<s>
Hyperpolarized	B-Algorithm
carbon-13	I-Algorithm
MRI	I-Algorithm
is	O
a	O
functional	B-Algorithm
medical	I-Algorithm
imaging	I-Algorithm
technique	O
for	O
probing	O
perfusion	O
and	O
metabolism	O
using	O
injected	O
substrates	O
.	O
</s>
<s>
In	O
contrast	O
with	O
other	O
metabolic	O
imaging	O
methods	O
such	O
as	O
positron	B-Application
emission	I-Application
tomography	I-Application
,	O
hyperpolarized	B-Algorithm
carbon-13	I-Algorithm
MRI	I-Algorithm
provides	O
chemical	O
as	O
well	O
as	O
spatial	O
information	O
,	O
allowing	O
this	O
technique	O
to	O
be	O
used	O
to	O
probe	O
the	O
activity	O
of	O
specific	O
metabolic	O
pathways	O
.	O
</s>
<s>
Hyperpolarized	B-Algorithm
carbon-13	I-Algorithm
MRI	I-Algorithm
is	O
currently	O
being	O
developed	O
as	O
a	O
potentially	O
cost	O
effective	O
diagnostic	O
and	O
treatment	O
progress	O
tool	O
in	O
various	O
cancers	O
,	O
including	O
prostate	O
cancer	O
.	O
</s>
<s>
Spectroscopic	O
imaging	O
techniques	O
enable	O
chemical	O
information	O
to	O
be	O
extracted	O
from	O
hyperpolarized	B-Algorithm
carbon-13	I-Algorithm
MRI	I-Algorithm
experiments	O
.	O
</s>
<s>
This	O
technique	O
also	O
allows	O
different	O
flip	B-Algorithm
angles	I-Algorithm
to	O
be	O
applied	O
to	O
each	O
metabolite	O
,	O
</s>
<s>
A	O
number	O
of	O
approaches	O
exist	O
for	O
modeling	O
the	O
evolution	O
of	O
magnetization	O
within	O
a	O
single	O
voxel	B-Algorithm
.	O
</s>
<s>
where	O
is	O
the	O
flip	B-Algorithm
angle	I-Algorithm
and	O
is	O
the	O
repetition	O
time	O
.	O
</s>
<s>
Time-varying	O
flip	B-Algorithm
angle	I-Algorithm
sequences	O
can	O
also	O
be	O
used	O
,	O
but	O
require	O
that	O
the	O
dynamics	O
be	O
modeled	O
as	O
a	O
hybrid	O
system	O
with	O
discrete	O
jumps	O
in	O
the	O
system	O
state	O
.	O
</s>
<s>
The	O
goal	O
of	O
many	O
hyperpolarized	B-Algorithm
carbon-13	I-Algorithm
MRI	I-Algorithm
experiments	O
is	O
to	O
map	O
the	O
activity	O
of	O
a	O
particular	O
metabolic	O
pathway	O
.	O
</s>
<s>
When	O
noise	O
is	O
independent	O
and	O
identically	O
distributed	O
and	O
Gaussian	O
,	O
parameters	O
can	O
be	O
fit	O
using	O
non-linear	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
estimation	O
.	O
</s>
<s>
The	O
spatial	O
distribution	O
of	O
metabolic	O
rates	O
can	O
be	O
visualized	O
by	O
estimating	O
metabolic	O
rates	O
corresponding	O
to	O
the	O
time	O
series	O
from	O
each	O
voxel	B-Algorithm
,	O
and	O
plotting	O
a	O
heat	B-Application
map	I-Application
of	O
the	O
estimated	O
rates	O
.	O
</s>
