Journal of Biomechanics 44 (2011) 1909–1913

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Journal of Biomechanics

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Viscoelastic properties of human cerebellum using magneticresonance elastography

John Zhang a,b, Michael A. Green a, Ralph Sinkus c, Lynne E. Bilston a,d,n

a Neuroscience Research Australia, Barker Street, Randwick NSW 2031, Australiab Faculty of Medicine University of New South Wales, Kensington, NSW 2052, Australiac INSERM U773, CRB3, Centre de Recherches Biomedicales Bichat-Beaujon, Paris, Franced Prince of Wales Clinical School, University of New South Wales, Kensington NSW 2052, Australia

a r t i c l e i n f o

Article history:

Accepted 19 April 2011Background: The cerebellum has never been mechanically characterised, despite its physiological

importance in the control of motion and the clinical prevalence of cerebellar pathologies. The aim of

Keywords:

Brain viscoelasticity

Shear modulus

Magnetic resonance imaging

In vivo measurements

90/$ - see front matter & 2011 Elsevier Ltd. A

016/j.jbiomech.2011.04.034

esponding author at: Neuroscience Research A

31, Australia.

ail address: L.Bilston@neura.edu.au (L.E. Bilsto

a b s t r a c t

this study was to measure the linear viscoelastic properties of the cerebellum in human volunteers

using Magnetic Resonance Elastography (MRE).

Methods: Coronal plane brain 3D MRE data was performed on eight healthy adult volunteers, at 80 Hz,

to compare the properties of cerebral and cerebellar tissues. The linear viscoelastic storage (G0) and loss

moduli (G00) were estimated from the MRE wave images by solving the wave equation for propagation

through an isotropic linear viscoelastic solid. Contributions of the compressional wave were removed

via application of the curl-operator.

Results: The storage modulus for the cerebellum was found to be significantly lower than that for the

cerebrum, for both white and grey matter. Cerebrum: white matter (mean7SD) G0 ¼2.4170.23 kPa,

grey matter G0 ¼2.3470.22 kPa; cerebellum: white matter, G0 ¼1.8570.18 kPa, grey matter G0 ¼1.7770.24 kPa; cerebrum vs cerebellum, po0.001. For the viscous behaviour, there were differences in

between regions and also by tissue type, with the white matter being more viscous than grey matter

and the cerebrum more viscous than the cerebellum. Cerebrum: white matter G00 ¼1.2170.21 kPa,

grey matter G00 ¼1.1170.03 kPa; cerebellum: white matter G00 ¼1.170.23 kPa, grey matter

G00 ¼0.9470.17 kPa.

Discussion: These data represent the first available data on the viscoelastic properties of cerebellum,

which suggest that the cerebellum is less physically stiff than the cerebrum, possibly leading to a

different response to mechanical loading. These data will be useful for modelling of the cerebellum for a

range of purposes.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The viscoelastic properties of brain tissue play a role in a varietyof neurological disorders and traumatic brain injury. It has beenpostulated that certain conditions, such as normal pressure hydro-cephalus, are influenced by a change in the mechanical properties ofthe brain tissue (Pang and Altschuler, 1994; Dutta-Roy et al., 2008),and those changes in the viscoelasticity of the brain may be amarker for neurodegenerative conditions such as Alzheimer’s dis-ease and multiple sclerosis (Kruse et al., 2008; Wuerfel et al., 2010).In addition, these parameters are vital for computational simulationssuch as Finite Element Analysis (FEA) of brain conditions, traumatic

ll rights reserved.

ustralia, Barker St, Randwick,

n).

brain injury, and surgical planning. To date, there have been a greatnumber of rheological studies of the viscoelastic properties of thebrain, generating data that vary by a considerable margin, reflectingthe heterogeneity in methods employed by different researchgroups. Researchers have performed ex-vivo studies of cadavericand animal brain tissues (e.g. (Bilston et al., 1997; Donnelly andMedige, 1997; Bilston et al., 2001; Miller and Chinzei, 2002; Hrapkoet al., 2006)), measured the poroelastic properties (e.g. (Franceschiniet al., 2006; Cheng and Bilston, 2007)), and developed manydifferent types of constitutive models (e.g. (Bilston et al., 2001;Darvish and Crandall, 2001; Brands et al., 2004; Hrapko et al.,2006)). Brain tissue mechanical properties have been recentlyreviewed in detail elsewhere (Cheng et al., 2008). While the earlieststudies only measured elastic properties of the brain (e.g. elasticshear modulus; McCracken et al., 2005), in recent years, the adventof Magnetic Resonance Elastography (MRE) has made possible thenon-invasive measurement of brain viscoelasticity in living human

J. Zhang et al. / Journal of Biomechanics 44 (2011) 1909–19131910

subjects. This has led to several studies targeted at the viscoelasticproperties of the brain (Green et al., 2008; Sack et al., 2008), whichprovide estimates of both the elastic (G0) and viscous (G00) compo-nents of the shear modulus. Results from MRE studies demonstratea greater level of congruence, but some discrepancies in measuredshear moduli persist due to differences in the methodologyemployed, particularly in the reconstruction algorithms used toextract the material properties from the MRE images.

