Mapping average axon diameters in porcine spinal cord white matter and rat corpuscallosum using d-PFG MRI

M.E. Komlosh a,b,⁎, E. Özarslan a,b,c, M.J. Lizak d, I. Horkayne-Szakaly e, R.Z. Freidlin f, F. Horkay a, P.J. Basser a

a Section on Tissue Biophysics and Biomimetics, PPITS, NICHD, National Institutes of Health, Bethesda, MD 20892, USAb Center for Neuroscience and Regenerative Medicine, Uniform Service University of the Health Sciences, Bethesda, MD 20814, USAc Dept. of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02215, USAd NIH MRI Research Facility, NINDS, NIH, Bethesda MD, 20892, USAe The Joint Pathology Center, Department of Defense, Silver Spring, MD 20910, USAf Center of Information Technology, NIH, Bethesda, MD 20892, USA

a b s t r a c ta r t i c l e i n f o

Article history:Accepted 28 March 2013Available online 10 April 2013

Keywords:MRIAverage axon diameterAADPulsed-field gradientPFGDouble wave vectord-PFGdPFG3D

Knowledge of microstructural features of nerve fascicles, such as their axon diameter, is crucial for under-standing normal function in the central and peripheral nervous systems as well as assessing changes dueto pathologies. In this study double-pulsed field gradient (d-PFG) filtered MRI was used to map the averageaxon diameter (AAD) in porcine spinal cord, which was then compared to AADs measured with optical mi-croscopy of the same specimen, as a way to further validate this new MRI method. A novel 3D d-PFG acqui-sition scheme was used to obtain AADs in each voxel of a coronal slice of rat brain corpus callosum. AADmeasurements were also acquired using optical microscopy performed on histological sections and validatedusing a glass capillary array phantom.

© 2013 Elsevier Inc. All rights reserved.

Introduction

The central nervous system (CNS) white matter consists of fasciclescontaining long bundles of myelinated axons, which serve as pathwaysto transfer impulses between gray matter regions within the brain, andfrom the cortex to other parts of the body and back (Kandel et al., 2000).Each fascicle comprises axons with a distribution of diameters whoserange can vary significantly. Since the diameter of a myelinated axonis linearly related to conduction velocity (Hursh, 1939; Tasaki et al.,1943), axon diameter helps determine the amount of informationtransferred along a pathway (Pajevic and Basser, 2013; Pajevic et al.,2008; Perge et al., 2012). Neuroanatomically, one finds axons in the spi-nal cord somatotopically organized into distinct clusters characterizedby different average diameters and diameter distributions, which en-able them to perform different functions. The ability to detect axon di-ameter non-invasively on a voxel-by-voxel basis in the spinal cordand in other white matter pathways would improve our understandingof both the normal function of the nervous system and many patholo-gies that may affect and be affected by changes in neuronal microstruc-ture. This information might also provide valuable insights about the

course of normal and abnormal development and changes that canoccur in aging and degeneration. Of particular interest is following pos-sible subtle pathological changes, which may occur in Traumatic BrainInjury (TBI), but which may be too small to detect using conventionaldiffusion MRI or other imaging methods.

Prior to the development of MRI-based methods, histological anal-ysis was the only means for measuring axon diameters. Histology,however, requires extracting tissue specimens, usually after sacrifice,and then cutting, fixing, sectioning, staining, mounting, and viewingthem with an optical or electron microscope. The microscope's resolu-tion needed to examine individual axons inherently limits the field ofview (FOV), requiring one to stitch together different swatches of tissueimages digitally to construct a quilt or cross-section of a large tissuestructure, such as the spinal cord, or a brainwhitematter pathway, suit-able for a more gross analysis.

CHARMED (Assaf et al., 2004) and AxCaliber (Assaf et al., 2008;Barazany et al., 2009) MRI were developed, in part, to overcome theinherent deficiencies of conventional histological analysis of whitematter structure and architecture. These in vivo MRI methods useconcepts of porous media NMR combined with MRI to measure, re-spectively, the average axon diameter (AAD) and the axon diameterdistribution (ADD) within nerve fascicles voxel by voxel. While thevoxel resolution of MRI is on the order of millimeters, the MR signalis sensitized to the microscopic diffusive or random motion of water

NeuroImage 78 (2013) 210–216

⁎ Corresponding author at: NIH, Bldg. 13 Rm. 3W16, 13 South Drive, Bethesda MD 20892,USA.

