POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres

Suleiman Banihani, Timon Rabczuk, Thakir Almomani

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.

Original languageEnglish
Article number386501
JournalMathematical Problems in Engineering
Volume2013
DOIs
Publication statusPublished - 2013 Dec 1

Fingerprint

Biological Tissue
Orthogonal Decomposition
Collocation Method
Tissue
Decomposition
Real-time
Model Order Reduction
Meshfree
Simulation
Reduced Order Model
Function Approximation
Data Storage
Numerical Techniques
Computational Efficiency
Surgery
Nonlinear Problem
Computational Cost
Boundary Value Problem
Physics
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres. / Banihani, Suleiman; Rabczuk, Timon; Almomani, Thakir.

In: Mathematical Problems in Engineering, Vol. 2013, 386501, 01.12.2013.

Research output: Contribution to journalArticle

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