All previous MRE studies of the brain have exclusivelyfocussed on the cerebrum, while no rheological measurementsof the cerebellum (using any method) have been made. Thecerebellum plays an important role in the control of motorfunctions; recent evidence suggests that it may also be involvedin higher cognitive functions (Cantelmi et al., 2008; Puget et al.,2009). The cerebellum is sometimes affected in traumatic braininjury even when the initial impact is directed elsewhere in thebrain, and mechanical forces caused by rapid deceleration arethought to be the cause of some of the pathological changes seenin the cerebellum (Gennarelli et al., 1982; Potts et al., 2009).Similarly, the biomechanics of the cerebellum is important inconditions where infratentorial herniation is a possibility. As forthe cerebral hemispheres, it is possible that disease processes inthe cerebellum might result in detectable mechanical changes. Itis therefore desirable to investigate the viscoelastic properties ofthe cerebellum, in order to understand better how cerebellartissues may respond to injuries and diseases. Current models ofbrain trauma typically assume that the cerebellum has similarmechanical properties to the remainder of the brain, in theabsence of cerebellum mechanical properties data. The presentstudy aims to characterize the viscoelastic properties of the livinghuman cerebellum in young healthy subjects, and to comparethese data to those from the cerebrum of the same subjects. Wehypothesised that the cerebellum would be softer than thecerebrum, based on the fine microstructure of the cerebellumtissue.

2. Methods

Eight healthy adult subjects (five males and three females, aged 22–43 years)

with no history of neurological or psychiatric disorders volunteered for this

study. Approval from the University of NSW Human Research Ethics Committee

was obtained prior to data collection, and all subjects gave written informed

consent.

The subjects were fitted into a custom made oscillatory transducer, which

produced a mechanical wave in the subjects’ brains through a mouthpiece. Details

of these methods have been described previously (Green et al., 2008). The transducer

was driven by a pulse generator triggered by the MRI spectrometer, in order to allow

the synchronisation of the MRI pulse sequence with the mechanical wave. Imaging

was conducted in the coronal plane, with the central slice located in the mid-region of

the cerebellum. A Philips 3T scanner (Achieva 3TX. Philips Medical Systems, Best, The

Fig. 1. Representative displacement images from typical subject in mm: (a) displacemen

The wave amplitude decreases towards the centre of the brain as waves propagate inw

Netherlands) was used. Imaging parameters were matrix 64�64, TE/TR¼50/700 ms,

seven slices, eight time dynamics, FOV¼192�192, 3 mm slice thickness, and

vibration frequency¼80 Hz. A matching T2 weighted anatomical image set

(256�256) was also collected for ROI selection.

The shear storage (G0) and loss moduli (G00), which represent the elastic and

viscous components of the shear modulus, respectively, were then reconstructed

from the 3D displacement field by solving the wave equation for propagation

through an isotropic linear viscoelastic solid, using the curl operator to remove the

contribution of the longitudinal waves. Full explanation of the theory behind the

reconstruction and details of its implementation are given in Sinkus et al. (2005)

and Green et al. (2008). The T2 anatomical images were used to manually select

regions of interest (ROIs) consisting of the cerebellum or the parenchyma of the

cerebral hemispheres, excluding the ventricles (see Fig. 2). ROIs were then copied

geometrically to maps of G0 and G00 , and mean viscoelastic properties for each

subject were calculated by taking the average of pixels contained within the ROIs.

Averages and standard deviations across all subjects were then calculated from

the individual subject data.

Statistical comparisons were performed using the generalised linear model

(GLM) method, with separate analyses for G0 and G00 . Comparisons were made for

the brain region (cerebrum vs cerebellum) and grey and white matter. Potential

interactions between region and tissue type were also tested. Significance was set

at a¼0.05.

