Impact Nola
of Section
M. Hylton,
Doubling
PhD
Ilya Simovsky, PhD Andrew J. Li, PhD James D. Hale, BA To improve the quality of projection angiograms generated from three-dimensional magnetic resonance (MR) angiography data, the authors applied voxel shifting to create intermediate sections (“section doubling”) prior to maximum
intensity
projection.
To
date,
the authors have processed MR angiography studies with and without section doubling in 20 cases. Section doubling resulted in improved vessel contrast and delineation of continuity (especially of small vessels) in all cases.
on
Radiology
S
1992;
OME
of
185:899-902
the
most
successful
magnetic
resonance
(MR) angiography techniques are based on three-dimensional (3D) Fourier transform (FT) acquisition schemes (1,2). In this form of imaging,
phase
encoding
in-plane
is used
resolution
definition.
D larger although
tions (and imaging time) increases in direct proportion to the amount of section thickness reduction; and (b) signalto-noise ratio (S/N) decreases as the square root of the section thickness changes for constant coverage (FOV in the section direction). In MR angiography, vessel connectivity can be difficult to appreciate through viewing of individual sections. This dif-
fect the conclusion) and a section thickness T. Figure 1 shows two extreme
mum
pixel
value
for projection
high
surface.
contrast
studies,
with
vessel
MR
a
of the
in a projec-
processing
used to reduce contrast registration in imaging lesions (3). We describe
has been due to mis-
loss
of small
brain
the application of voxel shifting to MR angiography and illustrate how the effects of misreg-
istration can be substantially reduced the use of voxel shifting along the section axis prior to vessel reformatting with MIP.
as for section
encoding
yields
Materials
and
Theoretical
by
MR angiogra-
tion of these
to
olution
two
the
vessels,
it is desirable
thickness.
This
has
along
MIP
thickness.
shifting From the Radiologic Imaging Laboratory, University of California, San Francisco, South San Francisco, CA 94080 (N.M.H., J.D.H.) and Toshiba America MRI, Inc, South San Francisco, Calif (IS., A.J.L.). Received March 24, 1992; revision requested May 13; revision received July 13; accepted August 18. Supported in part by Toshiba America MRI, Inc. and by grant no. HL 39171 from the National Heart, Lung, and Blood Institute, U.S. Department of Health and Human Services. Address reprint requests to N.M.H., Department of Radiology, University of California, San Francisco, I Irving St. San Francisco, CA 94143. 2 9* indicates generalized vein and artery involvement. (. RSNA, 1992
Volume
185
Number
#{149}
3
ate
interpolation intermediate pixel direction. If, instead,
is first
section
substantial dicted
of the in-plane axes to the section
used
planes
to create
prior
improvement
in vessel
edge
a
can be predefinition,
particu-
larly for thin vessels traveling in directions oblique to the section axis. Section
ization garding ity-related
thickness
in two
affects
principal
vessel
ways
visual-
(disre-
signal loss resulting from velocdephasing): through partial
volume averaging registration. To illustrate the
and
vessel-section
effects of partial volaveraging on vessel visualization, we present examples for a vessel of lumen diameter D (for convenience, with ume
aligned
in the
second
partial
case
(Fig
lb),
because
of
volume
averaging, the apparent vessel signal V = (D/T)V + ([T DJ/T) B. The contrast C becomes C = Va/ B 1 =C0(D/T)forD < TandC=C0for D T. Figure lc shows the contrast in the 90” case for T = 2D. In MR angiography sequences, attempts are made to have the vessel signal be much larger than the background, so that C may be approximated by C (D . V)/(T . B). Because of this, partial volume averaging is more forgiving in MR angiography than it is in other forms of imaging. Figure 2 shows the dependence of C on the ratio D/T for cases where V = 7 . B and V = 1.3 B. The first relationship is typical of MR angiography and the second is typical -
the vessel considering
example
only),
along for 0
the
also affects angle 0
and section axis the two-dimensional
the maximum
contrast
between C0 900. Furtherwill drop way, so that
vessel
will vary = O and C for 0 = more, the signal intensity from maximum in a linear
the intensity profile along the vessel will be triangular or trapezoidal, depending on the angle and the values of D, T, and R. This profile results from the
intermedi-
to projection,
the vessel
contrast
between (again
of
is used values voxel
Linear
to compute along this
I
one
is equivalent
2D, with
=
threshold is reached. Vessel-section registration vessel visualization. For any
