Corrections and Retraction

CORRECTIONS RETRACTION

EVOLUTION IMMUNOLOGY Correction for “Phylogenomic analyses reveal convergent pat- Retraction for “B7-DC cross-linking restores antigen uptake terns of adaptive evolution in elephant and human ancestries,” by and augments antigen-presenting cell function by matured den- Morris Goodman, Kirstin N. Sterner, Munirul Islam, Monica dritic cells” by Suresh Radhakrishnan, Esteban Celis, and Larry Uddin, Chet C. Sherwood, Patrick R. Hof, Zhuo-Cheng Hou, R. Pease, which appeared in issue 32, August 9, 2005, of Proc Natl Leonard Lipovich, Hui Jia, Lawrence I. Grossman, and Derek E. Acad Sci USA (102:11438–11443; first published online August 1, Wildman, which appeared in issue 49, December 8, 2009, of Proc 2005; doi: 10.1073/pnas.0501420102). The authors wish to note the Natl Acad Sci USA (106:20824–20829; first published November following: “After a re-examination of key findings underlying the 19, 2009; 10.1073/pnas.0911239106). reported conclusions that B7-DCXAb is an immune modulatory The authors note that the incorrect URL for accessing the reagent, we no longer believe this is the case. Using blinded pro- data in the Dryad database was published. The data discussed in tocols we re-examined experiments purported to demonstrate the this publication have been deposited in the Dryad Digital activation of dendritic cells, activation of cytotoxic T cells, induc- Repository database: http://hdl.handle.net/10255/dryad.908. tion of tumor immunity, modulation of allergic responses, breaking tolerance in the RIP-OVA diabetes model, and the reprogramming www.pnas.org/cgi/doi/10.1073/pnas.1003435107 of Th2 and T regulatory cells. Some of these repeated studies were direct attempts to reproduce key findings in the manuscript cited MEDICAL SCIENCES above. In no case did these repeat studies reveal any evidence that the B7-DCXAb reagent had the previously reported activity. In the Correction for “Sensitivity of MRI resonance frequency to the course of this re-examination, we were able to study all the anti- orientation of brain tissue microstructure,” by Jongho Lee, Karin bodies used in the various phases of our work spanning the last Shmueli, Masaki Fukunaga, Peter van Gelderen, Hellmut Merkle, 10 years. None of these antibodies appears to be active in any of our Afonso C. Silva, and Jeff H. Duyn, which appeared in issue 11, Proc Natl Acad Sci USA – fi repeat assays. We do not believe something has happened recently March 16, 2010, of (107:5130 5135; rst to the reagent changing its potency. Therefore, the authors seek to published March 2, 2010; 10.1073/pnas.0910222107). ” ’ retract this work. The authors note that due to a printer s error in adding an Suresh Radhakrishnan additional reference in the proof, beginning with the second ci- fi Esteban Celis tation for reference 12 on page 5130, right column, rst para- Larry R. Pease graph, fifth line, all numerical references should have appeared as one number higher, e.g., reference 12 becomes reference 13. www.pnas.org/cgi/doi/10.1073/pnas.1003319107 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 issue 9, March 3, 2009, of Proc Natl Acad Sci USA (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.

