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'''Spin–lattice relaxation in the rotating frame''' is the mechanism by which ''M<sub>xy</sub>'', the transverse component of the magnetization vector, exponentially decays towards its equilibrium value of zero, under the influence of a [[radio frequency]] (RF) field in [[nuclear magnetic resonance]] (NMR) and [[magnetic resonance imaging]] (MRI).   It is characterized by the spin–lattice relaxation '''time constant''' in the rotating frame, T<sub>1ρ</sub>. It is named in contrast to ''T<sub>1</sub>'', the [[spin-lattice relaxation time]].
 
T<sub>1ρ</sub> MRI is an alternative to conventional T<sub>1</sub> and T<sub>2</sub> MRI by its use of a long-duration, low-power [[radio frequency]] referred to as spin-lock (SL) pulse applied to the magnetization in the transverse plane. The magnetization is effectively spin-locked around an effective B<sub>1</sub> field created by the vector sum of the applied B<sub>1</sub> and any off-resonant component. The spin-locked magnetization will relax with a time constant T<sub>1ρ</sub>, which is the time it takes for the magnetic resonance signal to reach 37% (1/e) of its initial value, <math>M_{xy}(0)</math>.  Hence the relation:
<math>M_{xy}(t_{SL}) = M_{xy}(0) e^{-t_{SL}/T_{1rho}} \,</math>
, where t<sub>SL</sub> is the duration of the RF field.
 
==Measuring Spin–lattice relaxation in the rotating frame==
 
T<sub>1ρ</sub> can be quantified (relaxometry) by [[curve fitting]] the signal expression above as a function of the duration of the SL pulse while the amplitude of SL pulse (γB<sub>1</sub>~0.1-few kHz) is fixed. Quantitative T<sub>1ρ</sub> MRI relaxation maps reflect the biochemical composition of tissues.<ref>{{cite journal|last=Borthakur|first=A|coauthors=Mellon, E, Niyogi, S, Witschey, W, Kneeland, JB, Reddy, R|title=Sodium and T1rho MRI for molecular and diagnostic imaging of articular cartilage.|journal=NMR in biomedicine|date=2006 Nov|volume=19|issue=7|pages=781–821|pmid=17075961|doi=10.1002/nbm.1102|pmc=2896046}}</ref>
 
==''T<sub>1ρ</sub>'' MR images==
 
T<sub>1ρ</sub> MRI has been used to image tissues such as cartilage,<ref>{{cite journal|last=Li|first=X|coauthors=Benjamin Ma, C, Link, TM, Castillo, DD, Blumenkrantz, G, Lozano, J, Carballido-Gamio, J, Ries, M, Majumdar, S|title=In vivo T(1rho) and T(2) mapping of articular cartilage in osteoarthritis of the knee using 3 T MRI.|journal=Osteoarthritis and cartilage / OARS, Osteoarthritis Research Society|date=2007 Jul|volume=15|issue=7|pages=789–97|pmid=17307365|doi=10.1016/j.joca.2007.01.011|pmc=2040334}}</ref><ref>{{cite journal|last=Witschey|first=WR|coauthors=Borthakur, A, Fenty, M, Kneeland, BJ, Lonner, JH, McArdle, EL, Sochor, M, Reddy, R|title=T1rho MRI quantification of arthroscopically confirmed cartilage degeneration.|journal=Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine|date=2010 May|volume=63|issue=5|pages=1376–82|pmid=20432308|doi=10.1002/mrm.22272|pmc=2933515}}</ref> intervertebral discs,<ref>{{cite journal|last=Borthakur|first=A|coauthors=Maurer, PM, Fenty, M, Wang, C, Berger, R, Yoder, J, Balderston, RA, Elliott, DM|title=T1ρ magnetic resonance imaging and discography pressure as novel biomarkers for disc degeneration and low back pain.|journal=Spine|date=2011 Dec 1|volume=36|issue=25|pages=2190–6|pmid=21358489|doi=10.1097/BRS.0b013e31820287bf}}</ref> brain,<ref>{{cite journal|last=Borthakur|first=A|coauthors=Sochor, M, Davatzikos, C, Trojanowski, JQ, Clark, CM|title=T1rho MRI of Alzheimer's disease.|journal=NeuroImage|date=2008 Jul 15|volume=41|issue=4|pages=1199–205|pmid=18479942|doi=10.1016/j.neuroimage.2008.03.030}}</ref><ref>{{cite journal|last=Cai|first=K|coauthors=Haris, M, Singh, A, Kogan, F, Greenberg, JH, Hariharan, H, Detre, JA, Reddy, R|title=Magnetic resonance imaging of glutamate.|journal=Nature Medicine|date=2012 Jan 22|volume=18|issue=2|pages=302–6|pmid=22270722|doi=10.1038/nm.2615}}</ref> and heart,<ref>{{cite journal|last=Witschey|first=WR|coauthors=Pilla, JJ, Ferrari, G, Koomalsingh, K, Haris, M, Hinmon, R, Zsido, G, Gorman JH, 3rd, Gorman, RC, Reddy, R|title=Rotating frame spin lattice relaxation in a swine model of chronic, left ventricular myocardial infarction.|journal=Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine|date=2010 Nov|volume=64|issue=5|pages=1453–60|pmid=20677236|doi=10.1002/mrm.22543|pmc=2965811}}</ref> as well as certain types of cancers.<ref>{{cite journal|last=Li|first=LZ|coauthors=Zhou, R, Xu, HN, Moon, L, Zhong, T, Kim, EJ, Qiao, H, Reddy, R, Leeper, D, Chance, B, Glickson, JD|title=Quantitative magnetic resonance and optical imaging biomarkers of melanoma metastatic potential.|journal=Proceedings of the National Academy of Sciences of the United States of America|date=2009 Apr 21|volume=106|issue=16|pages=6608–13|pmid=19366661|doi=10.1073/pnas.0901807106|pmc=2672511}}</ref><ref>{{cite journal|last=Cai|first=K|coauthors=Shore, A, Singh, A, Haris, M, Hiraki, T, Waghray, P, Reddy, D, Greenberg, JH, Reddy, R|title=Blood oxygen level dependent angiography (BOLDangio) and its potential applications in cancer research.|journal=NMR in biomedicine|date=2012 Feb 2|pmid=22302557|doi=10.1002/nbm.2780}}</ref>
 
==References==
*{{cite book
|author = Malcolm H. Levitt
|title =  Spin Dynamics: Basics of Nuclear Magnetic Resonance
|publisher = Wiley
|year = 2001
|isbn =  978-0-471-48922-1
}}
 
{{Reflist}}
 
{{DEFAULTSORT:Spin-lattice relaxation in the rotating frame}}
[[Category:Magnetic resonance imaging]]
 
 
{{measurement-stub}}
{{electromagnetism-stub}}

Revision as of 18:00, 21 February 2014

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