phy sequences that exploit in-flow for contrast, the section axis is usually onented parallel to the vessel. MIP reformatting is commonly performed in a projection direction that is perpendicutar to the section axis, such that the res-
section
for T
size R, not af-
pixel
does
of MR imaging of small brain lesions. Notice that for a certain conspicuity threshold (eg, C = .2), the higher the C0, the lower the D/T value at which this
Methods methods-In
in-plane
shown, in the first case (Fig la), C0 between the vessel and background (C0 = V/B - 1, where V = vessel signal and B = background signal) is preserved in the image, while the
are extracted
anatomically
the
this assumption
example
angiography
structures
and presented tion view. Voxel shifting
onto
Because
than
at O (Fig la) and at 900 (Fig lb) to the section axis. For the two-dimensional
ficulty can be overcome through use of maximum intensity projection (MIP) processing, in which a projection of the anatomic structure of vessels is created by tracing parallel rays through the 3D volume of data and selecting the maxi-
the other axis of in-plane resolution). Although typically it is desirable to orient the section axis along the principal direction of flow, in practice, some yessels of interest will be aligned along directions that are close to orthogonal to the section axis. For reliable identificanarrow
cases
for one axis of
as well
(Frequency
Angiography’
deleterious effects: (a) For any given field of view (FOV), the number of sec-
two-dimensional Index terms: Angiography #{149} Magnetic resonance (MR), experimental, 9*12142 #{149} Magnetic resonance (MR), image processing #{149}Magnetic resonance (MR), three-dimensional, 9*1214 Magnetic resonance (MR), vascular studies, 9*1214
MR
changing sel cross
registration of section D/sinO thickness T. For a vessel the order of R, angulation thick section can produce tensity corresponding to
trapezoid or to one sult is a vessel with ance.
The
effect
for D = 1.2 are generated
the oblique yeswith the section of lumen D on through a pixels of inthe peak of the
of its edges.
fragmented is illustrated
re3
12#{176}. Two cases the example in Figure 3a by sampling with an R x R pixel size (Fig 3b) and R x 3R pixel size (Fig .
R and from
The
appearin Figure
0
3c). Linear interpolation cases to generate square
fectively
double
=
is used in both pixels and ef-
the display
matrix,
Radiology
as is 899
#{149}
00
R -
90#{176}
900
r
Section Axis I
I
Iftft
III III I I #{149}
I I I I I I I I 1I I I I I I I I
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIFFI
I Fl I I I I I I I I
I1111111111IIII-I-i- IIIIIIIII
I I I FI I I I I I I I I I I I I I I I I I I I I I I I I 1I I
I
II ill-..
T
IIIIIIIIII111111
F IIIIIIIIIII IIIIIIIIIIIIIIIIIIIIII
ji
‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘
IIIIIIIIIitiiii’ I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I I I I
IJ+IIIIIIIII 11111
FFFIIIIIIIIIII F-I-FII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIllI
IIIII)IIIII11IIIIIIIIIIIIIIIIIIIIIIII
D
-
FlIlll1lttllllllllllllllttJllllttllI
a.
b.
Figure 1. The lion axis, where background
to the
900
effect of partial T = the section signal) is preserved section axis and D =
volume
averaging
thickness, in a but
R varies
display terminal. A in contrast and in-
creased
vessel
width
on contrast
in-plane as
C
=
is demonstrated
pixel (D /T)
resolution, C0 for D
can
can
appreciate
that
the
effects
impractical,
but
the
exact
analogue can be achieved with postprocessing. In 1985, Leifer and Wiffley (4) pointed out that in 3D FT acquisition, if the time-domain data are multiplied by a linear phase shift as a function of time (in this case, pseudotime along the section-encoding direction), the FT will provide a sampling of the image space that is offset in position, depending on the slope of the phase shift. From a mathematical point of view, images generated after a finite 900
Radiology
#{149}
(c) Resulting
contrast
D aligned
C0
=
p
C
C
=
Co
2
0
D/T Figure
2.
The
ness
D/section
dependence
thickness
The higher
C0, the lower
conspicuity
threshold.
of contrast on the ratio T is shown for two values
the D/T value
required
vessel thickof contrast C0.
to obtain
a given
of
partial volume averaging and vesselsection registration are due to inherent sampling problems, irrespective of S/N levels and of the fidelity with which the imaging techniques represent flow. Section doubling by voxel shifting.-Registration errors can be reduced or eliminated by repeated imaging of the patient, with the patient advanced a fraction of the section thickness between procedures. Such a step is admittedly
T.
