U.S. patent application number 13/397813 was filed with the patent office on 2012-10-25 for system and method for retrospective correction of high order eddy-current-induced distortion in diffusion-weighted echo planar imaging.
Invention is credited to Bruce David Collick, Kevin F. King, Joseph K. Maier, Dan Xu.
Application Number | 20120271583 13/397813 |
Document ID | / |
Family ID | 47021995 |
Filed Date | 2012-10-25 |
United States Patent
Application |
20120271583 |
Kind Code |
A1 |
Xu; Dan ; et al. |
October 25, 2012 |
SYSTEM AND METHOD FOR RETROSPECTIVE CORRECTION OF HIGH ORDER
EDDY-CURRENT-INDUCED DISTORTION IN DIFFUSION-WEIGHTED ECHO PLANAR
IMAGING
Abstract
A computer is programmed to acquire calibration data from a
calibration scan, the calibration data configured to characterize
high order eddy current (HOEC) generated magnetic field error of an
imaging system. The computer is also programmed to process the
calibration data to generate a plurality of basis coefficients and
a plurality of time constants and to calculate a plurality of basis
correction coefficients based on the plurality of basis
coefficients, the plurality of time constants, and gradient
waveforms in a given pulse sequence. The computer is further
programmed to execute a diffusion-weighted imaging scan that
comprises application of a DW-EPI pulse sequence to acquire MR data
from an imaging subject and reconstruction of an image based on the
acquired MR data. The computer is also programmed to apply
HOEC-generated magnetic field error correction during image
reconstruction configured to reduce HOEC-induced distortion in the
reconstructed image.
Inventors: |
Xu; Dan; (Oconomowoc,
WI) ; Maier; Joseph K.; (Milwaukee, WI) ;
King; Kevin F.; (Menomonee Falls, WI) ; Collick;
Bruce David; (Madison, WI) |
Family ID: |
47021995 |
Appl. No.: |
13/397813 |
Filed: |
February 16, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61476936 |
Apr 19, 2011 |
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Current U.S.
Class: |
702/104 |
Current CPC
Class: |
G01R 33/56518 20130101;
G01R 33/5616 20130101; G01R 33/56341 20130101 |
Class at
Publication: |
702/104 |
International
Class: |
G06F 19/00 20110101
G06F019/00 |
Claims
1. An MRI apparatus comprising: a magnetic resonance imaging (MRI)
system having a plurality of gradient coils positioned about a bore
of a magnet, and an RF transceiver system and an RF switch
controlled by a pulse module to transmit RF signals to an RF coil
assembly to acquire MR images; and a computer programmed to:
acquire calibration data from a calibration scan, the calibration
data configured to characterize high order eddy current generated
magnetic field error of an imaging system; process the calibration
data to generate a plurality of basis coefficients and a plurality
of time constants; calculate a plurality of basis correction
coefficients based on the plurality of basis coefficients, the
plurality of time constants, and gradient waveforms in a given
pulse sequence; execute a diffusion-weighted imaging scan
comprising: applying a DW-EPI pulse sequence to acquire MR data
from an imaging subject; and reconstructing an image based on the
acquired MR data; and apply high order eddy-current-generated
magnetic field error correction during image reconstruction
configured to reduce high order eddy-current-induced distortion in
the reconstructed image.
2. The MRI apparatus of claim 1 wherein the computer is further
programmed to calculate a high order eddy-current-related field
map.
3. The MRI apparatus of claim 2 wherein the computer in being
programmed to calculate the high order eddy-current-related field
map, is programmed to calculate the high order eddy-current-related
field map based on the equation: f ( u , v ) = n c n ( t 0 ) B n (
u , v , w 0 ) , ##EQU00010## where c.sub.n(t.sub.0) are basis
correction coefficients of the plurality of basis correction
coefficients for a basis function at a time point t.sub.0 at which
the high order eddy current field is approximated, and B.sub.n(u,
v, w.sub.0) are polynomial bases.
4. The MRI apparatus of claim 2 wherein the computer is further
programmed to apply one of an intensity correction and a geometry
correction to data based on the high order eddy-current-related
field map.
5. The MRI apparatus of claim 4 wherein the computer in being
programmed to apply the one of the intensity correction and the
geometry correction, is programmed to apply the one of the
intensity correction and the geometry correction based on the
equation: I corrected ( u , v ) = ( 1 + .differential. h ( u , v )
.differential. v ) I distorted ( u , v + h ( u , v ) ) ,
##EQU00011## where h(u, v) is a pixel shift map.
6. The MRI apparatus of claim 4 wherein the computer is further
programmed to calculate a pixel shift map, h(u, v), based on the
high order eddy-current-related field map.
7. The MRI apparatus of claim 1 wherein the computer is programmed
to apply the high order eddy-current-generated magnetic field error
correction for an arbitrary imaging plane.
8. The MRI apparatus of claim 1 wherein the computer, in being
programmed to process the calibration data, is programmed to: apply
a 3D phase unwrapping to a phase angle of the calibration data;
scale the unwrapped calibration data to generate a magnetic field
data set; spatially fit the magnetic field data set to a harmonic
basis to generate basis coefficients; and temporally fit the basis
coefficients along a time axis using one of a single-exponential
model and a multi-exponential model.