3. Results

A representative displacement field is shown in Fig. 1, demon-strating good wave penetration into the deep portions of thecerebral hemispheres and the cerebellum despite the inevitablereduction in amplitude between the outer edges of the cerebralhemispheres to the deep white matter from attenuation due tothe viscoelasticity of brain tissue. Viscosity, in the context of wavepropagation, has this effect of reducing wave amplitude as thewave propagates. This can be seen clearly in Figs. 1 and 2(c).Wave amplitude in the cerebellum was similar to the cerebralhemispheres. Representative viscoelastic data from the samesubject are shown in Fig. 3, where one can differentiate betweenregions of high and low viscoelasticity, with low elasticity in theregion of the ventricles as expected from a liquid. A summary ofthe storage and loss moduli and results of the statistical analysisare shown in Tables 1 and 2, respectively.

For the storage modulus, the cerebellum was significantlysofter than the cerebrum (GLM, po0.001), but there were nosignificant differences between white and grey matter in eitherlocation. For the loss modulus (i.e. viscous properties), there weresignificant differences between the cerebrum and the cerebellum(p¼0.037) and also between white and grey matter (p¼0.04),but there was no significant interaction between region and whiteor grey matter (p40.5). In both regions, the white matterappeared to have a slightly higher loss modulus than the greymatter but this was not statistically significant. The means andstandard deviations for each tissue type and region are plotted inFig. 3.

t in X direction, (b) displacement in Y direction, and (c) displacement in Z direction.

ards, but waves are clearly visible throughout the brain and cerebellum.

Table 1Means and standard deviations for the storage and loss moduli by region and

tissue type.

Region Tissue type G0(kPa) G00(kPa)

Cerebellum Grey matter 1.7770.24 0.9470.17

White matter 1.8570.18 1.1070.23

Cerebrum Grey matter 2.3470.22 1.1170.03

White matter 2.4170.23 1.2170.21

Table 2Present data compared with previously published in vivo MRE data (mean7SD);

differences in the absolute values of the Shear Modulus reported could be due to

differences in experimental methodology and reconstruction algorithms.

Frequency (Hz) G0 (kPa) G00 (kPa)

Grey matter

Human—present study 80 2.3470.22 1.1170.03

Human—(Green et al., 2008) 90 3.0170.10 2.5070.20

Human—(Kruse et al., 2008) 100 5.2270.23*

Human—(McCracken et al., 2005) 80 5.3071.30*

White matter

Human—present study 80 2.4170.23 1.2170.21

Human—(Green et al., 2008) 90 2.7070.1 2.5070.20

Human—(Kruse et al., 2008) 100 13.670.66*

Human—(McCracken et al., 2005) 80 10.771.4*

WhiteþGrey matter

Human—(Hamhaber et al., 2007) 83.33 3.5071.33

Human—(Sack et al., 2009) 62.5 2.0170.23 0.8070.13

Human—(Klatt et al., 2007) 62.5 0.84–2.28 0.57–2.96

n These data were obtained using an elastic model, and this value is the elastic

shear modulus, G.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

CerebellumWhite

CerebellumGrey

CerebrumWhite

CerebrumGrey

Region

She

ar M

odul

i (kP

a)

G'G"

Fig. 3. Mean and standard deviation of G0 and G00 for the white and grey matter of

the cerebellum and cerebrum (N¼eight human subjects). Cerebellum is softer

than the cerebrum (G0 , po0.001, GLM). White matter is more viscous than grey

matter (G00 ,GLM, p¼0.04), and the cerebrum is more viscous than the cerebellum

(p¼0.037).

Fig. 2. Representative viscoelastic data: (a) T2 weighted anatomical image, (b) the Storage Modulus (G0 , in kPa), and (c) the Loss Modulus (G00 ,in kPa). Spatial averages were

generated for each ROI (examples shown in (a)) defined using T2 weighted images as shown (cyan¼grey matter, red¼white matter).

J. Zhang et al. / Journal of Biomechanics 44 (2011) 1909–1913 1911

4. Discussion

These results represent the first available dataset on theviscoelastic properties of the cerebellum. They suggest that thecerebellum is softer than the cerebral hemispheres, but that thereis no difference in viscosity between the two brain regions.

