5 Modelling of the Brain for Injury Simulation and Prevention
117
control these modes are tedious, and the reader is referred to relevant papers on
the subject, such as Hughes [36] and Yang [105]. Many software packages allow
changing the hourglass energy coefficient to adjust the extent hourglass energy. It
has been recommended that the hourglass energy should not exceed 10% of the total
energy in order to assure accuracy of simulation results [62].
5.3.4 Boundary Conditions
Representing the pia-arachnoid complex (PAC), within which the CSF flows,
remains an unresolved issue in brain modelling. Techniques used in the past
include a direct connection with no slip, direct coupling at the junction, sliding
interface with different coefficients of friction, or tie-break with a preset threshold.
A major reason for these selections is probably due to the fact that some researchers
were either unaware of or decided to ignore the existence of trabeculae within
the subarachnoid space. Also, the complex and random nature of the distribution
of trabeculae in the PAC makes it impossible to model them explicitly. While
the exact method to model the PAC and the CSF within it has not been agreed
upon, it has been noted that representing this layer by a gap cannot be used to
generate tension in the contrecoup site, thus making it unsuitable to model the
contrecoup phenomenon reported by clinicians. To accurately predict brain-skull
relative motion, it’s necessary to represent the meninges and the CSF that’s between
the arachnoid and the pia [98]. A recent study also suggested using fluid elements
to represent the CSF [112].
Experimental data reported by Jin et al. [42, 43] on bovine PAC showed that the
trabeculae in the CSF layer offer finite shear resistance; thus it would be a mistake
to model this layer as an incompressible fluid. A set of constitutive equations has
been developed for bovine PAC [45]. Effort should be devoted to determine inplane, traction, and shear loading responses in human pia-arachnoid samples using
methods similar to those reported by Jin et al. [42, 43]. Once a set of constitutive
equations is developed to represent the PAC and CSF, this combined structure can
be properly modelled. There is no evidence to suggest the need to model the CSF
surrounding the spinal cord. Unless there is new information to suggest otherwise,
the sliding of the cord relative to the surrounding dura can be represented by a
sliding interface.
The large oval opening in the occipital bone of the skull, or foramen magnum, is
frequently represented by a membrane in most head models. The material properties
selected for this membrane regulate the magnitude of intracranial pressure as a
flexible membrane would allow some deformation at the foramen and this increase
in brain volume will decrease the pressure within the skull. In other models, a set
of boundary conditions were assigned when modelling the foramen magnum. More
research is needed to determine the best way to model this anatomic opening.
117
control these modes are tedious, and the reader is referred to relevant papers on
the subject, such as Hughes [36] and Yang [105]. Many software packages allow
changing the hourglass energy coefficient to adjust the extent hourglass energy. It
has been recommended that the hourglass energy should not exceed 10% of the total
energy in order to assure accuracy of simulation results [62].
5.3.4 Boundary Conditions
Representing the pia-arachnoid complex (PAC), within which the CSF flows,
remains an unresolved issue in brain modelling. Techniques used in the past
include a direct connection with no slip, direct coupling at the junction, sliding
interface with different coefficients of friction, or tie-break with a preset threshold.
A major reason for these selections is probably due to the fact that some researchers
were either unaware of or decided to ignore the existence of trabeculae within
the subarachnoid space. Also, the complex and random nature of the distribution
of trabeculae in the PAC makes it impossible to model them explicitly. While
the exact method to model the PAC and the CSF within it has not been agreed
upon, it has been noted that representing this layer by a gap cannot be used to
generate tension in the contrecoup site, thus making it unsuitable to model the
contrecoup phenomenon reported by clinicians. To accurately predict brain-skull
relative motion, it’s necessary to represent the meninges and the CSF that’s between
the arachnoid and the pia [98]. A recent study also suggested using fluid elements
to represent the CSF [112].
Experimental data reported by Jin et al. [42, 43] on bovine PAC showed that the
trabeculae in the CSF layer offer finite shear resistance; thus it would be a mistake
to model this layer as an incompressible fluid. A set of constitutive equations has
been developed for bovine PAC [45]. Effort should be devoted to determine inplane, traction, and shear loading responses in human pia-arachnoid samples using
methods similar to those reported by Jin et al. [42, 43]. Once a set of constitutive
equations is developed to represent the PAC and CSF, this combined structure can
be properly modelled. There is no evidence to suggest the need to model the CSF
surrounding the spinal cord. Unless there is new information to suggest otherwise,
the sliding of the cord relative to the surrounding dura can be represented by a
sliding interface.
The large oval opening in the occipital bone of the skull, or foramen magnum, is
frequently represented by a membrane in most head models. The material properties
selected for this membrane regulate the magnitude of intracranial pressure as a
flexible membrane would allow some deformation at the foramen and this increase
in brain volume will decrease the pressure within the skull. In other models, a set
of boundary conditions were assigned when modelling the foramen magnum. More
research is needed to determine the best way to model this anatomic opening.