice relaxation time. It is the time it takes for the magnetic resonance signal to irreversibly decay to 37% (1/e) of its initial value after its generation by tipping the longitudinal magnetization towards the magnetic transverse plane.[4] Hence the relation
- .
T2 relaxation generally proceeds more rapidly than T1 recovery, and different samples and different biological tissues have different T2. For example, fluids have the longest T2 (on the order of seconds for protons), and water based tissues are in the 40–200 ms range, while fat based tissues are in the 10–100 ms range. Amorphous solids have T2 in the range of milliseconds, while the transverse magnetization of crystalline samples decays in around 1/20 ms.
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UQx Bioimg101x 5.3.7 Spin Echo and Relaxation
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MRI | Introduction In the Physics of MRI and It's Clinical Relevance
Transcription
Hello everyone. In the previous section we learnt about the origin of the MR signal, how it arises from the interaction of radio frequency pulses with the net magnetization and that it takes the form of a free induction decay detected in an RF coil. We discussed how the dephasing of the magnetization due to Bo field inhomogeneity causes loss of transverse magnetization and signal decay. So is it possible to reverse this dephasing in some way to recover this lost magnetization and regain the signal? It turns out that the dephasing of spin vectors can be reversed by applying a 180 degree pulse to the transverse magnetization. Initially, we create transverse magnetization with a 90 degree pulse, the spin vectors associated with different Larmor frequencies then begin to dephase. In our rotating frame of reference, the blue spins precessing faster than the Larmor frequency rotate clockwise about Bo and the red slower spins precess anticlockwise. If at a time tau after the 90 degree pulse, a 180 degree RF pulse aligned along the X-axis is applied to the transverse magnetization, we see that the vectors are rotated through 180 degrees around the X axis finishing back in the X' - Y' plane on the other side of the X' axis. After the pulse, the vectors then continue to precess around the Z axis in the same direction as they were precessing prior to the pulse. This means that after another time period of tau, the vectors will re-converge, this time aligned along the -Y' axis. This process is called refocusing and reverses the dephasing. Let's look at this again in its entirety. If we were to acquire the signal during this sequence, we would observe the transverse magnetization decay immediately following the 90 degree pulse, and then increase again when the Y-magnetization reforms as the vectors refocus. The signal then decays again once vectors continue to precess and dephase once more. This signal is known as a spin echo. This refocusing can also be achieved by applying a 180 degree pulse aligned along the Y' axis. Again, a 90 degree pulse is followed by a time tau for the spins to dephase, and then a 180 degree pulse along the Y' axis is applied. This time, the spin vectors are rotated 180 degrees around the Y' axis and then converge back along the +Y' axis. This would give rise to a spin echo, but with the opposite sign compared to the echo obtained with the 180 degree pulse along the X' axis. If the magnetization is allowed to dephase for a further time tau after the echo and another 180 degree pulse applied, the vectors will again be refocused forming a second echo. This process can be repeated to form multiple spin echoes. So now we have the basis of an RF pulse sequence. The 90 tau 180 tau series of pulses and delays is called a spin echo sequence and is the fundamental pulse sequence around which many MRI sequences are built. The top blue line represents the RF transmitter pulses, and the bottom yellow line the receiver and the signal that is detected. In this case the receiver is turned on after the 180 degree pulse and we detect the spin echo which reaches maximum intensity at the end of the second tau time. The time between the 90 degree excitation pulse and the echo maximum, that is 2 x tau, is called the echo time, or TE. TE is an important parameter in MRI that has a significant impact on image contrast as we will see later. So we have seen that dephasing of magnetic moments by Bo field inhomogeneity can be reversed by a 180 pulse. This is true provided that the Bo field does not change during the tau times. If the field changed in some way, then the precessional frequencies of the vectors before the 180 would not be the same after the pulse and so an echo would not form along the Y' axis at time 2 tau. Of course the formation of echoes cannot go on indefinitely or after long periods of precession time. At some point the system has to return to equilibrium. This process is known as relaxation, and occurs through other dephasing mechanisms that are not reversible. For transverse magnetization, this