4 Brain Tissue Mechanical Properties
87
However, there is still much that is either not yet known about brain tissue
mechanics or the subject of debate, due to inconsistent or contradictory data in the
literature. Some of the reasons for these inconsistencies are discussed below.
Despite the well-defined structural anisotropy of white matter arising from
the axonal fibre bundles, mechanical anisotropy has not been comprehensively
established. Some studies suggest that there is moderate mechanical anisotropy in
white matter under shear, with the axonal fibre direction up to twice as stiff as the
perpendicular direction [43, 80] and in tension [64], while others have not found
significant mechanical anisotropy in compression [55]. The strains used to estimate
properties are likely to have an influence, as increasing stretch of axons may stiffen
the tissue, as occurs in other fibrous soft tissues.
Regional variations in tissue properties across the brain have been suggested by
some studies [43, 80, 81], although the differences are not large, and some of these
studies suffer from methodological problems. A recent post-mortem human brain
study indicated some indication of small variations across different regions [82].
This modest, at best, regional variation is consistent with more recent MRE studies,
with the exception of the softer cerebellum [26].
Like most very soft hydrated tissues, brain tissue is usually assumed to be
incompressible, or nearly incompressible, due to its very high water content (e.g.
[52, 83]). There have been only a few studies that have directly examined this
assumption, and its validity almost certainly depends on the mechanical process
of interest. In very slow processes involving displacement of interstitial fluid within
the brain parenchyma, such as hydrocephalus or mass lesions in the brain involving
brain oedema, this assumption may not be valid, as there is time for fluid to
move within the brain tissue, and regions could locally appear compressible due
to fluid transfer. For processes at shorter time scales, there is no evidence that brain
tissue is significantly compressible, at least at macroscopic length scales. Indeed,
Franceschini et al. [61] report that the undrained (i.e. whole tissue) Poisson’s ratio
for brain tissue is 0.5, while the ‘drained’ compressibility is 0.496, lending credence
to the incompressibility assumption. A recent study used image correlation methods
to confirm that incompressibility holds, at least at slow loading rates [84].
Age dependence of brain tissue properties has also been described in a small
number of studies. Prange and Margulies [80] suggested neonatal brain tissue is
stiffer than in adults, as did Gefen and Margulies [85]. On the other hand, Thibault
and Margulies [86] found that shear modulus of the brain was significantly greater
for adult brain tissue than neonatal tissue. It is fair to say that this issue is not yet
settled and methodologically robust studies are required. As noted on p. 76 of this
Chapter, Sack et al. [21] found that brain tissue shear modulus decreases with age
from early adulthood to old age, using MR elastography in vivo, which has been
confirmed by other studies, which suggest such changes vary by brain region, e.g.
[23]. These studies also observed a small difference between females and males,
with female brain tissue being marginally stiffer [86].
Differences between measured properties of brain tissue in vivo and ex vivo have
been debated for decades. Some studies show significant drops in situ immediately
after death [45, 87, 88]. Weaver et al. attributed this change to drops in interstitial
87
However, there is still much that is either not yet known about brain tissue
mechanics or the subject of debate, due to inconsistent or contradictory data in the
literature. Some of the reasons for these inconsistencies are discussed below.
Despite the well-defined structural anisotropy of white matter arising from
the axonal fibre bundles, mechanical anisotropy has not been comprehensively
established. Some studies suggest that there is moderate mechanical anisotropy in
white matter under shear, with the axonal fibre direction up to twice as stiff as the
perpendicular direction [43, 80] and in tension [64], while others have not found
significant mechanical anisotropy in compression [55]. The strains used to estimate
properties are likely to have an influence, as increasing stretch of axons may stiffen
the tissue, as occurs in other fibrous soft tissues.
Regional variations in tissue properties across the brain have been suggested by
some studies [43, 80, 81], although the differences are not large, and some of these
studies suffer from methodological problems. A recent post-mortem human brain
study indicated some indication of small variations across different regions [82].
This modest, at best, regional variation is consistent with more recent MRE studies,
with the exception of the softer cerebellum [26].
Like most very soft hydrated tissues, brain tissue is usually assumed to be
incompressible, or nearly incompressible, due to its very high water content (e.g.
[52, 83]). There have been only a few studies that have directly examined this
assumption, and its validity almost certainly depends on the mechanical process
of interest. In very slow processes involving displacement of interstitial fluid within
the brain parenchyma, such as hydrocephalus or mass lesions in the brain involving
brain oedema, this assumption may not be valid, as there is time for fluid to
move within the brain tissue, and regions could locally appear compressible due
to fluid transfer. For processes at shorter time scales, there is no evidence that brain
tissue is significantly compressible, at least at macroscopic length scales. Indeed,
Franceschini et al. [61] report that the undrained (i.e. whole tissue) Poisson’s ratio
for brain tissue is 0.5, while the ‘drained’ compressibility is 0.496, lending credence
to the incompressibility assumption. A recent study used image correlation methods
to confirm that incompressibility holds, at least at slow loading rates [84].
Age dependence of brain tissue properties has also been described in a small
number of studies. Prange and Margulies [80] suggested neonatal brain tissue is
stiffer than in adults, as did Gefen and Margulies [85]. On the other hand, Thibault
and Margulies [86] found that shear modulus of the brain was significantly greater
for adult brain tissue than neonatal tissue. It is fair to say that this issue is not yet
settled and methodologically robust studies are required. As noted on p. 76 of this
Chapter, Sack et al. [21] found that brain tissue shear modulus decreases with age
from early adulthood to old age, using MR elastography in vivo, which has been
confirmed by other studies, which suggest such changes vary by brain region, e.g.
[23]. These studies also observed a small difference between females and males,
with female brain tissue being marginally stiffer [86].
Differences between measured properties of brain tissue in vivo and ex vivo have
been debated for decades. Some studies show significant drops in situ immediately
after death [45, 87, 88]. Weaver et al. attributed this change to drops in interstitial