9. The MRI apparatus of claim 1 wherein the computer, in being
programmed to process the calibration data, is programmed to: take
a time derivative on a phase angle of the calibration data to
obtain a magnetic field offset at a coil location; spatially fit
each time point of the magnetic field offset to a harmonic basis to
generate basis coefficients; and temporally fit the basis
coefficients along a time axis using one of a single-exponential
model and a multi-exponential model.
10. The MRI apparatus of claim 1 wherein the computer, in being
programmed to calculate the plurality of basis correction
coefficients, is programmed to calculate the plurality of basis
correction coefficients based on the equation: d n ( t ) = m = X ,
Y , Z G m .beta. mn .alpha. mn .tau. mn - t / .tau. mn ,
##EQU00012## where G.sub.m is the X, Y, or Z component of the
diffusion gradient amplitude, .beta..sub.mn is a pulse sequence
type and sequence timing related constant, .alpha..sub.mn are basis
coefficients, and .tau..sub.mn are time constants.
11. The MRI apparatus of claim 1 wherein the computer is further
programmed to display the reconstructed image to a user.
12. A method for correcting high order eddy-current-induced
distortions in diffusion-weighted echo planar imaging (DW-EPI)
comprising: acquiring calibration data from a calibration scan, the
calibration data configured to characterize high order eddy
currents of an imaging system; processing the calibration data to
generate a plurality of basis coefficients and a plurality of time
constants; calculating a plurality of basis correction coefficients
based on the plurality of basis coefficients and based on the
plurality of time constants; and applying a DW-EPI pulse sequence
to acquire MR data from an imaging subject; reconstructing an image
based on the acquired MR data; and wherein the reconstructing the
image comprises applying high order eddy-current-generated magnetic
field error correction configured to reduce high order
eddy-current-induced distortion in the image.
13. The method of claim 12 further comprising calculating a high
order eddy-current-related field map.
14. The method of claim 13 further comprising applying one of an
intensity correction and a geometry correction to data based on the
high order eddy-current-related field map.
15. The method of claim 14 further comprising generating the data
based on the high order eddy-current-related field map by
calculating a pixel shift map, h(u, v), based on the high order
eddy-current-related field map.
16. A non-transitory computer readable medium having stored thereon
a computer program comprising a set of instructions, which, when
executed by a computer, causes the computer to: acquire calibration
data from a calibration scan configured to characterize high order
eddy current generated magnetic field error of an imaging system;
process the calibration data; generate a plurality of basis
coefficients and a plurality of time constants based on the
processed calibration data; calculate a plurality of basis
correction coefficients based on the plurality of basis
coefficients, the plurality of time constants, and gradient
waveforms in a DW-EPI pulse sequence; apply the DW-EPI pulse
sequence to acquire MR data from an imaging subject; reconstruct an
image based on the acquired MR data; and apply high order
eddy-current-generated magnetic field error correction during
reconstruction of the image configured to reduce high order eddy
current induced distortion in the reconstructed image.
17. The computer readable medium of claim 16 wherein the set of
instructions further causes the computer to: calculate a high order
eddy-current-related field map; calculate a pixel shift map, h(u,
v), based on the high order eddy-current-related field map; and
apply an intensity and geometry correction to the pixel shift
map.
18. The computer readable medium of claim 17 wherein the set of
instructions that causes the computer to calculate the high order
eddy-current-related field map causes the computer to calculate the
high order eddy-current-related field map based on the equation: f
( u , v ) = n c n ( t 0 ) B n ( u , v , w 0 ) , ##EQU00013## where
c.sub.n(t.sub.0) are basis correction coefficients of the plurality
of basis correction coefficients for a basis function at a time
point t.sub.0 at which the high order eddy current field is
approximated, and B.sub.n(u, v, w.sub.0) are polynomial bases.
19. The method of claim 18 wherein the set of instructions that
causes the computer to calculate a pixel shift map causes the
computer to calculate the pixel shift map based on the equation: h
( u , v ) = f ( u , v ) G PE , ##EQU00014## where
G.sub.PE=1/(.gamma.TL) with .gamma. being the gyromagnetic ratio of
the nucleus of interest, T being the EPI echo spacing, and L being
the field of view in the phase encoding axis.
20. The method of claim 19 wherein the set of instructions that
causes the computer to apply the intensity and geometry correction
causes the computer to apply the intensity and geometry correction
based on the equation: I corrected ( u , v ) = ( 1 + .differential.
h ( u , v ) .differential. v ) I distorted ( u , v + h ( u , v ) )
. ##EQU00015##
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] The present application is a non-provisional of, and claims
priority to, U.S. Provisional Patent Application Ser. No.
61/476,936, filed Apr. 19, 2011, the disclosure of which is
incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] Embodiments of the invention relate generally to magnetic
resonance (MR) imaging and, more particularly, to correcting high
order eddy-current-induced distortion in diffusion-weighted echo
planar imaging.
