Tunay Ilker
Stereotaxis, Inc, 4320 Forest Park Ave, Suite 100 St Louis, Missouri 63108, USA.
Annu Int Conf IEEE Eng Med Biol Soc. 2011;2011:8344-7. doi: 10.1109/IEMBS.2011.6092058.
We discuss how to use special Cosserat rod theory for deriving distributed-parameter static equilibrium equations of magnetic catheters. These medical devices are used for minimally-invasive diagnostic and therapeutic procedures and can be operated remotely or controlled by automated algorithms. The magnetic material can be lumped in rigid segments or distributed in flexible segments. The position vector of the cross-section centroid and quaternion representation of an orthonormal triad are selected as DOF. The strain energy for transversely isotropic, hyperelastic rods is augmented with the mechanical potential energy of the magnetic field and a penalty term to enforce the quaternion unity constraint. Numerical solution is found by 1D finite elements. Material properties of polymer tubes in extension, bending and twist are determined by mechanical and magnetic experiments. Software experiments with commercial FEM software indicate that the computational effort with the proposed method is at least one order of magnitude less than standard 3D FEM.
我们讨论了如何使用特殊的柯西拉杆理论来推导磁导管的分布参数静态平衡方程。这些医疗设备用于微创诊断和治疗程序，可远程操作或由自动算法控制。磁性材料可以集中在刚性段或分布在柔性段。选择横截面质心的位置矢量和正交三轴的四元数表示作为自由度。对于横观各向同性的超弹性杆，应变能通过磁场的机械能和一个惩罚项来增强，以强制四元数单位约束。通过一维有限元找到数值解。聚合物管在拉伸、弯曲和扭转时的材料特性通过力学和磁性实验确定。使用商业有限元软件进行的软件实验表明，所提出方法的计算量比标准三维有限元至少少一个数量级。
