<s>
In	O
MRI	B-Algorithm
and	O
NMR	O
spectroscopy	O
,	O
an	O
observable	O
nuclear	O
spin	B-General_Concept
polarization	I-General_Concept
(	O
magnetization	O
)	O
is	O
created	O
by	O
a	O
homogeneous	O
magnetic	O
field	O
.	O
</s>
<s>
The	O
return	O
of	O
the	O
longitudinal	O
component	O
of	O
the	O
magnetization	O
to	O
its	O
equilibrium	O
value	O
is	O
termed	O
spin-lattice	B-Algorithm
relaxation	I-Algorithm
while	O
the	O
loss	O
of	O
phase-coherence	O
of	O
the	O
spins	O
is	O
termed	O
spin-spin	B-Algorithm
relaxation	I-Algorithm
,	O
which	O
is	O
manifest	O
as	O
an	O
observed	O
free	O
induction	O
decay	O
(	O
FID	O
)	O
.	O
</s>
<s>
The	O
energy	O
gap	O
between	O
the	O
spin-up	O
and	O
spin-down	O
states	O
in	O
NMR	O
is	O
minute	O
by	O
atomic	O
emission	O
standards	O
at	O
magnetic	O
fields	O
conventionally	O
used	O
in	O
MRI	B-Algorithm
and	O
NMR	O
spectroscopy	O
.	O
</s>
<s>
The	O
decay	O
of	O
RF-induced	O
NMR	O
spin	B-General_Concept
polarization	I-General_Concept
is	O
characterized	O
in	O
terms	O
of	O
two	O
separate	O
processes	O
,	O
each	O
with	O
their	O
own	O
time	O
constants	O
.	O
</s>
<s>
One	O
process	O
,	O
called	O
T1	B-Algorithm
,	O
is	O
responsible	O
for	O
the	O
loss	O
of	O
resonance	O
intensity	O
following	O
pulse	O
excitation	O
.	O
</s>
<s>
Stated	O
more	O
formally	O
,	O
T1	B-Algorithm
is	O
the	O
time	O
constant	O
for	O
the	O
physical	O
processes	O
responsible	O
for	O
the	O
relaxation	B-Algorithm
of	O
the	O
components	O
of	O
the	O
nuclear	O
spin	O
magnetization	O
vector	O
M	O
parallel	O
to	O
the	O
external	O
magnetic	O
field	O
,	O
B0	O
(	O
which	O
is	O
conventionally	O
designated	O
as	O
the	O
z-axis	O
)	O
.	O
</s>
<s>
T2	B-Algorithm
relaxation	I-Algorithm
affects	O
the	O
coherent	O
components	O
of	O
M	O
perpendicular	O
to	O
B0	O
.	O
</s>
<s>
In	O
conventional	O
NMR	O
spectroscopy	O
,	O
T1	B-Algorithm
limits	O
the	O
pulse	O
repetition	O
rate	O
and	O
affects	O
the	O
overall	O
time	O
an	O
NMR	O
spectrum	O
can	O
be	O
acquired	O
.	O
</s>
<s>
Values	O
of	O
T1	B-Algorithm
range	O
from	O
milliseconds	O
to	O
several	O
seconds	O
,	O
depending	O
on	O
the	O
size	O
of	O
the	O
molecule	O
,	O
the	O
viscosity	O
of	O
the	O
solution	O
,	O
the	O
temperature	O
of	O
the	O
sample	O
,	O
and	O
the	O
possible	O
presence	O
of	O
paramagnetic	O
species	O
(	O
e.g.	O
,	O
O2	O
or	O
metal	O
ions	O
)	O
.	O
</s>
<s>
The	O
longitudinal	O
(	O
or	O
spin-lattice	O
)	O
relaxation	B-Algorithm
time	O
T1	B-Algorithm
is	O
the	O
decay	O
constant	O
for	O
the	O
recovery	O
of	O
the	O
