9 Modelling of Cerebrospinal Fluid Flow by Computational Fluid Dynamics
223
The relative contributions of pia mater and ventricular wall motion to CSF
dynamics are unclear, in particular because there are no reliable quantitative data
on pia movement. While ventricular wall displacement is larger (as qualitatively
discernible in phase-based amplified MRI [46]), the pia mater surface area is much
bigger. Therefore, pia motion cannot necessarily be neglected. To account for the
effect of pia movement in an approximate fashion, simplified BC can be introduced.
One option is to prescribe uniform perpendicular flow across the pia, such that the
corresponding flow rate is equal to the difference between in- and outflow at the
aqueduct of Sylvius and the spinal canal [10]. This simplified BC is relatively easy
to implement but will lead to errors in the reported flow velocities close to the pia
surface.
The pulsatile motion of CSF is superimposed onto its steady flow caused by
production in the choroid plexus and removal through the arachnoid granulations,
extracranial lymphatic pathways and possibly through cerebral capillaries [3, 47].
The choroid plexus has a filamentous structure that cannot be acquired by MRI
in its full detail. For CFD modelling, its simplified macroscopic shape can be
segmented from MR images, and CSF flow rates corresponding to the production
value can be imposed on the idealized boundaries. Alternatively, the choroid plexus
geometry can be neglected altogether and inflow imposed at a part of the respective
ventricle wall. Combined CSF production rates in the choroid plexus of the third
and lateral ventricles can, principally, be obtained by integrating the MRI-acquired
CSF flow profile in the aqueduct of Sylvius over a cardiac cycle. While this method
is used throughout the literature, there is no conclusive data on the accuracy of
this approach. Obtaining CSF production rates in the fourth ventricle via MRI is
more difficult and would require measurement of flow through the small foramina
of Luschka and Magendie. This is not possible with a sufficient level of accuracy
on current clinical MRI scanners. In order to still take CSF production in the fourth
ventricle into account, a ratio between the production rates in this and the remaining
cerebral ventricles can be assumed.
Under physiologic conditions, the average rate of CSF removal is equal to the
production rate. While it is accepted that there are multiple locations of absorption
or drainage throughout the cranial and spinal cavity, there is no consensus on
the relative contributions of the individual exit routes. The classically purported
but increasingly questioned main locations of CSF reabsorption are the arachnoid
granulations that drain into the superior sagittal, transverse and sigmoid sinuses.
It is possible to locate large granulations through MRI, but most of the smaller
ones cannot be detected. Cadaver data on their distribution is available [48], and
areas of the arachnoid mater boundary can be assigned absorption functionality in
CFD simulations. Concretely, the arachnoid granulations can be assumed to act as
one-way differential pressure valves with associated permeability of approximately
92.5 μl . min –1. mmHg –1. cm −2 [49]. Recent studies in rodents have highlighted the
importance of lymphatic CSF drainage [47, 50, 51]. While it is unclear how these
findings translate to humans, it is reasonable that lymphatic drainage should be
considered in models of CSF dynamics. Further experimental work is needed to
obtain quantitative data on the connection between the two fluid spaces.
223
The relative contributions of pia mater and ventricular wall motion to CSF
dynamics are unclear, in particular because there are no reliable quantitative data
on pia movement. While ventricular wall displacement is larger (as qualitatively
discernible in phase-based amplified MRI [46]), the pia mater surface area is much
bigger. Therefore, pia motion cannot necessarily be neglected. To account for the
effect of pia movement in an approximate fashion, simplified BC can be introduced.
One option is to prescribe uniform perpendicular flow across the pia, such that the
corresponding flow rate is equal to the difference between in- and outflow at the
aqueduct of Sylvius and the spinal canal [10]. This simplified BC is relatively easy
to implement but will lead to errors in the reported flow velocities close to the pia
surface.
The pulsatile motion of CSF is superimposed onto its steady flow caused by
production in the choroid plexus and removal through the arachnoid granulations,
extracranial lymphatic pathways and possibly through cerebral capillaries [3, 47].
The choroid plexus has a filamentous structure that cannot be acquired by MRI
in its full detail. For CFD modelling, its simplified macroscopic shape can be
segmented from MR images, and CSF flow rates corresponding to the production
value can be imposed on the idealized boundaries. Alternatively, the choroid plexus
geometry can be neglected altogether and inflow imposed at a part of the respective
ventricle wall. Combined CSF production rates in the choroid plexus of the third
and lateral ventricles can, principally, be obtained by integrating the MRI-acquired
CSF flow profile in the aqueduct of Sylvius over a cardiac cycle. While this method
is used throughout the literature, there is no conclusive data on the accuracy of
this approach. Obtaining CSF production rates in the fourth ventricle via MRI is
more difficult and would require measurement of flow through the small foramina
of Luschka and Magendie. This is not possible with a sufficient level of accuracy
on current clinical MRI scanners. In order to still take CSF production in the fourth
ventricle into account, a ratio between the production rates in this and the remaining
cerebral ventricles can be assumed.
Under physiologic conditions, the average rate of CSF removal is equal to the
production rate. While it is accepted that there are multiple locations of absorption
or drainage throughout the cranial and spinal cavity, there is no consensus on
the relative contributions of the individual exit routes. The classically purported
but increasingly questioned main locations of CSF reabsorption are the arachnoid
granulations that drain into the superior sagittal, transverse and sigmoid sinuses.
It is possible to locate large granulations through MRI, but most of the smaller
ones cannot be detected. Cadaver data on their distribution is available [48], and
areas of the arachnoid mater boundary can be assigned absorption functionality in
CFD simulations. Concretely, the arachnoid granulations can be assumed to act as
one-way differential pressure valves with associated permeability of approximately
92.5 μl . min –1. mmHg –1. cm −2 [49]. Recent studies in rodents have highlighted the
importance of lymphatic CSF drainage [47, 50, 51]. While it is unclear how these
findings translate to humans, it is reasonable that lymphatic drainage should be
considered in models of CSF dynamics. Further experimental work is needed to
obtain quantitative data on the connection between the two fluid spaces.