考虑三维残余变形的主动脉生理稳态建模
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国家自然科学基金项目(82241208,82241207,11872267,82000436),上海市科委政府间国际科技合作项目(21410710500),福建省自然科学基金项目(2023J011687)


Modeling Method of Aortic Homeostasis Considering Three-Dimensional Residual Deformation
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    摘要:

    目的 考虑三维残余应力场,计算主动脉壁各个微观组分在生理稳态下的预拉伸。方法 将主动脉壁理想化为双层厚壁圆管。基于三维张开角实验计算血管壁的三维残余应力场,获得平均血压下在体应力的分布特征,进而拟合获得血管壁各微观组分在生理稳态下的预拉伸。根据在体测量得到的猪主动脉内压-半径关系构建反问题,以主动脉生理稳态为参考状态,在整合三维残余应力场的同时实现主动脉在体材料参数的反演识别。结果 未考虑残余应力时,中膜平均应力大于外膜;考虑残余应力时,外膜应力大于中膜,外膜对中膜起保护作用。考虑残余应力时,中膜各组分预拉伸小于未考虑残余应力时,而外膜各组分预拉伸大于未考虑残余应力时;生理稳态下,主动脉外膜内胶原纤维的预拉伸大于中膜内胶原纤维的预拉伸。以生理稳态作为参考构型在体识别主动脉材料参数,所得各组分占比与组织学实验结果一致。反之,以无加载零应力构型作为初始构型在体识别材料参数,所得外膜中弹性蛋白的占比被严重高估,与实验结果不符。结论 残余应力对主动脉壁各微观组分的预拉伸及生理稳态力学状态影响显著,故准确建立主动脉壁的生理稳态需要充分考虑残余应力的影响,材料参数的在体识别也需要充分考虑残余应力的三维特性和层特异性。

    Abstract:

    Objective To calculate the pre-stretching of the microscopic components of the aortic wall under physiological homeostasis by considering a three-dimensional (3D) residual stress field. Methods The aortic wall was simplified into a double-layer ideal circular tube, and the 3D residual stress field of the vascular wall was calculated based on a 3D expansion angle experiment. Then, the in vivo stress distribution characteristics under mean blood pressure and the pre-stretching of each microscopic constituent of the vascular wall under a physiologically steady state were obtained. The inverse problem was constructed according to the internal pressure-radius relationship measured in vivo. Physiological homeostasis of the aorta was considered the reference state, and inversion identification of the material parameters of the aorta in vivo was realized while integrating the three residual stress fields. Results When the residual stress was not considered, the mean stress of the middle membrane was greater than that of the outer membrane. When residual stress was considered, the outer membrane bore more stress than the middle membrane, and the outer membrane protected the middle membrane. The pre-stretching of the middle film with residual stress is lower than that without residual stress, whereas the pre-stretching of the outer film is higher than that without residual stress. Moreover, the pre-stretching of the outer membrane collagen fibers was greater than that of the middle membrane collagen fibers. The in vivo calculations of the material parameters of the aorta were performed using physiological homeostasis as the reference configuration, and the proportion of each component was consistent with the experimental results. However, the proportion of elastin in the outer membrane was significantly overestimated when the non-stress configuration was used as the initial configuration, which was inconsistent with the experimental results. Conclusions Residual stress significantly influences the pre-stretching and physiologically steady mechanical states of the microscopic components of the aortic wall. Therefore, it is necessary to fully consider the influence of residual stress to establish the physiologically steady state of the aortic wall accurately. Furthermore, it is also necessary to fully consider the 3D characteristics and layer specificity of residual stress in the in vivo identification of material parameters.

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高鹏,郭宝磊,张明,戴向晨,刘浩飞.考虑三维残余变形的主动脉生理稳态建模[J].医用生物力学,2024,39(3):510-517

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  • 收稿日期:2023-11-29
  • 最后修改日期:2023-12-24
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  • 在线发布日期: 2024-06-25
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