Department of Computer Graphics and Interface, Institute for Infocomm Research, Singapore, Singapore.
Int J Comput Assist Radiol Surg. 2011 Nov;6(6):829-38. doi: 10.1007/s11548-011-0560-x. Epub 2011 Apr 13.
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.
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.
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.
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.
为了实现手术模拟中的逼真软组织变形建模和触觉渲染，需要准确了解组织材料特性。我们对猪组织进行了生物力学实验，并开发了一种简化的准线性粘弹性模型来描述动脉壁的应变相关松弛行为。该信息用于手术模拟中，当用户握持处于不同水平拉伸状态的虚拟血管时，提供真实的强度降低感觉。
我们对 12 个猪腹主动脉样本进行了单轴拉伸和松弛测试，分别在环向和轴向方向进行。力学性能测试系统包括自动化环境控制、测试和数据采集机制。采用对数和多项式应变能方程的组合来模拟试件的弹性响应。通过整合有理方程作为校正因子，对简化松弛函数进行修正，以精确描述应变相关的松弛效应。
实验表明：（1）在加载速率较低时，动脉组织中的应力对应变速率不敏感；（2）动脉壁的应力松弛率对应变高度敏感。所提出的模型可以准确地描述实验数据。从组合应变能函数得出的应力-应变函数能够以 0.9995 在环向和 0.999 在轴向方向上的 R²拟合拉伸实验数据。修改后的简化松弛函数能够以 0.9686 在环向和 0.988 在轴向方向上的 R²拟合应变相关的松弛。
基于广泛的生物力学实验，所提出的模型可用于手术模拟中动脉变形的精确模拟和触觉渲染。所得模型能够确定在不同应变水平下的应力松弛状态。
