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Quasi-linear viscoelastic modeling of arterial wall for surgical simulation

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International Journal of Computer Assisted Radiology and Surgery Aims and scope Submit manuscript

Abstract

Purpose

Realistic soft tissue deformation modeling and haptic rendering for surgical simulation require accurate knowledge of tissue material characteristics. Biomechanical experiments on porcine tissue were performed, and a reduced quasi-linear viscoelastic model was developed to describe the strain-dependent relaxation behavior of the arterial wall. This information is used in surgical simulation to provide a realistic sensation of reduction in strength when the user holds a virtual blood vessel strained at different levels.

Materials and methods

Twelve pieces of porcine abdominal artery were tested with uniaxial elongation and relaxation test in both circumferential and longitudinal directions. The mechanical property testing system consists of automated environment control, testing, and data collection mechanism. A combined logarithm and polynomial strain energy equation was applied to model the elastic response of the specimens. The reduced relaxation function was modified by integrating a rational equation as a corrective factor to precisely describe the strain-dependent relaxation effects.

Results

The experiments revealed that (1) stress is insensitive to strain rate in arterial tissue when the loading rate is low, and (2) the rate of stress relaxation of arterial wall is highly strain dependent. The proposed model can accurately represent the experimental data. Stress–strain function derived from the combined strain energy function is able to fit the tensile experimental data with R 2 equals to 0.9995 in circumferential direction and 0.999 in longitudinal direction. Modified reduced relaxation function is able to model the strain-dependent relaxation with R 2 equals to 0.9686 in circumferential direction and 0.988 in longitudinal direction.

Conclusion

The proposed model, based on extensive biomechanical experiments, can be used for accurate simulation of arterial deformation and haptic rendering in surgical simulation. The resultant model enables stress relaxation status to be determined when subjected to different strain levels.

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Authors and Affiliations

  1. Department of Computer Graphics and Interface, Institute for Infocomm Research, Singapore, Singapore

    Tao Yang

  2. Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore

    Tao Yang, Chee Kong Chui & Jing Qin

  3. Department of Surgery, Yong Loo Lin School of Medicine National University of Singapore, Singapore, Singapore

    Rui Qi Yu

  4. Department of Surgery, National University Hospital, Singapore, Singapore

    Stephen K. Y. Chang

Authors
  1. Tao Yang
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  2. Chee Kong Chui
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  3. Rui Qi Yu
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  4. Jing Qin
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  5. Stephen K. Y. Chang
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Correspondence to Tao Yang.

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Yang, T., Chui, C.K., Yu, R.Q. et al. Quasi-linear viscoelastic modeling of arterial wall for surgical simulation. Int J CARS 6, 829–838 (2011). https://doi.org/10.1007/s11548-011-0560-x

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  • DOI: https://doi.org/10.1007/s11548-011-0560-x

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