Sensitivity of MRI resonance frequency to the orientation of brain tissue microstructure.

Abstract

Recent advances in high-field (>or=7 T) MRI have made it possible to study the fine structure of the human brain at the level of fiber bundles and cortical layers. In particular, techniques aimed at detecting MRI resonance frequency shifts originating from local variation in magnetic susceptibility and other sources have greatly improved the visualization of these structures. A recent theoretical study [He X, Yablonskiy DA (2009) Proc Natl Acad Sci USA 106:13558-13563] suggests that MRI resonance frequency may report not only on tissue composition, but also on microscopic compartmentalization of susceptibility inclusions and their orientation relative to the magnetic field. The proposed sensitivity to tissue structure may greatly expand the information available with conventional MRI techniques. To investigate this possibility, we studied postmortem tissue samples from human corpus callosum with an experimental design that allowed separation of microstructural effects from confounding macrostructural effects. The results show that MRI resonance frequency does depend on microstructural orientation. Furthermore, the spatial distribution of the resonance frequency shift suggests an origin related to anisotropic susceptibility effects rather than microscopic compartmentalization. This anisotropy, which has been shown to depend on molecular ordering, may provide valuable information about tissue molecular structure.

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Sensitivity of MRI resonance frequency to the
orientation of brain tissue microstructure
Jongho Leea,1, Karin Shmuelia, Masaki Fukunagaa, Peter van Gelderena, Hellmut Merklea, Afonso C. Silvab,
and Jeff H. Duyna
aAdvanced MRI Section andbCerebral Microcirculation Unit, Laboratory of Functional and Molecular Imaging, National Institute of Neurological Disorders
and Stroke, National Institutes of Health, Bethesda, MD 20892
Edited* by Adriaan Bax, National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, MD, and approved January 22, 2010 (received for review
September 29, 2009)
Recent advances in high-field (≥7 T) MRI have made it possible to
study the fine structure of the human brain at the level of fiber bun-
dles and cortical layers. In particular, techniques aimed at detecting
MRI resonance frequency shifts originating from local variation
in magnetic susceptibility and other sources have greatly improved
thevisualizationofthesestructures.Arecenttheoreticalstudy[HeX,
Yablonskiy DA (2009) Proc Natl Acad Sci USA 106:13558–13563] sug-
gests that MRI resonance frequency may report not only on tissue
composition, but also on microscopic compartmentalization of sus-
ceptibility inclusions and their orientation relative to the magnetic
field.Theproposedsensitivitytotissuestructuremaygreatlyexpand
the information available with conventional MRI techniques. To in-
vestigatethispossibility,westudiedpostmortemtissuesamplesfrom
human corpus callosum with an experimental design that allowed
separation of microstructural effects from confounding macrostruc-
tural effects. The results show that MRI resonance frequency does
depend on microstructural orientation. Furthermore, the spatial dis-
tribution of the resonance frequency shift suggests an origin related
to anisotropic susceptibility effects rather than microscopic compart-
mentalization. This anisotropy, which has been shown to depend on
molecular ordering, may provide valuable information about tissue
molecular structure.
MRI phase contrast|resonance frequency shift|anisotropic susceptibility|
magnetic susceptibility tensor|white matter fiber tracking
R
may substantially improve the visualization of fine-scale struc-
tural variation in the human brain. For example, many of the
brain’s major white matter fiber bundles and distinct cortical
lamination patterns have recently been visualized in vivo by
observing the signal phase that is proportional to the resonance
frequency in gradient-echo (GRE) MRI (1–4). Despite this
achievement and the potential clinical and scientific significance,
however, the mechanisms underlying magnetic resonance fre-
quency shifts remain poorly understood.
Several candidate mechanisms have been suggested and
investigated as sources for this frequency contrast (1, 5–8). A
primary candidate is an altered bulk magnetic susceptibility due
to such compounds as ferritin, myelin, and deoxyhemoglobin, all
of which are found throughout brain tissue. Strong support for
this mechanism comes from postmortem tissue analysis (9), and
from the observation that the phase distribution within and
between gray and white matter is consistent with calculations
from susceptibility models.†
An additional contribution to MRI resonance frequency may
come from the exchange processes between protons in water and
in amide groups on proteins or other exchangeable sites (8). The
frequency shifts arising from these mechanisms may provide
important information about the chemical composition of brain
tissues in vivo.
