9 Modelling of Cerebrospinal Fluid Flow by Computational Fluid Dynamics
225
whether turbulence modelling should be considered. In contrast to DNS, in which
also the smallest flow features are captured by employing very high spatial and
temporal resolution, turbulence models approximate the effect of these features,
thereby reducing computational cost [56].
9.3 Existing CFD Models
This section gives an overview of CFD models of CSF dynamics, starting with
the early studies that established the field. These initial models in particular
covered small subdomains of the expansive CSF space, beginning with parts of the
ventricular system, wherefrom the focus shifted over time to the subarachnoid and
perivascular spaces. The current trend goes towards both modelling multiple CSF
compartments at once and increasing the fidelity of smaller-scale models.
9.3.1 Ventricular Space
The first CFD study on flow in the CSF space was carried out by Jacobson and
co-workers in 1996, investigating fluid dynamics through a representation of the
aqueduct of Sylvius with stiff walls [6]. The same authors followed up with an
investigation of aqueduct stenosis in 1999, in which they approximated the geometry
of the aqueduct of Sylvius based on published anatomic data [57]. Several years
later, Fin and Grebe modelled the aqueduct wall as a deformable membrane and
compared these results to data attained with rigid walls [58]. The domain geometry
was obtained by MRI and CSF flow was calculated using finite element and
immersed boundaries methods. Under steady flow conditions, they obtained a 37%
lower pressure drop in the case with deformable walls compared to rigid walls.
This remarkable difference raises the question whether such a large influence of
boundary conditions on the results does not diminish the value of CFD, as the actual
aqueduct wall stiffness is not known. One may ask why the substantial additional
time and effort needed for CFD modelling should be invested compared to simple
bulk models. Bulk models will be sufficient if bulk values such as the pressure drop
across a simple structure are sought. If, however, one is interested in the effect of
local geometric features on flow, CFD models will provide added value. To be clear,
this still requires that the boundary conditions, which largely determine the accuracy
of the model, are well chosen.
After the CFD studies of the aqueduct of Sylvius, other researchers directed
their efforts at the remainder of the ventricular space, using varying levels of
detail both in the representation of the anatomy and in the acquisition of the
boundary conditions. In 2005, Kurtcuoglu et al. published results of simulations on
a simplified representation of the entire ventricular space, within which CSF flow
was driven by the expansion and contraction of the third ventricle walls [59], as
225
whether turbulence modelling should be considered. In contrast to DNS, in which
also the smallest flow features are captured by employing very high spatial and
temporal resolution, turbulence models approximate the effect of these features,
thereby reducing computational cost [56].
9.3 Existing CFD Models
This section gives an overview of CFD models of CSF dynamics, starting with
the early studies that established the field. These initial models in particular
covered small subdomains of the expansive CSF space, beginning with parts of the
ventricular system, wherefrom the focus shifted over time to the subarachnoid and
perivascular spaces. The current trend goes towards both modelling multiple CSF
compartments at once and increasing the fidelity of smaller-scale models.
9.3.1 Ventricular Space
The first CFD study on flow in the CSF space was carried out by Jacobson and
co-workers in 1996, investigating fluid dynamics through a representation of the
aqueduct of Sylvius with stiff walls [6]. The same authors followed up with an
investigation of aqueduct stenosis in 1999, in which they approximated the geometry
of the aqueduct of Sylvius based on published anatomic data [57]. Several years
later, Fin and Grebe modelled the aqueduct wall as a deformable membrane and
compared these results to data attained with rigid walls [58]. The domain geometry
was obtained by MRI and CSF flow was calculated using finite element and
immersed boundaries methods. Under steady flow conditions, they obtained a 37%
lower pressure drop in the case with deformable walls compared to rigid walls.
This remarkable difference raises the question whether such a large influence of
boundary conditions on the results does not diminish the value of CFD, as the actual
aqueduct wall stiffness is not known. One may ask why the substantial additional
time and effort needed for CFD modelling should be invested compared to simple
bulk models. Bulk models will be sufficient if bulk values such as the pressure drop
across a simple structure are sought. If, however, one is interested in the effect of
local geometric features on flow, CFD models will provide added value. To be clear,
this still requires that the boundary conditions, which largely determine the accuracy
of the model, are well chosen.
After the CFD studies of the aqueduct of Sylvius, other researchers directed
their efforts at the remainder of the ventricular space, using varying levels of
detail both in the representation of the anatomy and in the acquisition of the
boundary conditions. In 2005, Kurtcuoglu et al. published results of simulations on
a simplified representation of the entire ventricular space, within which CSF flow
was driven by the expansion and contraction of the third ventricle walls [59], as