Does Low B-value can Handle Q-ball and DTI Reconstructions?

Diffusion MRI Experiment of Ex-vivo Pigs Spinal Cord Phantom

Aleksandra Klimas

, Kamil Gorczewski

, Przemysław Pencak

, Zofia Drzazga

and Uwe Klose

Section for Experimental Methods for MR in the CNS, University of Tuebingen, Germany

Department of Medical Physics, University of Silesia, Katowice, Poland,

Radiology Department, Mielecki University Hospital of Silesian Medical University, Katowice, Poland

Keywords: Q-ball Reconstruction, Diffusion Tensor Imaging, Diffusion Phantom, Fibre Crossing.

Abstract The direction of axons in white matter can be estimated using a deterministic fibre tracking algorithms and

diffusion weighted imaging. The aim of this work was to evaluate the data, obtained from pig spines

phantom measurements with relatively low b-value, using two types of reconstructions: diffusion tensor

imaging (DTI) and q-ball approach. Pigs spines submerged in agar gel were used to prepare a phantom with

two crossing populations of fibres. The phantoms were measured in 3T MR scanned for b-value of 1000 and

2000 s/mm

for q-ball and 200-2000s/mm

for DTI reconstruction. Analysis of crossing and single fibre

population regions in the scanners showed that the median dispersions from the reference directions in case

of single fibre population were c.a. 4° and for crossing area c.a. 12° and 6.5° for b-value of 1000 s/mm

and

2000 s/mm

respectively. The q-ball approach was able to resolve crossing problem for both low b-values. It

was shown here that coherent results can be achieved even with lower b-values than proposed by the theory.

1 INTRODUCTION

The clinical applications of MR diffusion

measurement were suggested in 90s by LeBihan and

Basser when the development of echo planar

imaging (EPI) technique made MR imaging faster.

The diffusion measurement relays on MR signal

attenuation from water molecules. Those molecules

can move inside and in-between axons in the

presence of field gradient. The change in the spin

position results in phase shift in precession and

a signal loss. The obstacles, like cell membranes,

keep the phases coherent. The attenuation level is

proportional to the free path that molecules can

travel so the signal is attenuated along axons. The

anisotropic diffusion behaviour can be coupled to

the orientation of fibers what gives the possibility to

brain connectivity.

One can choose how strong images depend on

the diffusion using the diffusion-sensitizing factor,

called b-value, which can be calculated as follows:

b = (γδG)

(Δ-

) [s/mm

]

where: γ - gyromagnetic coefficient, δ - duration of

diffusion gradients, G - gradient strength, Δ - time

from the beginning of the first gradient to the

beginning of the second one.

There are several ways to evaluate the main

direction of diffusion from measured data. The most

common is diffusion tensor imaging (DTI) described

in details by Bammer (2003) and Jones in (2004),

which requires at least 7 measurements with gradient

applied in different directions. A diffusion tensor is

fitted to data to obtain only one direction of

diffusion. The degree of diffusion anisotropy,

enabling biological information about the integrity

and orientation of white matter tracts in the brain can

be determined by fractional anisotropy (FA) which

is independent of the orientation of the diffusion in

the voxel (FA = 0 – isotropic diffusion, FA = 1 –

infinite anisotropy). Some regions of brain white

matter such as the corpus callosum and the splenium

show very high FA (c.a. 0.8) while others have

considerably lower FA (Jellison et al. 2004);

(Masutani et al. 2003.). If the direction of diffusion

is known in each point of the brain it is possible to

follow those directions in order to reconstruct

pathway of connection. DTI provides just an

approximation of direction of diffusion, since the

real diffusion is more complex. The idea of using

excised animal nerve tissue to MR diffusion

measurements has already been introduced in

literature, in example by Madi et al. (2005).for the

401

Klimas A., Gorczewski K., Pencak P., Drzazga Z. and Klose U..

Does Low B-value can Handle Q-ball and DTI Reconstructions? - Diffusion MRI Experiment of Ex-vivo Pigs Spinal Cord Phantom.

DOI: 10.5220/0004329304010406

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2013), pages 401-406

ISBN: 978-989-8565-36-5

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

testing of diffusion sequences, to develop new fibre

tracking algorithms proposed by Campbell et al. in

2005, for the validation of diffusion models such as

the composite hindered and restricted model of

diffusion (CHARMED) described in details in 2004

by Y. Assaf et al. Another application of mentioned

nerve tissue was the method validation on phantom

showed by M. Perrin et al. in 2005, spherical

harmonics presented in 2007 by Descoteaux et al.

and tissue classification (Freidlin, et al., 2007).

