Paper:

# Moving Particle Semi-Implicit and Finite Element Method Coupled Analysis for Brain Shift Estimation

## Akito Ema^{*1}, Xiaoshuai Chen^{*2}, Kazuya Sase^{*3}, Teppei Tsujita^{*4}, and Atsushi Konno^{*1}

^{*1}Graduate School of Information Science and Technology, Hokkaido University

Kita 14, Nishi 9, Kita-ku, Sapporo, Hokkaido 060-0814, Japan

^{*2}Graduate School of Science and Technology, Hirosaki University

3 Bunkyo-cho, Hirosaki, Aomori 036-8560, Japan

^{*3}Faculty of Engineering, Tohoku Gakuin University

1-13-1 Chuo, Tagajo, Miyagi 980-8511, Japan

^{*4}Department of Mechanical Engineering, National Defense Academy of Japan

1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686, Japan

Neuronavigation is a computer-assisted technique for presenting three-dimensional images of a patient’s brain to facilitate immediate and precise lesion localization by surgeons. Neuronavigation systems use preoperative medical images of patients. In neurosurgery, when the dura mater and arachnoid membrane are incised and the cerebrospinal fluid (CSF) drains out, the brain loses the CSF buoyancy and deforms in the direction of gravity, which is referred to as *brain shift*. This brain shift yields inaccurate neuronavigation. To reduce this inaccuracy, an intraoperative brain shift should be estimated. This paper proposes a dynamic simulation method for brain-shift estimation combining the moving-particle semi-implicit (MPS) method and the finite element method (FEM). The CSF was modeled using fluid particles, whereas the brain parenchyma was modeled using finite elements (FEs). Node particles were attached to the surface nodes of the brain parenchyma in the FE model. The interaction between the CSF and brain parenchyma was simulated using the repulsive force between the fluid particles and node particles. Validation experiments were performed using a gelatin block. The gelatin block was dipped into silicone oil, which was then gradually removed; the block deformation owing to the buoyancy loss was measured. The experimental deformation data were compared with the results of the MPS-FEM coupled analysis. The mean absolute error (MAE) between the simulated deformation and the average across the four experiments was 0.26 mm, while the mean absolute percentage error (MAPE) was 27.7%. Brain-shift simulations were performed using the MPS-FEM coupled analysis, and the computational cost was evaluated.

*J. Robot. Mechatron.*, Vol.34, No.6, pp. 1306-1317, 2022.

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