2012 Proceedings - International Tissue Elasticity Conference

048 COMPRESSION SENSITIVE MAGNETIC RESONANCE ELASTOGRAPHY.
Sebastian Hirsch 1 , Frauke Beyer 1 , Jing Guo 1 , Sebastian Papazoglou 1 , Heiko Tzschätzsch 1 , Andreas
Fehlner 1 , Ingolf Sack 1 , Jürgen Braun 2 .
1 Radiology Department, 2 Institute of Medical Informatics, Charité – University Medicine Berlin,
Berlin, GERMANY.
Background: Tissue pressure is an important parameter for the diagnosis of various diseases from
hepatic hypertension, lung fibrosis to hydrocephalus. The intrinsic pressure of a material is related to its
effective compression modulus that scales volumetric strain to pressure [1]. According to the theory of
poroelasticity, volumetric strain in biological tissue may arise from the in– and outflow of compartmental
fluids like blood or CSF [2,3]. In order to measure compressibility, one needs to analyze local volumetric
strain given by the divergence of motion fields.
Aims: The purpose of this study is to test the sensitivity of the divergence of harmonic motion fields
measured by 3D MRE to tissue pressure. Tissue pressure is imposed by air pressure applied to agarose
phantoms made compressible through inclusion of air bubbles. Three experiments are demonstrated:
1) Rheometer experiments to measure compressibility by static compression; 2) MRE to measure the
divergence of the harmonic wave field at different values of excess air pressure and 3) MRE under normal
air pressure with increasing motion amplitude for imposing an increasing oscillating pressure.
Methods: Phantoms were built from 1.5% and 0.5% agarose solved in hot water. Gas bubbles were
created by adding different amounts of NaHCO3 and citric acid into the hot agarose–water solution,
yielding phantoms of variable density and reduced compression modulus as tested by a torsional
rheometry device (MCR 301, Anton Paar, Austria) equipped with a circular contact plate (Ø 5cm) and
operated in axial motion mode. For MRE, the phantoms were encased in a pressure chamber which was
placed in a head cradle [1] inside a 1.5T MR scanner (Siemens Sonata, Erlangen, Germany). 3D vector
field MRE was performed as described elsewhere [4]. The divergence of complex wave fields at vibration
frequency (50Hz) was calculated based on multi–dimensional derivative operators [5].
Results: Rheometer experiments illustrate that the compression modulus of agarose phantoms decreases
with the bulk density, indicating that gas bubbles contribute to the compressibility of the effective medium
(Figure 1A). The normalized displacement field divergence increases with external air pressure (Figure 1B),
the slope of that relation being correlated with the density of the effective medium (Figure 1C). The
expectation value of the magnitude of the oscillating displacement field divergence is linearly dependent on
the measured mean displacement field, as can be expected from theory (Figure 1D). The slope of this
relation is proportional to the inverse of the compression modulus, 1/K. The comparison of the lines for a
phantom with gas bubbles and a solid one yields a ratio of compression moduli of 3 (solid/bubble).
Conclusions: By measuring volumetric strain MRE is sensitive to the inherent pressure and the
compressibility of tissue. The introduced phantoms represent a valid model for compressible materials such as
lung tissue [1]. However, further work is necessary for modeling the permeation of biological tissue by fluid–filled
vessels which may result in a more complex pressure–strain relationship than the model introduced herein.
References:
[1] Hirsch et al.: Magn Reson Med, doi:10.1002/mrm.24294, 2012.
[2] Leiderman et al.: Phys Med Biol, 51, pp. 6291–313, 2006.
[3] Perrinez et al.: IEEE Trans Biomed Eng, 56, pp. 598–608, 2009.
[4] Romano et al.: Magn Reson Med, doi: 10.1002/mrm.24141, 2012.
[5] Anderssen and Hegland Math Comput, 68, pp. 1121–1141, 1999.
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Phantom 3
Phantom 2
Phantom 1
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Excess pressure in bar
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mean displacement amplitude in 10
Figure 1: A) Compression moduli of agarose phantom with different gas bubble concentrations obtained from rheometer
experiments. B) Dependence of the normalized displacement field divergence on external air pressure for 3 phantoms with
different gas bubble concentrations (1: lowest concentration, 3: highest concentration). C) Slopes of the fits from B) as a
function of bulk density. The density index is a relative measure of the bubble concentration derived from MRE
magnitude images. D) Relation between measured values of |div(u)| and the stimulated displacement amplitude.
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A) B) C) D)
Density index [a.u.]
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K in 106 K in 10 Pa 6 Pa
mean(|div(u)|)/mean(|u|) mean(|div(u)|)/mean(|u|) in 1/m
Slope from B) in 1/(bar∙m)
|div(u)| in 10-4 |div(u)| in 10-4 indicates Presenter