System and method for improved magnetic resonance fingerprinting using inner product space
A system and method is provided for improved magnetic resonance fingerprinting (MRF) data dictionary matching using an MRF dictionary having entries with an inner product storing tissue properties.
1. A method for generating a map of a tissue property in a subject using magnetic resonance fingerprinting (MRF) data, the method comprising:
accessing MRF data formed by acquiring a series of signal evolutions from tissue of a subject in a region of interest while performing an MRF process using a nuclear magnetic resonance (NMR) or magnetic resonance imaging (MRI) system;
accessing an MRF dictionary having entries that are a function of a tissue property vector given by q,d=d(q), wherein a given voxel is represented by q 0 , an acquired MRF signal evolution from the given voxel is given by s=d(q 0 )+e, where s is the MRF signal evolution and e is a noise term;
comparing the MRF data to the MRF dictionary to identify at least one tissue property of the region of interest by comparing inner product values between s and entries in the MRF dictionary; and
generating the map of the at least one tissue property based on the tissue in the region of interest of the subject.
2. The method of claim 1 , wherein identifying the tissue property is achieved upon finding a maximum in absolute value from the comparing of the inner product values between s and entries in the MRF dictionary.
3. The method of claim 1 , wherein the inner product can be approximated as a quadratic function.
4. The method of claim 1 , wherein the signal evolutions are described by:
S
E
=
∑
s
=
1
N
S
∏
i
=
1
N
A
∑
j
=
1
N
RF
R
i
(
α
)
R
RF
ij
(
α
,
ϕ
)
R
(
G
)
E
i
(
T
1
,
T
2
,
D
)
M
0
where SE is a signal evolution; N S is a number of spins; N A is a number of sequence blocks in a pulse sequence of the MRF process; N RF is a number of RF pulses in a sequence block in the pulse sequence; α is a flip angle in the pulse sequence; ϕ is a phase angle; R i (α) is a rotation due to off resonance; R RF ij (α,ϕ) is a rotation due to RF differences; R(G) is a rotation due to a magnetic field gradient; T 1 is a longitudinal, or spin-lattice, relaxation time; T 2 is a transverse, or spin-spin, relaxation time; D is diffusion relaxation; E i (T 1 ,T 2 ,D) is a signal decay due to relaxation differences; and M 0 is the magnetization in the default or natural alignment to which spins align when placed in a static magnetic field.
5. A magnetic resonance fingerprinting (MRF) system comprising:
a magnet system configured to generate a polarizing magnetic field about at least a portion of a subject;
a magnetic gradient system including a plurality of magnetic gradient coils configured to apply at least one magnetic gradient field to the polarizing magnetic field;
a radio frequency (RF) system configured to apply an RF field to the subject and to receive magnetic resonance signals from the subject using a coil array;
a computer system programmed to:
control the magnetic gradient system and the RF system to perform an MRF process to acquire MRF data formed by acquiring a series of signal evolutions from tissue of a subject in a region of interest;
access an MRF dictionary having entries that are a function of a tissue property vector given by q,d=d(q), wherein a given voxel is represented by q 0 , an acquired MRF signal evolution from the given voxel is given by s=d(q 0 )+e, where s is the MRF signal evolution and e is a noise term;
compare the MRF data to the MRF dictionary to identify a tissue property of the region of interest by comparing inner product values between s and each entry in the MRF dictionary; and
generate the map of the tissue property based on the tissue in the region of interest of the subject.
6. The system of claim 5 , wherein identifying the tissue property is achieved upon finding a maximum in absolute value from the comparing of the inner product values between s and entries in the MRF dictionary.
7. The system of claim 5 , wherein the inner product can be approximated as a quadratic function.
8. The system of claim 5 , wherein MRF process includes performing an MRF pulse sequence designed to elicit the series of signal evolutions.
9. The system of claim 8 , wherein the MRF pulse sequence includes a fast imaging with steady-state free precession (FISP) or balanced steady-state free precession (bSSFP) pulse sequence.
10. The system of claim 8 , wherein the signal evolutions are described by:
S
E
=
∑
s
=
1
N
S
∏
i
=
1
N
A
∑
j
=
1
N
RF
R
i
(
α
)
R
RF
ij
(
α
,
ϕ
)
R
(
G
)
E
i
(
T
1
,
T
2
,
D
)
M
0
where SE is a signal evolution; N S is a number of spins; N A is a number of sequence blocks in the pulse sequence; N RF is a number of RF pulses in a sequence block in the pulse sequence; α is a flip angle in the pulse sequence; ϕ is a phase angle; R i (α) is a rotation due to off resonance; R RF ij (α,ϕ) is a rotation due to RF differences; R(G) is a rotation due to a magnetic field gradient; T 1 is a longitudinal, or spin-lattice, relaxation time; T 2 is a transverse, or spin-spin, relaxation time; D is diffusion relaxation; E i (T 1 ,T 2 ,D) is a signal decay due to relaxation differences; and M 0 is the magnetization in the default or natural alignment to which spins align when placed in a static magnetic field.