occurs through interactions between the individual spins and so is called spin-spin relaxation. As we know, the proton is a spinning charged particle, and as such, will generate a local magnetic field of its own. Another proton nearby may be affected by the local field of the first. The effective field at the second proton could be altered by that of the first proton and so its Larmor frequency will change. The extent of this shift in frequency will depend on the proximity of the first proton and the direction of its local field at the second nucleus. Since water molecules are freely tumbling and rotating, this motion causes the local field at the second proton to fluctuate. This animation shows this spin-spin interaction. As the molecule tumbles, the local field at one proton passes through the other spin. The field changes at the second spin depends on the rate of molecular tumbling. If the fluctuations occur at a rate that approaches the Larmor frequency of the second spin, then that spin may be excited and an energy level transition may occur. This process is important for T1 relaxation which we discuss in the next section. So we can say that spin-spin relaxation will take place in a time dependent manner. The molecular motion is virtually random and so the variations in frequency are not constant with time throughout the spin echo sequence. Spin-spin relaxation is therefore an incoherent dephasing process and so dephasing of this type is not reversible. Other mechanisms also contribute to spin-spin relaxation, including chemical exchange where a proton on one water molecule exchanges for a proton on another through hydrogen bonding effects. So, we see that the spin echo sequence will only refocus magnetization dephased by magnetic field inhomogeneity. Spin-spin relaxation cannot be recovered and leads to irreversible loss of signal. The signal decays exponentially with time, and the rate at which this relaxation occurs is governed by a rate constant, the relaxation time, T2. T2 is a property of the nucleus that is dependent on a number of environmental and chemical factors and is the basis of one of the most important image contrast mechanisms that allow us to distinguish one form of tissue from another.
Origin
When excited nuclear spins—i.e., those lying partially in the transverse plane—interact with each other by sampling local magnetic field inhomogeneities on the micro- and nanoscales, their respective accumulated phases deviate from expected values.[4] While the slow- or non-varying component of this deviation is reversible, some net signal will inevitably be lost due to short-lived interactions such as collisions and random processes such as diffusion through heterogeneous space.
T2 decay does not occur due to the tilting of the magnetization vector away from the transverse plane. Rather, it is observed due to the interactions of an ensemble of spins dephasing from each other.[5] Unlike spin-lattice relaxation, considering spin-spin relaxation using only a single isochromat is trivial and not informative.
Determining parameters
Like spin-lattice relaxation, spin-spin relaxation can be studied using a molecular tumbling autocorrelation framework.[6] The resulting signal decays exponentially as the echo time (TE), i.e., the time after excitation at which readout occurs, increases. In more complicated experiments, multiple echoes can be acquired simultaneously in order to quantitatively evaluate one or more superimposed T2 decay curves.[6] The relaxation rate experienced by a spin, which is the inverse of T2, is proportional to a spin's tumbling energy at the frequency difference between one spin and another; in less mathematical terms, energy is transferred between two spins when they rotate at a similar frequency to their beat frequency, in the figure at right.[6] In that the beat frequency range is very small relative to the average rotation rate , spin-spin relaxation is not heavily dependent on magnetic field strength. This directly contrasts with spin-lattice relaxation, which occurs at tumbling frequencies equal to the Larmor frequency .[7] Some frequency shifts, such as the NMR chemical shift, occur at frequencies proportional to the Larmor frequency, and the related but distinct parameter T2* can be heavily dependent on field strength due to the difficulty of correcting for inhomogeneity in stronger magnet bores.[4]
Assuming isothermal conditions, spins tumbling faster through space will generally have a longer T2. Since slower tumbling displaces the spectral energy at high tumbling frequencies to lower frequencies, the relatively low beat frequency will experience a monotonically increasing amount of energy as increases, decreasing relaxation time.[6] The figure at the left illustrates this relationship. It is worth noting again that fast tumbling spins, such as those in pure water, have similar T1 and T2 relaxation times,[6] while slow tumbling spins, such as those in crystal lattices, have very distinct relaxation times.