These different MR diffusion methods were also

successfully applied in neuroimaging applications

and described by P. C. Sundgren et al. (2004).

However, some parts of the brain remained

untraceable. Disagreement between complex

diffusion situation and rather simple approximation

by one direction of diffusion leads to errors in

tracking.

Recently introduced methods of diffusion

measurements with high-angular-resolution

diffusion imaging (HARDI) allow to retrieve more

complex shape of diffusion than in case of DTI

showing more than one direction of diffusion. A

couple of reconstruction algorithms were proposed.

The first one was the q-ball evaluation by D. Tuch,

2004. Afterwards, other techniques were shown, like

a diffusion orientation transform (DOT) shown in

2006 by Ozarslan, et al., a spherical deconvolution

(Tournier et al. 2004) or PAS-MRI presented by

Parker and Alexander in 2005. In its original

proposed form, the q-ball methodology requires high

diffusion weighting (b-values > 3000 s/mm

) in

respect to those used in DTI. The spherical

deconvolution technique depends on the used b-

value (Tuch, 2004). For low b-values the angular

dependency of the signal (from layer which contains

both fibre directions) is relatively small and the

reconstruction of the fibre orientation distribution

function (ODF) is very sensitive to noise. When

using high b-values, the angular dependency is

better defined, but the noise is too big and it begins

to dominate. It was suggested that optimal value is

between 3000 and 4000 s/mm

because the strong

angular dependence is necessary to resolve the fibre

orientations without attenuating the signal down to

the noise level. However, the use of high b-value

causes the decrease of SNR. Therefore to obtain a

good quality images one has to increase averaging.

Diffusion tensor imaging calculations and q-ball

method require a quality control of the reconstructed

directions, but it is very difficult to produce an

artificial phantom, that could simulate anisotropy

levels found in a human brain. In case of q-ball

methods it is even more difficult because the

phantom should not only have high anisotropic

properties but also would simulate areas of crossing

fibre bundles. We examined the possibilities to

design a phantom using ex-vivo spinal cord from

slaughtered pigs.

The motivation for this work was the validation

of q-ball and diffusion tensor imaging reconstruction

accuracy of direction extraction using chosen

acquisition parameters. The aim was also to show

the comparison of both techniques presenting their

possibilities and limitations.

2 METHODS

2.1 Phantom Construction

Fresh samples of spinal cord from pigs were

obtained from the local slaughterhouse. The

phantom productions were performed within 6 hours

post mortem.

The pig spinal cords of 12 mm in diameter were

fixed in 2% agar-agar solution in a rectangular

container (suitable to insert into the head-coil of the

MR scanner) in order to create a cross. The crossing

spines were put in two layers – one above the other.

Only one spine went through the crossing area on

each layer, spines in second direction were just

approaching crossing region (which were cut in a

half) what is presented in detail in Figure 1.

Several phantoms were performed, in example

by A. Klimas et al. in 2008, with fibers crossing at

different angles but phantoms with 90° crossing

seem to be the best for studies due to minimization

of the influence of interaction between sampling

angle density and the fibres crossing angle (the 90°

can fulfill the Nyquist condition). The representative

model analyzed in this work showed the deviation

about 5,5° in Z and about 3,5° in X direction of the

MR system (see Figure 1).

2.2 Data Acquisition

The prepared phantom was inserted into head-coil of

3T MR system (Trio–Siemens, Erlangen, Germany).

Diffusion data were obtained in 252 directions,

equally distributed over the sphere. Gradient

directions were obtained by tessellation of an

icosahedron. A double refocusing spin echo MR

sequence was used as it was proposed in 2003 by

Reese, T. G et al. One unweighted image and 252

diffusion weighted images were acquired with

following parameters: TE=126ms, TR=2000ms, b-

values: 1000 and 2000 s/mm

BIOSIGNALS2013-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

402

Figure 1: Pigs spinal 90 crossing phantom. This way of construction was minimizing the partial volume effects and it was

assuring no fibres had to be bent during preparation. A) model of construction, B) photo of pigs spines submerged in agar

gel used in measurement.

Field of view (FoV) was 256mm with pixel size of

2mm. The slice thickness was set to 10mm in order

to cover fibres from both layers of phantom.

The diffusion measurement returns an average

signal over the full volume of the voxel. Phase-read

plane was aligned to XZ plane of the MR system.

Eight averages were taken for each image, resulting

in total acquisition time of c.a. 70min.

