Magnetic Resonance Im

DTI of trabecular bone marrow

Cristina Rossia,b,d, Silvia Capuanic,d, Fabrizio Fasanod,e, Marcella Alesiania,b,d,

Bruno Maravigliaa,b,d,TaIstituto Nazionale Fisica della Materia, Centro di Ricerca e Sviluppo SOFT (INFM CRS-SOFT) c/o Universita’ di Roma bLa SapienzaQ, I-00185 Roma, Italy

bPhysics Department, University bLa Sapienza,Q 00185 Rome, ItalycINFM CRS SOFT

dMuseo Storico della Fisica e Centro Studi e Ricerche bEnrico Fermi Q, Compendio Viminale I-00184 Roma, ItalyeLaboratory of Functional Neuroimaging, Fondazione Santa Lucia, IRCCS, 00179 Rome, Italy

Abstract

The development of NMR diffusion imaging and diffusion tensor imaging (DTI) has offered the possibility of studying the porous

structures beyond anatomical imaging. In fact, random molecular motions, within tissue components, probe tissue microstructures.

Up to now, the DTI method was mainly used to investigate cerebral morphology and study white matter diseases. In this study, it has

been applied to trabecular bone marrow analysis to obtain structural information on spongy bone tissue. Our first results show that DTI

could represent an important tool in studying the microstructural architecture of the trabecular bone as well as the microarchitecture of

porous media.

D 2005 Elsevier Inc. All rights reserved.

Keywords: DWI; DTI; Trabecular bone; Anisotropic diffusion; Restricted diffusion

1. Introduction

Diffusion is the process by which matter moves across a

system as a result of random molecular motions. As Einstein

explained in a 1905 article, in a dilute solution solvent,

molecules hit solute particles continuously and from all

sides. This results in a random motion known as the

brownian motion [1]. The self-diffusion coefficient D [1]

provides a complete description of diffusion in homoge-

neous and isotropic systems. When molecular diffusion

occurs in heterogeneous and anisotropic media, the mea-

sured diffusion coefficient value depends on observation

direction and measurement duration.

By means of suitable NMR pulse sequences such as the

pulsed gradient spin echo (PGSE) [2], it is possible to

measure an apparent diffusion coefficient value. This

coefficient is not a true measure of the intrinsic diffusion

because it depends on the interactions of the diffusing

molecules with tissue microstructures [3]. Furthermore,

0730-725X/$ – see front matter D 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.mri.2004.11.018

T Corresponding author. Physics Department, University bLa Sapi-

enza,Q Piazzale Aldo Moro 2, 00185 Rome, Italy. Tel.: +39 0649913473;

fax: +39 0649913484.

E-mail address: bruno.maraviglia@roma1.infn.it (B. Maraviglia).

because diffusion is a three-dimensional process, a diffusion

tensor,D [1], rather than a scalar, D, is needed to describe the

mobility of brownian particles along the different directions.

The estimate of diffusion tensor components from MR

images enables us to create parametric images where pixel

intensity is proportional either to mean diffusivity (MD) or

to the degree of anisotropy of the media. The set of all MRI

techniques that allow to determine the elements of such a

tensor and display the information it contains in each voxel

is known as diffusion tensor imaging (DTI) [4].

Since the early 1990s, diffusion-weighted imaging

(DWI) has assumed an important role both in clinical

routine and in the research environment [4–7] because of

its high sensitivity to changes in the displacement

characteristics of water molecules in human tissues.

Because of this property, DWI represents a powerful tool

in the field of brain studies and brain disease diagnosis. As

an example, a promising application is due to the ability of

DWI to detect an early cerebral infarct with respect to other

conventional MR imaging techniques. Furthermore, in

cerebral tissues, white matter containing fibrous compo-

nents, where diffusion of water molecules is much more

restricted across than along the fibers results in anisotropic

diffusion (i.e., the diffusion coefficient is dependent on the

aging 23 (2005) 245–248

rf

diff

slice

phase

read

90° 90° 90°

TE/2 TM TE/2

t

∆δ

Fig. 1. Schematic rf pulse and gradient sequence for diffusion-weighted

stimulated echo imaging using three 908 rf pulses in conjunction with a

magnetic field gradient for slice selection (slice). The stimulated echo

signal, which occurs at TE+TM, is acquired in the presence of a frequency-

encoding gradient (read) and the whole sequence is repeated with different

phase-encoding gradients (phase). Diffusion weighting is obtained by a pair

of diffusion gradients (diff). D is the separation of the diffusion gradients of

duration d.

C. Rossi et al. / Magnetic Resonance Imaging 23 (2005) 245–248246

direction of the applied field gradient [3]), DTI [6] has also

made imaging the fiber tracts in the white matter of the

brain possible.

Up to now, DTI was mainly used to investigate cerebral

morphology [3]. In fact, outside the brain, the short T2 values

of the other body tissues force the use of shorter TE than the

ones used for brain tissue in order to minimize T2 weighting.