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8498 | PNAS | May 4, 2010 | vol. 107 | no. 18 www.pnas.org Downloaded by guest on September 24, 2021 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 and bCerebral 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 tissue microstructure and its orientation relative to the main study the fine structure of the human brain at the level of fiber bun- magnetic field. The authors applied the Lorentzian cavity concept dles and cortical layers. In particular, techniques aimed at detecting (11, 12) to estimate the magnetic field induced by microscopic MRI resonance frequency shifts originating from local variation variations in magnetic susceptibilities. Using a nonspherical in magnetic susceptibility and other sources have greatly improved Lorentzian cavity, proposed earlier in (12, 13), to model the the visualization of these structures. A recent theoretical study [He X, compartmentalization of water protons in an anisotropic tissue Yablonskiy DA (2009) Proc Natl Acad Sci USA 106:13558–13563] sug- structure, the authors suggested the presence of a net (voxel- gests that MRI resonance frequency may report not only on tissue averaged) frequency shift that depends on the tissue’s orientation composition, but also on microscopic compartmentalization of sus- in the externally applied magnetic field. This mechanism could ceptibility inclusions and their orientation relative to the magnetic explain some of the strong frequency shifts observed in the major field. The proposed sensitivity to tissue structure may greatly expand fiber bundles (Fig. 1) and may have important implications for the the information available with conventional MRI techniques. To in- application and interpretation of the resonance frequency in vestigate this possibility, we studied postmortem tissue samples from GRE MRI. human corpus callosum with an experimental design that allowed The extent to which the Lorentzian cavity concept, which is separation of microstructural effects from confounding macrostruc- well established at the atomic (nanometer) scale for electric and MEDICAL SCIENCES tural effects. The results show that MRI resonance frequency does magnetic fields (11, 14), should be used to account for the field depend on microstructural orientation. Furthermore, the spatial dis- distributions at larger (micrometer) scales that may be present in tribution of the resonance frequency shift suggests an origin related brain structures is not clear, however. Furthermore, the exper- to anisotropic susceptibility effects rather than microscopic compart- imental evidence is sparse in the aforementioned study (9), and mentalization. This anisotropy, which has been shown to depend on interpretation of the results is confounded by large-scale geo- molecular ordering, may provide valuable information about tissue metric effects inherent to the susceptibility-related contrast molecular structure. mechanism. The purpose of the current study was to further investigate MRI phase contrast | resonance frequency shift | anisotropic susceptibility | the potential effect of brain microstructure on MRI resonance magnetic susceptibility tensor | white matter fiber tracking frequency. Results ecent high-field (≥7 T) human MRI studies have demon- Rstrated that contrast based on resonance frequency shifts The effect of tissue microstructure on MRI resonance frequency may substantially improve the visualization of fine-scale struc- was investigated by manipulating microstructure while minimally tural variation in the human brain. For example, many of the affecting macrostructure. Experiments were performed on an brain’s major white matter fiber bundles and distinct cortical elongated section of human corpus callosum, a major white lamination patterns have recently been visualized in vivo by matter fiber bundle of the human brain. A part of the corpus observing the signal phase that is proportional to the resonance callosum was chosen that had relatively uniform (micro- frequency in gradient-echo (GRE) MRI (1–4). Despite this structural) fiber orientation, with fibers running mostly parallel achievement and the potential clinical and scientific significance, to the long direction of the section (Fig. 2A). The section was cut however, the mechanisms underlying magnetic resonance fre- into five subsections, which were aligned parallel to the MRI fi quency shifts remain poorly understood. main magnetic eld (B0) in a sample holder. The section was Several candidate mechanisms have been suggested and imaged under two conditions: one in which all subsections were investigated as sources for this frequency contrast (1, 5–8). A placed in their original orientation (condition A; Fig. 2C), and the primary candidate is an altered bulk magnetic susceptibility