E-mail address: komloshm@mail.nih.gov (M.E. Komlosh).

1053-8119/$ – see front matter © 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.neuroimage.2013.03.074

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molecules, and to the size and shape of confining compartments thatcontain intra-axonal water, which are on the order of microns.

Both CHARMED and AxCaliber MRI employ a single pair ofStejskal–Tanner (Stejskal and Tanner, 1965) pulsed-field gradients(PFG) to measure the water proton spins' motion (Fig. 1a). Thelengthscale that they probe is characterized by the wave vectorq = γGδ/(2π) (where γ is the gyromagnetic ratio, G is the magneticfield gradient strength, and δ is the duration of the PFG), separatedby a diffusion time, Δ. These methods can detect microscopic net dis-placements of the tissue's water. In these methods the resulting signalattenuations can be correlated with the spins' 3D mean-squared netdisplacement, which can be used to infer the size of pores and confin-ing boundaries. In the case of CNS white matter, water diffusion is an-isotropic (Moseley et al., 1990). An idealized way to model axons is asmicrocapillaries whose diffusion is free (Gaussian) along the axial di-rection, and restricted within the axial plane (Avram et al., 2008).

In principle, for highly uniform aligned axons having a narrowADD, an effective way to measure the AADwould be from the positionof the first diffraction peak in a diffusion-diffraction experiment(Callaghan, 1996; Callaghan et al., 1991). However, these peaksarise only when the ADD is very narrow and the angle between theaxis of the fibers and the direction of the applied diffusion sensitizinggradient is close to 90° (Avram et al., 2004, 2008). Any small devia-tion of the applied gradient vector from orthogonality with respectto the fiber axis causes these peaks to disappear. Moreover, there isan inverse relationship between the pore or axon diameter and theq-value needed to probe it using the single-PFG MRI experiment, soextremely strong gradients are required (Ong et al., 2008) to measureaxon diameters in white matter, which are on the order of a few mi-crons. Such gradients are an order of magnitude stronger than what is

currently available on conventional clinical scanners, making suchmeasurements infeasible at this time (Basser, 2002).

Another approach to measuring pore diameter is to use thedouble-Pulsed Field Gradient (d-PFG) NMR method (Cheng andCory, 1999; Mitra, 1995; Özarslan and Basser, 2008) (Fig. 1b). Inher-ently, d-PFG MRI requires smaller gradients than the single PFGmethods described above to observe diffusion-diffraction effects.The d-PFG MRI employs two pairs (rather than one) of Stejskal–TannerPFG blocks separated by a mixing time, τm. The resulting signal loss isrelated to the correlation betweennet displacements during the twodif-fusion times rather than the net displacements themselves. With theaddition of a seconddisplacement dimension, numerousmicrostructur-al details can now be revealed, particularly as a function of τm. Forlong τm insight into microscopic (Komlosh et al., 2007, 2008; Lawrenzand Finsterbusch, 2011) and compartment shape anisotropy (Chengand Cory, 1999; Özarslan, 2009; Shemesh et al., 2012) can be gleaned,while for a negligibly short τm (Fig. 1c) (when τm = 0, the secondpulse of the first PFG block overlaps with the first pulse of the secondPFG block) the average pore diameter (Koch and Finsterbusch, 2008;Komlosh et al., 2011; Weber et al., 2009) can be obtained.

In this study we mapped the AAD voxel-by-voxel in an axial sec-tion of porcine spinal cord white matter using d-PFG MRI. For thefirst time the AAD obtained in spinal cord using d-PFG MRI was com-pared to the AAD obtained with optical microscopy of the same spec-imen, as a way to further validate this method. Moreover, a novel 3Dd-PFG MRI acquisition scheme was used to obtain the AAD in eachvoxel of a coronal slice of rat brain corpus callosum. Further studieswith well defined water-filled microcapillary arrays increase our con-fidence in the validity of this work.