at (a) 0#{176} and (b) 90 to the secV/B - 1 (V = vessel signal and B = for the case in which the vessel is aligned at
for a vessel of thickness D = ‘,4T. Contrast C =
be
seen for the larger voxel sampling size. Although these examples have assumed a rectangular rather than sinc point spread function, no important limitations are imposed on the conclusions. The appearance of Figure 3 is a result of the registration of the vessel with respect to the voxel changing from section to section for angles 0 other than O and 900. For 0 = 900, registration is always perfect, and for 0 = O, registration effects can change C by up to a factor of 2, since there are times when the vessel will straddle two sections. The consequence is that the values of C in Figure 2 can be anywhere between the value shown in Figure 3a and half that value. We
and
‘4T.
done on a typical greater reduction apparent
=
C-
phase shift has been applied to the time domain data are as “real” or valid as those reconstructed by application of a zero phase shift (ie, no phase shift). To obtain a true representation of the object, it is necessary that the object have finite support and a bandwidth that meets the Nyquist criterion of the acquisition, meaning that the object does not extend beyond the FOV and that there are no features with edges that are sharper than a pixel width. In practice, MR images do not always meet these conditions, and the consequences are familiar:
In the first
instance,
the
object
is seen to scroll around to the opposite side of the FOV. This is called aliasing. In the latter, “ringing” artifacts associated with the sharp-edged features are seen. The shifted images are subject to the same effects. The scrolling point of the data will move relative to the image, and the ringing artifacts (not object structures) may change character sub-
stantially. It must the “correctness”
obtained
be emphasized of the image
by displacing
that estimates
the subject
by section cause the
shifting is equivalent, same changes would
the object
had
same
value
been
as the
displaced shift.
The
and
beoccur
if
by the resolution
and S/N are maintained (3), as are the section profile characteristics of the 3D FT acquisition and reconstruction processes (5). It should be noted that similar results would be achieved by using sinc interpolation (6), although implementation of this method by using zero padding and performing the Fourier transform would be computationally more intensive and require more computer memory. Experimental
methods.-A
phantom
consisting of a fan of nine oil-filled tubes of 1.2 mm cross-sectional inside diameter was used in the section doubling experiment. The tubes were December
1992
placed
at 7#{176} intervals,
spanning
an angle
allel
and was imaged transaxially FT sequence, with the section
to the OO oil-filled tube. The sehad a section thickness of 3.5 in-plane resolution of 1.1 mm, sections obtained in 9.5 minutes.
quence mm and with 32 Images
of ±28#{176}. This phantom was placed with its plane horizontal to the patient bed with a 3D plane par-
were
obtained
with
permanent-magnet cess;
imaging
Toshiba
America
system
MRI,
(Ac-
South
San
Francisco, Calif). Patients underwent imaging with a O.35-T superconducting magnet imager (MRT 35; Toshiba America MRI); a 3D gradient-echo sequence was used. Sixtyfour 1-mm partitions were acquired
a O.064-T
with mm.
an in-plane resolution of 0.8 x 0.8 A repetition time (TR) of 60 msec, echo time of 7 msec, and flip angle of 30#{176} were employed. Flow compensation
was applied
directions, slab was excited structures. Image
P,
r
to the section-select and and a presaturation
readout
to remove venous reconstruction was
performed with the Access computer and MIP reformatting was performed in a similar computer with this latter software feature. #{149}
Section-doubled
3D image
reconby using intermediate section planes. An increase in reconstruction time of roughly a factor of two is required for section doubling. MIP
structions were generated voxel shifting to compute
projections orthogonal to the section axis were constructed from non-sectiondoubled structions
and section-doubled of the same data
parison.
Because
creases
two, MIP
the
section
number
doubling
of projected
the computation also
reconfor com-
set
time
inlines
by
for a single
doubles.
Results
a. Figure
b. 3.
(a-c)
Simulation
In the phantom comparison, reconstructions using zero, half-voxel, and quarter-voxel shifting were compared.
C-
changes when vessels are angulated with respect to the section axis (vessel thickness D = 1.2 x in-plane pixel size R, angulation (-) is at 12#{176}). The images in b and c are generated with an R x R and R x 3R pixel sampling size, respectively. Linear interpolation is used to create square pixels and double the display matrix. Greater contrast reduction and increased apparent vessel width results with the larger voxel sampling size.
a.
b.
4. Anteroposterior MIP projections created with (a) no voxel shifting, were generated from 3D data with the sections oriented perpendicular to the ness was 3.5 mm. Periodicity in size and contrast along the length of the tubes
the first stage
of voxel
angulation
Volume
185
shifting is apparent
Number
#{149}
3
and
is less appreciable
constructions
Variations described Figure of the
from
each
of the three
re-
are shown in Figure 4. in contrast and vessel width
in the simulated
example
3 are again seen along oil-filled tubes in Figure
of
the length 4. The
c.