A recent theoretical study from He and Yablonskiy (10) sug-
gests that resonance frequency shifts may also report on brain
ecent high-field (≥7 T) human MRI studies have demon-
strated that contrast based on resonance frequency shifts
tissue microstructure and its orientation relative to the main
magnetic field. The authors applied the Lorentzian cavity concept
(11, 12) to estimate the magnetic field induced by microscopic
variations in magnetic susceptibilities. Using a nonspherical
Lorentzian cavity, proposed earlier in (12, 13), to model the
compartmentalization of water protons in an anisotropic tissue
structure, the authors suggested the presence of a net (voxel-
averaged) frequency shift that depends on the tissue’s orientation
in the externally applied magnetic field. This mechanism could
explain some of the strong frequency shifts observed in the major
fiber bundles (Fig.1) andmay have important implications for the
application and interpretation of the resonance frequency in
GRE MRI.
The extent to which the Lorentzian cavity concept, which is
well established at the atomic (nanometer) scale for electric and
magnetic fields (11, 14), should be used to account for the field
distributions at larger (micrometer) scales that may be present in
brain structures is not clear, however. Furthermore, the exper-
imental evidence is sparse in the aforementioned study (9), and
interpretation of the results is confounded by large-scale geo-
metric effects inherent to the susceptibility-related contrast
mechanism.
The purpose of the current study was to further investigate
the potential effect of brain microstructure on MRI resonance
frequency.
Results
The effect of tissue microstructure on MRI resonance frequency
was investigated by manipulating microstructure while minimally
affecting macrostructure. Experiments were performed on an
elongated section of human corpus callosum, a major white
matter fiber bundle of the human brain. A part of the corpus
callosum was chosen that had relatively uniform (micro-
structural) fiber orientation, with fibers running mostly parallel
to the long direction of the section (Fig. 2A). The section was cut
into five subsections, which were aligned parallel to the MRI
main magnetic field (B0) in a sample holder. The section was
imaged under two conditions: one in which all subsections were
placed in their original orientation (condition A; Fig. 2C), and the
other in which two of the subsections (C2 and C4) were rotated by
90 degrees relative to B0(condition B; Fig. 2D). Microscopic fiber
orientationwasconfirmedbydiffusiontensorimaging(DTI)(15),
Authorcontributions: J.L., K.S., M.F.,andJ.H.D. designedresearch;J.L. performedresearch;
J.L., H.M., and A.C.S. contributed new reagents/analytic tools; J.L., K.S., M.F., P.v.G., and
J.H.D. analyzed data; and J.L., K.S., and J.H.D. wrote the paper.
The authors declare no conflict of interest.
*This Direct Submission article had a prearranged editor.
1To whom correspondence should be addressed. E-mail: jonghoyi@mail.nih.gov.
This article contains supporting information online at www.pnas.org/cgi/content/full/
0910222107/DCSupplemental.
†Shmueli K, et al. The dependenceof tissue phase contraston orientation canbe overcome
byquantitativesusceptibilitymapping.ProceedingsoftheAnnualMeetingoftheInterna-
tional Society of Magnetic Resonance Medicine, April 18–24, 2009, Honolulu, HI; p. 466.
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showing parallel orientation for condition A and alternating
parallel and perpendicular orientations for condition B (Fig. 3 A
and B). Macroscopic tissue orientation was parallel to B0, and the
overall shape was similar for both conditions.
Images representing signal amplitude and resonance fre-
quency from the two different microstructural orientations are
shown in Figs. 3 C–F. The average resonance frequency of the
tissues in condition A was −3.89 ± 0.76 Hz relative to the saline
solution. Under condition B, the resonance frequency of the
rotated segments C2 and C4 showed a positive shift of 0.56 ±
0.67 Hz (mean difference ± pooled SD over voxels) (Fig. 3F)
relative to condition A (Fig. 3E). This effect is shown more
clearly in Fig. 4, in which the average cross-sectional profile of
the difference image is plotted. The large SD is attributed to the
nonuniform phase shift within a tissue segment and the true
susceptibility variation within the tissue.