Materials and methods

Specimen preparation and MRI protocol

Spinal cordA porcine spinal cord was excised and put immediately in a 4%

formalin solution. Prior to performing MRI experiments a portionof the spine was saved for subsequent histology studies while therest was rehydrated with phosphate buffered saline (PBS) for MRI.The rehydrated spine was then immersed in perfluoropolyether(Fomblin LC/8, Solvay Solexis, Italy) and inserted into a 10 mmShigemi tube (Shigemi Inc., Japan) with a plunger matched to thesusceptibility of water. The tube was placed in a 14 T vertical-boreBruker AVANCE III MRI scanner equipped with a micro2.5 gradientsystem powered by GREAT 60 gradient amplifiers with a nominalgradient strength of 24.65 mT m!1 A!1 (Bruker BioSpin Corp.,Billerica, MA, USA).

Acquisition scheme and MRI protocol. Since the spinal cord white mat-ter consists of long aligned fibers with known orientation, the spinalcord specimen could be placed in the magnet so that its long axis isaligned with the main magnetic field. For such samples whose axisof free diffusion are known a priori and can be aligned with themain magnetic field, a circular two-dimensional (Fig. 2a) d-PFG gradi-ent sampling scheme can be performed. The gradients of the first PFGNMR block are fixed along the x-axis, perpendicular to the fiber's freediffusion axis (z), while the orientation of the gradients in the secondblock is varied by an angle ϕwith respect to the x-axis between 0 and2π within the x–y plane.

Multiple gradient strengths were used in this study since the MRsignal attenuations in the free and restricted compartments have dif-ferent dependencies on the gradient strength. Therefore, having datawith multiple gradient amplitudes yields more accurate estimates ofthe free and restricted volume fractions, which ultimately improvesthe accuracy of the inner diameter estimates, as well. Moreoverwhile at low gradient strengths the signal has high signal-to-noise

Fig. 1. The pulse sequences: a) single-PFG, b) double-PFG (d-PFG), c) d-PFG withτm = 0, the pulse sequence used in this study.

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ratio (SNR), the angular resolution (the difference between the min-imum (ϕ = 0) and maximum (ϕ = π)) is low. When the gradientstrength is large, the SNR is low but angular resolution is high. Theuse of multiple gradient strengths in the study thus allows us to sam-ple the signal in both the high SNR and high angular resolutionregimes.

The PFG NMR parameters were: δ = 3.15 ms, Δ = 60 ms, and Gwas varied between 0 and 664 mT m!1. The MRI parameters were:TR/TE = 3500/6.54 ms, FOV = 10.5 mm, matrix size = 128 ! 128,spatial resolution = 82 μm2, and slice thickness = 3.6 mm. Thetime required to acquire a single orientation was 2 h. Prior to thed-PFG MRI experiment a diffusion tensor imaging (DTI) (Basser etal., 1994; Pierpaoli et al., 1996) protocol was applied to verify/estab-lish the spine's orientation. The DTI parameters were: δ = 3 ms,Δ = 50 ms, 24 diffusion direction orientations with b-values of100 and 1000 s mm!2, TR/TE = 3500/57.3 ms, FOV = 10.5 mm,matrix size = 128 ! 128, spatial resolution = 82 μm2, and slicethickness = 3.6 mm. The experimental time was 6 h.

Rat corpus callosumA perfused rat brain was excised and placed in 4% paraformalde-

hyde (PFA) for 24 h and then rehydrated in phosphate buffered saline(PBS). The brain was immersed in perfluoropolyether (Fomblin LC/8,Solvay Solexis, Italy) and inserted into a 30-mm Falcon tube (BectonDickinson, NJ) with an Ultem (Ensinger, UK) plunger and bottomthat is susceptibility-matched to water to eliminate susceptibilityartifacts at the tube-plunger interface. The tube was placed in a 7 Tvertical bore Bruker DRX MRI scanner equipped with a micro2.5 gra-dient system powered by GREAT 60 gradient amplifiers with a nomi-nal gradient strength of 24.65 mT m!1 A!1 (Bruker BioSpin Corp.,Billerica, MA, USA).

