Chapter 11
Meshless Algorithms for Computational
Biomechanics of the Brain
Adam Wittek, Grand Roman Joldes, and Karol Miller
11.1 Introduction
In Chap. 10, we highlighted two important factors that limit application of finite
element method in predicting the brain responses for surgery simulation and pose
a significant challenge in application to injury biomechanics when the body tissues
undergo rupture/failure:
1. Time-consuming generation of patient-specific finite element meshes of the brain
and other body organs [1]
2. Deterioration of the solution accuracy and instability when the finite element
meshes undergo distortion induced by large localised deformations caused by
interactions between the organ and surgical tool [2] and by injury
Meshless algorithms [3–5], in which the analysed continuum is discretised by
nodes (where forces and displacements are calculated) with no assumed structure
for the interconnection of the nodes and integration points (where stresses and
strains are calculated) (Fig. 11.1), have been proposed in the literature for generating
computational grids of domains with complex geometry and providing reliable
results for large deformations [7–10].
Smoothed particle hydrodynamics (SPH) is regarded as the first meshless
method. It utilises a strong form of equations of continuum mechanics [11]. SPH
and other particle methods (such as material point method in which a strong form
of equations of continuum mechanics is used) were applied in injury biomechanics
[12–14]. However, the literature indicates several important shortcomings of the
SPH method, which includes instabilities in tension and accuracy inferior to that
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_11
273
Meshless Algorithms for Computational
Biomechanics of the Brain
Adam Wittek, Grand Roman Joldes, and Karol Miller
11.1 Introduction
In Chap. 10, we highlighted two important factors that limit application of finite
element method in predicting the brain responses for surgery simulation and pose
a significant challenge in application to injury biomechanics when the body tissues
undergo rupture/failure:
1. Time-consuming generation of patient-specific finite element meshes of the brain
and other body organs [1]
2. Deterioration of the solution accuracy and instability when the finite element
meshes undergo distortion induced by large localised deformations caused by
interactions between the organ and surgical tool [2] and by injury
Meshless algorithms [3–5], in which the analysed continuum is discretised by
nodes (where forces and displacements are calculated) with no assumed structure
for the interconnection of the nodes and integration points (where stresses and
strains are calculated) (Fig. 11.1), have been proposed in the literature for generating
computational grids of domains with complex geometry and providing reliable
results for large deformations [7–10].
Smoothed particle hydrodynamics (SPH) is regarded as the first meshless
method. It utilises a strong form of equations of continuum mechanics [11]. SPH
and other particle methods (such as material point method in which a strong form
of equations of continuum mechanics is used) were applied in injury biomechanics
[12–14]. However, the literature indicates several important shortcomings of the
SPH method, which includes instabilities in tension and accuracy inferior to that
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_11
273