Removing discontinuties in MRI-space data

Details Removing discontinuties in MRI-space data Removing discontinuties in MRI-space data

1998-09-14

2001-08-14

Oda, Christine (Department: 2862)

Electricity: measuring and testing

Particle precession resonance

Using a nuclear resonance spectrometer system

C324S307000

Reexamination Certificate

active

06275037

ABSTRACT:

FIELD OF THE INVENTION
The invention relates to the processing of k-space data in MRI imaging and to the removal of discontinuities in k-space data that occur at boundaries between sets of k-space data acquired for the same MRI image using different MRI techniques or operating conditions.
BACKGROUND OF THE INVENTION
In MRI imaging, a subject imaged is placed in a spatially and temporally varying magnetic field so that an imaging nucleus in the subject precesses around the magnetic field with a Larmor frequency &ohgr;({square root over (r)}, t)=&ggr;B({square root over (r)}, t), where &ggr; is the gyromagnetic moment of the imaging nucleus and B is the magnitude of the magnetic field at time t and at a point {square root over (r)} where the imaging nucleus is located. The dependence of the Larmor frequency on position is used to evaluate the spin density, &rgr;(x,y,z), of the imaging nuclei as a function of position in the imaged subject. Since &rgr;(x,y,z) is a function of the internal features and structures of the imaged subject these features and structures can be visualized.
The magnetic field B ({square root over (r)}, t) is generally of the form B
0
+G
x
x+G
y
y+G
z
z in a direction conventionally labeled as the z direction. B
0
is the magnitude of a large and constant homogeneous magnetic field parallel to the z direction, and G
x
, G
y
and G
z
are the x,y, and z gradients of gradient fields, also parallel to the z axis, added to B
0
., The time dependence of B ({square root over (r)}, t) is a function of the rise times of the gradients G
x
, G
y
, and G
z
and the timing sequence which governs when they are turned on and off.
A signal is elicited form the imaging nuclei by rotating their spins away from the z axis. This creates a component of spin density &rgr;(x,y,z) and associated magnetization density, m(x,y,z)=&ggr;&rgr;(x,y,z) which rotate perpendicular to the z axis with a frequency equal to the Larmor frequency of the imaging nuclei. The rotating magnetic density produces a signal SIG(t) which is sensed by an appropriate receiving antenna.
The relationship between SIG(t) and the spin density &rgr;(x,y,z) of the imaging nucleus can be written as SIG(t)=∫∫∫&rgr;(x,y,z)exp[i&ggr;(B
0
+G
x
x+G
y
y+G
z
z)t] dxdydz=exp[i&ohgr;
0
t]S(t), where &ohgr;
0
=&ggr;B
0
is the Larmor frequency of the imaging nucleus in B
0
and S(t) is the part of the integral dependent upon &rgr;(x,y,z). In the relationship, the relaxation of the magnitude of the spin density in the transverse plane to zero and the recovery of the spin density equilibrium value along the z axis is ignored, and it has been assumed that the angle of rotation of &rgr;(x,y,z) away from the z axis is &pgr;/2.
By changing variables so that k
x
=&ggr;G
x
t, k
y
=&ggr;G
y
t and k
z
=&ggr;G
z
t, S(t) can be written as a function of position in a “k-space”. S(t)→S(k
x
,k
y
,k
z
)=S({square root over (k)}), and:
S({square root over (k)})=∫∫∫&rgr;(x,y,z)exp[i(k
x
x+k
y
y+k
z
z)]dxdydz=∫∫∫&rgr;({square root over (r)})exp[i{square root over (k)}·{square root over (r)}]d
3
r.
This last integral is the Fourier transform of the spin density function &rgr;(x,y,z) of the imaging nucleus. S({square root over (k)}) is a “k-transform” of &rgr;(x,y,z) and {square root over (k)} and {square root over (r)} are conjugate variables so that &rgr;({square root over (r)})=∫∫∫S({square root over (k)})exp[i{square root over (k)}·{square root over (r)}]d
3
k.
When the imaging nuclei are first flipped away from the z axis they precess together coherently with a net spin density and magnetization density in the xy plane. With time, however, the coherence in the transverse xy plane decays to zero and the spin density relaxes to the equilibrium state where the imaging nuclei are polarized along the z axis. The decay of net transverse spin density and return to equilibrium along the z axis are characterized by different time constants known as T
2
and T
1
respectively. When inhomogenities in the magnetic field are present, the decay of transverse spin density is accelerated and is characterized by a time constant known as T
2
*. The relaxation times are related by the inequality T
2
*<T
2
<T
1
.
Many different techniques have been developed for MRI imaging. All involve procedures for acquiring values for the k-transform, S({square root over (k)}), of a subject imaged at many points, hereafter “read-points”, in a raster of points in k-space so that the Fourier transform of S({square root over (k)}) results in a proper evaluation of &rgr;({square root over (r)}).
Generally, the problem of evaluating S({square root over (k)}) over three dimensions in k-space is reduced to a two dimensional one. The k-transform S({square root over (k)}) is evaluated for a thin slice perpendicular to the z axis of the subject being imaged, so that S({square root over (k)})→S(k
x
,k
y
,Z
s
) where Z
s
is the constant z coordinate of the slice. A three dimensional image is built up from the two dimensional images of many adjacent thin slices acquired for a range of values of Z
s
.
Often, data for a k-transform S({square root over (k)}), is acquired using different MRI imaging techniques or operating conditions in different areas of k-space. Ideally the values of data acquired should be independent of data acquisition method. Sets of data acquired for a same k-transform S({square root over (k)}) using different techniques or operating conditions therefore should be consistent with each other. Consistency requires that, at boundaries between two areas in k-space where data for a k-transform is acquired in one of the k-space areas using a technique or conditions different from the technique or conditions used to acquire data for the same k-transform in the other k-space area, the data on either side of the boundaries approach the same values for points on the boundaries i.e. the data must be continuous at the boundaries.
If the data is not consistent, and has discontinuities at boundaries, the discontinuities cause artifacts such as ghosting or ringing. The scale and seriousness of the artifacts is an increasing function of the slope and magnitude of the discontinuities. These seriously degrade an MRI image constructed from the k-transform and generally, solutions are needed to remove or moderate them.
Many discontinuities and sources of discontinuities are removed by standard normalization and calibration procedures. These procedures remove from the data equipment biases and many types of timing errors. Additional corrections to the data are made by dividing out the T
1
and T
2
, decay envelope from the data. Finally, data is corrected for T
2
* effects arising from chemical shift and field inhomogenities.
Chemical shift and field inhomogeneity often lead to large discontinuous phase differences between data on opposite sides of a boundary between data sets acquired using different MRI techniques or operating conditions. This occurs when data on opposite sides of the boundary are acquired at significantly different echo times T
E
. The phase differences are proportional to the time difference between the echo times and the magnitudes of the chemical shift fields and the field inhomogenities.
One way to remove chemical shift and field inhomogeneity effects is to acquire all data at the same T
E
time. This is not possible except with the standard MRI spin echo technique. This technique however is slow and therefore not suitable for many procedures. The new fast imaging techniques must contend with chemical and field inhomogeneity phase effects.
It is possible to consider mathematically removing these effects. Removing the chemical shift and field inhomogeneity effects from the data mathematically requires the acquisition of data additional to the basic k-transform data, such as a magnetic field homogeneity map. This is often impra

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