Acquisition scheme andMRI protocol. Unlike the spinal cord white mat-ter, the brain white matter fibers do change orientation from voxel tovoxel. Thus, the 2D circular gradient sampling scheme that was usedon the spinal cord specimen could no longer be used to acquire thisd-PFGMRI data. To obtain the AAD for a fiber bundle with an arbitraryor variable orientation, a 3D gradient sampling scheme was devel-oped (Fig. 2b). The one employed in this study was designed not tobias any one direction over another by sampling 66 d-PFG-weightedMRIs over 3 shells. Gradient directions suggested by Sloane wereused (Sloane, 2000). The outermost shell (G1 = G2 = 591.6 mT/m)consisted of images with 11 distinct orientations of G1 sampling thehemisphere uniformly. For each of these 11 directions threeseparate images were acquired with ϕ = 0, π/2, and π resulting in11 ! 3 = 33 acquisitions. Similarly, the second shell consisted of6 ! 3 = 18 points with G = 443.7 mT m!1 and the inner shellconsisted of 3 ! 3 = 9 points with G = 221.85 mT m!1. The direc-tions along each shell are independent of the other shells, providingadditional spatial and directional information due to more homoge-neous sampling of the space. In the 3D acquisition scheme, the

experiment uses 22 independent DWI directions, which is consideredsufficient to map the fiber orientation (e.g., using DTI). While for ϕ = 0and π G1 uniquely defines G2, for ϕ = π/2 G2 could be somewhatambiguous. In this study for the first of the G1 vectors, the directionof G2 was selected randomly (from vectors that lie on the circle per-pendicular to G1). Then, the rotation matrix that transforms G1 intothe next G1 vector in the set was applied on the G2 vector as well. Toimprove the radial sampling resolution, six images were taken withG ranging from 0 to 591.6 mT m!1 with d-PFG NMR blocks with anorientation of ϕ = π.

The PFG NMR parameters were: δ = 3.15 ms, Δ = 30 ms. TheMRI parameters were: TR/TE = 3500/6.12 ms, FOV = 17 mm, ma-trix size = 100 ! 100, spatial resolution = 170 ! 170 μm2, andslice thickness = 1 mm. The time required to acquire a single orien-tation was 2 h.

An independent DTI protocol was also used to verify the brainwhite matter fiber orientation. The DTI parameters were: δ = 3 ms,Δ = 30 ms, 6 diffusion direction orientations with b-values of 100 and21 diffusion directions with b-values of 1600 s mm!2, TR/TE = 3500/37.1 ms. The experimental time was 17 h.

When the angle between the two d-PFG blocks is π, the middle gra-dient pulse vanishes, which results in a single PFG experiment wherethe diffusion time is now doubled. Consequently, the corpus callosumfiber orientation can potentially be obtained from these experimentsas well, and the DTI experiment performed prior to the d-PFG acquisi-tion can be omitted. We used a subset of twenty conventional diffusionweighted experiments taken from the d-PFG acquisition to obtain thecorpus callosum's fiber orientation.

Phantom validationIn order to assess the accuracy of the 3D sampling scheme, we

acquired d-PFG MRI data on a glass capillary array MRI phantom(Komlosh et al., 2011) using both 2D and 3D sampling schemes. Theglass capillary array phantom consists of a wafer 13 mm OD,0.5 mm thick with a parallel pack of fused capillary tubes of 5 μmnominal pore diameter filled with water. The d-PFG NMR parameterswere identical in both experiments: δ = 3.15 ms, Δ = 75 ms, and Gwas varied between 0 and 664 mT m!1. The MRI parameters were:TR/TE = 5000/14 ms, FOV = 17 mm, matrix size = 128 ! 128, spa-tial resolution = 133 ! 133 ! 500 μm3. The 2D and 3D samplingschemes followed the same pattern as the spinal cord and rat braincorpus callosum respectively. The time required to acquire a singleorientation was 21 minutes.

Modeling and analysis

Analysis of the white matter d-PFG MRI signal data involved theuse of a matrix operator formalism to predict the resulting signal asa function of the gradient pulse strength and the angle between thetwo PFG blocks (E(q,ϕ)). The model assumes the contribution to thesignal comes from two compartments. One contains aligned imper-meable cylindrical axons where the water diffusion within the fiberis restricted perpendicular to the cell wall and Gaussian along theaxis of the cylinder. The extracellular compartment is described by aGaussian displacement distribution. The model is used to estimatethe average pore diameter for each voxel. There is no exchange as-sumed between the two compartments.

