Method for correcting phase offsets in quantitative chemical shift encoded magnetic resonance imaging
Systems and methods for correcting phase errors in chemical shift encoded data are described. The technique is self-calibrated, without the need for specialized calibration data, and therefore may enable fat and iron quantification using data from clinical and research sites that do not have specialized pulse sequences.
1. A method for correcting phase errors in chemical shift encoded data acquired with a magnetic resonance imaging (MRI) system, the steps of the method comprising:
(a) acquiring chemical shift encoded data from a subject using an MRI system operating a pulse sequence that induces linear phase errors in multiple different echoes;
(b) generating first complex-valued estimates of a water image, a fat image, and a field map using a complex fitting of the acquired chemical shift encoded data, wherein the initial complex-valued estimates are indicative of a proton density fat fraction dynamic range of zero to one hundred percent;
(c) generating magnitude estimates of a water image and a fat image independently on a voxel-by-voxel basis using a magnitude fitting of the acquired chemical shift encoded data in which the first complex-valued estimates of the water image and the fat image are used as initial values;
(d) generating second complex-valued estimates of a water image and a fat image independently on a voxel-by-voxel basis using a complex fitting of the acquired chemical shift encoded data in which the first complex-valued estimates of the water image, the fat image, and the field map are used as initial values;
(e) producing a phase-corrected water image and a phase-corrected fat image by estimating linear phase offsets associated with the linear phase errors induced by the pulse sequence, wherein estimating the linear phase offsets is based on minimizing an objective function that includes a difference between the magnitude estimates of the water image and the fat image and the second complex-valued estimates of the water image and the fat image; and
(f) generating a proton density fat fraction map based on the phase-corrected water image and the phase-corrected fat image.
2. The method as recited in claim 1 , wherein step (b) further includes generating an initial complex-valued estimate of a parameter map and step (c) includes generating a magnitude estimate of the parameter map using the magnitude fitting in which the initial complex-valued estimate of the parameter is also used as an initial value.
3. The method as recited in claim 2 , wherein the parameter map is a transverse relaxation parameter map.
4. The method as recited in claim 3 , wherein the parameter map is a transverse relaxation rate (R 2 *) map.
5. The method as recited in claim 4 , wherein minimizing the objective function in step (e) is restricted to only minimize voxels having transverse relaxation rate values less than a threshold value.
6. The method as recited in claim 5 , wherein the threshold value is 100 per seconds (s −1 ).
7. The method as recited in claim 4 , wherein the objective function minimized in step (e) is,
min
ϕ
0
,
ϕ
1
{
∑
q
s
.
t
.
R
2
,
q
*
<
T
[
(
W
q
,
complex
-
W
q
,
mag
)
2
+
(
F
q
,
complex
-
F
q
,
mag
)
2
]
}
;
wherein ϕ 0 and ϕ 1 are the linear phase offsets; W q,complex is the second complex-valued estimate of the water image at voxel q; W q,mag is the magnitude estimate of the water image at voxel q; F q,complex is the second complex-valued estimate of the fat image at voxel q; F q,mag is the magnitude estimate of the fat image signal at voxel q; R 2,q * is the transverse relaxation rate at voxel q; and T is the threshold value.
8. The method as recited in claim 7 , wherein the threshold value is 100 per seconds (s −1 ).
9. The method as recited in claim 1 , wherein the pulse sequence includes bipolar readout gradients and the linear phase errors induced by the pulse sequence includes linear phase offsets associated with even-numbered echoes acquired in the chemical shift encoded data with the bipolar readout gradients.
10. The method as recited in claim 1 , wherein the pulse sequence includes forming unequally spaced echoes and the linear phase errors induced by the pulse sequence includes linear phase offsets associated with the unequally spaced echoes.
11. A method for producing a proton density fat fraction map from chemical shift encoded data acquired with a magnetic resonance imaging (MRI) system, the steps of the method comprising:
(a) acquiring chemical shift encoded data from a subject using an MRI system operating a pulse sequence that includes monopolar readout gradients;
(b) generating initial complex-valued estimates of a water image and a fat image using a complex fitting of the acquired chemical shift encoded data, wherein the initial complex-valued estimates are indicative of a proton density fat fraction dynamic range of zero to one hundred percent;
(c) generating magnitude estimates of a water image and a fat image independently on a voxel-by-voxel basis using a magnitude fitting of the acquired chemical shift encoded data in which the initial complex-valued estimates of the water image and the fat image are used as initial values; and
(d) generating a proton density fat fraction map based on the magnitude estimates of the water image and the fat image.
12. The method as recited in claim 11 , wherein step (b) further includes generating an initial complex-valued estimate of a parameter map and step (c) includes generating a magnitude estimate of the parameter map using the magnitude fitting in which the initial complex-valued estimate of the parameter is also used as an initial value.
13. The method as recited in claim 12 , wherein the parameter map is a transverse relaxation parameter map.
14. The method as recited in claim 13 , wherein the parameter map is a transverse relaxation rate (R 2 *) map.