Figure
changing
MIPs created
of contrast
between
the half-
and
(b) half-voxel shifting, and (c) quarter-voxel shifting. Projections phantom and parallel to the 0#{176} oil-filled tube. The section thickdecreases from a to c. The improvement is more dramatic with
quarter-pixel-shifted
projections.
The change
in periodicity
with
in a.
Radiology
901
#{149}
periodicity
of the artifact
increasing
angulation
with
with
increases respect
to
the 0#{176} (horizontal) axis. A reduction in the stairstep pattern can be appreciated between the unshifted and half-voxelshifted images. A less dramatic but noticeable reduction is evident between the images shifted by one-half and onequarter pixel. Anteroposterior projections created for non-section-doubled and sectiondoubled MR angiography data are compared in Figure 5 for a patient with an arteriovenous malformation. The improvement in vessel definition and contrast is especially noticeable in vessels oriented oblique to the section axis. In 3D time-of-flight MR angiography studies such as these, the persistence signal into the imaging volume
of flow
(in this case, arterial flow entering from the bottom of the slab) is limited by flow velocity, TR, and flip angle. A decrease in flow signal is seen with increasing distance from the entry. Section doubling is particularly beneficial in the more distat branches, allowing better visualization of these low-intensity structures through maximization of their contrast and improvement of their continuity. To date, MR angiographic studies in 20 patients have been processed with and without section doubling improved vessel delineation with section doubling resulted in all cases. Because a sampling
artifact
can
usually
fled by the periodicity trast
changes,
be identi-
of size and con-
no incident
of a false-
positive finding being corrected has occurred in our limited patient data. The improvement in vessel edge definition has allowed a more accurate assessment of the degree of vessel narrowing in the left carotid arteries of two patients. Discussion
902
doubling
Radiology
#{149}
time.
the
number
of sections,
If image
matrix
size
is limited,
gained by the
by voxel geometric
imaging
shifting will relationship
of vascular
features.
a.
a
reduced FOV might also result. Although resolution does not change with voxel shifting, an improvement in yessel-voxel registration can result in a new intensity maximum projected by the MIP process. This detection improvement is appreciated mainly at vessel edges and in imaging of small vessels, of a size on the order of the voxel dimension. Improvement is greatest for smalldiameter vessels and those with lower intrinsic contrast. Registration artifacts that occur for angulated vessels will be more severe for larger voxel dimensions. Clearly, the extent of the benefit be affected created in
b. Figure 5. section-doubled
1.
mation doubling improvement
appreciated at angles
4.
5.
W.
Three-dimensional Magn Reson
giography.
phase contrast anMed 1989; 9:139-
6.
with
and (b) nonsame data set
an artenovenous
demonstrate on projection
for views
U
Alfidi RJ, Masaryk TJ, Haacke EM, et al. MR angiography of peripheral, carotid and coronary arteries. AJR 1987; 149:1097-1109. Dumoulin CL, Souza SP, Walker MF, Wagle
(a) Section-doubled images of the
for a patient
References
2.
The technique of voxel shifting for creating intermediate sections in a 3D time-of-flight MR angiography study, thus
provides a substantial improvement in the visualization of small vessels in MIP projections. Artifactual variations in contrast and vessel width caused by registration changes as vessels cross sections obliquely are substantially reduced. Further improvement with smaller shift distances is limited, however, by the finite voxel sampling size, which this process does not address. Voxel shifting also requires increased data reconstruction and processing times, as well as increased demand for data storage. Given these considerations, we have found voxel shifting by one-half pixel to be most effective. The geometric relationships inherent in MR angiography make the section direction the most desirable for doubling. In-plane voxel shifting would also provide some benefit but will require the additional factor increase in imaging
orthogonal in vessel
the
impact angiograms
malforof section created
to the section delineation
axis. The is best
for the thinner vessels oriented oblique to the section axis.
Leifer MC, Wilfley BP. NMR volume imaging with half slice offsets (abstr). In: Book of abstracts: Society of Magnetic Resonance in Medicine 1985. Berkeley, Calif: Society of Magnetic Resonance in Medicine, 1985; 1013. Carlson JC, Crooks LE, Ortendahl DA, Kramer DM, Kaufman L. Signal-to-noise ratio and section thickness in two-dimensional versus three-dimensional Fourier transform MR imaging. Radiology 1988; 166: 266-270. Bracewell RN. The Fourier transform and its applications. 2nd ed. New York: McGraw-Hill, 1978; 194.
149. 3.
Kramer D, Li A, Simovsky I, Hawryszko C, Hale J, Kaufman L. Applications of voxel shifting in magnetic resonance imaging. Invest Radiol 1990; 25:1305-1310.