In order to estimate the axon diameter, the orientation of the fiberis estimated first. To this end, either a single-PFG DTI data set,acquired in tandem, is used or the fiber direction is calculated fromthe d-PFG experiments. In either case, the fiber orientation informa-tion is fed into the AAD estimation scheme, which employs athree-dimensional model of diffusion. The model implies a particularangular modulation in the plane perpendicular to the fiber orienta-tion; the fitting thus matches this modulation with the modulationpresent in the projection of the data onto the perpendicular plane.

Fig. 2. The d-PFG MRI acquisition schemes that were used in this study: a) 2D—for thespinal cord and b) 3D—for the rat corpus callosum.

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The d-PFG 3D acquisition scheme is acquired with no directional biasand then the fiber direction information is used along with the com-plete 3D data set to estimate the AAD.

The unknown parameters, which are estimated by fitting the modelare as follows: Axon diameter, S0_free (non-diffusion-weighted signalfor the free diffusion compartment), S0_rest (non-diffusion-weightedsignal for the restricted compartment), and diffusivity (assumed to bethe same in both compartments). For accurate estimation of these freeparameters, the number of d-PFG samples has to be significantly largerthan the number of unknowns, which was the case for all data sets.

All experimental parameters, including the use of “fat gradient” asopposed to infinitesimally short gradient pulses, are taken into ac-count when we estimate the free diffusion, the restricted compart-ment fraction and average pore diameter or AAD for each voxel.

A complete description of this modeling framework is containedin the following papers (Grebenkov, 2007; Özarslan et al., 2009,2011; Robertson, 1966; Shemesh et al., 2009).

Histology

Small sections of the spine were fixed in 3% glutaraldehyde, post-fixed in osmium tetroxide, and embedded in plastic (Finck, 1960;Freeman and Spurlock, 1962). One-micron thick sections were stainedwith toluidine blue and were scanned with an Olympus BX51 light mi-croscope with a resolution of 0.23 ! 0.23 μm2. The AAD values wereobtained using NIH ImageJ (Bethesda, MD).

To compare the AAD measured by both methods, regions of inter-est (ROI) analysis was performed on the AADmaps obtained from thed-PFG MRI experiments.

Results

Spinal cord

The results from the independent DTI acquisition performed onthe spinal cord specimen are shown in Fig. 3. Figs. 3a and b showthe DTI-derived Direction-Encoded Color (DEC) and the FractionalAnisotropy (FA) maps, respectively. The DEC maps show a uniformorientation of white matter aligned with the B0 field. The FA mapshows a fairly uniform level of high diffusion anisotropy in whitematter, and an expected reduction of FA in the “butterfly”-shapedgraymatter region. Neither map shows any significant variation with-in white matter. Therefore, for this specimen and its placement in themagnet, a d-PFG 2D MRI sampling scheme is appropriate to seewhether it can detect any regional variations within white matter.

Fig. 3c shows the AAD map calculated from the d-PFG filtered MRIexperiments. AADs are estimated between 3 and 5 μm. The darkpixels, which appear in the map, result from the noise in the data.Those pixels however, are rare and randomly scattered and thus donot obscure the general anatomy-dependent trends in this map. Fig. 3dshows the Toluidine blue sections thatwere taken from the ROIsmarkedin Fig. 3c.

Table 1 contains the AAD data obtained from the histological slicesshown in Fig. 3d and from the corresponding regions of the spinalcord using the ROIs shown in Fig. 3c.

Fig. 4 shows results obtained from the same specimen using ad-PFG-filtered MRI experiment. Fig. 4a shows the raw non-diffusionweighted d-PFG-filtered MRI. The image appears free of hardware ar-tifacts with a high SNR of 37.5. Fig. 4b, and c show the raw d-PFGMRIsfor the same specimen with gradients of 597 mT m!1 acquired with

Fig. 3. a) DEC and b) FA maps of spinal cord obtained from DTI using δ = 3 ms, Δ = 50 ms with b-values of 100 and 1000 s-mm!2. c) Average axon diameter map obtained fromd-PFG MRI data using δ = 3.15 ms, Δ = 60 ms, and G = 0–664 mT m!1. d) Toluidine blue light microscope images corresponding to the marked ROIs.

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collinear and perpendicular gradient blocks (i.e., ϕ = 0 and π, respec-tively). Due to the particular alignment of the fibers that allows a 2Dcircular sampling scheme, the difference between the two images isvery pronounced.