Apart from the frequency shift observed inside the rotated
tissue segments, subtle effects also were seen outside the rotated
tissue segments. For example, Fig. 3F shows a slightly positive
frequency shift in the fluid immediately lateral to the rotated
tissue segments. The frequency profile in Fig. 4 suggests the
presence of a shift in the unrotated segments (C1, C3, and C5) as
well, with the strongest effect seen in C3. Inside of C1 and C5,
the frequency gradually decreases close to the C1 side of the
C1–C2 boundary and the C5 side of the C4–C5 boundary. This
can be interpreted as the effect of C2 and C4 extending outside
of those tissue sections, with an amplitude that decreases with
distance. In summary, the results suggest that the orientation of
the microscopic structure affects MRI resonance frequency both
locally and remotely.
Discussion
Our findings represent direct experimental evidence for a de-
pendence of MRI resonance frequency on the orientation of
brain microstructure relative to the main magnetic field. Our
experimental design allowed the separation of microscopic and
macroscopic orientation effects that often coexist under general
in-vivo imaging conditions. Such effects have complicated the
Fig. 1.
2 mm slice thickness, axial slices) GRE frequency
images at 7 T (f0= 298.095 MHz) in vivo. Strong
contrast is seen in association with the major white
matter fiber bundles: (1) corpus callosum body; (2)
corona radiata; (3) corpus callosum splenium; (4)
optic radiation. Frequency was zeroed in areas with
low or absent NMR signal (e.g. outside the brain).
High-resolution (250 × 250-μm in-plane,
Fig. 2.
square cylindrical pieces of fixed tissue were sectioned along the primary
fiber orientation in the corpus callosum (coronal view). (B) The tissues were
placed in a groove at the bottom of a disk-shaped container. (C and D)
Representations of condition A (C) and condition B (D) showing fiber ori-
entations. The zoomed images show the detailed tissue structure.
Selection of white matter sections for postmortem MRI. (A) Five
Fig. 3.
C, and E) and rotated positions of fiber bundle segments C2 and C4 (condition
B: B, D, and F). (A and B) DTI confirmation of microstructure orientation of
segments, with red representing parallel orientations and blue representing
perpendicular (through-plane) orientations relative to B0. (C and D) Magnitude
images. (E and F) Frequency images. In F, rotation leads to a positive frequency
shift within and near the lateral edges of the rotated segments. A slightly
negative frequency shift is observed in unrotated segments. A few small dipole
field patterns, likely originating from air bubbles, are also seen in E. The
images are from coronal scans in which the slice selection was along the
physical y-axis, the readout gradient was along the physical z-axis, and the
phase encoding was along the physical x-axis. B0was along the z-axis.
Results of MRI frequency measurement at the original (condition A: A,
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interpretation of earlier studies (9, 16). The observed sensitivity
to orientation may result from different mechanisms (see below)
that could provide important clues about the cellular organ-
ization of the tissue.
The Nonspherical Lorentzian Cavity. Although the dependence on
microstructural orientation found in this study might appear
consistent with the theoretical predictions of He and Yablonskiy
(9), there is an obvious discrepancy that suggests inadequacy of
their theory. The nonspherical Lorentzian approach does not
explain the resonance frequency changes observed at the boun-
daries and outside of the tissues (e.g., the positive frequency near
the lateral edges of C2 and C4, and the decreased frequency in
C3 and at the C1–C2 and C4–C5 boundaries); rather, it predicts
a frequency shift that is purely local to the area of anisotropic
microstructure. We propose that the experimental observations
are better explained by a model of anisotropic susceptibility
rather than one of anisotropic compartmentalization.
Anisotropic Magnetic Susceptibility. Anisotropic magnetic sus-
ceptibility is a phenomenon commonly seen in crystals of highly
anisotropic atomic structure. It also has been noted in con-
stituents of biological tissues, including muscle fibers (17), retinal
rods (18), nucleic acids (19), proteins (20–23), and lipid bilayers
(24–27). Because the proteins and lipid bilayers associated with
white matter fibers are highly ordered, anisotropic susceptibility
may have contributed to our present findings.