December
1992
of Section
M. Hylton,
Doubling
PhD
Ilya Simovsky, PhD Andrew J. Li, PhD James D. Hale, BA To improve the quality of projection angiograms generated from three-dimensional magnetic resonance (MR) angiography data, the authors applied voxel shifting to create intermediate sections (“section doubling”) prior to maximum
intensity
projection.
To
date,
the authors have processed MR angiography studies with and without section doubling in 20 cases. Section doubling resulted in improved vessel contrast and delineation of continuity (especially of small vessels) in all cases.
on
Radiology
S
1992;
OME
of
185:899-902
the
most
successful
magnetic
resonance
(MR) angiography techniques are based on three-dimensional (3D) Fourier transform (FT) acquisition schemes (1,2). In this form of imaging,
phase
encoding
in-plane
is used
resolution
definition.
D larger although
tions (and imaging time) increases in direct proportion to the amount of section thickness reduction; and (b) signalto-noise ratio (S/N) decreases as the square root of the section thickness changes for constant coverage (FOV in the section direction). In MR angiography, vessel connectivity can be difficult to appreciate through viewing of individual sections. This dif-
fect the conclusion) and a section thickness T. Figure 1 shows two extreme
mum
pixel
value
for projection
high
surface.
contrast
studies,
with
vessel
MR
a
of the
in a projec-
processing
used to reduce contrast registration in imaging lesions (3). We describe
has been due to mis-
loss
of small
brain
the application of voxel shifting to MR angiography and illustrate how the effects of misreg-
istration can be substantially reduced the use of voxel shifting along the section axis prior to vessel reformatting with MIP.
as for section
encoding
yields
Materials
and
Theoretical
by
MR angiogra-
tion of these
to
olution
two
the
vessels,
it is desirable
thickness.
This
has
along
MIP
thickness.
shifting From the Radiologic Imaging Laboratory, University of California, San Francisco, South San Francisco, CA 94080 (N.M.H., J.D.H.) and Toshiba America MRI, Inc, South San Francisco, Calif (IS., A.J.L.). Received March 24, 1992; revision requested May 13; revision received July 13; accepted August 18. Supported in part by Toshiba America MRI, Inc. and by grant no. HL 39171 from the National Heart, Lung, and Blood Institute, U.S. Department of Health and Human Services. Address reprint requests to N.M.H., Department of Radiology, University of California, San Francisco, I Irving St. San Francisco, CA 94143. 2 9* indicates generalized vein and artery involvement. (. RSNA, 1992
Volume
185
Number
#{149}
3
ate
interpolation intermediate pixel direction. If, instead,
is first
section
substantial dicted
of the in-plane axes to the section
used
planes
to create
prior
improvement
in vessel
edge
a
can be predefinition,
particu-
larly for thin vessels traveling in directions oblique to the section axis. Section
ization garding ity-related
thickness
in two
affects
principal
vessel
ways
visual-
(disre-
signal loss resulting from velocdephasing): through partial
volume averaging registration. To illustrate the
and
vessel-section
effects of partial volaveraging on vessel visualization, we present examples for a vessel of lumen diameter D (for convenience, with ume
aligned
in the
second
partial
case
(Fig
lb),
because
of
volume
averaging, the apparent vessel signal V = (D/T)V + ([T DJ/T) B. The contrast C becomes C = Va/ B 1 =C0(D/T)forD < TandC=C0for D T. Figure lc shows the contrast in the 90” case for T = 2D. In MR angiography sequences, attempts are made to have the vessel signal be much larger than the background, so that C may be approximated by C (D . V)/(T . B). Because of this, partial volume averaging is more forgiving in MR angiography than it is in other forms of imaging. Figure 2 shows the dependence of C on the ratio D/T for cases where V = 7 . B and V = 1.3 B. The first relationship is typical of MR angiography and the second is typical -
the vessel considering
example
only),
along for 0
the
also affects angle 0
and section axis the two-dimensional
the maximum
contrast
between C0 900. Furtherwill drop way, so that
vessel
will vary = O and C for 0 = more, the signal intensity from maximum in a linear
the intensity profile along the vessel will be triangular or trapezoidal, depending on the angle and the values of D, T, and R. This profile results from the
intermedi-
to projection,
the vessel
contrast
between (again
of
is used values voxel
Linear
to compute along this
I
one
is equivalent
2D, with
=
threshold is reached. Vessel-section registration vessel visualization. For any