[0003] When a substance such as human tissue is subjected to a
uniform magnetic field (polarizing field B.sub.0), the individual
magnetic moments of the spins in the tissue attempt to align with
this polarizing field, but precess about it in random order at
their characteristic Larmor frequency. If the substance, or tissue,
is subjected to a magnetic field (excitation field B.sub.i) which
is in the x-y plane and which is near the Larmor frequency, the net
aligned moment, or "longitudinal magnetization", M.sub.z, may be
rotated, or "tipped", into the x-y plane to produce a net
transverse magnetic moment M.sub.t. A signal is emitted by the
excited spins after the excitation signal B.sub.1 is terminated and
this signal may be received and processed to form an image.
[0004] When utilizing these signals to produce images, magnetic
field gradients (G.sub.x, G.sub.y, and G.sub.z) are employed.
Typically, the region to be imaged is scanned by a sequence of
measurement cycles in which these gradients vary according to the
particular localization method being used. The resulting set of
received NMR signals are digitized and processed to reconstruct the
image using one of many well known reconstruction techniques.
[0005] It is well known that Diffusion-Weighted Echo Planar Imaging
(DW-EPI) often suffers from diffusion encoding direction dependent
distortions due to diffusion gradient generated eddy current field.
These distortions, if not corrected, can lead to mis-registration
among DW images of different directions and inaccuracies in any
post processing operations involving DW image combination. Dual
spin echo (also called twice refocused) DW-EPI has been proposed to
provide a certain level of inherent eddy current cancellation, but
with a significant increase in echo time and decrease in
signal-to-noise ratio (SNR). For example, a typical dual spin echo
protocol may generate about half as much SNR as the corresponding
single spin echo (also called Stejkal-Tanner sequence) protocol on
liver imaging at 3T. In many cases (e.g., whole body DW-EPI),
increasing NEX is not an option to increase SNR because of the
associated increase in scan time. Therefore, it is desirable to
keep single spin-echo while reducing the resulting distortion in
practice.
[0006] Conventional distortion correction methods have focused on
correcting only the linear and constant eddy currents (also called
B.sub.0 eddy currents), either by pre-emphasis or by explicitly
modifying gradient waveforms and receive frequency. However,
uncompensated eddy currents of high spatial order due to gradient
coil leakage field, or simply high order eddy currents (HOEC), can
also be significant with the desire for increased b values and the
increase of gradient amplitude and slew rate in modern MR scanners.
Because of the high spatial order, distortions generated by the
magnetic fields created by these eddy currents are not only
diffusion gradient direction dependent, but also slice
dependent.
[0007] It would therefore be desirable to have a system and method
capable of correcting distortion due to HOEC in DW-EPI.
BRIEF DESCRIPTION OF THE INVENTION
[0008] According to an aspect of the invention, an MRI apparatus
comprises a magnetic resonance imaging (MRI) system having a
plurality of gradient coils positioned about a bore of a magnet,
and an RF transceiver system and an RF switch controlled by a pulse
module to transmit RF signals to an RF coil assembly to acquire MR
images. The MRI apparatus also comprises a computer programmed to
acquire calibration data from a calibration scan, the calibration
data configured to characterize high order eddy-current-generated
magnetic field error of an imaging system. The computer is also
programmed to process the calibration data to generate a plurality
of basis coefficients and a plurality of time constants and to
calculate a plurality of basis correction coefficients based on the
plurality of basis coefficients, the plurality of time constants,
and gradient waveforms in a given pulse sequence. The computer is
further programmed to execute a diffusion-weighted imaging scan
that comprises application of a DW-EPI pulse sequence to acquire MR
data from an imaging subject and reconstruction of an image based
on the acquired MR data. The computer is also programmed to apply
high order eddy-current-generated magnetic field error correction
during image reconstruction configured to reduce high order
eddy-current-induced distortion in the reconstructed image.
[0009] According to another aspect of the invention, a method for
correcting high order eddy-current-induced distortions in
diffusion-weighted echo planar imaging (DW-EPI) comprises acquiring
calibration data from a calibration scan, the calibration data
configured to characterize high order eddy currents of an imaging
system, processing the calibration data to generate a plurality of
basis coefficients and a plurality of time constants, and
calculating a plurality of basis correction coefficients based on
the plurality of basis coefficients and based on the plurality of
time constants. The method also comprises applying a DW-EPI pulse
sequence to acquire MR data from an imaging subject, reconstructing
an image based on the acquired MR data, and wherein the
reconstructing the image comprises applying high order
eddy-current-generated magnetic field error correction configured
to reduce high order eddy-current-induced distortion in the
image.
[0010] According to yet another aspect of the invention, a
non-transitory computer readable medium having stored thereon a
computer program comprising a set of instructions, which, when
executed by a computer, causes the computer to acquire calibration
data from a calibration scan configured to characterize high order
eddy current generated magnetic field error of an imaging system
and to process the calibration data. The set of instructions also
causes the computer to generate a plurality of basis coefficients
and a plurality of time constants based on the processed
calibration data and to calculate a plurality of basis correction
coefficients based on the plurality of basis coefficients, the
plurality of time constants, and gradient waveforms in a DW-EPI
pulse sequence. The set of instructions also causes of the computer
to apply the DW-EPI pulse sequence to acquire MR data from an
imaging subject, to reconstruct an image based on the acquired MR
data, and to apply high order eddy-current-generated magnetic field
error correction during reconstruction of the image configured to
reduce high order eddy current induced distortion in the
reconstructed image.