Measurement
A spin echo experiment can be used to reverse time-invariant dephasing phenomena such as millimeter-scale magnetic inhomogeneities.[6] The resulting signal decays exponentially as the echo time (TE), i.e., the time after excitation at which readout occurs, increases. In more complicated experiments, multiple echoes can be acquired simultaneously in order to quantitatively evaluate one or more superimposed T2 decay curves.[6] In MRI, T2-weighted images can be obtained by selecting an echo time on the order of the various tissues' T2s.[8] In order to reduce the amount of T1 information and therefore contamination in the image, excited spins are allowed to return to near-equilibrium on a T1 scale before being excited again. (In MRI parlance, this waiting time is called the "repetition time" and is abbreviated TR). Pulse sequences other than the conventional spin echo can also be used to measure T2; gradient echo sequences such as steady-state free precession (SSFP) and multiple spin echo sequences can be used to accelerate image acquisition or inform on additional parameters.[6][8]
See also
References
- ^ Abragam, A. (1961). Principles of Nuclear Magnetism. Clarendon Press. p. 15. ISBN 019852014X.
- ^ Claridge, Timothy D.W. (2016). High Resolution NMR Techniques in Organic Chemistry, 3rd ed. Elsevier. p. 26-30. ISBN 978-0080999869.
- ^ Levitt, Malcolm H. (2016). Spin Dynamics: Basics of Nuclear Magnetic Resonance 2nd Edition. Wiley. ISBN 978-0470511176.
- ^ a b c Chavhan, Govind; Babyn, Paul; Thomas, Bejoy; Shroff, Manohar; Haacke, Mark (September 2009). "Principles, Techniques, and Applications of T2*-based MR Imaging and Its Special Applications". RadioGraphics. 29 (5): 1433–1449. doi:10.1148/rg.295095034. PMC 2799958. PMID 19755604.
- ^ Becker, Edwin (October 1999). High Resolution NMR (3rd ed.). San Diego, California: Academic Press. p. 209. ISBN 978-0-12-084662-7. Retrieved 8 May 2019.
- ^ a b c d e f g h Becker, Edwin (October 1999). High Resolution NMR (3rd ed.). San Diego, California: Academic Press. p. 228. ISBN 978-0-12-084662-7. Retrieved 8 May 2019.
- ^ Yury, Shapiro (September 2011). "Structure and dynamics of hydrogels and organogels: An NMR spectroscopy approach". Progress in Polymer Science. 36 (9): 1184–1253. doi:10.1016/j.progpolymsci.2011.04.002.
- ^ a b Basser, Peter; Mattiello, James; LeBihan, Denis (January 1994). "MR diffusion tensor spectroscopy and imaging". Biophysical Journal. 66 (1): 259–267. Bibcode:1994BpJ....66..259B. doi:10.1016/S0006-3495(94)80775-1. PMC 1275686. PMID 8130344.
- Ray Freeman (1999). Spin Choreography: Basic Steps in High Resolution NMR. Oxford University Press. ISBN 978-0-19-850481-8.
- Malcolm H. Levitt (2001). Spin Dynamics: Basics of Nuclear Magnetic Resonance. Wiley. ISBN 978-0-471-48922-1.
- Arthur Schweiger; Gunnar Jeschke (2001). Principles of Pulse Electron Paramagnetic Resonance. Oxford University Press. ISBN 978-0-19-850634-8.
- McRobbie D., et al. MRI, From picture to proton. 2003
- Hashemi Ray, et al. MRI, The Basics 2ED. 2004.
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This page was last edited on 7 April 2024, at 20:40