DTI data acquisition was made at wide range of

parameters: b-value 200–2000 s/mm

, TE 70–

110ms, TR 1300–1600ms. The orientation of

acquired slices was parallel to the direction of the

spinal cords. A high in-plane resolution of 2x2mm

was used, while a large slice thickness of 10mm was

chosen to obtain signals from both layers in the

crossing area. Twelve gradient directions were

derived from the vertices of an icosahedron as it was

shown in 2003 by T. G Reese et al.

2.3 Direction Estimation in Linear and

Crossing Region

Data were analyzed with MATLAB software

(MathWorks, MA, USA). The q-ball reconstruction

algorithm was implemented basing on the work

shown by Tuch (2004) with smoothing kernel

σ = 0.009 rad (0.5°). More details about used

algorithm and the smoothing kernel can be found in

the PhD thesis presented in 2010 by Gorczewski.

The directions of diffusion were obtained from

the orientation distribution function (ODF). The

maxima in ODF shapes were extracted using

following algorithm: starting from a random seed

point, it was advancing towards the direction of the

maximal gradient of ODF function. The procedure

was repeated for a hundred times starting from a

different seed point each time. In this way, the

algorithm was independent of starting point position.

The resulting directions were grouped into distinct

directions of diffusion present in the ODF shape.

Each maximum was treated as direction of diffusion.

The principal diffusion direction in q-ball shape was

the direction of the maximum with the highest value

of orientation distribution function.

The phantoms crossing area was in XZ plane.

The directions of diffusion were divided into two

groups: voxels with single fibre population pointing

X direction (group A) and voxels with single fibre

population pointing Z direction (group B).

An average direction from all voxels was

calculated in both groups. Dispersion of the

diffusion directions was estimated by a median

value.

The average directions of diffusion found in the

arms of the cross served as references in analysis of

reconstruction stability. The angles between

reference direction and directions of diffusion found

in each voxel belonging to the crossing area were

calculated. To estimate the angle dispersion in a

given diffusion direction a median from all angles

was calculated. The standard deviation cannot be

used since the distribution of angles is not a

Gaussian one. A median angle draws a cone

containing half of the reconstructed diffusion

directions. In this article, it is referred to as

dispersion cone angle (DCA). The more stable

direction, the narrower the cone is. Averaged

directions of diffusion were calculated in each group

and those directions were used to estimate the

dispersion. The results from the arms (single fibre

population) were compared with the corresponding

diffusion directions found in the crossing area (two

DoesLowB-valuecanHandleQ-ballandDTIReconstructions?-DiffusionMRIExperimentofEx-vivoPigsSpinalCord

Phantom

403

fibre populations).

3 RESULTS

3.1 Visualization of Diffusion in DTI

and Q-Ball

Q-ball reconstruction was able to identify regions of

higher anisotropy properly. Figure 2B and C shows

the q-ball reconstruction of the selected areas of

interest. Both low b-values visually reveal the

directional structure of the phantom. The ODF in

arms of the phantom have a peanut-shape which

represents the single fibre population as assumed.

However the directions of diffusion in each arm are

parallel.

Diffusion tensor imaging measurements reveal

high FA index of 0.7 in arm-regions proving validity

of constructed spine phantom for a clinical scanner.

DTI shapes within the voxel presented in Figure 2A

confirm that the detected orientations are coherent

with the underlying fibre directions.

3.2 Estimation of Diffusion Direction in

Single Fibre Population and

Crossing Area

A comparison between Figure 2A, B, and C

demonstrates how both methods deal with the

Figure 2: Visualization of phantom obtained by A) DTI with b-value of 800s/mm

, B) Q-ball shapes obtained with b-value

of 1000 s/mm

, C) Q-ball shapes obtained with b-value of 2000 s/mm

. D) Examples of reconstructed ODFs as a function

of smoothing kernels σ (2009 Gorczewski et al., modified).

BIOSIGNALS2013-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

404

multiple fibre populations. One can see that the main

direction of diffusion in arms in DTI reconstruction

can be clearly visible unlike in the crossing area

where obtained diffusion tensors have a plate-shape.

Q-ball technique gives better results in the crossing

area because the first diffusion direction is separated

from the second one.