[0011] Various other features and advantages will be made apparent
from the following detailed description and the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] The drawings illustrate embodiments presently contemplated
for carrying out embodiments of the invention.
[0013] In the drawings:
[0014] FIG. 1 is a schematic block diagram of an MR imaging system
for use with embodiments of the invention.
[0015] FIG. 2 is a pulse sequence diagram showing ideal gradient
and RF waveforms for a single spin echo diffusion-weighted EPI
scan.
[0016] FIG. 3 is a flowchart showing an HOEC correction technique
according to an embodiment of the invention.
[0017] FIG. 4 is a flowchart showing an HOEC calibration data
processing algorithm that may be used in the HOEC correction
technique of FIG. 3 according to an embodiment of the
invention.
[0018] FIG. 5 is a flowchart showing another HOEC data processing
algorithm that may be used in the HOEC correction technique of FIG.
3 according to an embodiment of the invention.
[0019] FIG. 6 is a flowchart showing an algorithm for calculating
HOEC terms that may be used in the HOEC correction technique of
FIG. 3 according to an embodiment of the invention.
[0020] FIG. 7 is a flowchart showing an algorithm for retrospective
compensation of HOEC terms that may be used in the HOEC correction
technique of FIG. 3 according to an embodiment of the
invention.
DETAILED DESCRIPTION
[0021] Referring to FIG. 1, the major components of a magnetic
resonance imaging (MRI) system 10 incorporating an embodiment of
the invention are shown. The operation of the system is controlled
for certain functions from an operator console 12 which in this
example includes a keyboard or other input device 13, a control
panel 14, and a display screen 16. The console 12 communicates
through a link 18 with a separate computer system 20 that enables
an operator to control the production and display of images on the
display screen 16. The computer system 20 includes a number of
modules which communicate with each other through a backplane 20a.
These modules include an image processor module 22, a CPU module 24
and a memory module 26, known in the art as a frame buffer for
storing image data arrays. The computer system 20 communicates with
a separate system control 32 through a high speed serial link 34.
The input device 13 can include a mouse, joystick, keyboard, track
ball, touch activated screen, light wand, voice control, card
reader, push-button, or any similar or equivalent input device, and
may be used for interactive geometry prescription.
[0022] The system control 32 includes a set of modules connected
together by a backplane 32a. These include a CPU module 36 and a
pulse generator module 38 which connects to the operator console 12
through a serial link 40. It is through link 40 that the system
control 32 receives commands from the operator to indicate the scan
sequence that is to be performed. The pulse generator module 38
operates the system components to carry out the desired scan
sequence and produces data which indicates the timing, strength and
shape of the RF pulses produced, and the timing and length of the
data acquisition window. The pulse generator module 38 connects to
a set of gradient amplifiers 42, to indicate the timing and shape
of the gradient pulses that are produced during the scan. The pulse
generator module 38 can also receive patient data from a
physiological acquisition controller 44 that receives signals from
a number of different sensors connected to the patient, such as ECG
signals from electrodes attached to the patient. And finally, the
pulse generator module 38 connects to a scan room interface circuit
46 which receives signals from various sensors associated with the
condition of the patient and the magnet system. It is also through
the scan room interface circuit 46 that a patient positioning
system 48 receives commands to move the patient to the desired
position for the scan.
[0023] The gradient waveforms produced by the pulse generator
module 38 are applied to the gradient amplifier system 42 having
Gx, Gy, and Gz amplifiers. Each gradient amplifier excites a
corresponding physical gradient coil in a gradient coil assembly
generally designated 50 to produce the magnetic field gradients
used for spatially encoding acquired signals. The gradient coil
assembly 50 forms part of a resonance assembly 52 which includes a
polarizing magnet 54 and a whole-body RF coil 56. A transceiver
module 58 in the system control 32 produces pulses which are
amplified by an RF amplifier 60 and coupled to the RF coil 56 by a
transmit/receive switch 62. The resulting signals emitted by the
excited nuclei in the patient may be sensed by the same RF coil 56
and coupled through the transmit/receive switch 62 to a
preamplifier 64. The amplified MR signals are demodulated,
filtered, and digitized in the receiver section of the transceiver
58. The transmit/receive switch 62 is controlled by a signal from
the pulse generator module 38 to electrically connect the RF
amplifier 60 to the coil 56 during the transmit mode and to connect
the preamplifier 64 to the coil 56 during the receive mode. The
transmit/receive switch 62 can also enable a separate RF coil (for
example, a surface coil) to be used in either the transmit or
receive mode.
[0024] The MR signals picked up by the RF coil 56 are digitized by
the transceiver module 58 and transferred to a memory module 66 in
the system control 32. A scan is complete when an array of raw
k-space data has been acquired in the memory module 66. This raw
k-space data is rearranged into separate k-space data arrays for
each image to be reconstructed, and each of these is input to an
array processor 68 which operates to Fourier transform the data
into an array of image data. This image data is conveyed through
the serial link 34 to the computer system 20 where it is stored in
memory. In response to commands received from the operator console
12 or as otherwise directed by the system software, this image data
may be archived in long term storage or it may be further processed
by the image processor 22 and conveyed to the operator console 12
and presented on the display 16.
