System and method for quantifying MR data acquired during a UTE sequence
A system and method for quantifying MR data acquired during a UTE sequence include a computer programmed to execute an MR scan comprising an application of an RF pulse, an echo time (TE) period, and an application of a data acquisition gradient pulse, wherein the TE period begins after the RF pulse and ends before the data acquisition gradient pulse. MR data of an imaging object are acquired during application of the data acquisition gradient pulse, and a phase image is reconstructed based on the acquired MR data. The computer is also programmed to calculate a first contribution of phase to the phase image during the application of the RF pulse, to calculate a second contribution of phase to the phase image by the application of the data acquisition gradient pulse, and to generate a frequency map based on the phase image and based on the first and second contributions of phase.
1. An MRI apparatus comprising:
a magnetic resonance imaging (MRI) system having a plurality of gradient coils positioned about a bore of a magnet, and an RF transceiver system and an RF switch controlled by a pulse module to transmit RF signals to an RF coil assembly to acquire MR images; and
a computer programmed to:
execute an MR scan comprising an application of an RF pulse, an echo time (TE) period, and an application of a data acquisition gradient pulse, wherein the TE period begins after the RF pulse and ends before the data acquisition gradient pulse;
acquire MR data of an imaging object during application of the data acquisition gradient pulse;
reconstruct a phase image based on the acquired MR data;
calculate a first contribution of phase to the phase image during the application of the RF pulse;
calculate a second contribution of phase to the phase image during the application of the data acquisition gradient pulse;
generate a frequency map based on the phase image and based on the first and second contributions of phase.
2. The MRI apparatus of claim 1 wherein the computer, in being programmed to execute the MR scan, is programmed to execute a center-out radial acquisition MR scan.
3. The MRI apparatus of claim 1 wherein the computer, in being programmed to generate the frequency map, is programmed to generate the frequency map according to the equation:
Φ=Φ RF +ω off ·TE+Φ DAQ ,
where Φ represents the phase image, Φ RF represents the first contribution of phase to the phase image during the application of the RF pulse, Φ DAQ represents the second contribution of phase to the phase image during the application of the data acquisition gradient pulse, and ω off represents an off-resonance frequency.
4. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the first contribution, is programmed to calculate the first contribution based on the equation:
Φ
(
τ
)
=
atan
(
M
x
M
y
)
=
atan
(
ω
off
[
1
-
cos
(
ω
2
τ
)
]
ω
2
sin
(
ω
2
τ
)
)
,
where ω off is an off-resonance frequency, τ is a duration of the RF pulse, ω 1 =γB 1 is an amplitude of the RF pulse, and M x and M y are spatial components of a thermal magnetization according to:
M
x
(
τ
)
=
M
0
ω
off
ω
1
ω
2
2
[
1
-
cos
(
ω
2
τ
)
]
M
y
(
τ
)
=
M
0
ω
1
ω
2
sin
(
ω
2
τ
)
,
where
ω 2 =√{square root over (ω 1 2 +ω off 2 )}, and M 0 is the thermal magnetization.
5. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the first contribution, is programmed to calculate the first contribution based on the equation:
Φ
(
τ
)
=
ω
off
τ
+
∠
{
∫
0
τ
B
1
(
t
)
exp
(
-
ⅈ
ω
off
t
)
ⅆ
t
}
,
where ω off is an off-resonance frequency, τ is a duration of the RF pulse, and the “∠” operator takes the phase angle of the expression in the brackets.
6. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the second contribution, is programmed to calculate the second contribution based on the equation:
Φ
(
x
=
0
)
=
∠
[
i
(
1
-
ⅇ
ⅈ
π
ω
off
γ
GL
)
]
≈
π
ω
off
2
γ
GL
,
where ω off is an off-resonance frequency, G is a gradient pulse, L is a length of a box function, γ is the gyromagnetic ratio, and the “∠” operator takes the phase angle of the expression in the brackets.
7. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the second contribution, is programmed to calculate the second contribution based on the equation:
Φ
(
x
=
0
)
≈
4
3
ω
off
π
2
γ
L
·
slew
,
where ω off is an off-resonance frequency, L is a length of a box function, γ is the gyromagnetic ratio, and slew is a gradient pulse slew rate.
8. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the second contribution, is programmed to calculate the second contribution based on the equation:
Φ
(
x
=
0
)
≈
4
3
ω
off
π
2
γ
L
·
slew
1
2
L
<
k
ramp
Φ
(
x
=
0
)
≈
ω
off
(
π
2
γ
GL
+
G
2
·
slew
)
=
ω
off
(
π
2
γ
GL
+
T
ramp
2
)
1
2
L
>
k
ramp
where ω off is an off-resonance frequency, G is a gradient pulse, slew is a slew rate of the gradient pulse, L is a length of a box function, γ is the gyromagnetic ratio, T ramp is a duration of a ramp sampling determined according to:
T
ramp
=
G
slew
.
k ramp is a magnitude of a k-space ramp signal determined according to:
k
ramp
=
γ
4
π
slew
·
T
ramp
2
.
9. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the second contribution, is programmed to calculate the second contribution based on the equation:
Φ
≈
8
5
ω
off
π
2
γ
L
·
slew
1
2
L
<
k
ramp
Φ
≈
ω
off
(
2
π
3
γ
GL
+
G
2
·
slew
)
=
ω
off
(
2
π
3
γ
GL
+
T
ramp
2
)
1
2
L
>
k
ramp
where ω off is an off-resonance frequency, G is a gradient pulse, slew is a slew rate of the gradient pulse, L is a length of a box function, γ is the gyromagnetic ratio, T ramp is a duration of a ramp sampling determined according to:
T
ramp
=
G
slew
,
and
k ramp is a magnitude of a k-space ramp signal determined according to:
k
ramp
=
γ
4
π
slew
·
T
ramp
2
.
10. The MRI apparatus of claim 1 wherein the computer, in being programmed to calculate the second contribution, is programmed to calculate the second contribution based on the equation:
Φ
≈
12
7
ω
off
π
2
γ
L
·
slew
1
2
L
<
k
ramp
Φ
≈
ω
off
(
3
π
4
γ
GL
+
G
2
·
slew
)
=
ω
off
(
3
π
4
γ
GL
+
T
ramp
2
)
1
2
L
>
k
ramp
where ω off is an off-resonance frequency, G is a gradient pulse, slew is a slew rate of the gradient pulse, L is a length of a box function, γ is the gyromagnetic ratio, T ramp is a duration of a ramp sampling determined according to:
T
ramp
=
G
slew
,
and
k ramp is a magnitude of a k-space ramp signal determined according to:
k
ramp
=
γ
4
π
slew
·
T
ramp
2
.
11. A method of generating quantitative data from MR data acquired during a UTE sequence, the method comprising:
prescribing an ultrashort TE (UTE) sequence comprising an application of an RF pulse, an echo time (TE) period, and an application of a data acquisition gradient pulse, wherein the TE period begins after the RF pulse and ends before the data acquisition gradient pulse;
executing an MR scan comprising the UTE sequence;
acquiring MR data of an imaging object during execution of the MR scan;
reconstructing a phase image based on the acquired MR data;
determining an RF phase contribution to the phase image during the application of the RF pulse;
determining an acquisition phase contribution of phase to the phase image during the application of the data acquisition gradient pulse;
creating a frequency map based on the phase image, the RF phase contribution, and the acquisition phase contribution.
12. The method of claim 11 further comprising displaying the frequency map to a user.
13. The method of claim 11 wherein executing the MR scan comprises executing a radial acquisition MR scan.
14. The method of claim 11 wherein executing the radial MR scan comprises executing a center-out radial acquisition MR scan.
15. The method of claim 11 wherein prescribing the UTE sequence comprises setting the TE period equal to a value in the range of 0 ms to 2 ms.