z	O
component	O
of	O
the	O
nuclear	O
spin	O
magnetization	O
,	O
Mz	O
,	O
towards	O
its	O
thermal	O
equilibrium	O
value	O
,	O
.	O
</s>
<s>
the	O
magnetization	O
recovers	O
to	O
63%	O
of	O
its	O
equilibrium	O
value	O
after	O
one	O
time	O
constant	O
T1	B-Algorithm
.	O
</s>
<s>
T1	B-Algorithm
relaxation	I-Algorithm
involves	O
redistributing	O
the	O
populations	O
of	O
the	O
nuclear	O
spin	O
states	O
in	O
order	O
to	O
reach	O
the	O
thermal	O
equilibrium	O
distribution	O
.	O
</s>
<s>
Hence	O
truly	O
isolated	O
nuclear	O
spins	O
would	O
show	O
negligible	O
rates	O
of	O
T1	B-Algorithm
relaxation	I-Algorithm
.	O
</s>
<s>
However	O
,	O
a	O
variety	O
of	O
relaxation	B-Algorithm
mechanisms	O
allow	O
nuclear	O
spins	O
to	O
exchange	O
energy	O
with	O
their	O
surroundings	O
,	O
the	O
lattice	O
,	O
allowing	O
the	O
spin	O
populations	O
to	O
equilibrate	O
.	O
</s>
<s>
The	O
fact	O
that	O
T1	B-Algorithm
relaxation	I-Algorithm
involves	O
an	O
interaction	O
with	O
the	O
surroundings	O
is	O
the	O
origin	O
of	O
the	O
alternative	O
description	O
,	O
spin-lattice	B-Algorithm
relaxation	I-Algorithm
.	O
</s>
<s>
Note	O
that	O
the	O
rates	O
of	O
T1	B-Algorithm
relaxation	I-Algorithm
(	O
i.e.	O
,	O
1/T1	B-Algorithm
)	O
are	O
generally	O
strongly	O
dependent	O
on	O
the	O
NMR	O
frequency	O
and	O
so	O
vary	O
considerably	O
with	O
magnetic	O
field	O
strength	O
B	O
.	O
</s>
<s>
Small	O
amounts	O
of	O
paramagnetic	O
substances	O
in	O
a	O
sample	O
speed	O
up	O
relaxation	B-Algorithm
very	O
much	O
.	O
</s>
<s>
By	O
degassing	O
,	O
and	O
thereby	O
removing	O
dissolved	O
oxygen	O
,	O
the	O
T1/T2	O
of	O
liquid	O
samples	O
easily	O
go	O
up	O
to	O
an	O
order	O
of	O
ten	O
seconds	O
.	O
</s>
<s>
Especially	O
for	O
molecules	O
exhibiting	O
slowly	O
relaxing	O
(	O
T1	B-Algorithm
)	O
signals	O
,	O
the	O
technique	O
spin	O
saturation	O
transfer	O
(	O
SST	O
)	O
provides	O
information	O
on	O
chemical	O
exchange	O
reactions	O
.	O
</s>
<s>
This	O
magnetization	O
transfer	O
technique	O
provides	O
rates	O
,	O
provided	O
that	O
they	O
exceed	O
1/T1	B-Algorithm
.	O
</s>
<s>
The	O
transverse	O
(	O
or	O
spin-spin	O
)	O
relaxation	B-Algorithm
time	O
T2	O
is	O
the	O
decay	O
constant	O
for	O
the	O
component	O
of	O
M	O
perpendicular	O
to	O
B0	O
,	O
designated	O
Mxy	O
,	O
MT	O
,	O
or	O
.	O
</s>
<s>
T2	B-Algorithm
relaxation	I-Algorithm
is	O
a	O
complex	O
phenomenon	O
,	O
but	O
at	O
its	O
most	O
fundamental	O
level	O
,	O
it	O
corresponds	O
to	O
a	O
decoherence	O
of	O
the	O
transverse	O
nuclear	O
