268
A. Wittek et al.
10.9 Conclusions
Modelling of the brain for injury simulation and computer-assisted neurosurgery
is a non-linear problem of continuum mechanics and involves large deformations,
very large strains (over 0.8 in compression during needle insertion [21]), non-linear
material models, complex loading and boundary conditions and complex geometry.
Various finite element (FE) algorithms have been applied for solving this problem.
Modelling of the brain for injury simulation has been often conducted with the
goal of using numerical surrogates of the human head in design of countermeasures
for traumatic brain injury mitigation. Such modelling has been almost exclusively
conducted using non-linear explicit dynamics (i.e. utilising explicit time stepping,
referred to in the literature also as explicit time integration [3, 4]) finite element
algorithms implemented in commercial finite element codes that are routinely used
in the automotive industry for transient dynamics problems involving rapid (impacttype) loading such as car structure responses during collision and sheet metal
forming.
However, the computational efficiency of the algorithms available in commercial
finite element codes is insufficient for computer-integrated neurosurgery where the
solution needs to be provided within the real-time constraints of neurosurgery. This
led to development of the specialised non-linear finite element algorithms aiming
at satisfying these constraints. We advocate application of non-linear finite element
algorithms utilising explicit time stepping (and therefore requiring no iteration for
non-linear problems) and Total Lagrangian incremental formulation of continuum
mechanics (as it allows precomputing of the derivatives with respect to the spatial
coordinates):
• Total Lagrangian Explicit Dynamics (TLED) finite element algorithm for time
accurate solution for surgery simulation.
• Dynamic Relaxation (DR) Total Lagrangian algorithm for computing steady state
deformations for neurosurgery modelling.
For hardware-based increase of computation speed, we propose the implementation of these algorithms on graphics processing units (GPUs) by using a GPU as a
coprocessor for the computer central processing unit (CPU). It has been shown in
Joldes et al. [64] that the implementation of the finite element Dynamic Relaxation
algorithm on NVIDIA Tesla C870 GPU performs 2000 iterations of the brain shift
simulation in under 2 s, offering real-time computation capabilities at a fraction of
a traditional supercomputer or PC cluster cost. It can be expected that for newer
generation of GPUs, this already excellent performance would appreciably improve
due to significant increase in the number of streaming processor cores (e.g. NVIDIA
Tesla C870 GPU had 128 cores while NVIDIA Quadro GV100 GPU released in
June 2017 has 5120 cores [62, 72]) and available memory (with 32 GB memory for
NVIDIA Quadro GV100) [62, 72]).
Application of even most efficient finite element algorithms in surgery simulation
and neurosurgery modelling is limited by time-consuming generation of patient-
A. Wittek et al.
10.9 Conclusions
Modelling of the brain for injury simulation and computer-assisted neurosurgery
is a non-linear problem of continuum mechanics and involves large deformations,
very large strains (over 0.8 in compression during needle insertion [21]), non-linear
material models, complex loading and boundary conditions and complex geometry.
Various finite element (FE) algorithms have been applied for solving this problem.
Modelling of the brain for injury simulation has been often conducted with the
goal of using numerical surrogates of the human head in design of countermeasures
for traumatic brain injury mitigation. Such modelling has been almost exclusively
conducted using non-linear explicit dynamics (i.e. utilising explicit time stepping,
referred to in the literature also as explicit time integration [3, 4]) finite element
algorithms implemented in commercial finite element codes that are routinely used
in the automotive industry for transient dynamics problems involving rapid (impacttype) loading such as car structure responses during collision and sheet metal
forming.
However, the computational efficiency of the algorithms available in commercial
finite element codes is insufficient for computer-integrated neurosurgery where the
solution needs to be provided within the real-time constraints of neurosurgery. This
led to development of the specialised non-linear finite element algorithms aiming
at satisfying these constraints. We advocate application of non-linear finite element
algorithms utilising explicit time stepping (and therefore requiring no iteration for
non-linear problems) and Total Lagrangian incremental formulation of continuum
mechanics (as it allows precomputing of the derivatives with respect to the spatial
coordinates):
• Total Lagrangian Explicit Dynamics (TLED) finite element algorithm for time
accurate solution for surgery simulation.
• Dynamic Relaxation (DR) Total Lagrangian algorithm for computing steady state
deformations for neurosurgery modelling.
For hardware-based increase of computation speed, we propose the implementation of these algorithms on graphics processing units (GPUs) by using a GPU as a
coprocessor for the computer central processing unit (CPU). It has been shown in
Joldes et al. [64] that the implementation of the finite element Dynamic Relaxation
algorithm on NVIDIA Tesla C870 GPU performs 2000 iterations of the brain shift
simulation in under 2 s, offering real-time computation capabilities at a fraction of
a traditional supercomputer or PC cluster cost. It can be expected that for newer
generation of GPUs, this already excellent performance would appreciably improve
due to significant increase in the number of streaming processor cores (e.g. NVIDIA
Tesla C870 GPU had 128 cores while NVIDIA Quadro GV100 GPU released in
June 2017 has 5120 cores [62, 72]) and available memory (with 32 GB memory for
NVIDIA Quadro GV100) [62, 72]).
Application of even most efficient finite element algorithms in surgery simulation
and neurosurgery modelling is limited by time-consuming generation of patient-