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Meshless Algorithms for Computational Biomechanics of the Brain

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Biomechanics of the Brain

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Abstract

In this chapter, we discuss meshless methods of computational biomechanics, which utilise computational grids in a form of clouds of points, in the context of computation of the brain deformations due to surgery and injury. We highlight that meshless discretisation may be regarded as a possible solution for overcoming the limitations of the finite element method. We advocate application of weak-form meshless methods that use background cells for spatial integration, explicit time stepping, and total Lagrangian formulation of continuum mechanics (where the derivatives with respect to the spatial coordinates can be pre-computed). We make specific recommendations regarding the following key aspects of the brain deformation computation using meshless methods: (1) shape functions that facilitate robust numerical solution for irregular node placement (a feature necessary to enable end-users who are not experts in computational mechanics to build patient-specific computational biomechanics models of the brain and other body organs), (2) ensuring the desired accuracy of Gaussian spatial integration for non-polynomial shape functions through adaptive integration schemes, and (3) determining a critical time step that ensures stability of the solution provided by explicit dynamics meshless algorithms. We also discuss soft tissue dissection simulation using a visibility criterion (where the model nodes located on the opposite sides of the dissection-induced crack cannot interact with each other) while leaving open the question about the method of choice for three-dimensional dissection simulation. We provide examples of verification of the discussed meshless algorithms against the reference solutions obtained using the well-established non-linear finite element procedures.

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Acknowledgements

This chapter uses the published results of research supported by the funding from the Australian Government through the Australian Research Council (ARC) (Discovery Project Grants DP160100714, DP1092893 and DP120100402) and National Health and Medical Research Council (NHMRC) (Project Grants APP1006031 and APP1144519). The authors thank Prof. King Hay Yang and Dr. Xin Jin of Bioengineering Centre and Biomedical Engineering Department of Wayne State University for providing the experimental data used in the reference[58].

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Authors and Affiliations

  1. Intelligent Systems for Medicine Laboratory, Department of Mechanical Engineering, The University of Western Australia, Perth, WA, Australia

    Adam Wittek, Grand Roman Joldes & Karol Miller

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  1. Adam Wittek
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  2. Grand Roman Joldes
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  3. Karol Miller
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Correspondence to Adam Wittek .

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  1. Intelligent Systems for Medicine Laboratory, The University of Western Australia, Perth, WA, Australia

    Karol Miller

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Wittek, A., Joldes, G.R., Miller, K. (2019). Meshless Algorithms for Computational Biomechanics of the Brain. In: Miller, K. (eds) Biomechanics of the Brain. Biological and Medical Physics, Biomedical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-04996-6_11

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