phy sequences that exploit in-flow for contrast, the section axis is usually onented parallel to the vessel. MIP reformatting is commonly performed in a projection direction that is perpendicutar to the section axis, such that the res-
section
for T
size R, not af-
pixel
does
of MR imaging of small brain lesions. Notice that for a certain conspicuity threshold (eg, C = .2), the higher the C0, the lower the D/T value at which this
Methods methods-In
in-plane
shown, in the first case (Fig la), C0 between the vessel and background (C0 = V/B - 1, where V = vessel signal and B = background signal) is preserved in the image, while the
are extracted
anatomically
the
this assumption
example
angiography
structures
and presented tion view. Voxel shifting
onto
Because
than
at O (Fig la) and at 900 (Fig lb) to the section axis. For the two-dimensional
ficulty can be overcome through use of maximum intensity projection (MIP) processing, in which a projection of the anatomic structure of vessels is created by tracing parallel rays through the 3D volume of data and selecting the maxi-
the other axis of in-plane resolution). Although typically it is desirable to orient the section axis along the principal direction of flow, in practice, some yessels of interest will be aligned along directions that are close to orthogonal to the section axis. For reliable identificanarrow
cases
for one axis of
as well
(Frequency
Angiography’
deleterious effects: (a) For any given field of view (FOV), the number of sec-
two-dimensional Index terms: Angiography #{149} Magnetic resonance (MR), experimental, 9*12142 #{149} Magnetic resonance (MR), image processing #{149}Magnetic resonance (MR), three-dimensional, 9*1214 Magnetic resonance (MR), vascular studies, 9*1214
MR
changing sel cross
registration of section D/sinO thickness T. For a vessel the order of R, angulation thick section can produce tensity corresponding to
trapezoid or to one sult is a vessel with ance.
The
effect
for D = 1.2 are generated
the oblique yeswith the section of lumen D on through a pixels of inthe peak of the
of its edges.
fragmented is illustrated
re3
12#{176}. Two cases the example in Figure 3a by sampling with an R x R pixel size (Fig 3b) and R x 3R pixel size (Fig .
R and from
The
appearin Figure
0
3c). Linear interpolation cases to generate square
fectively
double
=
is used in both pixels and ef-
the display
matrix,
Radiology
as is 899
#{149}
00
R -
90#{176}
900
r
Section Axis I
I
Iftft
III III I I #{149}
I I I I I I I I 1I I I I I I I I
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIFFI
I Fl I I I I I I I I
I1111111111IIII-I-i- IIIIIIIII
I I I FI I I I I I I I I I I I I I I I I I I I I I I I I 1I I
I
II ill-..
T
IIIIIIIIII111111
F IIIIIIIIIII IIIIIIIIIIIIIIIIIIIIII
ji
‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘
IIIIIIIIIitiiii’ I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I I I I
IJ+IIIIIIIII 11111
FFFIIIIIIIIIII F-I-FII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIllI
IIIII)IIIII11IIIIIIIIIIIIIIIIIIIIIIII
D
-
FlIlll1lttllllllllllllllttJllllttllI
a.
b.
Figure 1. The lion axis, where background
to the
900
effect of partial T = the section signal) is preserved section axis and D =
volume
averaging
thickness, in a but
R varies
display terminal. A in contrast and in-
creased
vessel
width
on contrast
in-plane as
C
=
is demonstrated
pixel (D /T)
resolution, C0 for D
can
can
appreciate
that
the
effects
impractical,
but
the
exact
analogue can be achieved with postprocessing. In 1985, Leifer and Wiffley (4) pointed out that in 3D FT acquisition, if the time-domain data are multiplied by a linear phase shift as a function of time (in this case, pseudotime along the section-encoding direction), the FT will provide a sampling of the image space that is offset in position, depending on the slope of the phase shift. From a mathematical point of view, images generated after a finite 900
Radiology
#{149}
(c) Resulting
contrast
D aligned
C0
=
p
C
C
=
Co
2
0
D/T Figure
2.
The
ness
D/section
dependence
thickness
The higher
C0, the lower
conspicuity
threshold.
of contrast on the ratio T is shown for two values
the D/T value
required
vessel thickof contrast C0.
to obtain
a given
of
partial volume averaging and vesselsection registration are due to inherent sampling problems, irrespective of S/N levels and of the fidelity with which the imaging techniques represent flow. Section doubling by voxel shifting.-Registration errors can be reduced or eliminated by repeated imaging of the patient, with the patient advanced a fraction of the section thickness between procedures. Such a step is admittedly
T.
