流固耦合分析颈椎生理活动对椎动脉血流动力学的影响

目的 建立椎动脉（vertebral artery, VA）流体有限元模型，进行流固耦合计算，以深入了解颈椎活动与VA血流流体力学之间生物力学关系。方法 基于正常人颈椎（C0~T1）及双侧椎动脉三维有限元模型，模拟颈椎前屈、后伸、左右侧弯、左右旋转，观察颈椎活动对VA血管壁应力的影响，并通过流固耦合计算血管壁与流体相互作用，获取血流动力学参数。结果颈椎活动过程中，VA血管壁的最大应力通常集中在两侧C2横突孔处（入颅方向的第2个弯曲），后伸和侧弯较旋转活动时血管壁最大应变最为明显，应变比值分别为23.04%和35.5%。侧弯活动时，血管最大应力位于对侧横突孔；旋转活动时，血管应变位于同侧横突孔。颈椎活动度方面，最低流速值几乎均出现在生理活动范围的30%~40%。颈椎前屈、后伸活动时，双侧VA流速-时间变化曲线相似，且在0.5 s内，都完成了2次流速增减的循环。侧弯时，同侧VA的波峰和波谷早于对侧VA出现；而旋转时，同侧VA的波峰和波谷晚于对侧VA出现。结论 双侧VA血管壁所受应力特点、血流速-时间变化曲线等结果能与其他实验结果相互验证，并能合理解释相关临床现象。建立的VA模型将为VA相关疾病研究提供较理想的平台。

Fluid-structure interaction analysis on hemodynamics of vertebral arteries during physiological activities of cervical spine

Objective To further understand the biomechanical relationship between activities of cervical spine and blood flow of vertebral artery (VA) by developing the VA finite element model and calculating the fluid-structure interaction. Methods Based on the normal model of cervical spine and the developed C0-T1 finite element model with bilateral VA, the flexion and extension, right and left lateral bending, right and left axial rotation movement of cervical spine at physiological velocity were simulated. The effects of cervical activities on stress of vertebral arterial wall were observed, and the biomechanical interaction between the vessel wall and fluid was calculated by fluid-structure interaction equation to obtain the hemodynamic parameters. Results The maximum stress was usually concentrated on the both sides of C2 transverse foramen, where the second arc of vertebral arterial wall protruded into the cranial direction during cervical activities. The maximum strain of the vessel wall was most obvious during the extension and lateral bending movement, with strain ratio of 23.04% and 35.5%, respectively. The maximum stress on the vessel was located in the position of contralateral transverse foramen during lateral bending movement, while the maximum strain on the vessel was located in the position of ipsilateral transverse foramen during rotation movement. In aspect of cervical spine range of motion (ROM), the minimum volume flow rate occurred within 30%-40% of the physiological ROM. The volume flow rate-time curve of bilateral VA was similar during flexion and extension movement, when the circulation of flow rate was completed for two times within 0.5 s. The peak and valley of ipsilateral blood flow in volume flow rate-time curve occurred earlier than that of contralateral blood flow during lateral bending movement, while the results of rotation movement were opposite. Conclusions The obtained stress features of bilateral VA vessel and the law of the volume flow rate-time curve validated the experimental results with those in the literature, which could reasonably explain the clinical phenomenon. The established model would provide an ideal platform for researches on vertebral artery-related diseases.