Chapter 10
Finite Element Algorithms for
Computational Biomechanics
of the Brain
Adam Wittek, Grand Roman Joldes, and Karol Miller
10.1 Introduction
Modelling of the brain biomechanical responses due to injury-causing transients and
surgery is a problem of continuum mechanics that involves irregular geometry, complex loading and boundary conditions, non-linear materials and large deformations
(see Chaps. 5 and 6). Finding a solution for such a problem requires computational
algorithms of non-linear continuum mechanics.
As stated in Chap. 5, modelling for brain injury simulation has been driven
by the idea that numerical surrogates of the human brain can be applied in the
design of countermeasures mitigating the traumatic brain injury. Such modelling
has been done with significant contribution and involvement of the automotive
manufacturers [1] and participation of organisations responsible for traffic safety
(e.g. National Highway Traffic Safety Administration (NHTSA)) [2]. Because of
this industrial links and implications, modelling of the brain for injury simulation
has been dominated by the explicit dynamics (i.e. utilising explicit time stepping
referred to in the literature also as explicit time integration [3, 4]) non-linear finite
element algorithms available in commercial finite element codes, such as LS-DYNA
[5], PAM-SAFE [6], RADIOSS [7] and ABAQUS [8], which are routinely used by
the automotive industry.
In computational biomechanics for medicine, on the other hand, significant
research effort has been directed to development of specialised algorithms that can
provide the results within the real-time constraints of surgery. For instance, great
interest was given to mass-spring method [9, 10] in which the analysed continuum is
modelled as a discrete system of nodes (where the mass is concentrated) and springs.
A. Wittek () · G. R. Joldes · K. Miller
Intelligent Systems for Medicine Laboratory, Department of Mechanical Engineering,
The University of Western Australia, Perth, WA, Australia
e-mail: adam.wittek@uwa.edu.au; karol.miller@uwa.edu.au
© Springer Nature Switzerland AG 2019
K. Miller (ed.), Biomechanics of the Brain, Biological and Medical Physics,
Biomedical Engineering, https://doi.org/10.1007/978-3-030-04996-6_10
243
Finite Element Algorithms for
Computational Biomechanics
of the Brain
Adam Wittek, Grand Roman Joldes, and Karol Miller
10.1 Introduction
Modelling of the brain biomechanical responses due to injury-causing transients and
surgery is a problem of continuum mechanics that involves irregular geometry, complex loading and boundary conditions, non-linear materials and large deformations
(see Chaps. 5 and 6). Finding a solution for such a problem requires computational
algorithms of non-linear continuum mechanics.
As stated in Chap. 5, modelling for brain injury simulation has been driven
by the idea that numerical surrogates of the human brain can be applied in the
design of countermeasures mitigating the traumatic brain injury. Such modelling
has been done with significant contribution and involvement of the automotive
manufacturers [1] and participation of organisations responsible for traffic safety
(e.g. National Highway Traffic Safety Administration (NHTSA)) [2]. Because of
this industrial links and implications, modelling of the brain for injury simulation
has been dominated by the explicit dynamics (i.e. utilising explicit time stepping
referred to in the literature also as explicit time integration [3, 4]) non-linear finite
element algorithms available in commercial finite element codes, such as LS-DYNA
[5], PAM-SAFE [6], RADIOSS [7] and ABAQUS [8], which are routinely used by
the automotive industry.
In computational biomechanics for medicine, on the other hand, significant
research effort has been directed to development of specialised algorithms that can
provide the results within the real-time constraints of surgery. For instance, great
interest was given to mass-spring method [9, 10] in which the analysed continuum is
modelled as a discrete system of nodes (where the mass is concentrated) and springs.
A. Wittek () · G. R. Joldes · K. Miller
Intelligent Systems for Medicine Laboratory, Department of Mechanical Engineering,
The University of Western Australia, Perth, WA, Australia
e-mail: adam.wittek@uwa.edu.au; karol.miller@uwa.edu.au
© Springer Nature Switzerland AG 2019
K. Miller (ed.), Biomechanics of the Brain, Biological and Medical Physics,
Biomedical Engineering, https://doi.org/10.1007/978-3-030-04996-6_10
243