232
V. Kurtcuoglu et al.
without fine anatomic structures [121]. Their approach involved calculation of the
steady streaming velocity field over one CSF flow cycle and using it to predict
drug concentration in the entire spinal domain over several hours. The authors
predicted that there would be no clear difference in drug distribution range for
a bolus injection versus slow infusion. By using different models for phenomena
occurring at different time scales, they were able to progress towards a potentially
clinically relevant CFD application in the CSF space.
Since then, a number of studies have been carried out to help understand factors
that could impact intrathecal drug spread, including CSF waveform [122], drug
injection rate and volume [123, 124], catheter position within the SAS [123],
impact of trabecular microstructure [125], drug diffusivity [123] and absorption into
CNS tissue [126–128]. Tangen et al. conducted the first CFD study to investigate
clearance of blood from the CSF following subarachnoid haemorrhage by a lumbar
drain [129, 130]. The authors conducted rigorous in vitro verification of results,
adding confidence to the study findings. In combination, these studies found that
drug properties, bolus size, injection rate, injection location, CSF flow pulsation
amplitude, macroscale anatomy and microscale anatomy can play a role in CSF
solute transport and that these factors require further detailed investigation.
Computational modelling has also been applied to help understand how radionuclide studies of molecules injected into the CSF indicate a net CSF flow direction
[131], while MRI studies appear to show zero net CSF flow. Combined CFD and
bulk models were also used to assess the relation between changes in CSF net flow
and increase in CSF protein concentration [132]. Sanchez et al. used an anatomically
idealized spinal SAS model without spinal cord nerve roots or curvature, showing
that CSF steady streaming can be produced by convective acceleration depending on
the degree of spinal cord eccentricity [133]. This finding was also observed by Khani
et al. within an anatomically detailed model of the SAS with spinal cord nerve roots
and non-uniform subject-specific CSF flow waveform along the spine [69]. Asgari
et al. formulated a one-dimensional model of protein dispersion in the spinal SAS,
determining dispersion coefficients using a 3D advection-diffusion model [132].
They investigated two hypothesized causes of increased CSF albumin levels, finding
blood-brain barrier dysfunction to be a more likely cause than a reduction in the
rate of CSF outflow. This finding may help in the clinical interpretation of Reiber
diagrams.
9.3.3 Perivascular Space
Starting in 2003 with the work of Bilston et al. [134], CFD modelling of perivascular
CSF flow was initially driven by the desire to understand the pathophysiology
of syringomyelia. Bilston idealized the perivascular space with a 2D rectangular
domain with no-slip boundary conditions at the walls and prescribed pressure
boundary conditions at the inlet and outlet. Transient deformation was prescribed
on the wall representing the boundary closer to the artery lumen, whereas the outer
V. Kurtcuoglu et al.
without fine anatomic structures [121]. Their approach involved calculation of the
steady streaming velocity field over one CSF flow cycle and using it to predict
drug concentration in the entire spinal domain over several hours. The authors
predicted that there would be no clear difference in drug distribution range for
a bolus injection versus slow infusion. By using different models for phenomena
occurring at different time scales, they were able to progress towards a potentially
clinically relevant CFD application in the CSF space.
Since then, a number of studies have been carried out to help understand factors
that could impact intrathecal drug spread, including CSF waveform [122], drug
injection rate and volume [123, 124], catheter position within the SAS [123],
impact of trabecular microstructure [125], drug diffusivity [123] and absorption into
CNS tissue [126–128]. Tangen et al. conducted the first CFD study to investigate
clearance of blood from the CSF following subarachnoid haemorrhage by a lumbar
drain [129, 130]. The authors conducted rigorous in vitro verification of results,
adding confidence to the study findings. In combination, these studies found that
drug properties, bolus size, injection rate, injection location, CSF flow pulsation
amplitude, macroscale anatomy and microscale anatomy can play a role in CSF
solute transport and that these factors require further detailed investigation.
Computational modelling has also been applied to help understand how radionuclide studies of molecules injected into the CSF indicate a net CSF flow direction
[131], while MRI studies appear to show zero net CSF flow. Combined CFD and
bulk models were also used to assess the relation between changes in CSF net flow
and increase in CSF protein concentration [132]. Sanchez et al. used an anatomically
idealized spinal SAS model without spinal cord nerve roots or curvature, showing
that CSF steady streaming can be produced by convective acceleration depending on
the degree of spinal cord eccentricity [133]. This finding was also observed by Khani
et al. within an anatomically detailed model of the SAS with spinal cord nerve roots
and non-uniform subject-specific CSF flow waveform along the spine [69]. Asgari
et al. formulated a one-dimensional model of protein dispersion in the spinal SAS,
determining dispersion coefficients using a 3D advection-diffusion model [132].
They investigated two hypothesized causes of increased CSF albumin levels, finding
blood-brain barrier dysfunction to be a more likely cause than a reduction in the
rate of CSF outflow. This finding may help in the clinical interpretation of Reiber
diagrams.
9.3.3 Perivascular Space
Starting in 2003 with the work of Bilston et al. [134], CFD modelling of perivascular
CSF flow was initially driven by the desire to understand the pathophysiology
of syringomyelia. Bilston idealized the perivascular space with a 2D rectangular
domain with no-slip boundary conditions at the walls and prescribed pressure
boundary conditions at the inlet and outlet. Transient deformation was prescribed
on the wall representing the boundary closer to the artery lumen, whereas the outer