at (a) 0#{176} and (b) 90 to the secV/B - 1 (V = vessel signal and B = for the case in which the vessel is aligned at
for a vessel of thickness D = ‘,4T. Contrast C =
be
seen for the larger voxel sampling size. Although these examples have assumed a rectangular rather than sinc point spread function, no important limitations are imposed on the conclusions. The appearance of Figure 3 is a result of the registration of the vessel with respect to the voxel changing from section to section for angles 0 other than O and 900. For 0 = 900, registration is always perfect, and for 0 = O, registration effects can change C by up to a factor of 2, since there are times when the vessel will straddle two sections. The consequence is that the values of C in Figure 2 can be anywhere between the value shown in Figure 3a and half that value. We
and
‘4T.
done on a typical greater reduction apparent
=
C-
phase shift has been applied to the time domain data are as “real” or valid as those reconstructed by application of a zero phase shift (ie, no phase shift). To obtain a true representation of the object, it is necessary that the object have finite support and a bandwidth that meets the Nyquist criterion of the acquisition, meaning that the object does not extend beyond the FOV and that there are no features with edges that are sharper than a pixel width. In practice, MR images do not always meet these conditions, and the consequences are familiar:
In the first
instance,
the
object
is seen to scroll around to the opposite side of the FOV. This is called aliasing. In the latter, “ringing” artifacts associated with the sharp-edged features are seen. The shifted images are subject to the same effects. The scrolling point of the data will move relative to the image, and the ringing artifacts (not object structures) may change character sub-
stantially. It must the “correctness”
obtained
be emphasized of the image
by displacing
that estimates
the subject
by section cause the
shifting is equivalent, same changes would
the object
had
same
value
been
as the
displaced shift.
The
and
beoccur
if
by the resolution
and S/N are maintained (3), as are the section profile characteristics of the 3D FT acquisition and reconstruction processes (5). It should be noted that similar results would be achieved by using sinc interpolation (6), although implementation of this method by using zero padding and performing the Fourier transform would be computationally more intensive and require more computer memory. Experimental
methods.-A
phantom
consisting of a fan of nine oil-filled tubes of 1.2 mm cross-sectional inside diameter was used in the section doubling experiment. The tubes were December
1992
placed
at 7#{176} intervals,
spanning
an angle
allel
and was imaged transaxially FT sequence, with the section
to the OO oil-filled tube. The sehad a section thickness of 3.5 in-plane resolution of 1.1 mm, sections obtained in 9.5 minutes.
quence mm and with 32 Images
of ±28#{176}. This phantom was placed with its plane horizontal to the patient bed with a 3D plane par-
were
obtained
with
permanent-magnet cess;
imaging
Toshiba
America
system
MRI,
(Ac-
South
San
Francisco, Calif). Patients underwent imaging with a O.35-T superconducting magnet imager (MRT 35; Toshiba America MRI); a 3D gradient-echo sequence was used. Sixtyfour 1-mm partitions were acquired
a O.064-T
with mm.
an in-plane resolution of 0.8 x 0.8 A repetition time (TR) of 60 msec, echo time of 7 msec, and flip angle of 30#{176} were employed. Flow compensation
was applied
directions, slab was excited structures. Image
P,
r
to the section-select and and a presaturation
readout
to remove venous reconstruction was
performed with the Access computer and MIP reformatting was performed in a similar computer with this latter software feature. #{149}
Section-doubled
3D image
reconby using intermediate section planes. An increase in reconstruction time of roughly a factor of two is required for section doubling. MIP
structions were generated voxel shifting to compute
projections orthogonal to the section axis were constructed from non-sectiondoubled structions
and section-doubled of the same data
parison.
Because
creases
two, MIP
the
section
number
doubling
of projected
the computation also
reconfor com-
set
time
inlines
by
for a single
doubles.
Results
a. Figure
b. 3.
(a-c)
Simulation
In the phantom comparison, reconstructions using zero, half-voxel, and quarter-voxel shifting were compared.
C-
changes when vessels are angulated with respect to the section axis (vessel thickness D = 1.2 x in-plane pixel size R, angulation (-) is at 12#{176}). The images in b and c are generated with an R x R and R x 3R pixel sampling size, respectively. Linear interpolation is used to create square pixels and double the display matrix. Greater contrast reduction and increased apparent vessel width results with the larger voxel sampling size.
a.
b.
4. Anteroposterior MIP projections created with (a) no voxel shifting, were generated from 3D data with the sections oriented perpendicular to the ness was 3.5 mm. Periodicity in size and contrast along the length of the tubes
the first stage
of voxel
angulation
Volume
185
shifting is apparent
Number
#{149}
3
and
is less appreciable
constructions
Variations described Figure of the
from
each
of the three
re-
are shown in Figure 4. in contrast and vessel width
in the simulated
example
3 are again seen along oil-filled tubes in Figure
of
the length 4. The
c.