Anisotropic white matter susceptibility could lead to a shift in
susceptibility on rotation of the microscopic fiber orientation, as
occurred in tissue segments C2 and C4 in the experiment
described above. Computer simulations suggest that anisotropic
susceptibility would lead to a pattern of resonance frequency
shifts closely resembling the experimental observation, including
the effects outside the rotated segments (Fig. 5). Assuming that
the frequency shifts were caused entirely by anisotropy of the
magnetic susceptibility, the magnitude of this effect was calcu-
lated using simulations. When the primary fiber orientation in all
of the tissue sections was parallel to B0, the susceptibility value
(χk) that gave the best match between the experiment and the
simulation was −9.093 ppm. The susceptibility value χ⊥that gave
the minimum residual error between simulations and measure-
ments made of the difference between condition A and condition
B was −9.105 ppm. This value is more diamagnetic than χk(both
relative to saline solution). These results suggest that the effect
of microstructure orientation on the resonance frequency in
white matter can be explained by a model based on anisotropic
magnetic susceptibility with a microstructural orientation–
dependent susceptibility difference (χk− χ⊥) of 0.012 ppm. Note
that this model does not include any contribution of the mo-
lecular exchange effect to the frequency shift; If that were taken
into account, the absolute susceptibility values could change. The
anisotropic susceptibility difference (χk− χ⊥) would not change,
however, because it is based on the exchange-averaged frequency
difference images.
Fig. 6 shows the susceptibility difference profile calculated
directly from the frequency difference image. The measured
susceptibility difference (χk− χ⊥) between the tissue segments
varies from 0.006 ± 0.007 ppm (mean difference ± pooled SD
over voxels between C4 and C5) to 0.010 ± 0.007 ppm (between
C2 and C3). We attribute the large SD to the true susceptibility
variation within the tissue and/or the noise amplification occur-
ring during the inversion process that is required to convert
frequency distributions into susceptibility distributions (16).
Despite the large SDs, the susceptibility difference was highly
statistically significant between all χkand χ⊥tissue combinations
with P values <10−16when averaged over the voxels.
One possible source of this susceptibility anisotropy is the
phospholipid bilayers in myelin. The susceptibility anisotropy
(χk− χ⊥) measured in the corpus callosum is ∼3–5 times smaller
than the anisotropy measured in the lipid bilayers of lecithin
membranes (24, 25). This range is reasonable considering the
smaller lipid fraction (∼16%) in white matter (28) and potential
confounds, such as the differences in the molecular composition
of the bilayers and differences in cellular structure.
Fig. 4.
(condition B − condition A). The rotated segments (C2 and C4) show positive
frequency shifts compared with the unrotated segments (C1, C3, and C5).
Error bars represent SE. The scanner frequency was 300.390 MHz.
Averaged cross-sectional profile of the frequency difference image
Fig. 5.
(solid line) and the simulated frequency (dashed line). The simulated frequency image in A shows a strong similarity to the experimental results shown in Fig.
3F. The average cross-sectional profile (dashed in B) also agrees well with the experimental results (Fig. 4).
Simulation results for anisotropic susceptibility. (A) simulation result for condition B. (B) Cross-sectional profile of the best-fit susceptibility model
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Although the qualitative agreement between the frequency
distribution determined in the experiments and that predicted by
the anisotropic susceptibility model is striking, the possible
contribution of other sources to the observed dependence of
MRI resonance frequency on microstructure cannot be ruled
out. Further research is needed to confirm the effect size of the
anisotropic susceptibility.
Experimental Considerations. One limitation of the current
experiment is that the resonance frequency images (Fig. 3 E and
F) and the cross-sectional profiles (Fig. 4 and Fig. S1) could have
been somewhat affected by the cut surfaces and the gaps
between the tissue segments. However, these effects are limited
in space and fail to explain the overall negative frequency shift in
unrotated C3 (Fig. 4 and Fig. S1) and the positive frequency
shifts observed in the fluid lateral to C2 and C4 (Fig. 3F). In
addition, a gap should create a mirrored profile outside the gap
and centered on it; however, the profiles around the C1–C2 and
C4–C5 gaps in Fig. S1B are not mirrored, indicating that the
effect of the gaps does not dominate the profile or explain the
profile change between conditions.
