# US 9,519,039 B2 · Determining the form of RF pulses for selective excitation in magnetic resonance imaging

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- Number: US 9,519,039 B2
- Document ID: US9519039B2
- Status: Granted
- Kind: B2
- Application number: 14/000,493
- Filed: 2012-02-15
- Published: 2015-02-12
- Granted: 2016-12-13
- Earliest claimed: 2011-02-20
- Assignees: Siemens Healthcare GmbH
- Applicants: Rene Gumbrecht; Kaveh Vahedipour; Tony Stoecker; Nadim Joni Shah
- Inventors: Rene Gumbrecht; Kaveh Vahedipour; Tony Stoecker; Nadim Joni Shah
- Web page: https://patentgrep.com/patent/US9519039B2

## CPC

- G01R 33/4833: {using spatially selective excitation of the volume of interest, e.g. selecting non-orthogonal or inclined slices}
- G01R 33/385: using gradient magnetic field coils
- G01R 33/4818: {MR characterised by data acquisition along a specific k-space trajectory or by the temporal order of k-space coverage, e.g. centric or segmented coverage of k-space}
- G01R 33/56: Image enhancement or correction, e.g. subtraction or averaging techniques {, e.g. improvement of signal-to-noise ratio and resolution}
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)

## Abstract

The invention relates to a magnetic resonance method involving the generation of high-frequency pulses and magnetic gradients (gx, gy, gz) for the selective excitation of an object to be examined. According to the invention, the magnetic resonance method is characterized in that a magnetic resonance signal s(t) according to the following signal equation is generated: s ⁡ ( t ) = ∫ V ⁢ m ( r r , T ) ⁢ exp ⁡ [ t ⁢ / ⁢ T 2 ] ⁢ exp ⁡ [ ⅈ ⁢ ⁢ t ⁢ ⁢ ω s ] ⁢ exp ⁡ [ - ⅈ ⁢ ⁢ k r ⁡ ( T - t ) · r r ] ⁢ ⁢ ⅆ 3 ⁢ r wherein stands for a desired transversal magnetization after the selective excitation, t stands for a time, {right arrow over (r)} stands for a position vector and T stands for a duration of a pulse, and whereby s(t) stands for a magnetic resonance signal, V stands for a volume that is to be examined, T2 stands for a transversal relaxation time, and ωs stands for a shift of the resonance frequency. The invention also relates to a nuclear spin tomograph for carrying out the magnetic resonance method.

## Claims

### Claim 1

A magnetic resonance method involving the generation of high-frequency pulses and magnetic gradients (gx, gy, gz) for the selective excitation of an object that is to be examined, whereby the magnetic resonance method comprises the following steps:
providing a transversal magnetization m({right arrow over (r)}, T) which is described by
m
(
r
->
,
T
)
=
ⅈγ
⁢
⁢
m
0
⁢
exp
⁡
[
-
T
⁢
/
⁢
T
2
]
⁢
exp
⁡
[
-
ⅈ
⁢
⁢
T
⁢
⁢
ω
s
]
⁢
∫
0
T
⁢
exp
⁡
[
t
⁢
/
⁢
T
2
]
⁢
exp
⁡
[
ⅈ
⁢
⁢
t
⁢
⁢
ω
s
]
⁢
b
1
⁡
(
t
)
⁢
exp
[
ⅈ
⁢
⁢
k
->
⁡
(
t
)
·
r
->
]
⁢
⁢
ⅆ
t
wherein i stands for an imaginary unit, γ stands for a gyromagnetic ratio, m0 stands for an equilibrium magnetization, t stands for a time, {right arrow over (r)}; stands for a position vector and T stands for a duration of a pulse, T2 stands for a transversal relaxation time, ωs stands for a shift of the resonance frequency, b1(t) stands for a high-frequency pulse, and {right arrow over (k)}(t) stands for a vector of the k-space trajectory that is given by the magnetic gradients,
determining the high-frequency pulse by means of a signal equation s(t) according to:
s
⁡
(
t
)
=
∫
V
⁢
m
(
r
->
,
T
)
⁢
exp
⁡
[
t
⁢
/
⁢
T
2
]
⁢
exp
⁡
[
ⅈ
⁢
⁢
t
⁢
⁢
ω
s
]
⁢
exp
⁡
[
-
ⅈ
⁢
⁢
k
->
⁡
(
T
-
t
)
·
r
->
]
⁢
⁢
ⅆ
3
⁢
r
wherein V stands for a volume that is to be examined, so that, except for factors, the high-frequency pulse is obtained as:
b
1
⁡
(
t
)
=
J
⁡
(
t
)
ⅈγ
⁢
⁢
m
0
⁢
s
⁡
(
T
-
t
)
wherein J(t) is a Jacobi determinant that, under the premise of the bijectivity of k(t) onto a value range of t, yields the dependence of the coordinate transformation between the time parameterization and the k-space parameterization,
using the high-frequency pulse to excite the volume that is to be examined,
detecting the measured signal generated by the high-frequency pulse in the volume that is to be examined, and
evaluating the measured signal.