This involves the use of short diffusion gradient pulses

and requires hardware modification (such as gradient

strength and gradient shape) and ad hoc pulse sequence

[e.g., the pulsed gradient stimulated echo (PGSTE) se-

quence is better than the PGSE one] and parameters (such as

the diffusion time D and or the gradient pulse duration d)especially in media characterized by an high degree of

anisotropy and restricted diffusion such as porous media.

In this study, the DTI method was used for the first time to

obtain anisotropic information on trabecular bone tissue.

Parametric images representing the MD and the degree of

anisotropy [fractional anisotropy (FA)] were obtained sam-

pling an excised bovine spongy bone at 7 T. Our first results

show the great potentiality of DTI methods to study bone

tissue microstructure and tissue architecture arrangement.

Fig. 2. (A) MD map of a portion of celery. This map underlines the

differences in molecular diffusion regimes inside the sample. The bbulkQ ofthe vegetable (parenchyma) appears isointense, as we can expect for an

isotropic medium. On the other hand, the pixels that correspond to the

fibers appear less intense as a result of restricted diffusion regime. The MD

provides, in fact, a description of the overall diffusion in different sample

regions. The MD value is reported in mm2/s. (B) The FA map confirms the

goodness of the experimental protocol. In fact, the pixels that correspond to

the fibers are characterized by a great intensity, as we expect from an axial

geometry, while the map is darker in the parenchyma region, as we expect

from isotropic diffusion.

2. Methods and materials

The diffusion tensor D [8,9] is a symmetric tensor and its

elements are all positive, so it is possible to diagonalize it to

obtain the eigenvalues D1, D2 and D3 and the corresponding

eigenvectors k1, k2 and k3. The local frame of reference is

an orthogonal coordinate system with axes that are parallel

to the tensor eigenvectors. In such frame of reference, the

anisotropy can be visualized by means of the diffusion

ellipsoid, where D1, D2 and D3 are the principal diffusiv-

ities. The diffusion ellipsoid is a three-dimensional repre-

sentation of the diffusion distance covered in space by

molecules in a given diffusion time.

It is possible to define a set of scalar quantities that

enable visualization of the diffusion properties of the tissue.

Some of these quantities are invariant with respect to the

rotation of the coordinate system and, thus, are independent

from the laboratory frame in which the tensor components

are measured [9].

In this study, we considered the MD [9,10]:

MD ¼ D1þD2þD3

3ð1Þ

which corresponds to the average ellipsoid’s size and is

proportional to the tensor’s trace. It is a scalar invariant that

Fig. 3. T2-weighted image of an axial slice of a portion of bovine epiphysis

extracted by a bovine femur covered by a layer of fat. Signal from fat is

more intense due to its higher T2 value compared with spin–spin relaxation

time of marrow within the bony porous structure.

ig. 4. MD and FA maps of an axial slice of a portion of epiphysis covered

y a layer of fat. (A) The signal intensity of the MD map varies according to

e MD variation inside the fat and the spongy bone. The MD value is

ported in mm2/s. (B) The FA map confirms the highly isotropic molecular

iffusion inside the fat, where the pixels appear less intense. In the FA map,

e intensity of the pixels from the spongy bone is characterized by a great

ariability that suggests a variation in pore size and trabecular bone

rientation. As suggested by the comparison with the T2-weighted image

ported in Fig. 3, such structure-related features are only observable from

arametric maps obtained with DTI techniques.

C. Rossi et al. / Magnetic Resonance Imaging 23 (2005) 245–248 247

allows us to monitor the overall mean-squared displacement

of molecules, which is mainly determined by the presence

and distribution of obstacles to diffusion.

The FA [9,10]:

FA ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3½ðD1�MDÞ2þðD2�MDÞ2þðD3�MDÞ2�

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 D2

1þD22þD2

3

��q ð2Þ

measures the degree of anisotropy and is related to the

presence of oriented structures. Geometrically, it is propor-

tional to the ellipsoid’s eccentricity.

In our study, the PGSTE sequence [2] was used to obtain

a series of MR images from bovine spongy bone marrow.

The intensity of the gradient was varied for each of the

seven directions of the diffusion-encoding gradients to

collect a set of diffusion-weighted images along at least

six noncollinear gradient directions [11,12]. One unweight-

ed image (i.e., an image acquired without a diffusion-

encoding gradient) was also acquired to estimate the

components of D in each voxel and obtain the parametric

MD and FA images by means of a homemade software. All

images were obtained on the same slices (5-mm thickness).

The PGSTE sequence is especially suited for spin

systems characterized by T2bT1 [3]. It is therefore useful

to investigate restricted diffusion at different diffusion times.

