Quadratic species separation using balanced SSFP MRI
View Patent ↗MRI signals from two species such as water and fat are separated by using two SSFP acquisitions (S 1 , S 2 ) with the two species signals having two different phase differences (e.g., 180°, 90°) and binomial quadratic expansion in which the species are determined based on magnitude and sign of S 1 and the magnitude of S 2 .
1. A method of separating MRI signals (Sp 1 , Sp 2 ) from two species in an object being imaged comprising the steps of:
a) acquiring MRI signals (S 1 , S 2 ) using two balanced SSFP acquisitions in which the two species are at respective phase differences, φ and ν, and in which echo times TE 1 and TE 2 differ, with
S 1 =( S p1 −S p2 ) e iφ
S 2 =( S p1 −e iν S p2 ) e iφ e 2πi(TE 2 −TE 1 )f
where f is a frequency corresponding to field inhomogeniety and susceptibility variations,
b) estimating a phase, {circumflex over (φ)}, for voxels in a field of view, and defining species differences as
{circumflex over (d)}=Sp 1 −Sp 2 =S 1 e −1{circumflex over (φ)} , and
c) using a quadratic expression
| S 2 | 2 =S p1 2 +S p2 2 +2 S p1 ·S p2 cos ν
and substituting species difference, {circumflex over (d)},
estimating
S
^
p2
=
-
1
2
ⅆ
^
+
1
2
ⅆ
^
2
+
2
❘
S
2
2
-
ⅆ
^
2
1
+
cos
v
and
S
^
p1
=
ⅆ
^
+
S
^
p2
.
2. The method of claim 1 wherein the two species are water and fat with signal magnitude W and F, respectively.
3. The method of claim 2 where first echo time, TE 1 , is one-half repetition time, TR/2, and the second echo time,
TE2
is
TR
/
2
+
v
2
π
Δ
f
cs
,
where ν is phase difference between water signals and fat signals in the second acquisition, and Δf cs is chemical shift frequency difference between water and fat.
4. The method of claim 3 wherein phase difference between fat and water in S 1 is 180° and in S 2 is 90°.
5. The method of claim 4 wherein
F
^
=
-
1
2
ⅆ
^
+
1
2
2
S
2
2
-
ⅆ
^
2
.
6. The method of claim 5 where a field map is calculated after estimating the two species.
7. The method of claim 6 where species and field map estimates are calculated using reduced-resolution images to reduce imaging time.
8. The method of claim 1 wherein S 1 and S 2 are acquired multiple times with different phase increments in SSFP to reduce the effects of dark bands.
9. The method of claim 1 wherein multiple coils are used, and the coil sensitivities are used to reconstruct signals S 1 and S 2 for different coils or combinations of coils.
10. The method of claim 1 where signals S 1 and S 2 are both acquired in a “multi-echo” sequence, using a single RF excitation.
11. The method of claim 1 where S 1 is acquired using a pulse sequence that results in water and fat being opposed-phase.
12. The method of claim 1 where TE 1 =(2k+1)/(2f cs ) where k is an integer and f cs is the frequency difference between species.