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Soft tissue modelling through autowaves for surgery simulation

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Abstract

Modelling of soft tissue deformation is of great importance to virtual reality based surgery simulation. This paper presents a new methodology for simulation of soft tissue deformation by drawing an analogy between autowaves and soft tissue deformation. The potential energy stored in a soft tissue as a result of a deformation caused by an external force is propagated among mass points of the soft tissue by non-linear autowaves. The novelty of the methodology is that (i) autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal forces, and (ii) non-linear materials are modelled with non-linear autowaves other than geometric non-linearity. Integration with a haptic device has been achieved to simulate soft tissue deformation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply changing diffusion coefficients.

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Acknowledgments

This research is supported by the Australian Research Council (ARC) Discovery grant (ARC Discovery: DP034946).

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Authors and Affiliations

  1. Robotics and Mechatronics Research Laboratory, Department of Mechanical Engineering, Monash University, P.O. Box 31, Clayton Campus, Clayton, VIC, 3800, Australia

    Yongmin Zhong & Bijan Shirinzadeh

  2. School of Mechanical, Materials, and Mechatronics Engineering, University of Wollongong, Wollongong, NSW, 2522, Australia

    Gursel Alici

  3. Department of Surgery, Monash Medical Centre, Monash University, Clayton, VIC, 3800, Australia

    Julian Smith

Authors
  1. Yongmin Zhong
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  2. Bijan Shirinzadeh
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Correspondence to Yongmin Zhong.

Appendix

Appendix

Consider two adjacent points \({\vec{P}_i}\) and \(\vec{P}_{j},\) where the potentials are \(U_{{\vec{P}_{i}}}\) and \(U_{{\vec{P}_{j}}},\) respectively. The potential at any point \(\vec{P}\) between these two points is regarded as a function of the distance between point \(\vec{P}_{i}\) and point \(\vec{P}.\) Therefore, the following relationships can be written:

$$ \begin{aligned}& U = U(l) \\& l = {\left\| {\vec{P} - \vec{P}_{i}} \right\|} \\ \end{aligned}. $$
(27)

Thus:

$$ \nabla _{{\vec{P}_{i}}} U = \frac{{{\rm d}U}}{{{\rm d}l}}\nabla _{{\vec{P}_{i}}} l = - \frac{{{\left| {U_{{\vec{P}_{j}}} - U_{{\vec{P}_{i}}}} \right|}}}{{{\left\| {\vec{P}_{j} - \vec{P}_{i}} \right\|}}}{{\overrightarrow{P_{i} P_{j}}}}, $$
(28)

where \({{\overrightarrow{P_{i} P_{j}}}} = \frac{{\vec{P}_{j} - \vec{P}_{i}}}{{{\left\| {\vec{P}_{j} - \vec{P}_{i}} \right\|}}}\) and \({\left| {U_{{\vec{P}_{j}}} - U_{{\vec{P}_{i}}}} \right|}\) is the magnitude of the potential change between point \({\vec{P}_i}\) and point \(\vec{P}_{j}.\)

Substituting Eq. 28 into Eq. 17, the force between point \({\vec{P}_i}\) and point \(\vec{P}_{j}\) is

$$ \vec{f}_{{ij}} = D\frac{{{\left| {U_{{\vec{P}_{j}}} - U_{{\vec{P}_{i}}}} \right|}}}{{{\left\| {\vec{P}_{j} - \vec{P}_{i}} \right\|}}}{{\overrightarrow{P_{i}P_{j}}}}. $$
(29)

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Zhong, Y., Shirinzadeh, B., Alici, G. et al. Soft tissue modelling through autowaves for surgery simulation. Med Bio Eng Comput 44, 805–821 (2006). https://doi.org/10.1007/s11517-006-0084-7

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