[0025] Embodiments of the invention correct high order eddy current
(HOEC) induced diffusion gradient direction dependent distortion in
Diffusion-Weighted Echo Planar Imaging (DW-EPI). As used herein,
"high order" means spatial order higher than or equal to 2, as
compared to linear and constant orders, which mean order 1 and 0,
respectively. However, embodiments of the invention can also be
applied to linear and constant orders as well. The distortions due
to HOEC may strongly affect the acquired data, especially for body
applications where large FOV is used and large slice coverage is
desired. As discussed herein, a system calibration may be used to
characterize eddy currents of spatial orders less than or equal to
P, where P is usually 3 to 5, but can be any order in general.
DW-EPI pulse sequence with correction amplitudes for gradients in
readout, phase encoding, and slice axes, and receiver frequency on
a per-slice basis may be played to prospectively remove the effect
of the quasi-linear HOEC terms.
[0026] Referring to FIG. 2, a DW-EPI pulse sequence 70 is shown
including 90.degree. and 180.degree. RF pulses 72 and 74,
respectively. RF pulses 72, 74 can be transmitted by RF coil 56 to
generate an echo signal 76, which can be encoded with spatial
information. Echo signal 76 can also be received by coil 56 or by
another coil, such as a surface coil, for use in reconstructing an
image.
[0027] To spatially encode echo signal 76 in accordance with echo
planar imaging, the sequence shown in FIG. 2 further includes
read-out, phase-encoding, and slice-selection gradients G.sub.ro,
G.sub.pe, and G.sub.sl, respectively. Readout gradient G.sub.ro
comprises a pre-phasing pulse 78 and read-out pulses 80. Similarly,
phase-encoding gradient G.sub.pe comprises a pre-phasing pulse 82
and phase-encoding pulses 84. Slice-selection gradient G.sub.sl
comprises slice selection pulses 86 for the 90.degree. RF pulse 72
and 88 for the 180.degree. RF pulse 74, as well as 86a for slice
refocusing.
[0028] Still referring to FIG. 2, there is shown
diffusion-weighting gradient G.sub.d, used in a diffusion-weighted
EPI scan. Diffusion-weighting gradient G.sub.d comprises two
equivalent trapezoidal pulses 90 and 92, placed at either side of
the 180.degree. RF pulse 74. Note that in general, G.sub.d can
contain components on all three logical axes. In the following, the
read-out, phase-encoding, and slice axes (i.e., the logical axes)
are denoted as u, v, and w respectively, and the components of
G.sub.d in u, v, and w axes are denoted as G.sub.u, G.sub.v, and
G.sub.w, respectively. The physical axes are denoted as x, y, and
z.
[0029] FIG. 3 shows an HOEC correction technique 94 according to an
embodiment of the invention. Technique 94 begins at block 96 by
performing an HOEC calibration to characterize the
eddy-current-generated magnetic field error of a particular imaging
system such as MRI system 10 of FIG. 1. The calibration can either
be phantom-based or local-pickup-coil-based. In the phantom-based
method, gradient echo images are often collected at multiple time
points following an eddy current generating gradient. In the
local-pickup-coil-based method, a number of local coils, each with
a small sample, are used to obtain free induction decay signals at
their respective spatial locations. To use the local pickup coil
method for HOEC measurement, multiple data acquisitions are often
needed where the coil fixture is repositioned at each acquisition
so that sufficient data are obtained for HOEC characterization. The
HOEC calibration can be done as frequently as needed, but is in
general only needed once per system installation or when there are
significant system hardware (e.g., gradient coil) changes. A
4-dimensional (3D in space and 1D in time) eddy current field data
set is generated after HOEC calibration scan.
[0030] At block 98, data from the HOEC calibration of block 96 are
first preprocessed and then fitted to mathematical models to
characterize the underlying HOEC according to an algorithm based on
which of the abovementioned calibration methods is used in block
96. FIGS. 4 and 5 illustrate HOEC data processing algorithms 116,
118 that may be used in block 98 of the HOEC correction technique
94 of FIG. 3 according to an embodiment of the invention.
[0031] Referring to FIG. 4, HOEC data processing algorithm 116 is
used when the HOEC calibration of block 96 of technique 94 is
performed using the phantom-based method as described above. Data
from the HOEC calibration scan are acquired at block 120. At block
122, a 3D phase unwrapping is applied to the phase angle of the
data, and the phase angle is scaled at block 124 by a factor
proportional to the echo time to yield a magnetic field data set.
Each time point of the magnetic field data set is then spatially
fitted at block 126 to polynomial or spherical harmonic bases of
order up to P to generate basis coefficients, where P is usually 3
to 5, but can be any order in general. Note that magnitude weights
or masks can be optionally used during the spatial fitting.
[0032] The resulting basis coefficients are then temporal fitted
along the time axis at block 128 using a single-exponential or
multi-exponential model. The end results of HOEC data processing is
a set of (.alpha..sub.mn, .tau..sub.mn) pairs, where .alpha..sub.mn
are basis coefficients and .tau..sub.mn are time constants (for
notational simplicity, a single exponential is assumed) of the nth
spatial basis function B.sub.n(x, y, z), n=1,2, . . . , N, with
diffusion donor axis m, where m is the x, y, or z axis. B.sub.n(x,
y, z) are assumed to be polynomial bases for convenience of
discussion. Note that this is without any loss of generalization
because spherical harmonic bases are linear combinations of
polynomial bases and can be easily converted into polynomials. Note
also that the total number of bases N=(P+1)(P+2)(P+3)/6. The
(.alpha..sub.mn, .tau..sub.mn) pairs are saved or stored on the
host computer of the scanner for future use at block 130.
