University of Florida, Gainesville, FL, 32611, USA.
Int J Comput Assist Radiol Surg. 2022 Dec;17(12):2183-2192. doi: 10.1007/s11548-022-02742-9. Epub 2022 Sep 16.
Soft-tissue manipulations, such as collecting, stretching or tearing tissue, are a common component of surgery. When too much force is applied, these manipulations result in a residual plastic deformation that surgeons should be aware of and that should be modeled by surgical simulation.
Many tissues, vessels and organs can be modeled as offsets of curved simple shapes with primary directions, e.g., radial and axial for cylinders yield a rectangular mesh whose normal offset naturally yields a hexahedral mesh that can serve as a thick shell. Other organs are easy to embed into and deform following a hex mesh. We extend existing code for the volumetric finite element method (FEM) to model tissue plasticity as hexahedral thick shells or embedded organs. Specifically, the work extends the open source Simulation Open Framework Architecture and its newest hyperelastic deformation addition, Caribou, with focus on surgical simulation. The extension factors deformation gradients into (corotational or hyperelastic) elastic factors and plastic factors and enforces volume preservation. Limits on per-element twist, twist torque, material hardening and bounds on plasticity where elements invert avoid the need for re-meshing.
Our hexahedral FEM avoids the biased outcomes of asymmetric coarsely-partitioned tetrahedral FEM. Caribou's hyperelastic FEM is extended to hex-FEM stretching plasticity. Our high-order accurate blended-vertex deformation enables coarse hex meshes to model large plastic rotational and stretch deformations without re-meshing. We compare a vertex-blended to a cell-centered piecewise constant approach; contrast plasticity based on corotational FEM and hyperelastic FEM; and test the computation under mesh refinement. The volume is preserved also for large deformations.
On-the-fly generated hexahedral meshes can directly be used as finite element domains for plastic deformation based on corotational or hyperelastic elasticity. The outcome is suitable for surgical simulation.
软组织操作，如组织的采集、拉伸或撕裂，是手术的常见组成部分。当施加的力过大时，这些操作会导致剩余的塑性变形，外科医生应该注意到这一点，并通过手术模拟对其进行建模。
许多组织、血管和器官可以建模为具有主方向的弯曲简单形状的偏移，例如，圆柱的径向和轴向产生一个矩形网格，其法向偏移自然产生一个六面体网格，可以用作厚壳。其他器官很容易嵌入并跟随六面体网格变形。我们将体积有限元方法（FEM）的现有代码扩展到组织塑性建模作为六面体厚壳或嵌入器官。具体来说，这项工作扩展了开源 Simulation Open Framework Architecture 及其最新的超弹性变形添加 Caribou，重点是手术模拟。扩展因素将变形梯度分解为（共旋或超弹性）弹性因子和塑性因子，并强制体积保持。每个元素的扭转限制、扭转扭矩、材料硬化和元素反转的塑性限制避免了重新网格化的需要。
我们的六面体 FEM 避免了非对称粗部分化四面体 FEM 的有偏结果。Caribou 的超弹性 FEM 被扩展到六面体 FEM 拉伸塑性。我们的高精度混合顶点变形使粗六面体网格能够在不重新网格化的情况下对大塑性旋转和拉伸变形进行建模。我们比较了顶点混合与单元中心分片常数方法；对比了基于共旋 FEM 和超弹性 FEM 的塑性；并在网格细化下进行了测试。即使在大变形下，体积也得到了保持。
即时生成的六面体网格可以直接用作基于共旋或超弹性弹性的塑性变形的有限元域。结果适用于手术模拟。
