9 Modelling of Cerebrospinal Fluid Flow by Computational Fluid Dynamics
229
with a non-uniformly moving boundary method to more accurately reproduce the
axial distribution of CSF flow measured by MRI [87]. This study was followed
up in 2018 with a similar model of the human spinal SAS but with 31 pairs of
anatomically realistic spinal cord nerve roots [12, 69]. Results showed that the
complex geometry resulted in considerable steady streaming of CSF, which was
greatly impacted by the presence of spinal cord nerve roots.
In combination, the CFD studies representing normal physiologic conditions
indicate that small anatomic structures such as nerve roots and trabeculae must be
accounted for to reproduce in vivo CSF velocity profiles accurately. However, they
also show that it is difficult to directly validate CFD results with MRI measurements
due to a lack of spatial resolution and noise in the experiments [82, 83].
9.3.2.2 Syringomyelia
Syringomyelia is a spinal cord disorder characterized by formation of a fluid-filled
cyst within the cord tissue that can progressively expand over time and cause
neurological damage [88, 89]. The exact mechanism underlying cyst formation and
progression remains unclear. Thus, numerical modelling has been applied to identify
mechanical factors that could help explain cyst pathogenesis and/or investigate the
plausibility of various hypotheses brought forth by clinicians [70].
The first study to apply numerical modelling to investigate syringomyelia, and
perhaps the first model to investigate spinal SAS CSF dynamics, was conducted
by Lockey et al. in 1975 [90]. This study used 1D analytic models of wave
propagation to predict the impact of a spinal stenosis on cough-related pressure
pulse propagation along the spinal SAS. Since that time, many numerical models
of syringomyelia have been formulated with varying degrees of anatomic and
physiologic complexity. From 1999 to 2003, Carpenter, Berkouk and colleagues
published a series of fluid-filled elastic coaxial tube models and proposed an “elastic
jump” hypothesis for syringomyelia pathogenesis based on a wave steepening effect
that could potentially greatly increase pressure pulse along the spinal SAS [91–
93]. However, Bertram et al. [64, 94] and subsequently Elliott et al. found the
elastic jump hypothesis to be quantitatively implausible [95]. Chang and Nakagawa
constructed an electric circuit analogue for syringomyelia with the cystic cavity
connected to the fourth ventricle by the obex [96].
These models opened many questions on the relevance of mechanical properties
of the tissue, such as viscoelasticity and porosity, as well as tissue geometry. To
answer these, a number of 1D and 2D numerical models of spinal SAS wave propagation were formulated, including those brought forth by Bertram and colleagues
[97–99], Elliott et al. [100–102], Cirovic et al. [103–105] and Bilston, Cheng and
colleagues [106–108]. Bertram used the finite element method to investigate wave
phenomena and anatomic conditions such as spinal arachnoiditis that could lead
to a pressure environment favourable for cystic growth. Elliott et al. built on these
models by investigating the importance of tissue permeability and how permeability,
in combination with wave propagation, could lead to cyst formation. Cirovic et al.
229
with a non-uniformly moving boundary method to more accurately reproduce the
axial distribution of CSF flow measured by MRI [87]. This study was followed
up in 2018 with a similar model of the human spinal SAS but with 31 pairs of
anatomically realistic spinal cord nerve roots [12, 69]. Results showed that the
complex geometry resulted in considerable steady streaming of CSF, which was
greatly impacted by the presence of spinal cord nerve roots.
In combination, the CFD studies representing normal physiologic conditions
indicate that small anatomic structures such as nerve roots and trabeculae must be
accounted for to reproduce in vivo CSF velocity profiles accurately. However, they
also show that it is difficult to directly validate CFD results with MRI measurements
due to a lack of spatial resolution and noise in the experiments [82, 83].
9.3.2.2 Syringomyelia
Syringomyelia is a spinal cord disorder characterized by formation of a fluid-filled
cyst within the cord tissue that can progressively expand over time and cause
neurological damage [88, 89]. The exact mechanism underlying cyst formation and
progression remains unclear. Thus, numerical modelling has been applied to identify
mechanical factors that could help explain cyst pathogenesis and/or investigate the
plausibility of various hypotheses brought forth by clinicians [70].
The first study to apply numerical modelling to investigate syringomyelia, and
perhaps the first model to investigate spinal SAS CSF dynamics, was conducted
by Lockey et al. in 1975 [90]. This study used 1D analytic models of wave
propagation to predict the impact of a spinal stenosis on cough-related pressure
pulse propagation along the spinal SAS. Since that time, many numerical models
of syringomyelia have been formulated with varying degrees of anatomic and
physiologic complexity. From 1999 to 2003, Carpenter, Berkouk and colleagues
published a series of fluid-filled elastic coaxial tube models and proposed an “elastic
jump” hypothesis for syringomyelia pathogenesis based on a wave steepening effect
that could potentially greatly increase pressure pulse along the spinal SAS [91–
93]. However, Bertram et al. [64, 94] and subsequently Elliott et al. found the
elastic jump hypothesis to be quantitatively implausible [95]. Chang and Nakagawa
constructed an electric circuit analogue for syringomyelia with the cystic cavity
connected to the fourth ventricle by the obex [96].
These models opened many questions on the relevance of mechanical properties
of the tissue, such as viscoelasticity and porosity, as well as tissue geometry. To
answer these, a number of 1D and 2D numerical models of spinal SAS wave propagation were formulated, including those brought forth by Bertram and colleagues
[97–99], Elliott et al. [100–102], Cirovic et al. [103–105] and Bilston, Cheng and
colleagues [106–108]. Bertram used the finite element method to investigate wave
phenomena and anatomic conditions such as spinal arachnoiditis that could lead
to a pressure environment favourable for cystic growth. Elliott et al. built on these
models by investigating the importance of tissue permeability and how permeability,
in combination with wave propagation, could lead to cyst formation. Cirovic et al.