<s>
In	O
physics	O
and	O
chemistry	O
,	O
specifically	O
in	O
nuclear	O
magnetic	O
resonance	O
(	O
NMR	O
)	O
,	O
magnetic	B-Algorithm
resonance	I-Algorithm
imaging	I-Algorithm
(	O
MRI	B-Algorithm
)	O
,	O
and	O
electron	O
spin	O
resonance	O
(	O
ESR	O
)	O
,	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
are	O
a	O
set	O
of	O
macroscopic	O
equations	O
that	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	I-Algorithm
T1	B-Algorithm
and	O
T2	O
are	O
present	O
.	O
</s>
<s>
They	O
are	O
analogous	O
to	O
the	O
Maxwell	O
–	O
Bloch	B-Algorithm
equations	I-Algorithm
.	O
</s>
<s>
Then	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
read	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>
With	O
no	O
relaxation	B-Algorithm
(	O
that	O
is	O
both	O
T1	B-Algorithm
and	O
T2	O
→	O
∞	O
)	O
the	O
above	O
equations	O
simplify	O
to	O
:	O
</s>
<s>
The	O
relaxation	B-Algorithm
terms	O
,	O
</s>
<s>
represent	O
an	O
established	O
physical	O
process	O
of	O
transverse	O
and	O
longitudinal	O
relaxation	B-Algorithm
of	O
nuclear	O
magnetization	O
M	O
.	O
</s>
<s>
Bloch	B-Algorithm
equations	I-Algorithm
are	O
macroscopic	O
:	O
they	O
describe	O
the	O
equations	O
of	O
motion	O
of	O
macroscopic	O
nuclear	O
magnetization	O
that	O
can	O
be	O
obtained	O
by	O
summing	O
up	O
all	O
nuclear	O
magnetic	O
moment	O
in	O
the	O
sample	O
.	O
</s>
<s>
Opening	O
the	O
vector	O
product	O
brackets	O
in	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
leads	O
to	O
:	O
</s>
<s>
The	O
Bloch	B-Algorithm
equations	I-Algorithm
can	O
be	O
recast	O
in	O
matrix-vector	O
notation	O
:	O
</s>
<s>
there	O
are	O
no	O
longitudinal	O
and	O
transverse	O
relaxations	B-Algorithm
(	O
that	O
is	O
T1	B-Algorithm
and	O
T2	O
→	O
∞	O
)	O
.	O
</s>
<s>
Then	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
are	O
simplified	O
to	O
:	O
</s>
<s>
Substitute	O
from	O
the	O
Bloch	B-Algorithm
equation	I-Algorithm
in	O
laboratory	O
frame	O
of	O
reference	O
:	O
</s>
<s>
It	O
is	O
also	O
the	O
term	O
that	O
is	O
behind	O
MRI	B-Algorithm
:	O
it	O
is	O
generated	O
by	O
the	O
gradient	O
coil	O
system	O
.	O
</s>
<s>
T1	B-Algorithm
and	O
T2	O
→	O
∞	O
.	O
</s>
<s>
Practically	O
this	O
means	O
that	O
τ	O
≪	O
T1	B-Algorithm
and	O
T2	O
.	O
</s>
<s>
The	O
Bloch	O
–	O
Torrey	O
equation	O
is	O
a	O
generalization	O
of	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
,	O
which	O
includes	O
added	O
terms	O
due	O
to	O
the	O
transfer	O
of	O
magnetization	O
by	O
diffusion	O
.	O
</s>
