4 Brain Tissue Mechanical Properties
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procedures. However, there is also considerable intra-study variability in reported
brain mechanical properties data, to which biological variation is likely to be at
least a substantial contributor. A key flaw of many early studies of shear properties
in the literature was the (sometimes unstated) assumption of linear viscoelastic
behaviour and therefore flawed interpretation of large amplitude oscillatory data.
The appropriate approach is to first identify the linear viscoelastic limit for a tissue,
conduct tests to characterise the linear viscoelastic response, and then conduct
appropriate large-amplitude (nonlinear) tests with appropriate analysis methods.
Shear response of a viscoelastic material is characterised in terms of the shear
modulus, usually denoted by the symbol G. This quantity represents the unit stress
response to a unit shear strain and is constant for a given frequency in linear
viscoelastic materials. The relaxation shear modulus represents the temporal stress
response to a unit shear strain and is typically denoted G(t). The storage and
loss moduli represent the elastic (G’) and viscous (G”) components of the linear
viscoelastic shear modulus, respectively, and are a function of loading rate, often
reported as frequency.
4.2.1 Linear Viscoelastic Properties
The traditional rheological approach to measuring viscoelastic properties of complex materials is to first establish the linear viscoelastic limit and characterise the
material behaviour at or below this limit. In the linear viscoelastic region, the stress
generated is proportional to the strain applied, so that the shear modulus is constant.
4.2.1.1 Oscillatory Loading
Oscillatory testing of tissues is most often carried out using parallel plate geometries, where one plate is fixed, while the other is moved sinusoidally parallel to
the fixed plate, while torque is recorded. Parallel plates are used because of the
difficulty of cutting brain tissue samples to fit the cone-and-plate setup that is often
used for viscoelastic fluids. The moving plate is typically either rotated about an axis
perpendicular to the plates, as in traditional rotational rheometers, or moved linearly
parallel to the fixed plate. Other methods have been used, including an eccentrically
loaded sample in a rotational rheometry setup [10], and shear wave propagation
methods such as magnetic resonance elastography [11].
Oscillatory loading results are typically reported as the storage (G’) and loss (G”)
moduli, which represent the elastic and viscous components of the dynamic shear
modulus (G* = G’ + iG”). This complex notation is used for the shear modulus
to indicate that the stress associated with the viscous response is temporally out of
phase with the elastic response and the input sinusoidal displacement (by π /2).
Figure 4.1 summarises the data reported in the literature within the linear
viscoelastic region [10, 12–15]. From this, it can be seen that brain tissue is a very
73
procedures. However, there is also considerable intra-study variability in reported
brain mechanical properties data, to which biological variation is likely to be at
least a substantial contributor. A key flaw of many early studies of shear properties
in the literature was the (sometimes unstated) assumption of linear viscoelastic
behaviour and therefore flawed interpretation of large amplitude oscillatory data.
The appropriate approach is to first identify the linear viscoelastic limit for a tissue,
conduct tests to characterise the linear viscoelastic response, and then conduct
appropriate large-amplitude (nonlinear) tests with appropriate analysis methods.
Shear response of a viscoelastic material is characterised in terms of the shear
modulus, usually denoted by the symbol G. This quantity represents the unit stress
response to a unit shear strain and is constant for a given frequency in linear
viscoelastic materials. The relaxation shear modulus represents the temporal stress
response to a unit shear strain and is typically denoted G(t). The storage and
loss moduli represent the elastic (G’) and viscous (G”) components of the linear
viscoelastic shear modulus, respectively, and are a function of loading rate, often
reported as frequency.
4.2.1 Linear Viscoelastic Properties
The traditional rheological approach to measuring viscoelastic properties of complex materials is to first establish the linear viscoelastic limit and characterise the
material behaviour at or below this limit. In the linear viscoelastic region, the stress
generated is proportional to the strain applied, so that the shear modulus is constant.
4.2.1.1 Oscillatory Loading
Oscillatory testing of tissues is most often carried out using parallel plate geometries, where one plate is fixed, while the other is moved sinusoidally parallel to
the fixed plate, while torque is recorded. Parallel plates are used because of the
difficulty of cutting brain tissue samples to fit the cone-and-plate setup that is often
used for viscoelastic fluids. The moving plate is typically either rotated about an axis
perpendicular to the plates, as in traditional rotational rheometers, or moved linearly
parallel to the fixed plate. Other methods have been used, including an eccentrically
loaded sample in a rotational rheometry setup [10], and shear wave propagation
methods such as magnetic resonance elastography [11].
Oscillatory loading results are typically reported as the storage (G’) and loss (G”)
moduli, which represent the elastic and viscous components of the dynamic shear
modulus (G* = G’ + iG”). This complex notation is used for the shear modulus
to indicate that the stress associated with the viscous response is temporally out of
phase with the elastic response and the input sinusoidal displacement (by π /2).
Figure 4.1 summarises the data reported in the literature within the linear
viscoelastic region [10, 12–15]. From this, it can be seen that brain tissue is a very