due other in which two of the subsections (C2 and C4) were rotated by D fi to such compounds as ferritin, myelin, and deoxyhemoglobin, all 90 degrees relative to B0 (condition B; Fig. 2 ). Microscopic ber fi of which are found throughout brain tissue. Strong support for orientation was con rmed by diffusion tensor imaging (DTI) (15), 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 Author contributions: J.L., K.S., M.F., and J.H.D. designed research; J.L. performed research; † J.L., H.M., and A.C.S. contributed new reagents/analytic tools; J.L., K.S., M.F., P.v.G., and from susceptibility models. J.H.D. analyzed data; and J.L., K.S., and J.H.D. wrote the paper. An additional contribution to MRI resonance frequency may The authors declare no conflict of interest. come from the exchange processes between protons in water and *This Direct Submission article had a prearranged editor. in amide groups on proteins or other exchangeable sites (8). The 1To whom correspondence should be addressed. E-mail: [email protected]. frequency shifts arising from these mechanisms may provide This article contains supporting information online at www.pnas.org/cgi/content/full/ important information about the chemical composition of brain 0910222107/DCSupplemental. tissues in vivo. † Shmueli K, et al. The dependence of tissue phase contrast on orientation can be overcome A recent theoretical study from He and Yablonskiy (10) sug- by quantitative susceptibility mapping. Proceedings of the Annual Meeting of the Interna- gests that resonance frequency shifts may also report on brain tional Society of Magnetic Resonance Medicine, April 18–24, 2009, Honolulu, HI; p. 466. www.pnas.org/cgi/doi/10.1073/pnas.0910222107 PNAS Early Edition | 1of6 Fig. 1. High-resolution (250 × 250-μm in-plane, 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). showing parallel orientation for condition A and alternating well, with the strongest effect seen in C3. Inside of C1 and C5, parallel and perpendicular orientations for condition B (Fig. 3 A the frequency gradually decreases close to the C1 side of the and B). Macroscopic tissue orientation was parallel to B0, and the C1–C2 boundary and the C5 side of the C4–C5 boundary. This overall shape was similar for both conditions. can be interpreted as the effect of C2 and C4 extending outside Images representing signal amplitude and resonance fre- of those tissue sections, with an amplitude that decreases with quency from the two different microstructural orientations are distance. In summary, the results suggest that the orientation of shown in Figs. 3 C–F. The average resonance frequency of the the microscopic structure affects MRI resonance frequency both − ± tissues in condition A was 3.89 0.76 Hz relative to the saline locally and remotely. solution. Under condition B, the resonance frequency of the rotated segments C2 and C4 showed a positive shift of 0.56 ± Discussion 0.67 Hz (mean difference ± pooled SD over voxels) (Fig. 3F) Our findings represent direct experimental evidence for a de- E relative to condition A (Fig. 3 ). This effect is shown more pendence of MRI resonance frequency on the orientation of fi clearly in Fig. 4, in which the average cross-sectional pro le of brain microstructure relative to the main magnetic field. Our the difference image is plotted. The large SD is attributed to the experimental design allowed the separation of microscopic and nonuniform phase shift within a tissue segment and the true macroscopic orientation effects that often coexist under general susceptibility variation within the tissue. in-vivo imaging conditions. Such effects have complicated the 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

Fig. 3. Results of MRI frequency measurement at the original (condition A: A, C,andE) and rotated positions of fiber bundle segments C2 and C4 (condition B: B, D,andF). (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 Fig. 2. Selection of white matter sections for postmortem MRI. (A) Five shift within and near the lateral edges of the rotated segments. A slightly square cylindrical pieces of fixed tissue were sectioned along the primary negative frequency shift is observed in unrotated segments. A few small dipole fiber orientation in the corpus callosum (coronal view). (B) The tissues were field patterns, likely originating from air bubbles, are also seen in E.The placed in a groove at the bottom of a disk-shaped container. (C and D) images are from coronal scans in which the slice selection was along the Representations of condition A (C) and condition B (D) showing fiber ori- physical y-axis, the readout gradient was along the physical z-axis, and the entations. The zoomed images show the detailed tissue structure. phase encoding was along the physical x-axis. B0 was along the z-axis.

