Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
1999-11-09
2002-02-26
Patidar, Jay (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
C324S309000, C324S300000
Reexamination Certificate
active
06351121
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention is directed to magnetic resonance imaging (MRI) apparatus and methods, and particularly to apparatus and methods which increase the accuracy and/or resolution of MRI images, and/or decrease the time required to obtain an MRI image.
MRI is based on solving the Bloch Equations
dM
x
/dt=−&ggr;H
z
M
y
−M
x
/T
2
, (1.1)
dM
y
/dt=−&ggr;H
z
M
x
−M
y
/T
2
, (1.2)
and
dM
z
/dt
=−(
M
0
−M
z
)/
T
1
, (1.3)
which gives the magnetization M=M
x
x+M
y
y+M
z
z of magnetic nuclei (typically protons) in the presence of a magnetic field H=H
z
z. Standard nuclear magnetic resonance (NMR) uses a homogeneous magnetic field, but to obtain the spatial resolution required for image mapping, gradient magnetic fields must be added. The interaction of the magnetic spins with the environment is given in terms of the transverse relaxation time T
2
which determines the rate of decay of the M
x
and M
y
components of the magnetization M to zero, and the longitudinal relaxation time T
1
which determines the rate of decay of the M
z
component of the magnetization M to the value M
0
. It has been previously shown (Prolongation of Proton Spin Lattice Relaxation Times in Regionally Ischemic Tissue from Dog Hearts, E. S. Williams, J. I. Kaplan, F. Thatcher, G. Zimmerman and S. B. Knoebel, Journal of Nuclear Medicine, May 1980, Vol. 21, No. 5) that T
1
is different in normal and ischemic heart muscle by about 10%. Using the inversion recovery technique (which is described in detail in U.S. Pat. No. 4,383,219, entitled Nuclear Magnetic Resonance Spatial Mapping, issued May 10, 1983 to Jerome I. Kaplan, and is incorporated herein by reference) the 10% difference in the relaxation times can be amplified into a 25% differentiation in the magnetization in the normal and ischemic regions of the heart. Thus mapping this difference in magnetization allows for a mapping of the normal and ischemic regions of the heart.
High-resolution MRI images of non-moving body parts are routinely obtained. However, an added difficulty with the heart arises from its large scale rapid motion at about one beat per second. To avoid blurring, the MRI image must therefore be obtained in less than {fraction (1/20)}th of a second.
As is shown in the present specification, standard mapping procedures do not permit a high-resolution mapping for times of less than {fraction (1/20)}th of a second. An advantage of the present invention is that high-resolution images may be obtained for mappings where the data is acquired in a short period of time.
The mapping procedure of the present invention is as follows:
1) A radio frequency pulse or pulse sequence rotates the magnetization M(x,y) of the actual object density &rgr;(x,y) from its equilibrium direction along the z-axis (i.e., the direction of the large applied static magnetic field) to the x-y plane. The magnetization M(x,y) precesses at a frequency &ohgr;(x,y) about the local gradient fields at position (x,y).
2) The total magnetization is recorded by monitoring the induced voltage in the receiver coils. The relation between the total magnetization M and the actual object density &rgr;(x,y) is described by the transform F(t,x,y) according to
M
(
t
)=∫
F
(
t,x,y
)&rgr;(
x,y
)
dxdy,
(1.4)
3) An estimated mapping object density &rgr;*(x,y) is obtained from the magnetization M(t) by application of a transform E according to
&rgr;*(
x,y
)=&Sgr;
t
E
(
t,x,y
)
M
(
t
). (1.5)
For long mapping times, the estimated object density &rgr;*(x,y) is a relatively accurate map of the actual object density &rgr;(x,y) using this standard procedure. However, for shorter mapping times, the estimated object density &rgr;*(x,y) becomes a less accurate mapping of the actual object density &rgr;(x,y).