[0033] Referring to FIG. 5, HOEC data processing algorithm 118 is
used when the HOEC calibration of block 96 of technique 94 is
performed using the local-pickup-coil-based method as described
above. Data from the HOEC calibration scan are acquired at block
132. At block 134, time derivatives are taken on the phase angle of
the data to obtain the magnetic field offset at a coil location.
Each time point of the magnetic field offset is then spatially
fitted at block 136 to polynomial or spherical harmonic bases of
order up to P to generate basis coefficients, where P is usually 3
to 5, but can be any order in general. As noted above, magnitude
weights or masks can be optionally used during the spatial
fitting.
[0034] Similar to that described above with respect to HOEC data
processing algorithm 116, the resulting basis coefficients are then
temporal fitted along the time axis at block 138, and a set of
(.alpha..sub.mn, .tau..sub.mn) pairs is generated. The
(.alpha..sub.mn, .tau..sub.mn) pairs are saved or stored on the
host computer of the scanner for future use at block 140.
[0035] Similar to the HOEC calibration scan of block 96 of
technique 94, the HOEC data processing performed in HOEC data
processing algorithms 116 and 118 only needs to be done once per
system installation. However, algorithms 116 and 118 can be
performed as frequently as needed.
[0036] Referring back to FIG. 3, DW-EPI protocol dependent HOEC
terms are calculated at block 100. Note that block 100 can handle
arbitrary imaging planes. As used herein, an arbitrary imaging
plane means straight axial, coronal, or sagittal scan plane, as
well as any oblique plane. As shown in FIG. 6, an algorithm 142 for
calculating the HOEC terms for block 100 of FIG. 3 is shown. At
block 144, the diffusion gradient components G.sub.u, G.sub.v,
G.sub.w of the DW-EPI pulse sequence to be used are obtained. At
block 145, logical gradients G.sub.u, G.sub.v, G.sub.w are
converted to physical components G.sub.x, G.sub.y, G.sub.z by
applying the 3.times.3 axis rotation matrix R:
[ G x G y G z ] = R [ G u G v G w ] , where ##EQU00001## R = [ r 11
r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33 ] , ##EQU00001.2##
Note that R is a unitary matrix (i.e., R.sup.-1=R.sup.T).
[0037] At block 146, the (.alpha..sub.mn, .tau..sub.mn) pairs
determined via block 98 from the HOEC calibration scan at block 96
of technique 94 are obtained, and the pulse sequence type and
sequence timing dependent constant, .beta..sub.nm, is calculated at
block 148.
[0038] Derivation of .beta..sub.mn can either be analytical or
using convolution. Although all gradient waveforms can be included
to obtain .beta..sub.nm, contributions from the diffusion gradients
are often dominant, which allow for simplified analysis to obtain
.beta..sub.mn. For example, when single spin echo DW-EPI is used
such as that shown in FIG. 2, it can be derived that:
.beta. mn = ( 1 - t 1 .tau. mn ) ( 1 - t 2 .tau. mn ) ( 1 + t 3
.tau. mn ) t 1 , ( Eqn . 1 ) ##EQU00002##
where t.sub.1, t.sub.2, and t.sub.3 are sequence timing related
constants shown in FIG. 2. Note that .beta..sub.nm for other pulse
sequences such as the dual spin echo or stimulated echo DW-EPI can
also be determined analytically.
[0039] At block 149, the HOEC physical basis coefficients
d.sub.n(t) for the nth basis function .beta..sub.n(x, y, z) at time
t after the last diffusion gradient are calculated based on the
equation:
d n ( t ) = m = x , y , z G m .beta. mn .alpha. mn .tau. mn - t /
.tau. mn , ( Eqn . 2 ) ##EQU00003##
where G.sub.m is the x, y, or z component of the diffusion gradient
amplitude.
[0040] At block 150, the transpose of another rotation matrix, the
basis rotation matrix F, is applied to d.sub.1(t), d.sub.2(t), . .
. , d.sub.N(t) to convert them into HOEC logical basis coefficients
c.sub.1(t), c.sub.2(t), . . . , c.sub.N(t):
[ c 1 ( t ) c 2 ( t ) c N ( t ) ] = F T [ d 1 ( t ) d 2 ( t ) d N (
t ) ] , ##EQU00004##
where "T" denotes matrix transpose. F is an N.times.N matrix that
transforms polynomial bases from logical to physical coordinates.