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.0910222107 Lee et al. 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 − χk Fig. 4. Averaged cross-sectional profile of the frequency difference image B was 9.105 ppm. This value is more diamagnetic than (both (condition B − condition A). The rotated segments (C2 and C4) show positive relative to saline solution). These results suggest that the effect frequency shifts compared with the unrotated segments (C1, C3, and C5). of microstructure orientation on the resonance frequency in Error bars represent SE. The scanner frequency was 300.390 MHz. 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 interpretation of earlier studies (9, 16). The observed sensitivity that this model does not include any contribution of the mo- to orientation may result from different mechanisms (see below) lecular exchange effect to the frequency shift; If that were taken that could provide important clues about the cellular organ- into account, the absolute susceptibility values could change. The ization of the tissue. anisotropic susceptibility difference (χk − χ⊥) would not change, however, because it is based on the exchange-averaged frequency The Nonspherical Lorentzian Cavity. Although the dependence on difference images. microstructural orientation found in this study might appear Fig. 6 shows the susceptibility difference profile calculated MEDICAL SCIENCES consistent with the theoretical predictions of He and Yablonskiy directly from the frequency difference image. The measured (9), there is an obvious discrepancy that suggests inadequacy of susceptibility difference (χk − χ ) between the tissue segments their theory. The nonspherical Lorentzian approach does not ⊥ varies from 0.006 ± 0.007 ppm (mean difference ± pooled SD explain the resonance frequency changes observed at the boun- ± daries and outside of the tissues (e.g., the positive frequency near 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 the lateral edges of C2 and C4, and the decreased frequency in fi C3 and at the C1–C2 and C4–C5 boundaries); rather, it predicts variation within the tissue and/or the noise ampli cation occur- a frequency shift that is purely local to the area of anisotropic ring during the inversion process that is required to convert microstructure. We propose that the experimental observations frequency distributions into susceptibility distributions (16). are better explained by a model of anisotropic susceptibility Despite the large SDs, the susceptibility difference was highly statistically significant between all χk and χ⊥ tissue combinations rather than one of anisotropic compartmentalization. − with P values <10 16 when averaged over the voxels. Anisotropic Magnetic Susceptibility. Anisotropic magnetic sus- One possible source of this susceptibility anisotropy is the ceptibility is a phenomenon commonly seen in crystals of highly phospholipid bilayers in myelin. The susceptibility anisotropy anisotropic atomic structure. It also has been noted in con- (χk − χ⊥) measured in the corpus callosum is ∼3–5 times smaller stituents of biological tissues, including muscle fibers (17), retinal than the anisotropy measured in the lipid bilayers of lecithin rods (18), nucleic acids (19), proteins (20–23), and lipid bilayers membranes (24, 25). This range is reasonable considering the (24–27). Because the proteins and lipid bilayers associated with smaller lipid fraction (∼16%) in white matter (28) and potential white matter fibers are highly ordered, anisotropic susceptibility confounds, such as the differences in the molecular composition may have contributed to our present findings. of the bilayers and differences in cellular structure.

Fig. 5. Simulation results for anisotropic susceptibility. (A) simulation result for condition B. (B) Cross-sectional profile of the best-fit susceptibility model (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).

Lee et al. PNAS Early Edition | 3of6 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 T1 and T2 values and water diffusivity to values closer to those found Fig. 6. fi Cross-sectional pro le of the calculated magnetic susceptibility. Note in vivo (29). A cylindrical PVC container (62 mm diameter, 54 mm deep) was that the relative susceptibility of C1, C3, and C5 is not 0, because the result designed with a bottom plate with a central groove (59 mm long, 5.5 mm was obtained from the frequency difference images. Error bars represent SE. 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 Although the qualitative agreement between the frequency with saline solution. The tissue pieces fitted tightly into the groove while distribution determined in the experiments and that predicted by leaving a large portion of the tissue above the groove. The two long pieces the anisotropic susceptibility model is striking, the possible (C1 and C5) were placed at the ends, holding the three cubes (C2–C4) in contribution of other sources to the observed dependence of place, as shown in Fig. 2B. MRI resonance frequency on microstructure cannot be ruled The fiber orientation in the two long pieces (C1 and C5) and the middle cube out. Further research is needed to confirm the effect size of the (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 anisotropic susceptibility. the