spin	O
magnetization	O
.	O
</s>
<s>
Because	O
T2	B-Algorithm
relaxation	I-Algorithm
involves	O
only	O
the	O
phases	O
of	O
other	O
nuclear	O
spins	O
it	O
is	O
often	O
called	O
"	O
spin-spin	O
"	O
relaxation	B-Algorithm
.	O
</s>
<s>
T2	O
values	O
are	O
generally	O
much	O
less	O
dependent	O
on	O
field	O
strength	O
,	O
B	O
,	O
than	O
T1	B-Algorithm
values	O
.	O
</s>
<s>
In	O
fact	O
,	O
for	O
most	O
magnetic	O
resonance	O
experiments	O
,	O
this	O
"	O
relaxation	B-Algorithm
"	O
dominates	O
.	O
</s>
<s>
However	O
,	O
decoherence	O
because	O
of	O
magnetic	O
field	O
inhomogeneity	O
is	O
not	O
a	O
true	O
"	O
relaxation	B-Algorithm
"	O
process	O
;	O
it	O
is	O
not	O
random	O
,	O
but	O
dependent	O
on	O
the	O
location	O
of	O
the	O
molecule	O
in	O
the	O
magnet	O
.	O
</s>
<s>
For	O
molecules	O
that	O
are	O
n't	O
moving	O
,	O
the	O
deviation	O
from	O
ideal	O
relaxation	B-Algorithm
is	O
consistent	O
over	O
time	O
,	O
and	O
the	O
signal	O
can	O
be	O
recovered	O
by	O
performing	O
a	O
spin	O
echo	O
experiment	O
.	O
</s>
<s>
The	O
corresponding	O
transverse	O
relaxation	B-Algorithm
time	O
constant	O
is	O
thus	O
T2*	O
,	O
which	O
is	O
usually	O
much	O
smaller	O
than	O
T2	O
.	O
</s>
<s>
The	O
T2*	O
relaxation	B-Algorithm
time	O
is	O
always	O
shorter	O
than	O
the	O
T2	B-Algorithm
relaxation	I-Algorithm
time	O
and	O
is	O
typically	O
milliseconds	O
for	O
water	O
samples	O
in	O
imaging	O
magnets	O
.	O
</s>
<s>
Bloch	O
equations	O
are	O
used	O
to	O
calculate	O
the	O
nuclear	O
magnetization	O
M	O
=	O
(	O
Mx	O
,	O
My	O
,	O
Mz	O
)	O
as	O
a	O
function	O
of	O
time	O
when	O
relaxation	B-Algorithm
times	O
T1	B-Algorithm
and	O
T2	O
are	O
present	O
.	O
</s>
<s>
It	O
is	O
present	O
in	O
magnetic	B-Algorithm
resonance	I-Algorithm
imaging	I-Algorithm
and	O
helps	O
with	O
the	O
spatial	O
decoding	O
of	O
the	O
NMR	O
signal	O
.	O
</s>
<s>
The	O
equation	O
listed	O
above	O
in	O
the	O
section	O
on	O
T1	B-Algorithm
and	O
T2	B-Algorithm
relaxation	I-Algorithm
are	O
those	O
in	O
the	O
Bloch	O
equations	O
.	O
</s>
<s>
Solomon	O
equations	O
are	O
used	O
to	O
calculate	O
the	O
transfer	O
of	O
magnetization	O
as	O
a	O
result	O
of	O
relaxation	B-Algorithm
in	O
a	O
dipolar	O
system	O
.	O
</s>
<s>
Following	O
is	O
a	O
table	O
of	O
the	O
approximate	O
values	O
of	O
the	O
two	O
relaxation	B-Algorithm
time	O
constants	O
for	O
hydrogen	O
nuclear	O
spins	O
in	O
nonpathological	O
human	O
tissues	O
.	O
</s>
<s>
Following	O
is	O
a	O
table	O
of	O
the	O
approximate	O
values	O
of	O
the	O
two	O