Glass capillary array MRI phantom

Figs. 5a and b show the pore diameter map of the glass capillaryarray – a proxy for the AAD – obtained using the 2D and 3D acquisi-tion schemes, respectively. An ROI analysis of the maps yielded anAAD of 4.88 ± 0.04 μm and 4.86 ± 0.3 μm for the 2D and 3D acquisi-tion schemes, respectively.

Rat corpus callosum

Figs. 6a and b show the DEC and FA maps calculated from the DTIdata obtained on a coronal slice of rat brain (arrows mark the corpuscallosum). The corpus callosum is very visible in these images. Thevariation in color in the DEC map in the corpus callosum clearlyshows the change in fiber orientation of this structure within theimage plane.

Fig. 6c shows the corresponding AAD map in the corpus callosumobtained from the 3D d-PFG MRI experiment. The fiber orientationwas first obtained from the DTI experiment prior to the d-PFGMRI ac-quisition and the signal attenuation perpendicular to the eigenvectorassociated with the largest eigenvalue – the purported fiber direction

(Basser et al., 1994) – was used to estimate the axons' orientation.The FA map in Fig. 6b appears fairly homogeneous as expected froma coronal slice of the corpus callosumwhile the AADs ranged between1 and 3 μm with a mean AAD of 1.5 μm. Figs. 6d and e show experi-mental fits for two pixels in the map, ADD 2.08 μm and 3.58 μm.The solid line depicts the values implied by the model while the sym-bols correspond to the observed signal arranged in decreasing order.The profiles of those figures show a significant difference, which re-flects the variation in the AAD map.

Fig. 7a shows a DEC map obtained from the set d-PFG MRI exper-iments where ϕ = π. Even though the map is noisy and inferior inquality to the same map obtained by DTI, the corpus callosum(marked with arrows) is well defined. The AADmap, which employedthe fiber orientations obtained from the d-PFG experiments (Fig. 7b)look remarkably similar to the one in Fig. 6c with the same mean di-ameter of 1.5 μm.

Discussion

D-PFG size measurements are based on the angular modulation ofthe signal when both gradients are applied perpendicular to the fiberorientation. For certain specimens such as the spinal cord, the orien-tation of white-matter fibers is known approximately a priori. Whenthis is the case, the d-PFG acquisition can be performed using the sim-ple 2D (circular) sampling scheme to provide the sought after angularmodulation. Any deviation due to the small mismatch between thereal fiber orientation and the one assumed by the circular samplingscheme can be accounted for by feeding the fiber orientation informa-tion obtained through an independent (e.g., DTI) measurement intothe analysis. In a recent study (Özarslan et al., 2011), we discussedthis topic in greater detail. We observed some change in the fiber di-ameter estimates when the DTI-based fiber orientation information isincorporated even when the angular deviation was a few degrees(Özarslan et al., 2012).

The spinal cord AAD map, obtained from the d-PFG MRI experi-ments clearly shows variations in white matter microstructure thatare not visible in the corresponding DTI-derived maps. The d-PFG

Table 1Average axon diameter (AAD) and the standard deviation for the ROIs marked inFig. 6a. The AAD obtained from multiple Toluidine blue histological sections weretaken from the marked ROI. The d-PFG AADs were obtained from similar ROIs in thed-PFG map.

ROI AAD histology (μm) AAD d-PFG map (μm)

A 4.53 ± 2.0 4.5 ± 0.2B 2.67 ± 2.1 3.4 ± 0.3C 3.92 ± 1.4 3.6 ± 0.4D 4.42 ± 1.9 4.1 ± 0.2

Fig. 5. Average pore diameter map obtained from the glass capillary array using d-PFG MRI data, with δ = 3.15 ms, Δ = 75 ms, and G = 0–664 mT m!1. a) 2D and b) 3D acquisitionscheme.

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MRI AAD maps agree well with and follow the known anatomy of thespinal cordwhere the various regions of the cross section can be identi-fied (Snell, 2001). The AAD map obtained from the d-PFG MRI experi-ments also agrees very well with the corresponding AADs obtainedfrom our own histological analysis of corresponding ROIs.