effects of microstructure and allow separation of these effects from large- scale shape effects, these two cubes of tissue were later rotated by 90 degrees Experimental Considerations. One limitation of the current such that their primary fiber orientation was parallel to B0 (condition A). The experiment is that the resonance frequency images (Fig. 3 E and entire container was placed in a custom-designed passive PVC shim set, similar F) and the cross-sectional profiles (Fig. 4 and Fig. S1) could have to that described previously,§ to reduce the large-scale field effects from the been somewhat affected by the cut surfaces and the gaps shape of the container (in air). The long axis of the entire square cylindrical between the tissue segments. However, these effects are limited tissue assembly was placed parallel to B0 to minimize the contribution of the in space and fail to explain the overall negative frequency shift in geometry of the tissue assembly to the measured phase. unrotated C3 (Fig. 4 and Fig. S1) and the positive frequency Data Acquisition. shifts observed in the fluid lateral to C2 and C4 (Fig. 3F). In Fig. 1 was acquired using a 7-T (f0 = 298.095 MHz)/94-cm addition, a gap should create a mirrored profile outside the gap human whole-body system (GE), whereas all other MRI images were acquired in a 7-T (f = 300.390 MHz)/30-cm MRI system (Bruker BioSpin) and centered on it; however, the profiles around the C1–C2 and 0 – B equipped with a 15-cm gradient set (Resonance Research). A 12-cm linear C4 C5 gaps in Fig. S1 are not mirrored, indicating that the homebuilt birdcage coil was used for excitation, and a four-element effect of the gaps does not dominate the profile or explain the homebuilt phased array coil (each of 28 mm diameter) was used for signal profile change between conditions. reception. First, the tissue was localized using a three-plane localizer Because the current study was performed on a fixed tissue sequence, and region-of-interest–based shimming (MAPSHIM; Bruker Bio- sample that had been preserved in formalin, some of the bio- Spin) was performed to increase the magnetic field homogeneity in and logical parameters may not accurately reflect values in vivo. A around the tissues. Then a DTI was performed to confirm the fiber ori- recent study suggested that washing fixed tissues for 12 h helps 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 restore MRI parameters (T1,T2, and diffusivity) to close to their resolution, 0.5 × 0.5 mm2; slice thickness, 0.5 mm; slice gap, 0.05 mm; values in vivo (29). We followed a similar procedure to restore acquisition bandwidth, 10 kHz; flip angle, 90 degrees; repetition time (TR), 3 the MRI parameters. The DTI results indicate that the micro- s; echo time (TE), 56.4 ms. Four axial slices were acquired over 3 h using a structure was preserved even after fixation, as was suggested by spin-echo sequence with 20 diffusion gradient directions based on the Sun et al. (30). Moreover, frequency contrasts quantitatively downhill simplex method (35), with a b value of 3,000 s/mm2. Three addi- similar to those observed in vivo have been observed in fixed tional baseline images were acquired with no diffusion gradients. tissues (31). Nevertheless, further research is needed to inves- After the DTI scan, a 2D GRE sequence (FOV, 60 × 60 mm2; in-plane res- × 2 tigate the effects of fixation on resonance frequency contrast. olution, 0.2 0.2 mm ; 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 fi Implications. The finding of microstructure orientation–dependent to acquire phase images over four axial slices over 15 min. After the rst GRE fi scan, the container was removed from the magnet, and the two cubes of resonance frequency shifts may have signi cant implications for the tissue (C2 and C4) that originally had a main fiber orientation perpendicular study of brain structures with MRI. First, it should improve the to B0 (condition B) were rotated by 90 degrees such that their primary fiber understanding of previous observations of frequency shifts in high- orientation was parallel to B0 (condition A). When the cubic tissue sections resolution brain images (1), which may lead to improved method- were rotated, great care was taken to avoid moving the other tissue sec- ology for their detection. Second, the microstructural information tions. In this way, only the microstructural orientation was altered, leaving available through this mechanism could complement data available the overall geometry and shape of the tissues undisturbed. The tissue with MRI measures of water diffusion (32). Interpreting resonance phantom was carefully placed back into the scanner, and the three-plane frequency data directly remains challenging, given the presence of localization was repeated to ensure the that the tissue sections were located multiple contributing mechanisms. Nonetheless, when combined with other information such as T * (33) and magnetization transfer 2 § contrast (34), these resonance frequency data could be used to 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- extract microstructural information for use in various clinical and icine Workshop on High Field Systems and Applications, October 15-17, 2008, Rome, scientific applications (e.g., high-resolution fiber tracking). Italy; p. 47.

