System and method for flip angle determination in magnetic resonance imaging
A system and method for calculating a flip angle schedule is provided. The technique includes selecting an initial condition, providing a function for calculating flip angles, calculating flip angles, assessing the flip angles, and repeating the calculation of the flip angles by adjusting the function until a desired flip angle schedule is obtained.
1. A magnetic resonance imaging (MRI) system comprising: an MRI scanner, a control unit, and a processing unit,
the processing unit performing operations comprising:
a) selecting an initial condition relating to a first phase of an echo train, the initial condition including initial values of a first flip angle, a last flip angle, and a first characteristic parameter;
b) providing a first function corresponding to the first phase echo train, the first function relating to at least one of the first flip angle, the last flip angle, or the first characteristic parameter;
c) calculating, based on the first function, one or more flip angles corresponding to one or more spin echoes of the first phase;
d) assessing the one or more flip angles of the first phase according to a first criterion; and
e) if the first criterion is not satisfied,
revising the first function by adjusting at least one of the first flip angle, the last flip angle, or the first characteristic parameter, and repeating (c) and (d);
wherein the first function provides a flip angle schedule corresponding to the first phase of the echo train for MRI, and
the control unit controlling the MRI scanner according to the flip angle schedule,
wherein the first function includes:
α
n
=
α
M
+
(
α
0
-
α
N
-
1
)
·
e
(
(
M
-
n
)
2
P
2
)
-
1
e
(
(
N
-
1
)
2
P
2
)
-
1
,
where α 0 is the first flip angle of the first phase, α N-1 is the last flip angle of the first phase, N is a number of echoes in the first phase, P is the characteristic parameter of the first phase, α n is the one or more flip angles of the first phase, n=0, 1, . . . , N−1;
where M=0 if α N-1 ≥α 0 , or M=N−1 if α 0 >α N-1 .
2. The MRI system of claim 1 , the assessing of the one or more flip angles of the first phase comprising:
calculating, based on the one or more flip angles of the first phase, a first signal evolution; and
evaluating the first signal evolution according to the first criterion.
3. The MRI system of claim 2 ,
the first criterion comprising a first threshold, and
the assessing of the one or more flip angles of the first phase comprising determining whether a maximum signal in the first signal evolution equals to or exceeds the first threshold.
4. The MRI system of claim 1 , the processing unit further performing:
(f) providing a reference signal schedule corresponding to the first phase, the reference signal schedule comprising one or more reference signals corresponding to the one or more spin echoes of the first phase.
5. The MRI system of claim 4 , the assessing of the one or more flip angles of the first phase comprising:
calculating, based on the one or more flip angles of the first phase, a first signal evolution; and
comparing the first signal evolution with the reference signal schedule.
6. The MRI system of claim 4 , the reference signal schedule relating to T1 or T2 of a tissue to be imaged using the flip angle schedule corresponding to the first phase of the echo train for magnetic resonance imaging.
7. The MRI system of claim 1 , the processing unit further performing:
g) selecting a second initial condition relating to a second phase of the echo train, the second initial condition including initial values of a third flip angle, a fourth flip angle, and a second characteristic parameter;
h) providing a second function corresponding to the second phase, the second function relating to at least one of the third flip angle, the fourth flip angle, or the second characteristic parameter;
i) calculating; based on the second function, one or more flip angles corresponding to one or more spin echoes of the second phase;
j) assessing the one or more flip angles of the second phase according to a second criterion; and
k) if the second criterion is not satisfied,
revising the second function by adjusting at least one of the third flip angle; the fourth flip angle, or the second characteristic parameter, and repeating (i) and (j);
wherein the second function provides a flip angle schedule corresponding to the second phase of the echo train for magnetic resonance imaging.
8. The MRI system of claim 7 ; the third flip angle being the same as the initial value of the last flip angle or the adjusted last flip angle.
9. A method comprising:
a) selecting an initial condition relating to a first phase of an echo train, the initial condition including initial values of a first flip angle, a last flip angle, and a first characteristic parameter;
b) providing a first function corresponding to the first phase of the echo train, the first function relating to at least one of the first flip angle, the last flip angle, or the first characteristic parameter;
c) calculating, based on the first function, one or more flip angles corresponding to one or more spin echoes of the first phase;
d) assessing the one or more flip angles of the first phase according to a first criterion; and
e) if the first criterion is not satisfied,
revising the first function by adjusting at least one of the first flip angle, the last lip angle, or the first characteristic parameter, and repeating (c) and (d);
wherein the first function provides a flip angle schedule corresponding to the first phase of the echo train for MRI,
wherein the first function includes:
α
n
=
α
M
+
(
α
0
-
α
N
-
1
)
·
e
(
(
M
-
n
)
2
P
2
)
-
1
e
(
(
N
-
1
)
2
P
2
)
-
1
,
where α 0 is the first flip angle of the first phase, α N-1 is the last flip angle of the first phase, N is a number of echoes in the first phase, P is the characteristic parameter of the first phase, α n is the one or more flip angles of the first phase, n=0, 1, . . . , N−1;
where M=0 if α N-1 ≥α 0 , or M=N−1 if α 0 >α N-1 .
10. The method of claim 9 , the assessing of the one or more flip angles of the first phase comprising:
calculating, based on the one or more flip angles of the first phase, a first signal evolution; and
evaluating the first signal evolution according to the first criterion.
11. The method of claim 10 , the calculating of the first signal evolution comprising using the Bloch equation or the EPG algorithm.
12. The method of claim 10 ,
the first criterion comprising a first threshold, and
the assessing of the one or more flip angles of the first phase comprising determining whether a maximum signal in the first signal evolution equals to or exceeds a first threshold.
13. The method of claim 9 further comprising:
(f) providing a reference signal schedule corresponding to the first phase, the reference signal schedule comprising one or more reference signals corresponding to the one or more spin echoes of the first phase.
14. The method of claim 13 , the assessing of the one or more flip angles of the first phase comprising:
calculating, based on the one or more flip angles of the first phase, a first signal evolution; and
comparing the first signal evolution with the reference signal schedule.
15. The method of claim 9 , the magnetic resonance imaging comprising T1 weighted imaging, T2 weighted imaging, or proton density weighted imaging.
16. The method of claim 9 , the adjusting of the at least one of the first flip angle, the last flip angle, or the first characteristic parameter comprising using recursion, a bisection method, an exhaustive search, a greedy algorithm, a divide and conquer algorithm, a dynamic programming method, an iterative method, a branch-and-bound algorithm, or a backtracking algorithm.
17. The method of claim 9 further comprising:
g) selecting a second initial condition including initial values of a third flip angle, a fourth flip angle, and a second characteristic parameter;
h) providing a second function corresponding to a second phase, the second function relating to the third flip angle, the fourth flip angle, and the second characteristic parameter;
i) calculating, based on the second function, one or more flip angles corresponding to one or more spin echoes of the second phase;
j) assessing the one or more flip angles of the second phase according to a second criterion; and
k) if the second criterion is not satisfied,
revising the second function by adjusting at least one of the third flip angle, the fourth flip angle, or the second characteristic parameter, and repeating (i) and (j);
wherein the second function provides a flip angle schedule corresponding to the second phase of the echo train for magnetic resonance imaging.
18. The method of claim 9 , the initial condition relating to the first phase comprising at least one of an echo train duration time, an echo train length, or a phase number.
19. The method of claim 17 , wherein the second function is different from the first function.