Because the current study was performed on a fixed tissue
sample that had been preserved in formalin, some of the bio-
logical parameters may not accurately reflect values in vivo. A
recent study suggested that washing fixed tissues for 12 h helps
restore MRI parameters (T1, T2, and diffusivity) to close to their
values in vivo (29). We followed a similar procedure to restore
the MRI parameters. The DTI results indicate that the micro-
structure was preserved even after fixation, as was suggested by
Sun et al. (30). Moreover, frequency contrasts quantitatively
similar to those observed in vivo have been observed in fixed
tissues (31). Nevertheless, further research is needed to inves-
tigate the effects of fixation on resonance frequency contrast.
Implications. The finding of microstructure orientation–dependent
resonancefrequencyshiftsmayhavesignificantimplicationsforthe
study of brain structures with MRI. First, it should improve the
understanding of previous observations of frequency shifts in high-
resolution brain images (1), which may lead to improved method-
ology for their detection. Second, the microstructural information
availablethroughthismechanismcouldcomplementdataavailable
with MRI measures ofwater diffusion (32). Interpreting resonance
frequency data directly remains challenging, given the presence of
multiple contributing mechanisms. Nonetheless, when combined
with other informationsuch as T2* (33)and magnetization transfer
contrast (34), these resonance frequency data could be used to
extract microstructural information for use in various clinical and
scientific applications (e.g., high-resolution fiber tracking).
Materials and Methods
Experimental Setup. Because the aim of the present study was to investigate
the effect of tissue microstructure and its orientation on MRI resonance
frequency, we selected a section of white matter known to have a relatively
uniform fiber orientation. The experiment was carefully designed to separate
out any effects of tissue microstructure from well-known larger-scale geo-
metric shape effects.
A square cylindrical piece of corpus callosum was sectioned from a coronal
slice of a fixed human brain from a 70-year-old female with no history of
neurologic disorders, preserved in 10% formalin (Fig. 2A). The piece of corpus
callosum was cut such that the main white matter fiber orientation was
parallel to the piece’s long axis. The square cylindrical piece was then laid
flat and cut into five square cylindrical subsections with a surgical knife: two
long pieces (C1 and C5, with a short side of ∼5.6 mm and a long side of
∼16–18 mm) and three cubic pieces (C2–C4, with sides of ∼5.6 mm) (Fig. 2B).
Before MRI scanning, the tissue was soaked in saline solution for >48 h to
restore T1and T2values and water diffusivity to values closer to those found
in vivo (29). A cylindrical PVC container (62 mm diameter, 54 mm deep) was
designed with a bottom plate with a central groove (59 mm long, 5.5 mm
wide, 1.5 mm deep) (Fig. 2B). When the container was placed inside of the
scanner, the cylindrical axis of the container was perpendicular to B0, and
the orientation of central groove was parallel to B0. The container was filled
with saline solution. The tissue pieces fitted tightly into the groove while
leaving a large portion of the tissue above the groove. The two long pieces
(C1 and C5) were placed at the ends, holding the three cubes (C2–C4) in
place, as shown in Fig. 2B.
Thefiberorientationinthetwolongpieces(C1andC5)andthemiddlecube
(C3) was parallel to B0, whereas the other two cubes (C2 and C4) initially had a
primary fiber orientation perpendicular to B0(condition B). To demonstrate
theeffectsofmicrostructureandallowseparationoftheseeffectsfromlarge-
scale shape effects, these two cubes of tissue were later rotated by 90 degrees
such that their primary fiber orientation was parallel to B0(condition A). The
entirecontainerwas placedinacustom-designedpassivePVCshimset,similar
to that described previously,§to reduce the large-scale field effects from the
shape of the container (in air). The long axis of the entire square cylindrical
tissue assembly was placed parallel to B0to minimize the contribution of the
geometry of the tissue assembly to the measured phase.