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.0910222107 Lee et al. sufficiently close to their previous positions to obviate the need for any bility. Square cylindrical structures were designed to match the tissue pieces image coregistration in later processing of the two sets of images. Another used in the experiment. The matrix size was 300 × 300 × 300, with 28 × 28 × set of 2D GRE images was acquired with identical parameters, and the DTI 28 voxels for C2, C3, and C4; 28 × 28 × 93 voxels for C1; and 28 × 28 × 81 for scan was repeated as well. 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 Data Analysis. The DTI data were reconstructed by taking the root sum of value to each tissue section and performing a Fourier-based field calculation squares of the individual coil magnitude images. The reconstructed images (39). An initial susceptibility model was set up for condition A in which all of were processed further using DTIFIT (36) to generate eigenvectors, eigen- the tissues had their primary fiber orientation parallel to B0 and all of the values, and fractional anisotropy (FA) maps. The FA maps, multiplied by the tissue sections were assigned the same susceptibility value (χk). The simu- primary eigenvector maps, were displayed as red-green-blue color-coded lation was repeated, varying χk from −9.085 ppm to −9.105 ppm in steps of images in which each voxel was assigned a color based on the direction of its 10−3 ppm to see which value gave a minimum root mean squared error primary eigenvector and an intensity proportional to its FA. between the calculated and measured frequency images (the central 4 mm The GRE magnitude images were reconstructed using the root sum of of the tissues excluding air bubbles and tissue boundaries). Once χk was squares method. Phase images were calculated from the complex sum of the chosen, another computer model was designed to simulate condition B. In individual coil data after correcting for each coil’s phase offset (37). A circular this second model, C1, C3, and C5 were assigned χk, whereas the suscepti- mask (32 mm diameter) around the tissue region was chosen in which to bility value for C2 and C4 (χ⊥) was varied between −9.090 ppm and −9.110 perform all further phase processing and analysis (Fig. 3, dashed circles). The − ppm in steps of 10 3 ppm. Both C2 and C4 were assumed to have the same phase was unwrapped (38), and large-scale background phase variations were susceptibility value. A frequency difference image was calculated by sub- removed by subtracting an eighth-order polynomial fitted to the data (in 2D) tracting the results of the two simulations. The calculated and measured within the mask. During the polynomial fitting procedure, the tissue sections frequency difference images were then compared within the central 4 mm and nearby areas were not included in the fitting mask, to prevent the of the tissue section over all four slices, excluding air bubbles and the tissue removal of phase contrast caused by the tissue structures. The difference boundaries. The susceptibility value that gave a minimum root mean 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- squared error between the measured and calculated frequency difference χ ference image was obtained by subtracting the unwrapped phase images, not images was chosen as ⊥: the susceptibility of tissue sections with a micro- the data fitted with an eighth-order polynomial. The background phase structure perpendicular to B0. variation was removed from the difference image using the procedure In addition to the simulations, in which each tissue section was assumed to described earlier, but with a second-order polynomial fit. This procedure was have a single susceptibility value, the susceptibility difference between the necessary due to the significant drift in the scanner gradient and/or shim tissue sections was calculated directly from the measured frequency differ- systems between the two acquisitions. The resulting difference image was ence image. The inverse-Fourier method (16) was applied to the frequency more reliable than the original phase images because any orientation inde- difference image, and the susceptibility was calculated using a truncation pendent molecular exchange contrast would be canceled out in the differ- value of 5 for the k-space deconvolution filter (16). Note that in this method MEDICAL SCIENCES ence image. Also, the large-scale background phase variations and poly- and in the previous Fourier-based frequency map calculation, the suscepti- nomial fitting procedure had less effect on the difference images. A cross- bility value in a voxel is constrained to be single-valued and, therefore, is a sectional profile of the difference image—the average within the central 4 partial volume-averaged quantity. For the susceptibility calculation, a mm of the tissue over all four slices—was plotted (excluding air bubbles). In slightly larger circular mask (40 mm diameter) was used to avoid effects due the profile, the values in C1 and C5 were affected by the order of background to excluding the edges of the tissue sections. Air bubbles were excluded polynomial fitting and the choice of mask (including the tissues or not) and from the calculation to reduce streaking artifacts. A cross-sectional profile were less reliable than the values in C2, C3, and C4. All phase images and through the calculated susceptibility difference map in the original 32 mm fi π × pro les were scaled (by dividing by 2 TE) to give frequency images or mask was plotted as the average within the central 4 mm of the tissue over fi pro les in Hz. To calculate the frequency shift in each tissue, the central 20 all four slices. The susceptibility of each tissue segment was calculated as the × × (width) 23 (length) 4 (slices) voxels were averaged, excluding air bubble mean within this central 4 mm by 4.6 mm over all slices (20 × 23 × 4 voxels in ± areas. The resulting frequency shift measurements are given as mean SD or each segment), excluding air bubble areas. mean difference ± pooled SD. ACKNOWLEDGMENTS. We thank Dr. Ara Kocharyan and Dr. Kant M. Simulation for Anisotropic Susceptibility and Susceptibility Calculation. A Matsuda for tissue preparation. This research was supported by the Intra- computer simulation was performed to test the hypothesis that the observed mural Research Program of the National Institutes of Health, National resonance frequency changes could be explained by anisotropic suscepti- Institute of Neurological Disorders and Stroke.

