76
L. E. Bilston
modulus. In the simplest implementation, the local wavelength is used to estimate
the ‘elastic’ shear modulus of the tissue, according to Muthupillai et al. [17]:
G = ν
2 λ
2 ρ,
where ν = frequency, λ = the local wavelength, and ρ = density.
More advanced implementations solve the full wave equation over the threedimensional image domain. Some of these techniques use a correspondence principle approach, whereby the shear modulus is considered to be a complex quantity
in the wave equation, allowing both the elastic and viscous components (G’ and
G”, respectively) of the shear modulus to be extracted, if a sufficiently high signal
to noise ratio is present in the image data. This relies on the attenuation of the
propagating wave as it penetrates the brain parenchyma to estimate the viscous
damping.
The estimated shear moduli for healthy brain tissue that has been gathered
using MRE, while not as widely varying as some of the early ex vivo brain data,
are nevertheless somewhat variable, due in large part to the different analytical
approaches taken to estimating the elastic and/or viscoelastic properties and data
quality. Although there is still considerable debate about the best methods of both
wave induction in brain elastography and data analysis, numerous studies have used
MRE to examine both healthy populations and also several clinical populations.
Selected data from a selection of brain MRE studies in healthy adults is shown in
Fig. 4.3.
Many of the early brain MRE studies used small sample sizes, but more recently,
larger studies have been performed, giving greater confidence in their findings. Such
studies have suggested that brain shear modulus may decline slightly with age and
that females may have very slightly stiffer brains than males [21, 23]. The practical
significance of these small differences is not yet clear. Some research groups have
Fig. 4.3 Brain shear
modulus measurements made
using MR elastography. (Data
from [11, 18–22])
0
1
2
3
4
5
6
7
8
9
0
50
100
150
200
Frequency (Hz)
Shear Modulus (KPa)
G'
G"
L. E. Bilston
modulus. In the simplest implementation, the local wavelength is used to estimate
the ‘elastic’ shear modulus of the tissue, according to Muthupillai et al. [17]:
G = ν
2 λ
2 ρ,
where ν = frequency, λ = the local wavelength, and ρ = density.
More advanced implementations solve the full wave equation over the threedimensional image domain. Some of these techniques use a correspondence principle approach, whereby the shear modulus is considered to be a complex quantity
in the wave equation, allowing both the elastic and viscous components (G’ and
G”, respectively) of the shear modulus to be extracted, if a sufficiently high signal
to noise ratio is present in the image data. This relies on the attenuation of the
propagating wave as it penetrates the brain parenchyma to estimate the viscous
damping.
The estimated shear moduli for healthy brain tissue that has been gathered
using MRE, while not as widely varying as some of the early ex vivo brain data,
are nevertheless somewhat variable, due in large part to the different analytical
approaches taken to estimating the elastic and/or viscoelastic properties and data
quality. Although there is still considerable debate about the best methods of both
wave induction in brain elastography and data analysis, numerous studies have used
MRE to examine both healthy populations and also several clinical populations.
Selected data from a selection of brain MRE studies in healthy adults is shown in
Fig. 4.3.
Many of the early brain MRE studies used small sample sizes, but more recently,
larger studies have been performed, giving greater confidence in their findings. Such
studies have suggested that brain shear modulus may decline slightly with age and
that females may have very slightly stiffer brains than males [21, 23]. The practical
significance of these small differences is not yet clear. Some research groups have
Fig. 4.3 Brain shear
modulus measurements made
using MR elastography. (Data
from [11, 18–22])
0
1
2
3
4
5
6
7
8
9
0
50
100
150
200
Frequency (Hz)
Shear Modulus (KPa)
G'
G"