relaxation	B-Algorithm
time	O
constants	O
for	O
chemicals	O
that	O
commonly	O
show	O
up	O
in	O
human	O
brain	O
magnetic	B-Algorithm
resonance	I-Algorithm
spectroscopy	I-Algorithm
(	O
MRS	O
)	O
studies	O
,	O
physiologically	O
or	O
pathologically	O
.	O
</s>
<s>
+	O
At	O
a	O
main	O
field	O
of	O
1.5	O
T	O
Signals	O
of	O
chemical	O
groups	O
Relative	O
resonance	O
frequency	O
Approximate	O
T1	B-Algorithm
value	O
(	O
ms	O
)	O
Approximate	O
T2	O
value	O
(	O
ms	O
)	O
Creatine	O
(	O
Cr	O
)	O
and	O
Phosphocreatine	O
(	O
PCr	O
)	O
Chemicals	O
of	O
brain	O
relaxation	B-Algorithm
time	O
at	O
1.5T	O
.	O
</s>
<s>
Metabolite	O
Concentrations	O
"	O
Journal	O
of	O
Magnetic	O
Resonance	O
,	O
Series	O
B	O
102	O
(	O
1993	O
)	O
:	O
9-19	O
3.0	O
ppm	O
gray	B-Device
matter	I-Device
:	O
1150-1340	O
,	O
white	O
matter	O
:	O
1050-1360	O
gray	B-Device
matter	I-Device
:	O
198-207	O
,	O
white	O
matter	O
:	O
194-218N-Acetyl	O
group	O
(	O
NA	O
)	O
,	O
mainly	O
from	O
N-acetylaspartate	O
(	O
NAA	O
)	O
2.0	O
ppm	O
gray	B-Device
matter	I-Device
:	O
1170-1370	O
,	O
white	O
matter	O
:	O
1220-1410	O
gray	B-Device
matter	I-Device
:	O
388-426	O
,	O
white	O
matter	O
:	O
436-519	O
—	O
CH3	O
group	O
ofLactateLactate	O
relaxation	B-Algorithm
time	O
at	O
1.5	O
T	O
.	O
Isobe	O
T	O
,	O
Matsumura	O
A	O
,	O
Anno	O
I	O
,	O
Kawamura	O
H	O
,	O
Muraishi	O
H	O
,	O
Umeda	O
T	O
,	O
Nose	O
T	O
.	O
"	O
Effect	O
of	O
J	O
coupling	O
and	O
T2	B-Algorithm
Relaxation	I-Algorithm
in	O
Assessing	O
of	O
Methyl	O
Lactate	O
Signal	O
using	O
PRESS	O
Sequence	O
MR	O
Spectroscopy.	O
"	O
</s>
<s>
The	O
discussion	O
above	O
describes	O
relaxation	B-Algorithm
of	O
nuclear	O
magnetization	O
in	O
the	O
presence	O
of	O
a	O
constant	O
magnetic	O
field	O
B0	O
.	O
</s>
<s>
This	O
is	O
called	O
relaxation	B-Algorithm
in	O
the	O
laboratory	O
frame	O
.	O
</s>
<s>
Another	O
technique	O
,	O
called	O
relaxation	B-Algorithm
in	O
the	O
rotating	O
frame	O
,	O
is	O
the	O
relaxation	B-Algorithm
of	O
nuclear	O
magnetization	O
in	O
the	O
presence	O
of	O
the	O
field	O
B0	O
together	O
with	O
a	O
time-dependent	O
magnetic	O
field	O
B1	O
.	O
</s>
<s>
Under	O
these	O
circumstances	O
the	O
relaxation	B-Algorithm
of	O
the	O
magnetization	O
is	O
similar	O
to	O
laboratory	O
frame	O
relaxation	B-Algorithm
in	O
a	O
field	O
B1	O
.	O
</s>
<s>
The	O
decay	O
constant	O
for	O
the	O
recovery	O
of	O
the	O
magnetization	O
component	O
along	O
B1	O
is	O
called	O
the	O
spin-lattice	B-Algorithm
relaxation	I-Algorithm
time	I-Algorithm
in	O
the	O
rotating	O
frame	O