The actual form of F depends on the polynomial order and how the
basis functions are numbered. Without loss of generality, the bases
are in the following order: 1, x, y, z, x.sup.2,xy, xz, y.sup.2,
yz, z.sup.2, x.sup.3, x.sup.2y, x.sup.2z, xy.sup.2, xyz, xz.sup.2,
y.sup.3, y.sup.2z, yz.sup.2, z.sup.3, . . . , where lower order
bases lead higher order bases, and for bases that have the same
polynomial order, the ones that have higher x exponent lead, or, in
case of the same x exponent, the ones that have higher y exponent
lead. F can be determined by the relationship between B.sub.n(x, y,
z) and B.sub.n(u, v, w), where
[ x y z ] = R [ u v w ] . ##EQU00005##
[0041] For example, for up to 3.sup.rd order polynomials,
F = [ 1 0 0 0 0 0 0 0 0 0 0 r 11 r 12 r 13 0 0 0 0 0 0 0 r 21 r 22
r 23 0 0 0 0 0 0 0 r 31 r 32 r 33 0 0 0 0 0 0 0 0 0 0 r 11 2 r 12 2
r 13 2 2 r 11 r 12 2 r 11 r 13 2 r 12 r 13 0 0 0 0 r 21 2 r 22 2 r
23 2 2 r 21 r 22 2 r 21 r 23 2 r 22 r 23 0 0 0 0 r 31 2 r 32 2 r 33
2 2 r 31 r 32 2 r 31 r 33 2 r 32 r 33 0 0 0 0 r 11 r 21 r 12 r 22 r
13 r 23 r 13 r 22 + r 12 r 21 r 11 r 23 + r 13 r 21 r 12 r 23 + r
13 r 22 0 0 0 0 r 11 r 31 r 13 r 32 r 11 r 32 r 11 r 32 + r 12 r 31
r 11 r 33 + r 13 r 31 r 12 r 33 + r 13 r 32 0 0 0 0 r 21 r 31 r 22
r 32 r 23 r 33 r 21 r 32 + r 22 r 31 r 21 r 33 + r 23 r 31 r 22 r
33 + r 23 r 32 ] . ##EQU00006##
At block 151, all HOEC logical basis coefficients are saved for
future use.
[0042] Referring back to FIG. 3, the protocol dependent HOEC terms
can be compensated for in technique 94 retrospectively.
Retrospective compensation includes applying a DW-EPI pulse
sequence to acquire data from the imaging subject at block 102.
Then, during image reconstruction at block 104, the HOEC terms are
retrospectively compensated for. FIG. 7 illustrates a retrospective
compensation algorithm 162 for block 104 according to an embodiment
of the invention. Note that due to the application of F, bases are
now in logical axes.
[0043] Image distortion due to HOEC fields can be corrected using a
field map based method in image reconstruction according to this
embodiment. Algorithm 162 does distortion correction in the image
domain on a per-slice basis. For simplicity, the w dependency in
the notation is dropped. Denote the eddy current field as f(u, v).
At w=w.sub.0, the value of the HOEC related field map f(x, y) can
be calculated at block 164 by the equation:
f ( u , v ) = n c n ( t 0 ) B n ( u , v , w 0 ) , ( Eqn . 3 )
##EQU00007##
where the summation is done over all the spatial basis functions
and t.sub.0 is the time point at which the HOEC field is
approximated. The choice of t.sub.0 can be arbitrary, but it is
preferable to be chosen at the time when the k-space center data is
acquired (i.e., at the echo time).
[0044] The eddy current field is then normalized by the effective
gradient in the phase encoding axis G.sub.PE to obtain the pixel
shift map h(u, v) at block 166 by the equation:
h ( u , v ) = f ( u , v ) G PE , ( Eqn . 4 ) ##EQU00008##
where G.sub.PE=1/(.gamma.TL) with .gamma. being the gyromagnetic
ratio of the nucleus of interest, T being the EPI echo spacing and
L being the field of view in the phase encoding axis.
[0045] Denote the image under normal image reconstruction (i.e.,
without retrospective correction) as I.sub.distorted(u, v). The
image after retrospective correction I.sub.corrected(u, v) can be
obtained at block 168 by the equation:
I corrected ( u , v ) = ( 1 + .differential. h ( u , v )
.differential. v ) I distorted ( u , v + h ( u , v ) ) , ( Eqn . 5
) ##EQU00009##
where the first term is the intensity correction and the second
term is the geometry correction. Note that both I.sub.distorted(u,
v) and I.sub.corrected(u, v) could be magnitude or complex images.
According to Eqns. 3 and 4, h(u, v) are linear combinations of
B.sub.n(u, v, w.sub.0). Because B.sub.n(u, v, w.sub.0) are
polynomial bases, it is straightforward to obtain the analytical
form of .differential.h(u, v)/.differential.v, which makes it easy
to obtain the intensity correction factor in Eqn. 5. Evaluation of
the geometry correction term can be accomplished by image domain
interpolation. HOEC-corrected image results from performing
algorithm 162.
[0046] One can see that this technique can be applied to multishot
EPI (top-down or bottom-up interleaved acquisition) as well. For
S-shot EPI, the effective echo spacing becomes T/S and G.sub.PE in
Eqn. 4 becomes S/(.gamma.TL), which scales the overall distortion
by a factor of 1/S. Note that multishot EPI can reduce TE versus
single shot EPI, leading to a different t.sub.0 in Eqn. 3.
[0047] Referring again to FIG. 3, the image reconstructed at block
104 may be displayed to a user or stored on an image storage
database for future use at block 106.