In fact, in the PGSTE sequence, the diffusion time is limited

by the value of the mixing time, TM, during which the

longitudinal component of the magnetization decays with

the spin-lattice relaxation time, T1. In this work, the choice

of using a PGSTE sequence is related to the short T2 that

characterizes the sample. In fact, for fat’s hydrogen nuclei in

bovine bone sample, we obtain a T2 equal to about 31 ms

and a T1 equal to about 390 ms.

All the measurements were implemented and performed

on a 7 T Bruker Biospec horizontal magnet, equipped with

gradient unit with a maximum intensity of 280 mT/m, 300 Asrise time. An Avance digital spectrometer, with XWINNMR

and ParaVision 2.1 software version, was employed for data

acquisition and analysis. The experimental results were

obtained by using a microimaging probe (12 mm internal

diameter) for RF transmission and signal detection.

The experimental procedure was first tested on a fresh ce-

lery sample and then applied on a portion of extracted bovine

epiphysis excised from distal femur, covered by a layer of fat.

The trabecular bone consists of a three-dimensional

network where bone marrow is dispersed in the interstitial

F

b

th

re

d

th

v

o

re

p

C. Rossi et al. / Magnetic Resonance Imaging 23 (2005) 245–248248

spaces. The heterogeneous structure of spongy bone

exhibits simultaneously anatomical site dependence and

directional anisotropy of mechanical properties and archi-

tecture. In such a structure, marrow is trapped inside pores

of 50 Am–1 mm diameter, while the separation between

pores is about 200 Am: this geometry causes an aniso-

tropic molecule diffusion of the bone marrow in contrast

with the homogeneous structure represented by the fat

layer covering.

3. Results

The experimental procedure and our homemade software

that allowed reconstructing the MD and the FA maps were

tested and optimized on a standard phantom made of a fresh

celery portion. The conventional PGSTE sequence provided

with the appropriate slice, phase and read encoding gradients

for the imaging (Fig. 1) (d=4 ms, D=43 ms, TE=26.1 ms,

TR=6 s) was used, with the b values ranging from 0 to about

1550 s/mm2. The MD map in Fig. 2 confirms the isotropy of

molecular diffusion inside the vegetable inner part (paren-

chyma). On the other hand, the pixels corresponding to the

fibers appear less intense in brightness as a consequence of

the restricted molecular diffusion along the fiber axis. A

strong diffusion anisotropy inside the fibers (FA about 1)

and a large diffusion isotropy in the bulk of the sample (FA

about 0) were found in the FA map, in good agreement with

the expected trend.

The DWI sequence was then applied to obtain a series of

MR images from bovine bone samples. The sample was

extracted from the most extreme region of the spongy bone,

the epiphysis. The sample is constituted by a portion of

trabecular bone, filled with bone marrow and covered by a

layer of fat. So, both porous anisotropic system (trabecular

bone) and homogeneous isotropic system (fat) are present in

the sample. The T2-weighted image in Fig. 3 shows a great

difference between fat and bone marrow signals but does

not show any difference inside the trabecular structure.

To obtain the MD and FA maps shown in Fig. 4, d=4 ms

and D=220 ms were chosen for each gradient direction (x,

y, z, xy, yz, xz, xyz). Experimental b values ranged from 40

to 12000 s/mm2 (TR=5 s, TE=28 ms). The MD map in

Fig. 4A and the FA map in Fig. 4B show a great variability

in the intensity inside the trabecular structure. These results

can be explained by supposing a variation in pore size,

bigger near the fat and smaller at the bottom of the sample.

The FA image shows a typical artefact probably arising

from uncorrected eddy currents-induced distortions [13]. In

fact, the parametric image of the sample is characterized by

a hem of high anisotropy.

The absence of such an artefact in the celery FA map

may confirm our guess; in fact, we expect that the smaller

the diffusion gradient strength is, the better the eddy

currents compensation is and the smaller the artefact is.

The MD and FA images show different contrasts with

respect to conventional T2-weighted image, particularly in

the trabecular bone region. In particular, in epiphysis regions,

because of different contrasts in the FA image, different

microstructural rearrangement orientations are present. On

the other hand, the isotropy of diffusion in the fat region of

the sample is underlined by FA values around 0.

4. Conclusion

In this study, the DTI contrast between differently

structured areas of bovine spongy bone was investigated.

Because of bone marrow in the trabecular bone T2bT1,

PGSTE-based imaging sequences were used to obtain MD

and FA parametric images. Our preliminary results show

that MD and FA maps are more sensitive than conventional

NMR imaging techniques to bone trabecular network

microstructure. However, it is important to point out that,

in our experiments, the selected diffusion range of about

10 Am is less wide than the average dimension of the pores

in the trabecular bone (equal to 50–200 Am).

DTI proved to be a potential tool in studying bone

architecture and, in general, in assessing the geometrical

organization of porous systems. In fact, the MD map

underlines the difference in restricted diffusion (smaller or

bigger pores) while the FA map emphasizes the anisotropy

in a porous network.

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