Data Acquisition. Fig. 1 was acquired using a 7-T (f0= 298.095 MHz)/94-cm
human whole-body system (GE), whereas all other MRI images were
acquired in a 7-T (f0= 300.390 MHz)/30-cm MRI system (Bruker BioSpin)
equipped with a 15-cm gradient set (Resonance Research). A 12-cm linear
homebuilt birdcage coil was used for excitation, and a four-element
homebuilt phased array coil (each of 28 mm diameter) was used for signal
reception. First, the tissue was localized using a three-plane localizer
sequence, and region-of-interest–based shimming (MAPSHIM; Bruker Bio-
Spin) was performed to increase the magnetic field homogeneity in and
around the tissues. Then a DTI was performed to confirm the fiber ori-
entation in the corpus callosum tissue sections. The sequence parameters for
the DTI scan were as follows: field of view (FOV), 60 × 60 mm2; in-plane
resolution, 0.5 × 0.5 mm2; slice thickness, 0.5 mm; slice gap, 0.05 mm;
acquisition bandwidth, 10 kHz; flip angle, 90 degrees; repetition time (TR), 3
s; echo time (TE), 56.4 ms. Four axial slices were acquired over 3 h using a
spin-echo sequence with 20 diffusion gradient directions based on the
downhill simplex method (35), with a b value of 3,000 s/mm2. Three addi-
tional baseline images were acquired with no diffusion gradients.
After the DTI scan, a 2D GRE sequence (FOV, 60 × 60 mm2; in-plane res-
olution, 0.2 × 0.2 mm2; slice thickness, 0.5 mm; slice gap, 0.05 mm; acquis-
ition bandwidth, 26 kHz; flip angle, 90 degrees; TR, 3 s; TE, 10 ms) was used
to acquire phase images over four axial slices over 15 min. After the first GRE
scan, the container was removed from the magnet, and the two cubes of
tissue (C2 and C4) that originally had a main fiber orientation perpendicular
to B0(condition B) were rotated by 90 degrees such that their primary fiber
orientation was parallel to B0(condition A). When the cubic tissue sections
were rotated, great care was taken to avoid moving the other tissue sec-
tions. In this way, only the microstructural orientation was altered, leaving
the overall geometry and shape of the tissues undisturbed. The tissue
phantom was carefully placed back into the scanner, and the three-plane
localization was repeated to ensure the that the tissue sections were located
Fig. 6.
that the relative susceptibility of C1, C3, and C5 is not 0, because the result
was obtained from the frequency difference images. Error bars represent SE.
Cross-sectional profile of the calculated magnetic susceptibility. Note
§van Gelderen P, Merkle H, de Zwart JA, Duyn JH. Passive shimming for a cylindrical brain-
sample container. Proceedings of the International Society of Magnetic Resonance Med-
icine Workshop on High Field Systems and Applications, October 15-17, 2008, Rome,
Italy; p. 47.
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sufficiently close to their previous positions to obviate the need for any
image coregistration in later processing of the two sets of images. Another
set of 2D GRE images was acquired with identical parameters, and the DTI
scan was repeated as well.
Data Analysis. The DTI data were reconstructed by taking the root sum of
squares of the individual coil magnitude images. The reconstructed images
were processed further using DTIFIT (36) to generate eigenvectors, eigen-
values, and fractional anisotropy (FA) maps. The FA maps, multiplied by the
primary eigenvector maps, were displayed as red-green-blue color-coded
images in which each voxel was assigned a color based on the direction of its
primary eigenvector and an intensity proportional to its FA.
The GRE magnitude images were reconstructed using the root sum of
squares method. Phase images were calculated from the complex sum of the
individual coil data after correcting for each coil’s phase offset (37). A circular
mask (32 mm diameter) around the tissue region was chosen in which to
perform all further phase processing and analysis (Fig. 3, dashed circles). The
phasewasunwrapped(38),andlarge-scalebackgroundphasevariationswere
removed by subtracting an eighth-order polynomial fitted to the data (in 2D)
within the mask. During the polynomial fitting procedure, the tissue sections
and nearby areas were not included in the fitting mask, to prevent the
removal of phase contrast caused by the tissue structures. The difference
image of conditions A and B was calculated to demonstrate the effect on the
phase contrast of changing the orientation of the microstructure. This dif-
ferenceimagewasobtainedbysubtractingtheunwrappedphaseimages,not
the data fitted with an eighth-order polynomial. The background phase
variation was removed from the difference image using the procedure
described earlier, but with a second-order polynomial fit. This procedure was
necessary due to the significant drift in the scanner gradient and/or shim
systems between the two acquisitions. The resulting difference image was
more reliable than the original phase images because any orientation inde-
pendent molecular exchange contrast would be canceled out in the differ-
ence image. Also, the large-scale background phase variations and poly-
nomial fitting procedure had less effect on the difference images. A cross-
sectional profile of the difference image—the average within the central 4
mm of the tissue over all four slices—was plotted (excluding air bubbles). In
the profile, the values in C1 and C5 were affected by the order of background
polynomial fitting and the choice of mask (including the tissues or not) and
were less reliable than the values in C2, C3, and C4. All phase images and
profiles were scaled (by dividing by 2π × TE) to give frequency images or
profiles in Hz. To calculate the frequency shift in each tissue, the central 20
(width) × 23 (length) × 4 (slices) voxels were averaged, excluding air bubble
areas. The resulting frequency shift measurements are given as mean ± SD or
mean difference ± pooled SD.
