Abstract
Modeling the coupled fluid and elastic mechanics of blood perfused soft tissues is important for medical applications. In particular, the current study aims to capture the effect of tissue swelling and the transport of blood through damaged tissue under bleeding or hemorrhaging conditions. The soft tissue is considered a dynamic poro-hyperelastic material with blood-filled voids. A biphasic formulation—effectively, a generalization of Darcy’s law—is utilized, treating the phases as occupying fractions of the same volume. A Stokes-like friction force and a pressure that penalizes deviations from volume fractions summing to unity serve as the interaction force between solid and liquid phases. The resulting equations for both phases are discretized with the method of smoothed particle hydrodynamics (SPH). The solver is validated separately on each phase and demonstrates good agreement with exact solutions in test problems. Simulations of oozing, hysteresis, swelling, drying and shrinkage, and tissue fracturing and hemorrhage are shown in the paper.
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We gratefully acknowledge the support of the US Army Medical Research Acquisition Activity (grant no. W81XWH-15-1-0147) and the US Office of Naval Research (grant no. N00014-13-C-0357).
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Appendix: Kernel functions
Appendix: Kernel functions
The cubic spline kernel
where κ = 2 and α0 = 2/(3h), 10/(7πh2), 1/(πh3) in 1, 2, and 3 dimensions, respectively.
The third-degree polynomial kernel
where κ = 1 and α0 = 10/(3πh2), 15/(2πh3) in 2 and 3 dimensions, respectively.
The sixth-degree polynomial kernel
where κ = 1 and α0 = 35/(16h), 4/(πh2), 315/(64πh3) in 1, 2, and 3 dimensions, respectively.
The spiky kernel:
where κ = 1 and α0 = 4/h, 10/(πh2), 15/(πh3) in 1, 2, and 3 dimensions, respectively.
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Chang, YJ., Benharash, P., Dutson, E.P. et al. Smoothed particle hydrodynamics simulation of biphasic soft tissue and its medical applications. Med Biol Eng Comput 59, 227–242 (2021). https://doi.org/10.1007/s11517-020-02283-w
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DOI: https://doi.org/10.1007/s11517-020-02283-w