1. Duyn JH, et al. (2007) High-field MRI of brain cortical substructure based on signal 12. Lorentz HA (1909) The Theory of Electrons and Its Applications to the Phenomena of phase. Proc Natl Acad Sci USA 104:11796–11801. Light and Radiant Heat (B.G. Teubner, Leipzig). 2. Deistung A, et al. (2008) Susceptibility-weighted imaging at ultra-high-magnetic field 13. Luckhurst GR, Zannoni C (1975) A theory of dielectric relaxation in anisotropic strengths: Theoretical considerations and experimental results. Magn Reson Med 60: systems. Proc R Soc Lond A 343:389–398. 1155–1168. 14. Aravamudhan S (2005) Magnetized materials: Contributions inside Lorentz ellipsoids. 3. Thomas BP, et al. (2008) High-resolution 7-T MRI of the human hippocampus in vivo. J Indian J Phys 79:985–989. Magn Reson Imaging 28:1266–1272. 15. Kittel C (1976) Introduction to Solid-State Physics (Wiley, New York), pp 407. 4. Marques JP, Maddage R, Mlynarik V, Gruetter R (2009) On the origin of the MR image 16. Basser PJ, Pierpaoli C (1996) Microstructural and physiological features of tissues – phase contrast: An in vivo MR microscopy study of the rat brain at 14.1 T. Neuroimage elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B 111:209 219. 17. Shmueli K, et al. (2009) Magnetic susceptibility mapping of brain tissue in vivo using 46:345–352. MRI phase data. Magn Reson Med 62:1510–1522. 5. Ogg RJ, Langston JW, Haacke EM, Steen RG, Taylor JS (1999) The correlation between 18. Arnold W, Steele R, Mueller H (1958) On the magnetic asymmetry of muscle fibers. phase shifts in gradient-echo MR images and regional brain iron concentration. Magn Proc Natl Acad Sci USA 44:1–4. Reson Imaging 17:1141–1148. 19. Hong FT, Mauzerall D, Mauro A (1971) Magnetic anisotropy and the orientation of 6. Haacke EM, et al. (2005) Imaging iron stores in the brain using magnetic resonance retinal rods in a homogeneous magnetic field. Proc Natl Acad Sci USA 68:1283–1285. imaging. Magn Reson Imaging 23:1–25. 20. Maret G, Schickfus M, Mayer A, Dransfeld K (1975) Orientation of nucleic acids in high 7. Lee J, Hirano Y, Fukunaga M, Silva AC, Duyn JH (2010) On the contribution of deoxy- magnetic fields. Phys Rev Lett 35:397–400. – fi hemoglobin to MRI gray white matter phase contrast at high eld. Neuroimage 49: 21. Tolman JR, Flanagan JM, Kennedy MA, Prestegard JH (1995) Nuclear magnetic dipole – 193 198. interactions in field-oriented proteins: Information for structure determination in 8. Zhong K, Leupold J, von Elverfeldt D, Speck O (2008) The molecular basis for gray and solution. Proc Natl Acad Sci USA 92:9279–9283. – white matter contrast in phase imaging. Neuroimage 40:1561 1566. 22. Torbet J, Freyssinet JM, Hudry-Clergeon G (1981) Oriented fibrin gels formed by fi 9. Fukunaga M, et al. Layer-speci c variation of iron content in cerebral cortex as a polymerization in strong magnetic fields. Nature 289:91–93. source of MRI contrast, Proc Natl Acad Sci USA, 10.1073/pnas.0911177107. 