and	O
is	O
denoted	O
T1ρ	O
.	O
</s>
<s>
Relaxation	B-Algorithm
in	O
the	O
rotating	O
frame	O
is	O
useful	O
because	O
it	O
provides	O
information	O
on	O
slow	O
motions	O
of	O
nuclei	O
.	O
</s>
<s>
Relaxation	B-Algorithm
of	O
nuclear	O
spins	O
requires	O
a	O
microscopic	O
mechanism	O
for	O
a	O
nucleus	O
to	O
change	O
orientation	O
with	O
respect	O
to	O
the	O
applied	O
magnetic	O
field	O
and/or	O
interchange	O
energy	O
with	O
the	O
surroundings	O
(	O
called	O
the	O
lattice	O
)	O
.	O
</s>
<s>
Several	O
other	O
relaxation	B-Algorithm
mechanisms	O
also	O
exist	O
.	O
</s>
<s>
The	O
chemical	O
shift	O
anisotropy	O
(	O
CSA	O
)	O
relaxation	B-Algorithm
mechanism	O
arises	O
whenever	O
the	O
electronic	O
environment	O
around	O
the	O
nucleus	O
is	O
non	O
spherical	O
,	O
the	O
magnitude	O
of	O
the	O
electronic	O
shielding	O
of	O
the	O
nucleus	O
will	O
then	O
be	O
dependent	O
on	O
the	O
molecular	O
orientation	O
relative	O
to	O
the	O
(	O
fixed	O
)	O
external	O
magnetic	O
field	O
.	O
</s>
<s>
The	O
spin	O
rotation	O
(	O
SR	O
)	O
relaxation	B-Algorithm
mechanism	O
arises	O
from	O
an	O
interaction	O
between	O
the	O
nuclear	O
spin	O
and	O
a	O
coupling	O
to	O
the	O
overall	O
molecular	O
rotational	O
angular	O
momentum	O
.	O
</s>
<s>
The	O
nuclear	O
quadrupole	O
has	O
an	O
interaction	O
with	O
the	O
electric	O
field	O
gradient	O
at	O
the	O
nucleus	O
which	O
is	O
again	O
orientation	O
dependent	O
as	O
with	O
the	O
other	O
mechanisms	O
described	O
above	O
,	O
leading	O
to	O
the	O
so-called	O
quadrupolar	O
relaxation	B-Algorithm
mechanism	O
.	O
</s>
<s>
According	O
to	O
quantum	O
mechanics	O
,	O
time-dependent	O
interaction	O
energies	O
cause	O
transitions	O
between	O
the	O
nuclear	O
spin	O
states	O
which	O
result	O
in	O
nuclear	O
spin	O
relaxation	B-Algorithm
.	O
</s>
<s>
The	O
application	O
of	O
time-dependent	O
perturbation	O
theory	O
in	O
quantum	O
mechanics	O
shows	O
that	O
the	O
relaxation	B-Algorithm
rates	O
(	O
and	O
times	O
)	O
depend	O
on	O
spectral	B-Algorithm
density	I-Algorithm
functions	I-Algorithm
that	O
are	O
the	O
Fourier	O
transforms	O
of	O
the	O
autocorrelation	O
function	O
of	O
the	O
fluctuating	O
magnetic	O
dipole	O
interactions	O
.	O
</s>
<s>
The	O
form	O
of	O
the	O
spectral	B-Algorithm
density	I-Algorithm
functions	I-Algorithm
depend	O
on	O
the	O
physical	O
system	O
,	O
but	O
a	O
simple	O
approximation	O
called	O
the	O
BPP	O
theory	O
is	O
widely	O
used	O
.	O
</s>
<s>
Another	O
relaxation	B-Algorithm
mechanism	O
is	O
the	O
electrostatic	O