16. The method of claim 11 wherein creating the frequency map comprises creating the frequency map according to the equation:
Φ=Φ RF +ω off ·TE+Φ DAQ ,
where Φ represents the phase image, Φ RF represents the first contribution of phase to the phase image during the application of the RF pulse, Φ DAQ represents the second contribution of phase to the phase image during the application of the data acquisition gradient pulse, and ω off represents an off-resonance frequency.
17. A non-transitory computer readable medium having stored thereon a computer program comprising instructions which when executed by a computer cause the computer to:
execute an MR scan comprising an ultrashort TE (UTE) sequence comprising:
an application of an RF pulse;
an echo time (TE) period; and
an application of a data acquisition gradient pulse, wherein the TE period begins after the RF pulse and ends before the data acquisition gradient pulse;
acquire MR data of an imaging object during execution of the MR scan;
reconstruct a phase image based on the acquired MR data;
determine an RF phase contribution to the phase image during the application of the RF pulse;
determine an acquisition phase contribution of phase to the phase image during the application of the data acquisition gradient pulse;
create a frequency map based on the phase image, the RF phase contribution, and the acquisition phase contribution.
18. The non-transitory computer readable medium of claim 17 wherein the instructions that cause the computer to create the frequency map cause the computer to create a relative frequency map.
19. The non-transitory computer readable medium of claim 17 wherein the instructions that cause the computer to create the relative frequency map cause the computer to create a relative frequency map according to the equation:
Φ=Φ RF +ω off ·TE+Φ DAQ ,
where Φ represents the phase image, Φ off represents the first contribution of phase to the phase image during the application of the RF pulse, Φ DAQ represents the second contribution of phase to the phase image during the application of the data acquisition gradient pulse, and ω off represents an off-resonance frequency.
20. The non-transitory computer readable medium of claim 17 wherein the instructions that cause the computer to determine the acquisition phase contribution of phase cause the computer to determine the acquisition phase contribution of phase based on one of a first equation, a second equation, a third equation, a fourth equation, and a fifth equation;
wherein the first equation comprises:
Φ
(
x
=
0
)
=
∠
[
i
(
1
-
ⅇ
ⅈ
π
ω
off
γ
GL
)
]
≈
π
ω
off
2
γ
GL
;
wherein the second equation comprises:
Φ
(
x
=
0
)
≈
4
3
ω
off
π
2
γ
L
·
slew
wherein the third equation comprises:
Φ
(
x
=
0
)
≈
4
3
ω
off
π
2
γ
L
·
slew
1
2
L
<
k
ramp
Φ
(
x
=
0
)
≈
ω
off
(
π
2
γ
GL
+
G
2
·
slew
)
=
ω
off
(
π
2
γ
GL
+
T
ramp
2
)
1
2
L
>
k
ramp
wherein the fourth equation comprises:
Φ
≈
8
5
ω
off
π
2
γ
L
·
slew
1
2
L
<
k
ramp
Φ
≈
ω
off
(
2
π
3
γ
GL
+
G
2
·
slew
)
=
ω
off
(
2
π
3
γ
GL
+
T
ramp
2
)
1
2
L
>
k
ramp
;
wherein the fifth equation comprises:
Φ
≈
12
7
ω
off
π
2
γ
L
·
slew
1
2
L
<
k
ramp
Φ
≈
ω
off
(
3
π
4
γ
GL
+
G
2
·
slew
)
=
ω
off
(
3
π
4
γ
GL
+
T
ramp
2
)
1
2
L
>
k
ramp
;
and
where ω off is an off-resonance frequency, G is a gradient pulse, slew is a slew rate of the gradient pulse, L is a length of a box function, γ is the gyromagnetic ratio, T ramp is a duration of a ramp sampling determined according to:
T
ramp
=
G
slew
,
and
k ramp is a magnitude of a k-space ramp signal determined according to:
k
ramp
=
γ
4
π
slew
·
T
ramp
2
.