For specimens that can be aligned in the magnet (such as the spinalcord) a 2Dd-PFGMRI sampling scheme is suitable. N.B. Determining theorientation of the sample is crucial for the success of the d-PFG analysisand a DTI experiment is recommended to measure fiber orientationprior to the 2D d-PFGMRI. However, for tissueswhere the fiber orienta-tion may vary from voxel to voxel, such as in the brain or in the periph-eral nervous system, a 3Dd-PFGMRI acquisition scheme should be usedwhere the gradient orientations are distributed over various shells. Thehigh degree of similarity of the pore diametermaps and values obtainedin the glass capillary array using the 2D and 3D acquisition schemes val-idate the use of the 3D spherical d-PFGMRI acquisition. We also antici-pate that a similar type of phantom will be useful in validating newin vivo methods for measuring AAD distributions within the brainusing quadruple and other multiple PFGMRImethods, such as were re-cently demonstrated in (Avram et al., 2012).

The AADmap of the rat corpus callosum follows the known anatomyof the rat brain (Kruger et al., 1995), and yields the expected distribu-tion of AADs (Barazany et al., 2009). The 3D d-PFGMRI acquisition con-tains enough single diffusion weighted images (DWIs) to obtain areasonably high-quality fiber orientation map using DTI because eachtime the angle between the successive PFG blocks is π, the middle gra-dient pulses vanish, resulting in a single PFG experimentwith twice thediffusion time. Therefore, a separate DTI experiment is no longer need-ed. The d-PFG experiments were time consuming because of low SNR(due to short T2 of the fixed tissue), which requires multiple averages,and the use of a slow (spin-echo) imaging block. Using fast imagingtechniques such as EPI for the imaging block can greatly reduce the ex-periment time.

Conclusions

D-PFG MRI is an emerging tool for revealing the underlying micro-structure of axons in the peripheral and central nervous system. Assum-ing a simple bi-compartmental model, with no a priori assumptionsabout the form of the axon diameter distribution, one can accurately

Fig. 6. a) DEC and b) FA maps of a coronal slice of fixed rat brain obtained from DTI using δ = 3 ms, Δ = 30 ms with b-values of 100 and 1600 s-mm!2 c) AAD map for the corpuscallosum obtained from d-PFG data, overlay a T2-weighted image, using δ = 3.15 ms, Δ = 30 ms, and G = 0–591.6 mT m!1. Fiber orientations were obtained from the prior DTIexperiment. d) and e) experimental data (symbols) and their estimated values (solid line) for two pixels in the map, arranged in their intensity order.

Fig. 7. a) DEC map obtained from the 3D d-PFG MRI experiment. b) AAD map obtained from d-PFG data overlay a T2 image. Fiber orientations were obtained from the d-PFGexperiment only.

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obtain an AAD map. Consequently, this method has the potential tocharacterize features or possibly changes in brain microstructure dueto geneticmanipulations (knock-in or knock outmodels), neurotrauma,degenerative diseases or disorders (such asMS or ALS), and cognitive orbehavioral disorders where a neuroanatomical substrate may besuspected or neuroanatomic sequelae occur, even if these cannot bedetected by more conventional MRI methods. We have presentedd-PFG MRI acquisition scheme appropriate for studying tissues withknown a priori axonal orientation and for making these measurementsmore robustly in the brain and other tissues where the axon orientationis not known a priori and can be assumed to change fromvoxel to voxel.

Acknowledgments

MK and EÖ were supported by funds from the CNRM and HenryJackson Foundation. EÖ was supported in part by NIH R01MH074794.PJB and FH were supported by the Intramural Research Programof the Eunice Kennedy Shriver National Institute of Child Health andHuman Development, NIH. RZF was supported by the Center for Infor-mation Technology, NIH. We are grateful to Mr. R. R. Clevenger, Mr. T.J. Hunt, Mrs. Joni Taylor, Ms. G. J. Zywicke, Mr. A. D. Zetts, Mrs. K. Keeran,Mr. S. M. Kozlov, and Mr. K. R. Jeffries, from LAMS, NHLBI, and Dr. M. D.Budde from the Department of Neurosurgery, Medical College ofWisconsin for obtaining the specimens. We would also like to thankDr. Doug Morris from the NMRF/NINDS for assistance with the instru-mentation and Dan Benjamini for fruitful discussions.

Conflict of interest

There is no conflict of interest.

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