The moduli for the cerebrum are comparable to the publisheddata from the literature. Green et al. (2008) found the G0 and G00 ofcerebral grey matter to be 3.1 and 2.5 kPa, respectively, and the G0

and G00 of cerebral white matter to be 2.7 and 2.5 kPa, using a

similar reconstruction technique at an oscillatory frequency of90 Hz, which is slightly higher than that used in the current study.Higher frequency would be expected to increase the shearmodulus estimates slightly due to the frequency dependence ofbrain mechanical properties (Cheng et al., 2008). Other MREstudies of brain tissue include McCracken et al. (2005), whodetermined the elastic shear moduli of grey and white matter tobe 5.3 and 10.7 kPa, respectively, at 80 Hz; and Kruse et al. (2008),who determined the elastic shear moduli of grey and whitematter to be 5.2 and 13.6 kPa, respectively, at 100 Hz. SomeMRE studies have not distinguished between grey and whitematter; these include Sack et al. (2009) who found the G0 and G00

of brain tissue to be 2.01 and 0.8 kPa, respectively, at 62.5 Hz; andKlatt et al. (2007) who used a number of different viscoelasticmodels to calculate the G0 and G00 of brain tissue to be between0.84 and 2.28, and 0.57 and 2.96 kPa, respectively, at 62.5 Hz.Lastly, Hamhaber et al. (2007) found G0 ¼3.5 kPa at 83 Hz. Presentdata is compared to these results in Table 2. There is no priorpublished data on the viscoelastic properties of cerebellum. Whilethe cerebrum data are at the lower end of the published range andconsistent with the data from the Berlin group (Klatt et al. 2007;Hamhaber et al. 2007) there are differences in reconstructiontechnique that might account for the higher values obtained bythe Mayo Clinic group (McCracken et al. 2005; Kruse et al. 2008).The McCracken et al. (2005) and Kruse et al. (2008) studies use an

J. Zhang et al. / Journal of Biomechanics 44 (2011) 1909–19131912

analytical technique that tends to overestimate the elastic shearmodulus in regions of low signal-to-noise ratio, such as thedeeper brain structures. This can be seen in their data (seeFigure 4 in (Kruse et al., 2008)). Also that technique does notestimate the viscoelastic properties, as the tissue is assumed to bepurely elastic without any loss component.

The finding that the cerebellum is slightly (�23–24%) softerthan the cerebrum is consistent with our initial hypothesis. Onepossible explanation for this lies in the delicate, branchingultrastructure of cerebellum, including the molecular layer andgranular cell layers. This can be readily observed in histology ofthe cerebellum (Young and Wheater, 2006). There are alsoproportionally many fewer glial cells in the cerebellum than thecerebral cortex, and thus the cells may be less tightly boundtogether (Azevedo et al., 2009) and all of these factors mayinfluence the mechanical properties, although the details of whythis might be the case are not known. The apparent differences inviscous properties do not have an obvious explanation, andfurther studies are needed to confirm whether this is a realdifference or a chance finding.

There are several limitations of the study to keep in mindwhen considering these results. Firstly, due to the fine structure ofthe cerebellum, it was not possible to perfectly separate whiteand grey matter in much of this region without partial volumeeffects, due to the voxel size (3 mm) required for good signalquality. These effects were minimised as much as possible bycareful ROI selection. Moreover, due to the very fine structure ofthe sulci of the cerebellum, it is not possible to be completelycertain that there is not a small amount of CSF in the cerebellumregions of interest for grey matter. This is unlikely to account forthe differences in observed mechanical properties as this affectedonly the grey matter, and similar differences were seen in thedeeper white matter where this is unlikely to be a significanteffect. This is also true for the cerebral hemispheres, but to alesser extent, since the sulci are larger and thus easier to excludefrom the regions of interest. Lastly, the method employed in thisstudy assumes the brain to be isotropic in nature, despite ofevidence that white matter at least should be treated as aniso-tropic (Prange and Margulies, 2002). Methods of analysing aniso-tropic tissues in MRE are still under development (Green et al.,2009).

Despite these limitations, these results represent the firstavailable data on the viscoelastic properties of the cerebellum.They suggest that the cerebellum is less physically stiff than thecerebrum, and these data may assist in other research efforts tounderstand the brain’s response to mechanical loading, includingstudies of injury and structural neurological disorders. Furtherresearch is needed to confirm these findings, and to investigatewhy the cerebellum is less stiff than the cerebrum, and whether itresponds differently to the same forces.

5. Conclusion

MR elastographic measurements on eight healthy adult sub-jects were analysed to compare the viscoelasticity of the cere-brum and the cerebellum. It was found that G0 (elastic shearmodulus) of the cerebellum is lower than that of the cerebralhemispheres. The results suggest that the cerebellum mayrespond differently to mechanical loading than the cerebrum.

Conflict of interest statement

None declared.

Acknowledgements

The authors would like to thank the staff of the NeuroscienceResearch Australia imaging centre for their assistance withimaging experiments. This research was funded by a discoveryGrant from the Australian Research Council. Lynne Bilston issupported by an NHMRC senior research fellowship.

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