In the q-ball approach the analysis of the

directions acquired with b-value 1000 s/mm

in arm-

regions shows that the median is equal to 4.0° for X

(group A) and 4.4° for Z direction (group B). In case

of b-value 2000 s/mm

both medians are equal to

3.8°. Stability of diffusion direction estimation for

double fibre population resulted in a DCA of 12.7°

in X, 10.8° in Z for 1000 s/mm

and 6.6° in X, 5.5°

in Z direction for 2000 s/mm

The influence of the reconstruction stability was

examined by calculating DCA in the crossing area

against the smoothing kernel σ from reconstruction

algorithm like in the work of D. Tuch, 2004. The

example of the blurring influence is shown in Figure

2D. Two initially distinct directions of diffusion in

q-ball shape disappear when the σ is increased. As

we can observe, the two directions are replaced by

one, averaged diffusion direction. Reasonably low

smoothing kernels should be used to maintain good

directional data quality.

4 DISCUSSION

Fibre tracking becomes an effective tool in clinical

practice as well as in research combined with

functional imaging. Recent development of methods

for multiple diffusion direction extraction prepares

even better data for connectivity exploration. New

methods of water molecules diffusion measurement

with HARDI methods provide more detailed

information about the structure of the white matter.

The tensor model for single fibre populations works

very well. The error estimation and its propagation

in relation to acquisition factors such as sampling

directions, b-value or SNR was shown earlier in

2004 by Jones D.K. The tensor approach was

successfully used in clinical routine (the sequence

duration was acceptable) but it cannot fulfill all of

the assumptions of the theoretical model. In case of

multiple fibre population the tensor model shows a

decrease of FA and two eigenvalues of similar

amplitude manifesting in a plate-shape of diffusion

tensors. In this way only a plane of crossing was

determined, but it was impossible to retrieve

information about the directions of the crossing

fibres. In our study the diffusion directions provided

by tensor model were successfully applied in single

fibre population unlike to in crossing area. The q-

ball algorithm has an assumption about high b-value,

which cannot be fulfilled in clinical due to the long

measurement time - a clinical routine always have to

consider a trade between quality of measurement

and time. The building time of the b-value is

dependent on the integral over the gradients

amplitudes. Using short gradient time implies TE

shorting, so stronger signal is acquired and less

averages is needed.

It was shown here, that even not being strict with

the assumptions of the q-ball measurement theory

gives coherent results. When acquiring patients, it is

important to reduce time of acquisition as much as it

is reasonably possible.

Moreover it should be noted that the decrease of

b-value, which has a major impact on the acquisition

time, still provides data that can be used to resolve

fibre crossing problem.

Another possibility to shorten the time of the

measurements is the reduction of diffusion direction

number. According to the Nyquist condition

sampling frequency should be at least 2n+1, where n

is the highest expected frequency in data.

Decreasing the angular resolution double the

minimal angle that can be distinguished. It is better

to speed up acquisition by other means, than by

losing the angular resolution. That is the reason why

the reduction of the diffusion directions is unwanted.

However, recently the Nyquist theorem has been

improved as was shown in 2011 by McEwen and

Wiaux an successfully applied in the same year by

A. Daducci et al.

Half of the diffusion directions felt into 5 degree

wide cone for a single fibre bundle case. The fibre

crossing area was successfully resolved. Two pairs

of maxima were present in all voxels.

This work deals with the reconstruction of data

from phantom measurements whereas a comparison

between diffusion tensor imaging and q-ball results

obtained from in-vivo measurements can be found in

the work shown by Gorczewski et al. in 2009.

5 CONCLUSIONS

To conclude, we show that even if the condition of

high b-value is not met q-ball reconstruction can

successfully retrieve proper directions of diffusion in

single as well as in multi fibre population cases. The

stability of this evaluation is still in ranges of

degrees. The data measured in lower b-values ranges

can be properly processed by fibre tracking

DoesLowB-valuecanHandleQ-ballandDTIReconstructions?-DiffusionMRIExperimentofEx-vivoPigsSpinalCord

Phantom

405

algorithms.

REFERENCES

Le Bihan D., Turner R., Douek P., Patronas N. (1992).

Diffusion MR imaging: clinical applications.

American Journal of Roentgenology,159(3), 591-599.

Basser P. J., Mattiello J., LeBihan D. (1994). Estimation

of the effective self-diffusion tensor from the NMR

spin echo. Journal of Magnetic Resonance - Series B,

103(3), 247-254.

Bammer R. (2003). Basic principles of diffusion-weighted

imaging. European Journal of Radiology, 45(3), 169-

184.

Jones D.K. (2004). The Effect of Gradient Sampling

Schemes on Measures Derived From Diffusion Tensor

MRI: A Monte Carlo Study. Magnetic Resonance in

Medicine. 51(4), 807-815.