23. Worcester DL (1978) Structural origins of diamagnetic anisotropy in proteins. Proc 10. He X, Yablonskiy DA (2009) Biophysical mechanisms of phase contrast in gradient Natl Acad Sci USA 75:5475–5477. echo MRI. Proc Natl Acad Sci USA 106:13558–13563. 24. Torbet J (1987) Using magnetic orientation to study structure and assembly. Trends 11. Chu SC, Xu Y, Balschi JA, Springer CS, Jr (1990) Bulk magnetic susceptibility shifts in Biochem Sci 12:327–330. NMR studies of compartmentalized samples: Use of paramagnetic reagents. Magn 25. Boroske E, Helfrich W (1978) Magnetic anisotropy of egg lecithin membranes. Biophys Reson Med 13:239–262. J 24:863–868.

Lee et al. PNAS Early Edition | 5of6 26. Scholz F, Boroske E, Helfrich W (1984) Magnetic anisotropy of lecithin membranes: A 34. Li TQ, et al. (2009) Characterization of T(2)* heterogeneity in human brain white new anisotropy susceptometer. Biophys J 45:589–592. matter. Magn Reson Med 62:1652–1657. 27. Speyer JB, Sripada PK, Das Gupta SK, Shipley GG, Griffin RG (1987) Magnetic 35. Wolff SD, Balaban RS (1989) Magnetization transfer contrast (MTC) and tissue water – orientation of sphingomyelin-lecithin bilayers. Biophys J 51:687–691. proton relaxation in vivo. Magn Reson Med 10:135 144. 28. Naito A, et al. (2002) Dynorphin induced magnetic ordering in lipid bilayers as studied 36. Skare S, Hedehus M, Moseley ME, Li TQ (2000) Condition number as a measure of 31 noise performance of diffusion tensor data acquisition schemes with MRI. J Magn by P NMR spectroscopy. Biochim Biophys Acta 1558:34–44. – 29. O’Brien JS, Sampson EL (1965) Lipid composition of the normal human brain: Gray Reson 147:340 352. 37. Smith SM, et al. (2004) Advances in functional and structural MR image analysis and matter, white matter, and myelin. J Lipid Res 6:537–544. implementation as FSL. Neuroimage 23:208–219. 30. Shepherd TM, Thelwall PE, Stanisz GJ, Blackband SJ (2009) Aldehyde fixative solutions alter 38. de Zwart JA, van Gelderen P, Kellman P, Duyn JH (2002) Application of sensitivity- the water relaxation and diffusion properties of nervous tissue. Magn Reson Med 62:26–34. encoded echo-planar imaging for blood oxygen level–dependent functional brain 31. Sun SW, et al. (2005) Formalin fixation alters water diffusion coefficient magnitude imaging. Magn Reson Med 48:1011–1020. – but not anisotropy in infarcted brain. Magn Reson Med 53:1447 1451. 39. Jenkinson M (2003) Fast, automated, N-dimensional phase-unwrapping algorithm. fi 32. Yao B, et al. (2009) Susceptibility contrast in high eld MRI of human brain as a Magn Reson Med 49:193–197. function of tissue iron content. Neuroimage 44:1259–1266. 40. Marques JP, Bowtell R (2005) Application of a Fourier-based method for rapid 33. Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A (2000) In vivo fiber tractography calculation of field inhomogeneity due to spatial variation of magnetic susceptibility. using DT-MRI data. Magn Reson Med 44:625–632. Concepts Magn Reson B 25:65–78.

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