Figure
changing
MIPs created
of contrast
between
the half-
and
(b) half-voxel shifting, and (c) quarter-voxel shifting. Projections phantom and parallel to the 0#{176} oil-filled tube. The section thickdecreases from a to c. The improvement is more dramatic with
quarter-pixel-shifted
projections.
The change
in periodicity
with
in a.
Radiology
901
#{149}
periodicity
of the artifact
increasing
angulation
with
with
increases respect
to
the 0#{176} (horizontal) axis. A reduction in the stairstep pattern can be appreciated between the unshifted and half-voxelshifted images. A less dramatic but noticeable reduction is evident between the images shifted by one-half and onequarter pixel. Anteroposterior projections created for non-section-doubled and sectiondoubled MR angiography data are compared in Figure 5 for a patient with an arteriovenous malformation. The improvement in vessel definition and contrast is especially noticeable in vessels oriented oblique to the section axis. In 3D time-of-flight MR angiography studies such as these, the persistence signal into the imaging volume
of flow
(in this case, arterial flow entering from the bottom of the slab) is limited by flow velocity, TR, and flip angle. A decrease in flow signal is seen with increasing distance from the entry. Section doubling is particularly beneficial in the more distat branches, allowing better visualization of these low-intensity structures through maximization of their contrast and improvement of their continuity. To date, MR angiographic studies in 20 patients have been processed with and without section doubling improved vessel delineation with section doubling resulted in all cases. Because a sampling
artifact
can
usually
fled by the periodicity trast
changes,
be identi-
of size and con-
no incident
of a false-
positive finding being corrected has occurred in our limited patient data. The improvement in vessel edge definition has allowed a more accurate assessment of the degree of vessel narrowing in the left carotid arteries of two patients. Discussion
902
doubling
Radiology
#{149}
time.
the
number
of sections,
If image
matrix
size
is limited,
gained by the
by voxel geometric
imaging
shifting will relationship
of vascular
features.
a.
a
reduced FOV might also result. Although resolution does not change with voxel shifting, an improvement in yessel-voxel registration can result in a new intensity maximum projected by the MIP process. This detection improvement is appreciated mainly at vessel edges and in imaging of small vessels, of a size on the order of the voxel dimension. Improvement is greatest for smalldiameter vessels and those with lower intrinsic contrast. Registration artifacts that occur for angulated vessels will be more severe for larger voxel dimensions. Clearly, the extent of the benefit be affected created in
b. Figure 5. section-doubled
1.
mation doubling improvement
appreciated at angles
4.
5.
W.
Three-dimensional Magn Reson
giography.
phase contrast anMed 1989; 9:139-
6.
with
and (b) nonsame data set
an artenovenous
demonstrate on projection
for views
U
Alfidi RJ, Masaryk TJ, Haacke EM, et al. MR angiography of peripheral, carotid and coronary arteries. AJR 1987; 149:1097-1109. Dumoulin CL, Souza SP, Walker MF, Wagle
(a) Section-doubled images of the
for a patient
References
2.
The technique of voxel shifting for creating intermediate sections in a 3D time-of-flight MR angiography study, thus
provides a substantial improvement in the visualization of small vessels in MIP projections. Artifactual variations in contrast and vessel width caused by registration changes as vessels cross sections obliquely are substantially reduced. Further improvement with smaller shift distances is limited, however, by the finite voxel sampling size, which this process does not address. Voxel shifting also requires increased data reconstruction and processing times, as well as increased demand for data storage. Given these considerations, we have found voxel shifting by one-half pixel to be most effective. The geometric relationships inherent in MR angiography make the section direction the most desirable for doubling. In-plane voxel shifting would also provide some benefit but will require the additional factor increase in imaging
orthogonal in vessel
the
impact angiograms
malforof section created
to the section delineation
axis. The is best
for the thinner vessels oriented oblique to the section axis.
Leifer MC, Wilfley BP. NMR volume imaging with half slice offsets (abstr). In: Book of abstracts: Society of Magnetic Resonance in Medicine 1985. Berkeley, Calif: Society of Magnetic Resonance in Medicine, 1985; 1013. Carlson JC, Crooks LE, Ortendahl DA, Kramer DM, Kaufman L. Signal-to-noise ratio and section thickness in two-dimensional versus three-dimensional Fourier transform MR imaging. Radiology 1988; 166: 266-270. Bracewell RN. The Fourier transform and its applications. 2nd ed. New York: McGraw-Hill, 1978; 194.
149. 3.
Kramer D, Li A, Simovsky I, Hawryszko C, Hale J, Kaufman L. Applications of voxel shifting in magnetic resonance imaging. Invest Radiol 1990; 25:1305-1310.
December
1992