[0048] According to embodiments of the invention, compensation of
HOEC-induced distortions for DW-EPI can make single spin echo
DW-EPI more practical. While, single spin echo has SNR and scan
time benefits over dual spin echo DWI, embodiments of the invention
can also be applied to dual spin echo and other variants of DW-EPI
sequences to reduce distortion. Embodiments of the invention can
produce a significant leverage of whole body DWI, which may have a
long scan time, low SNR, and large image distortions. Brain DWI may
benefit as well, especially for high b-value, large parallel
imaging factor cases where SNR can be a problem.
[0049] A technical contribution for the disclosed method and
apparatus is that it provides for a computer implemented correction
of high order eddy-current-induced distortion in diffusion-weighted
echo planar imaging.
[0050] One skilled in the art will appreciate that embodiments of
the invention may be interfaced to and controlled by a computer
readable storage medium having stored thereon a computer program.
The computer readable storage medium includes a plurality of
components such as one or more of electronic components, hardware
components, and/or computer software components. These components
may include one or more computer readable storage media that
generally stores instructions such as software, firmware and/or
assembly language for performing one or more portions of one or
more implementations or embodiments of a sequence. These computer
readable storage media are generally non-transitory and/or
tangible. Examples of such a computer readable storage medium
include a recordable data storage medium of a computer and/or
storage device. The computer readable storage media may employ, for
example, one or more of a magnetic, electrical, optical,
biological, and/or atomic data storage medium. Further, such media
may take the form of, for example, floppy disks, magnetic tapes,
CD-ROMs, DVD-ROMs, hard disk drives, and/or electronic memory.
Other forms of non-transitory and/or tangible computer readable
storage media not list may be employed with embodiments of the
invention.
[0051] A number of such components can be combined or divided in an
implementation of a system. Further, such components may include a
set and/or series of computer instructions written in or
implemented with any of a number of programming languages, as will
be appreciated by those skilled in the art. In addition, other
forms of computer readable media such as a carrier wave may be
employed to embody a computer data signal representing a sequence
of instructions that when executed by one or more computers causes
the one or more computers to perform one or more portions of one or
more implementations or embodiments of a sequence.
[0052] Therefore, according to an embodiment of the invention, an
MRI apparatus comprises a magnetic resonance imaging (MRI) system
having a plurality of gradient coils positioned about a bore of a
magnet, and an RF transceiver system and an RF switch controlled by
a pulse module to transmit RF signals to an RF coil assembly to
acquire MR images. The MRI apparatus also comprises a computer
programmed to acquire calibration data from a calibration scan, the
calibration data configured to characterize high order
eddy-current-generated magnetic field error of an imaging system.
The computer is also programmed to process the calibration data to
generate a plurality of basis coefficients and a plurality of time
constants and to calculate a plurality of basis correction
coefficients based on the plurality of basis coefficients, the
plurality of time constants, and gradient waveforms in a given
pulse sequence. The computer is further programmed to execute a
diffusion-weighted imaging scan that comprises application of a
DW-EPI pulse sequence to acquire MR data from an imaging subject
and reconstruction of an image based on the acquired MR data. The
computer is also programmed to apply high order
eddy-current-generated magnetic field error correction during image
reconstruction configured to reduce high order eddy-current-induced
distortion in the reconstructed image.
[0053] According to another embodiment of the invention, a method
for correcting high order eddy-current-induced distortions in
diffusion-weighted echo planar imaging (DW-EPI) comprises acquiring
calibration data from a calibration scan, the calibration data
configured to characterize high order eddy currents of an imaging
system, processing the calibration data to generate a plurality of
basis coefficients and a plurality of time constants, and
calculating a plurality of basis correction coefficients based on
the plurality of basis coefficients and based on the plurality of
time constants. The method also comprises applying a DW-EPI pulse
sequence to acquire MR data from an imaging subject, reconstructing
an image based on the acquired MR data, and wherein the
reconstructing the image comprises applying high order
eddy-current-generated magnetic field error correction configured
to reduce high order eddy-current-induced distortion in the
image.
[0054] According to yet another embodiment of the invention, a
non-transitory computer readable medium having stored thereon a
computer program comprising a set of instructions, which, when
executed by a computer, causes the computer to acquire calibration
data from a calibration scan configured to characterize high order
eddy current generated magnetic field error of an imaging system
and to process the calibration data. The set of instructions also
causes the computer to generate a plurality of basis coefficients
and a plurality of time constants based on the processed
calibration data and to calculate a plurality of basis correction
coefficients based on the plurality of basis coefficients, the
plurality of time constants, and gradient waveforms in a DW-EPI
pulse sequence. The set of instructions also causes of the computer
to apply the DW-EPI pulse sequence to acquire MR data from an
imaging subject, to reconstruct an image based on the acquired MR
data, and to apply high order eddy-current-generated magnetic field
error correction during reconstruction of the image configured to
reduce high order eddy current induced distortion in the
reconstructed image.
[0055] This written description uses examples to disclose
embodiments of the invention, including the best mode, and also to
enable any person skilled in the art to practice the embodiments of
the invention, including making and using any devices or systems
and performing any incorporated methods. The patentable scope of
embodiments of the invention is defined by the claims, and may
include other examples that occur to those skilled in the art. Such
other examples are intended to be within the scope of the claims if
they have structural elements that do not differ from the literal
language of the claims, or if they include equivalent structural
elements with insubstantial differences from the literal languages
of the claims.
* * * * *