### Claim 2 (depends on 1)

The magnetic resonance method according to claim 1, characterized in that N coils having a different spatial transmission characteristic are used for the excitation.

### Claim 3 (depends on 2)

The magnetic resonance method according to claim 2, characterized in that the high-frequency pulse b1(t, {right arrow over (r)}) is generated taking the following formula into account:
b
1
(
t
,
r
->
)
=
∑
n
=
1
N
⁢
⁢
σ
n
(
r
->
)
⁢
b
n
⁡
(
t
)
wherein
σn(r) stands for a sensitivity of the nth channel,
b1,n(t) is determined by the formula
b
1
,
n
⁡
(
t
)
=
J
⁡
(
t
)
ⅈγ
⁢
⁢
M
0
⁢
s
n
⁡
(
T
-
t
)
and designates the sought high-frequency pulses of the individual N transmission channels,
b1(t,r) stands for the superposition of the individual sensitivity-weighted pulses, and
b1,n(t) stands for r at all locations.

### Claim 4 (depends on 3)

The magnetic resonance method according to claim 3, characterized in that the sensitivity σn(r) is determined on the basis of a numerical calculation.

### Claim 5 (depends on 1, 3)

The magnetic resonance method according to claim 3, characterized in that complexly conjugated receiving sensitivities, σn*(r), are determined:
s
n
⁡
(
t
)
=
∫
V
⁢
σ
n
*
(
r
->
)
⁢
M
(
r
->
)
⁢
exp
⁡
[
t
⁢
/
⁢
T
2
]
⁢
exp
⁡
[
ⅈ
⁢
⁢
t
⁢
⁢
ω
s
]
⁢
exp
⁡
[
-
ⅈ
⁢
⁢
k
->
⁡
(
T
-
t
)
·
r
->
]
⁢
ⅆ
3
⁢
r
wherein the N high-frequency pulses b1,n according to claim 1 can be calculated on the basis of
b
1
,
n
⁡
(
t
)
=
J
⁡
(
t
)
ⅈγ
⁢
⁢
M
0
⁢
s
n
⁡
(
T
-
t
)
.

### Claim 6 (depends on 5)

The magnetic resonance method according to claim 5, characterized in that the sensitivity σn(r) is determined by means of one or more measurements of a magnetic resonance signal of the object that is to be examined, so that the high-frequency pulse is determined on the basis of the one or more preceding measurements.

### Claim 7 (depends on 1)

A nuclear spin tomograph having a means for generating magnetic gradients, a means for generating high-frequency pulses, and a means for generating a static main magnetic field, and having a means for data acquisition, characterized in that it comprises control electronics for carrying out the magnetic resonance method according to one of claim 1.

### Claim 8 (depends on 7)

The nuclear spin tomograph according to claim 7, characterized in that it comprises N coils having a different spatial transmission characteristic for generating N excitation channels, whereby the number N is greater than 1 and fundamentally not limited upwards.