Immersed finite element method and its applications to biological systems

Wing K Liu*, Yaling Liu, David Farrell, Lucy Zhang, X. Sheldon Wang, Yoshio Fukui, Neelesh A Patankar, Yongjie Zhang, Chandrajit Bajaj, Junghoon Lee, Juhee Hong, Xinyu Chen, Huayi Hsu

*Corresponding author for this work

Research output: Contribution to journalArticle

186 Scopus citations

Abstract

This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid sub-domains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility.

Original languageEnglish (US)
Pages (from-to)1722-1749
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
Volume195
Issue number13-16
DOIs
StatePublished - Feb 15 2006

Keywords

  • Aggregation
  • Cardiovascular system
  • Cell motility
  • Cytoskeletal dynamics
  • Fluid-structure interaction
  • Immersed finite element method
  • Micro-circulation
  • Nano-electro-mechanical-sensors
  • Red blood cell
  • Reproducing Kernel particle method
  • Surgical corrective procedures
  • Thrombosis

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Immersed finite element method and its applications to biological systems'. Together they form a unique fingerprint.

  • Cite this

    Liu, W. K., Liu, Y., Farrell, D., Zhang, L., Wang, X. S., Fukui, Y., Patankar, N. A., Zhang, Y., Bajaj, C., Lee, J., Hong, J., Chen, X., & Hsu, H. (2006). Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering, 195(13-16), 1722-1749. https://doi.org/10.1016/j.cma.2005.05.049