Titze Ingo R, Alipour Fariborz, Blake Douglas, Palaparthi Anil
National Center for Voice and Speech, 136 South Main Street, Suite 320, Salt Lake City, Utah 84101, USA.
J Acoust Soc Am. 2017 Sep;142(3):1376. doi: 10.1121/1.5001055.
A fiber-gel vocal fold model is compared to a transversely isotropic stiffness model in terms of normal mode vibration. The fiber-gel finite element model (FG-FEM) consists of a series of gel slices, each with a two-dimensional finite element mesh, in a plane transverse to the tissue fibers. The gel slices are coupled with fibers under tension in the anterior-posterior dimension. No vibrational displacement in the fiber-length direction is allowed, resulting in a plane strain state. This is consistent with the assumption of transverse displacement of a simple string, offering a wide range of natural frequencies (well into the kHz region) with variable tension. For low frequencies, the results compare favorably with the natural frequencies of a transversely isotropic elastic stiffness model (TISM) in which the shear modulus in the longitudinal plane is used to approximate the effect of fiber tension. For high frequencies, however, the natural frequencies do not approach the string mode frequencies unless plane strain is imposed on the TISM model. The simplifying assumption of plane strain, as well as the use of analytical closed-form shape functions, allow for substantial savings in computational time, which is important in clinical and exploratory applications of the FG-FEM model.
在简正模式振动方面,将一种纤维 - 凝胶声带模型与横向各向同性刚度模型进行比较。纤维 - 凝胶有限元模型(FG - FEM)由一系列凝胶切片组成,每个凝胶切片在垂直于组织纤维的平面内具有二维有限元网格。凝胶切片在前后维度上与处于张力下的纤维相连。不允许在纤维长度方向上有振动位移,从而产生平面应变状态。这与简单弦的横向位移假设一致,在可变张力下可提供广泛的固有频率(高达kHz区域)。对于低频,结果与横向各向同性弹性刚度模型(TISM)的固有频率相比具有优势,在TISM模型中,纵向平面内的剪切模量用于近似纤维张力的影响。然而,对于高频,除非在TISM模型上施加平面应变,否则固有频率不会接近弦模式频率。平面应变的简化假设以及解析封闭形式形状函数的使用,使得计算时间大幅节省,这在FG - FEM模型的临床和探索性应用中很重要。