9 Modelling of Cerebrospinal Fluid Flow by Computational Fluid Dynamics
217
The procedural steps in CFD modelling of cerebrospinal fluid dynamics are
similar to those encountered in generic problems of incompressible, isothermal
internal flows. In a first step, the model domain must be defined, which consists
of at least one fluid domain and, if the deformation of surrounding tissue is to be
modelled, one or more solid domains. In the second step, these domains must be
discretized, which includes choosing a spatial discretization scheme and generating
a computational grid. Depending on the manageable grid size, which is primarily
determined by the available computer resources, and expected flow conditions, a
turbulence modelling scheme may be necessary as well. Next, the behaviour of
the fluids and solids at their respective domain boundaries must be prescribed,
i.e. corresponding pressures, velocities or their derivatives in those areas must be
determined a priori and set accordingly. In the fourth step, the physical properties
of the fluids and solids (rheology, material properties) have to be set. Finally, the
Navier-Stokes, continuity and, if considered, transport equations must be solved
based on appropriate initial conditions. If the problem is transient, a suitable
temporal discretization scheme is required. The following section discusses these
steps for the case of subject-specific CSF flow simulations based on MRI data.
9.2 Procedural Steps in CFD Modelling of CSF Dynamics
9.2.1 Obtaining the Model Domain
The cerebrospinal fluid spaces consist of a number of connected compartments (Fig.
9.1). For modelling purposes, MRI is the most widely used method for determining
their shapes and the anatomies of associated blood vessels. Due to limits in
resolution, the largest part of the cerebral vasculature cannot be acquired in sufficient
detail for CFD. If the interaction between blood and CSF flow is to be taken into
account explicitly by calculating the transient displacements of the arterial walls
and transmission to the CSF space, smaller vessels have to be simulated via lowerorder models. These models can be coupled to the CFD representations of larger
vessels. However, this coupling poses numerical and computational challenges [7].
MRI partial volume effects also limit CSF space representation of small features
such as the foramina of Monro, Luschka and Magendie, posterior horns of the
lateral ventricles, aqueduct of Sylvius and recesses of the third and fourth ventricle
[8]. Nevertheless, the overall size of these entities is large enough that lowerorder modelling is not required. In contrast, the SAS features minute structures
such as nerve roots, denticulate ligaments and arachnoid trabeculae that cannot
be imaged adequately or captured at all by current clinical MRI systems. Despite
their small sizes, these entities may increase the pressure drop along the SAS
substantially [9, 10]. Nerve roots and similar structures can be integrated into the
computational domain artificially by computer-aided design based on generic highresolution anatomy data [11, 12]. The contribution of arachnoid trabeculae to flow
217
The procedural steps in CFD modelling of cerebrospinal fluid dynamics are
similar to those encountered in generic problems of incompressible, isothermal
internal flows. In a first step, the model domain must be defined, which consists
of at least one fluid domain and, if the deformation of surrounding tissue is to be
modelled, one or more solid domains. In the second step, these domains must be
discretized, which includes choosing a spatial discretization scheme and generating
a computational grid. Depending on the manageable grid size, which is primarily
determined by the available computer resources, and expected flow conditions, a
turbulence modelling scheme may be necessary as well. Next, the behaviour of
the fluids and solids at their respective domain boundaries must be prescribed,
i.e. corresponding pressures, velocities or their derivatives in those areas must be
determined a priori and set accordingly. In the fourth step, the physical properties
of the fluids and solids (rheology, material properties) have to be set. Finally, the
Navier-Stokes, continuity and, if considered, transport equations must be solved
based on appropriate initial conditions. If the problem is transient, a suitable
temporal discretization scheme is required. The following section discusses these
steps for the case of subject-specific CSF flow simulations based on MRI data.
9.2 Procedural Steps in CFD Modelling of CSF Dynamics
9.2.1 Obtaining the Model Domain
The cerebrospinal fluid spaces consist of a number of connected compartments (Fig.
9.1). For modelling purposes, MRI is the most widely used method for determining
their shapes and the anatomies of associated blood vessels. Due to limits in
resolution, the largest part of the cerebral vasculature cannot be acquired in sufficient
detail for CFD. If the interaction between blood and CSF flow is to be taken into
account explicitly by calculating the transient displacements of the arterial walls
and transmission to the CSF space, smaller vessels have to be simulated via lowerorder models. These models can be coupled to the CFD representations of larger
vessels. However, this coupling poses numerical and computational challenges [7].
MRI partial volume effects also limit CSF space representation of small features
such as the foramina of Monro, Luschka and Magendie, posterior horns of the
lateral ventricles, aqueduct of Sylvius and recesses of the third and fourth ventricle
[8]. Nevertheless, the overall size of these entities is large enough that lowerorder modelling is not required. In contrast, the SAS features minute structures
such as nerve roots, denticulate ligaments and arachnoid trabeculae that cannot
be imaged adequately or captured at all by current clinical MRI systems. Despite
their small sizes, these entities may increase the pressure drop along the SAS
substantially [9, 10]. Nerve roots and similar structures can be integrated into the
computational domain artificially by computer-aided design based on generic highresolution anatomy data [11, 12]. The contribution of arachnoid trabeculae to flow