78
L. E. Bilston
using MR elastography at an intermediate frequency of 1 kHz, obtaining values of
approximately 10–15 kPa, still well below the values obtained by high-frequency
ultrasound. Ultrasound shear wave elastography has also recently been applied to
brain tissue in vivo in human subjects [41] and ex vivo porcine samples [42],
yielding tissue shear modulus estimates more in keeping with MRE measures.
In summary, the linear viscoelastic properties of brain tissue, while a fundamental
stepping stone for understanding the more complex nonlinear properties, have
been measured using reliable techniques in only a small number of studies, and
methodologically flawed data sets are common. There is still room for more robust
characterisation of these properties under a wider range of loading conditions,
including further cross-validation of data from one testing mode against another
(e.g. oscillation vs relaxation or tension vs compression). The former has rarely
been done (e.g. see Bilston et al. [12]) and would create greater confidence in the
quality and reliability of the data.
4.2.2 Nonlinear Viscoelastic Properties
Most soft biological tissues are thought to be nonlinearly viscoelastic at moderate
to large amplitudes of loading [16]. Nonlinear viscoelastic materials require more
complex mechanical testing protocols in order to characterise the behaviour of the
material, in order to ascertain how the properties change with loading type, loading
amplitude, and loading rate. Brain tissue has a very low linear viscoelastic limit,
rendering it nonlinearly viscoelastic at most strains of practical interest.
4.2.2.1 Oscillatory Response
While there are several reports of oscillatory response of brain tissue in the literature
[13, 43–45], most of these have interpreted data without proper analysis of the
nonlinear viscoelastic effects and are thus of questionable validity. The key problem
is that in the nonlinear viscoelastic regime, the shear modulus is a function of strain
and not independent of strain as it is within the linear viscoelastic regime. In the
case of brain tissue, there is substantial shear thinning at strains beyond the linear
viscoelastic regime, and the shear modulus estimated from larger amplitude test
data can be significantly underestimated (as discussed above). In this context, shear
thinning is observed as a decreasing shear modulus with increasing applied shear
strain. Oscillatory tests at large amplitude require analysis of the full loading and
unloading cycle, which is non-sinusoidal at large amplitudes, and thus the simple
calculation of G’ and G” from the phase difference between the peak torque and the
peak shear strain is no longer valid. In addition, the decomposition of the complex
modulus into the storage and loss modulus is typically based on the phase difference
between the peak input shear strain and the peak torque generated. If the torque
signal is non-sinusoidal, decomposition of the shear modulus based on this method
will give erroneous values. Newer rheometers have the capacity to measure the full
L. E. Bilston
using MR elastography at an intermediate frequency of 1 kHz, obtaining values of
approximately 10–15 kPa, still well below the values obtained by high-frequency
ultrasound. Ultrasound shear wave elastography has also recently been applied to
brain tissue in vivo in human subjects [41] and ex vivo porcine samples [42],
yielding tissue shear modulus estimates more in keeping with MRE measures.
In summary, the linear viscoelastic properties of brain tissue, while a fundamental
stepping stone for understanding the more complex nonlinear properties, have
been measured using reliable techniques in only a small number of studies, and
methodologically flawed data sets are common. There is still room for more robust
characterisation of these properties under a wider range of loading conditions,
including further cross-validation of data from one testing mode against another
(e.g. oscillation vs relaxation or tension vs compression). The former has rarely
been done (e.g. see Bilston et al. [12]) and would create greater confidence in the
quality and reliability of the data.
4.2.2 Nonlinear Viscoelastic Properties
Most soft biological tissues are thought to be nonlinearly viscoelastic at moderate
to large amplitudes of loading [16]. Nonlinear viscoelastic materials require more
complex mechanical testing protocols in order to characterise the behaviour of the
material, in order to ascertain how the properties change with loading type, loading
amplitude, and loading rate. Brain tissue has a very low linear viscoelastic limit,
rendering it nonlinearly viscoelastic at most strains of practical interest.
4.2.2.1 Oscillatory Response
While there are several reports of oscillatory response of brain tissue in the literature
[13, 43–45], most of these have interpreted data without proper analysis of the
nonlinear viscoelastic effects and are thus of questionable validity. The key problem
is that in the nonlinear viscoelastic regime, the shear modulus is a function of strain
and not independent of strain as it is within the linear viscoelastic regime. In the
case of brain tissue, there is substantial shear thinning at strains beyond the linear
viscoelastic regime, and the shear modulus estimated from larger amplitude test
data can be significantly underestimated (as discussed above). In this context, shear
thinning is observed as a decreasing shear modulus with increasing applied shear
strain. Oscillatory tests at large amplitude require analysis of the full loading and
unloading cycle, which is non-sinusoidal at large amplitudes, and thus the simple
calculation of G’ and G” from the phase difference between the peak torque and the
peak shear strain is no longer valid. In addition, the decomposition of the complex
modulus into the storage and loss modulus is typically based on the phase difference
between the peak input shear strain and the peak torque generated. If the torque
signal is non-sinusoidal, decomposition of the shear modulus based on this method
will give erroneous values. Newer rheometers have the capacity to measure the full