Simulation for Anisotropic Susceptibility and Susceptibility Calculation. A
computer simulation was performed to test the hypothesis that the observed
resonance frequency changes could be explained by anisotropic suscepti-
bility. Square cylindrical structures were designed to match the tissue pieces
used in the experiment. The matrix size was 300 × 300 × 300, with 28 × 28 ×
28 voxels for C2, C3, and C4; 28 × 28 × 93 voxels for C1; and 28 × 28 × 81 for
C5. The susceptibility value for the saline was assumed to be that of water
(−9.05 ppm). Frequency maps were calculated by assigning a susceptibility
value to each tissue section and performing a Fourier-based field calculation
(39). An initial susceptibility model was set up for condition A in which all of
the tissues had their primary fiber orientation parallel to B0and all of the
tissue sections were assigned the same susceptibility value (χk). The simu-
lation was repeated, varying χkfrom −9.085 ppm to −9.105 ppm in steps of
10−3ppm to see which value gave a minimum root mean squared error
between the calculated and measured frequency images (the central 4 mm
of the tissues excluding air bubbles and tissue boundaries). Once χkwas
chosen, another computer model was designed to simulate condition B. In
this second model, C1, C3, and C5 were assigned χk, whereas the suscepti-
bility value for C2 and C4 (χ⊥) was varied between −9.090 ppm and −9.110
ppm in steps of 10−3ppm. Both C2 and C4 were assumed to have the same
susceptibility value. A frequency difference image was calculated by sub-
tracting the results of the two simulations. The calculated and measured
frequency difference images were then compared within the central 4 mm
of the tissue section over all four slices, excluding air bubbles and the tissue
boundaries. The susceptibility value that gave a minimum root mean
squared error between the measured and calculated frequency difference
images was chosen as χ⊥: the susceptibility of tissue sections with a micro-
structure perpendicular to B0.
In addition to the simulations, in which each tissue section was assumed to
have a single susceptibility value, the susceptibility difference between the
tissue sections was calculated directly from the measured frequency differ-
ence image. The inverse-Fourier method (16) was applied to the frequency
difference image, and the susceptibility was calculated using a truncation
value of 5 for the k-space deconvolution filter (16). Note that in this method
and in the previous Fourier-based frequency map calculation, the suscepti-
bility value in a voxel is constrained to be single-valued and, therefore, is a
partial volume-averaged quantity. For the susceptibility calculation, a
slightly larger circular mask (40 mm diameter) was used to avoid effects due
to excluding the edges of the tissue sections. Air bubbles were excluded
from the calculation to reduce streaking artifacts. A cross-sectional profile
through the calculated susceptibility difference map in the original 32 mm
mask was plotted as the average within the central 4 mm of the tissue over
all four slices. The susceptibility of each tissue segment was calculated as the
mean within this central 4 mm by 4.6 mm over all slices (20 × 23 × 4 voxels in
each segment), excluding air bubble areas.
ACKNOWLEDGMENTS. We thank Dr. Ara Kocharyan and Dr. Kant M.
Matsuda for tissue preparation. This research was supported by the Intra-
mural Research Program of the National Institutes of Health, National
Institute of Neurological Disorders and Stroke.