In a first preferred embodiment, the present invention therefore includes the following additional steps:
4A) A kernel function A which describes the relationship between the estimated object density &rgr;*(x,y) and the actual object density &rgr;(x,y) is estimated, i.e.,
&rgr;*(
x,y
)=∫
A
(
x,y,x′y′
)&rgr;(
x′,y′
)
dx′dy′,
(1.6)
where the kernel function is given by
A
(
x,y,x′y′
)=&Sgr;
t
E
(
t,x,y
)
F
(
t,x′,y′
). (1.7)
5A) The kernel function A is discretized to form a kernel matrix B describing the relationship between the estimated object density pixel values &rgr;*(x,y) and the actual object density pixel values &rgr;(x,y), i.e.,
ρ
*
(
x
,
y
)
=
∑
x
′
,
y
′
B
(
x
,
y
,
x
′
,
y
′
)
ρ
(
x
′
,
y
′
)
.
(
1.8
)
6A) The inverse of the kernel matrix B is applied to the estimated object density &rgr;*(x,y) to produce an increased-accuracy object density &rgr;**(x,y) which more accurately represents the actual object density &rgr;(x,y), i.e.,
ρ
**
(
x
,
y
)
=
∑
x
′
,
y
′
B
-
1
(
x
′
,
y
′
)
ρ
*
(
x
′
,
y
′
)
.
(
1.9
)
This procedure allows for high-resolution mapping of a moving subject, such as an organ like the heart. It should also be noted that the application of the inverse of the kernel matrix B to the estimated object density &rgr;*(x,y) to provide the increased-accuracy object density &rgr;**(x,y) is also useful in producing increased accuracy images in situations where there are no time constraints.
In a second preferred embodiment of the present invention, information regarding the object density is utilized to increase the accuracy of the estimate of the transform E(t,x,y). The second preferred embodiment of the present invention therefore includes the following additional steps:
4B) Ischemic and normal regions of the myocardium are mapped according to the estimated object density &rgr;*(x,y).
5B) The transform E(t,x,y) is corrected to form corrected transform E
c
(t,x,y) based on the locations of the ischemic and normal regions of the myocardium obtained from the estimated object density &rgr;*(x,y).
6B) The corrected transform E
c
(t,x,y) is used to calculate a corrected estimated object density &rgr;
c
*(x,y) according to
&rgr;
c
*(
x,y
)=&Sgr;
t
E
c
(
t,x,y
)
M
(
t
). (1.10)
According to a third preferred embodiment of the present invention a combination of the techniques of the first two preferred embodiments is used. The process of the third preferred embodiment of the present invention includes a modification of step 3, described above, as follows:
3C) A current-best estimated object density &rgr;
b
*(x,y) is obtained from the magnetization M(t) by application of a current-best transform E
b
according to
&rgr;
b
*(
x,y
)=&Sgr;
t
E
b
(
t,x,y
)
M
(
t
). (1.11)
The currently-best transform E
b
is based on an average value of the actual object density &rgr;, unless a corrected transform E
c
based on an estimation of the normal and ischemic regions has been calculated. Furthermore, the process of the third preferred embodiment of the present invention includes the following steps:
4C) When an estimated object density &rgr;*(x,y) is calculated or updated to provide a current-best estimated object density &rgr;
b
*(x,y), then a choice is made to either (i) use the current-best estimated object density &rgr;
b
*(x,y) to produce an estimate of the ischemic and normal regions, as described in step 6C below, or (ii) use the current-best estimated object density &rgr;
b
*(x,y) to produce a current-best corrected object density &rgr;
b
**(x,y), as described in step 5C below.
5C) The inverse of a best kernel matrix B
b
is applied to the current-best estimated object density &rgr;
b
*(x,y) to produce a current-best increased-accuracy object density &rgr;
b
**(x,y), which more accurately represents the actual object density &rgr;(x,y), according to
ρ
b
**
(
x
,
y
)
=
∑
k
,
l
[
B
b
(
x
,
y
,
x
′
,
y
&
Integral Patent Associates
Patidar Jay
Shrivastav Brij B.
LandOfFree
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