Jellison B. J., Field A. S., Medow J., Lazar M., M. Shariar

Salamat and Alexander A. L. (2004). Diffusion Tensor

Imaging of Cerebral White Matter: A Pictorial Review

of Physics, Fiber Tract Anatomy, and Tumor Imaging

Patterns. American Journal of Neuroradiology. 25,

356–369.

Masutani Y., Aoki S., Abe O., Hayashi N., Otomo K.

(2003). MR diffusion tensor imaging: recent advance

and new techniques for diffusion tensor visualization.

European Journal of Radiology, 46, 53-/66.

Madi, S., Hasan, K. M., Narayana, P. A. (2005). Diffusion

tensor imaging of in vivo and excised rat spinal cord at

7 T with an icosahedral encoding scheme. Magnetic

Resonance in Medicine, 53, 118-125.

Campbell, J. S., Siddiqi, K., Rymar, V. (2005). Flow-

based fiber tracking with diffusion tensor and q-ball

data: validation and comparison to principal diffusion

direction techniques. Neuroimage; 27(4) 725-736.

Assaf, Y., Freidlin, R. Z., Rohde, G. K., Basser, P. J.

(2004). New Modeling and Experimental Framework

to Characterize Hindered and Restricted Water

Diffusion in Brain White Matter. Magnetic Resonance

in Medicine, 52, 965–978.

Perrin, M., Poupon, C., Rieul, B., Leroux, P. (2005).

Validation of q-ball imaging with a diffusion fibre-

crossing phantom on a clinical scanner. Philosophical

Transactions of the Royal Society B: Biological

Sciences, 360, 881-891.

Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.

(2007). Regularized, Fast, and Robust Analytical Q-

Ball Imaging. Magnetic Resonance in Medicine, 58,

497–510.

Freidlin, R. Z., Ozarslan, E., Komlosh, M. E., Chang, L.

(2007). Parsimonious Model Selection for DTI Tissue

Segmentation and Classification: Study on Simulated

and Experimental Data. IEEE Transactions on

Medical Imaging,26(11), 1576-1584.

Sundgren, P. C., Dong, Q., Gómez-Hassan, D., Mukherji

(2004). Diffusion tensor imaging of the brain: review

of clinical applications. Neuroradiology,

46, 339-350.

Tuch D. S. (2004). Q-ball imaging. Magnetic Resonance

in Medicine, 52( 6), 1358-1372.

Ozarslan, E., Shepherd, T. M., Vemuri, B. C., Blackband,

S. J. (2006). Resolution of complex tissue

microarchitecture using the diffusion orientation

transform (DOT). Neuroimage, 31(3), 1086-1103.

Tournier, J. D., Calamante, F., Gadian, D. G., Connelly,

A. (2004). Direct estimation of the fiber orientation

density function from diffusion-weighted MRI data

using spherical deconvolution. Neuroimage, 23( 3),

1176-1185.

Parker, G. J., Alexander, D. C. (2005). Probabilistic

anatomical connectivity derived from the microscopic

persistent angular structure of cerebral tissue.

Philosophical Transactions of the Royal Society B:

Biological Sciences, 360, 893-902.

Klimas, A., Gorczewski, K., Klose, U., Drzazga, Z.

(2008). Preparation and validation of an easy-to-make

organic DTI phantom. 41st Polish Seminar on Nuclear

Magnetic Resonance and Its Applications.

Reese, T. G., Heid, O., Weisskoff, R. M., Wedeen, V. J.

(2003). Reduction of eddy-current-induced distortion

in diffusion MRI using a twice-refocused spin echo.

Magnetic Resonance in Medicine, 49(1), 177-182.

Gorczewski K. (2010). Multi-directional diffusion

weighted imaging: Implementation, verification and

clinical application, PhD thesis.

McEwen J. D., Wiaux Y. (2011). A novel sampling

theorem on the sphere. IEEE Transactions on Signal

Processing, 59, 5876–5887.

Daducci A., McEwen J., Van De Ville D., Thiran J. P.,

Wiaux Y. (2011). Harmonic analysis of spherical

sampling in diffusion MRI. Proceedings of the

International Society for Magnetic Resonance in

Medicine, 3929.

Gorczewski, K., Mang, S, Klose, U. (2009).

Reproducibility and consistency of evaluation

techniques for HARDI data. Magnetic Resonance

Materials in Physics Biology and Medicine, 22(1), 63-

70.

BIOSIGNALS2013-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

406