interaction	O
between	O
a	O
nucleus	O
with	O
an	O
electric	O
quadrupole	O
moment	O
and	O
the	O
electric	O
field	O
gradient	O
that	O
exists	O
at	O
the	O
nuclear	O
site	O
due	O
to	O
surrounding	O
charges	O
.	O
</s>
<s>
In	O
1948	O
,	O
Nicolaas	O
Bloembergen	O
,	O
Edward	O
Mills	O
Purcell	O
,	O
and	O
Robert	O
Pound	O
proposed	O
the	O
so-called	O
Bloembergen-Purcell-Pound	O
theory	O
(	O
BPP	O
theory	O
)	O
to	O
explain	O
the	O
relaxation	B-Algorithm
constant	O
of	O
a	O
pure	O
substance	O
in	O
correspondence	O
with	O
its	O
state	O
,	O
taking	O
into	O
account	O
the	O
effect	O
of	O
tumbling	O
motion	O
of	O
molecules	O
on	O
the	O
local	O
magnetic	O
field	O
disturbance	O
.	O
</s>
<s>
This	O
theory	O
makes	O
the	O
assumption	O
that	O
the	O
autocorrelation	O
function	O
of	O
the	O
microscopic	O
fluctuations	O
causing	O
the	O
relaxation	B-Algorithm
is	O
proportional	O
to	O
,	O
where	O
is	O
called	O
the	O
correlation	B-Algorithm
time	I-Algorithm
.	O
</s>
<s>
From	O
this	O
theory	O
,	O
one	O
can	O
get	O
T1	B-Algorithm
>	O
T2	O
for	O
magnetic	O
dipolar	O
relaxation	B-Algorithm
:	O
</s>
<s>
is	O
the	O
correlation	B-Algorithm
time	I-Algorithm
of	O
the	O
molecular	O
tumbling	O
motion	O
.	O
</s>
<s>
Taking	O
for	O
example	O
the	O
H2O	O
molecules	O
in	O
liquid	O
phase	O
without	O
the	O
contamination	O
of	O
oxygen-17	O
,	O
the	O
value	O
of	O
K	O
is	O
1.02	O
×1010	O
s−2	O
and	O
the	O
correlation	B-Algorithm
time	I-Algorithm
is	O
on	O
the	O
order	O
of	O
picoseconds	O
=	O
s	O
,	O
while	O
hydrogen	O
nuclei	O
1H	O
(	O
protons	B-Application
)	O
at	O
1.5	O
tesla	O
precess	O
at	O
a	O
Larmor	O
frequency	O
of	O
approximately	O
64	O
MHz	O
(	O
Simplified	O
.	O
</s>
<s>
which	O
is	O
close	O
to	O
the	O
experimental	O
value	O
,	O
3.6	O
s	O
.	O
Meanwhile	O
,	O
we	O
can	O
see	O
that	O
at	O
this	O
extreme	O
case	O
,	O
T1	B-Algorithm
equals	O
T2	O
.	O
</s>
<s>
As	O
follows	O
from	O
the	O
BPP	O
theory	O
,	O
measuring	O
the	O
T1	B-Algorithm
times	O
leads	O
to	O
internuclear	O
distances	O
r	O
.	O
One	O
of	O
the	O
examples	O
is	O
accurate	O
determinations	O
of	O
the	O
metal	O
–	O
hydride	O
(	O
M-H	O
)	O
bond	O
lengths	O
in	O
solutions	O
by	O
measurements	O
of	O
1H	O
selective	O
and	O
non-selective	O
T1	B-Algorithm
times	O
in	O
variable-temperature	O
relaxation	B-Algorithm
experiments	O
via	O
the	O
equation	O
:	O
</s>
<s>
where	O
r	O
,	O
frequency	O
and	O
T1	B-Algorithm
are	O
measured	O
in	O
Å	O
,	O
MHz	O
and	O
s	O
,	O
respectively	O
,	O
and	O
IM	O
is	O
the	O
spin	O
of	O
M	O
.	O
</s>