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Corrections and Retraction
CORRECTIONS
EVOLUTION
Correction for “Phylogenomic analyses reveal convergent pat-
terns of adaptive evolution in elephant and human ancestries,” by
Morris Goodman, Kirstin N. Sterner, Munirul Islam, Monica
Uddin, Chet C. Sherwood, Patrick R. Hof, Zhuo-Cheng Hou,
Leonard Lipovich, Hui Jia, Lawrence I. Grossman, and Derek E.
Wildman, which appeared in issue 49, December 8, 2009, of Proc
Natl Acad Sci USA (106:20824–20829; first published November
19, 2009; 10.1073/pnas.0911239106).
The authors note that the incorrect URL for accessing the
data in the Dryad database was published. The data discussed in
this publication have been deposited in the Dryad Digital
Repository database: http://hdl.handle.net/10255/dryad.908.
www.pnas.org/cgi/doi/10.1073/pnas.1003435107
MEDICAL SCIENCES
Correction for “Sensitivity of MRI resonance frequency to the
orientation of brain tissue microstructure,” by Jongho Lee, Karin
Shmueli, Masaki Fukunaga, Peter van Gelderen, Hellmut Merkle,
Afonso C. Silva, and Jeff H. Duyn, which appeared in issue 11,
March 16, 2010, of Proc Natl Acad Sci USA (107:5130–5135; first
published March 2, 2010; 10.1073/pnas.0910222107).
The authors note that due to a printer’s error in adding an
additional reference in the proof, beginning with the second ci-
tation for reference 12 on page 5130, right column, first para-
graph, fifth line, all numerical references should have appeared
as one number higher, e.g., reference 12 becomes reference 13.
This is with the exception of reference 1 on page 5133, left
column, last paragraph, fifth line.
www.pnas.org/cgi/doi/10.1073/pnas.1003440107
NEUROSCIENCE
Correction for “Phosphorylation of Rap1GAP, a striatally en-
riched protein, by protein kinase A controls Rap1 activity and
dendritic spine morphology,” by Thomas McAvoy, Ming-ming
Zhou, Paul Greengard, and Angus C. Nairn, which appeared in
issue9,March3,2009,ofProcNatlAcadSciUSA(106:3531–3536;
first published February 13, 2009; 10.1073/pnas.0813263106).
The authors note that in the abstract of their paper, the sen-
tence, “Phosphorylation of Rap1GAP is also associated with in-
creased dendritic spine head size in cultured neurons” should
instead appear as “Phosphorylation of Rap1GAP is also asso-
ciated with decreased dendritic spine head size in cultured neu-
rons.” This error does not affect the conclusions of the article.
www.pnas.org/cgi/doi/10.1073/pnas.1003564107
RETRACTION
IMMUNOLOGY
Retraction for “B7-DC cross-linking restores antigen uptake
and augments antigen-presenting cell function by matured den-
dritic cells” by Suresh Radhakrishnan, Esteban Celis, and Larry
R. Pease, which appeared in issue 32, August 9, 2005, of Proc Natl
Acad Sci USA (102:11438–11443; first published online August 1,
2005;doi:10.1073/pnas.0501420102).Theauthorswishtonotethe
following: “After a re-examination of key findings underlying the
reported conclusions that B7-DCXAb is an immune modulatory
reagent, we no longer believe this is the case. Using blinded pro-
tocols we re-examined experiments purported to demonstrate the
activation of dendritic cells, activation of cytotoxic T cells, induc-
tionoftumorimmunity,modulationofallergicresponses,breaking
toleranceintheRIP-OVAdiabetesmodel,andthereprogramming
ofTh2 andT regulatory cells.Some oftheserepeatedstudieswere
direct attempts to reproduce key findings in the manuscript cited
above. In no case did these repeat studies reveal any evidence that
theB7-DCXAbreagenthadthepreviouslyreportedactivity.Inthe
course of this re-examination, we were able to study all the anti-
bodies used in the various phases of our work spanning the last
10years.Noneoftheseantibodiesappearstobeactiveinanyofour
repeatassays. We donotbelieve something has happened recently
tothe reagent changing itspotency.Therefore, theauthors seek to
retract this work.”
Suresh Radhakrishnan
Esteban Celis
Larry R. Pease
www.pnas.org/cgi/doi/10.1073/pnas.1003319107
8498
| PNAS
| May 4, 2010
| vol. 107
| no. 18www.pnas.org