Maftoon Nima, Funnell W Robert J, Daniel Sam J, Decraemer Willem F
Department of BioMedical Engineering, McGill University, 3775 rue University, Montréal, QC, H3A 2B4, Canada.
Department of Otolaryngology-Head and Neck Surgery, McGill University, Montréal, QC, Canada.
J Assoc Res Otolaryngol. 2015 Oct;16(5):547-67. doi: 10.1007/s10162-015-0531-y. Epub 2015 Jul 22.
We present a finite-element model of the gerbil middle ear that, using a set of baseline parameters based primarily on a priori estimates from the literature, generates responses that are comparable with responses we measured in vivo using multi-point vibrometry and with those measured by other groups. We investigated the similarity of numerous features (umbo, pars-flaccida and pars-tensa displacement magnitudes, the resonance frequency and break-up frequency, etc.) in the experimental responses with corresponding ones in the model responses, as opposed to simply computing frequency-by-frequency differences between experimental and model responses. The umbo response of the model is within the range of variability seen in the experimental data in terms of the low-frequency (i.e., well below the middle-ear resonance) magnitude and phase, the main resonance frequency and magnitude, and the roll-off slope and irregularities in the response above the resonance frequency, but is somewhat high for frequencies above the resonance frequency. At low frequencies, the ossicular axis of rotation of the model appears to correspond to the anatomical axis but the behaviour is more complex at high frequencies (i.e., above the pars-tensa break-up). The behaviour of the pars tensa in the model is similar to what is observed experimentally in terms of magnitudes, phases, the break-up frequency of the spatial vibration pattern, and the bandwidths of the high-frequency response features. A sensitivity analysis showed that the parameters that have the strongest effects on the model results are the Young's modulus, thickness and density of the pars tensa; the Young's modulus of the stapedial annular ligament; and the Young's modulus and density of the malleus. Displacements of the tympanic membrane and manubrium and the low-frequency displacement of the stapes did not show large changes when the material properties of the incus, stapes, incudomallear joint, incudostapedial joint, and posterior incudal ligament were changed by ±10 % from their values in the baseline parameter set.
我们展示了一个沙鼠中耳的有限元模型，该模型使用一组主要基于文献中先验估计的基线参数，生成的响应与我们使用多点振动测量法在体内测量的响应以及其他研究小组测量的响应相当。我们研究了实验响应中众多特征（鼓膜脐、松弛部和紧张部位移大小、共振频率和破裂频率等）与模型响应中相应特征的相似性，而不是简单地计算实验响应和模型响应之间逐频率的差异。就低频（即远低于中耳共振频率）的大小和相位、主要共振频率和大小以及共振频率以上响应的滚降斜率和不规则性而言，模型的鼓膜脐响应在实验数据的变化范围内，但在共振频率以上的频率时略高。在低频时，模型的听骨旋转轴似乎与解剖轴相对应，但在高频（即高于紧张部破裂频率）时行为更为复杂。模型中紧张部的行为在大小、相位、空间振动模式的破裂频率以及高频响应特征的带宽方面与实验观察结果相似。敏感性分析表明，对模型结果影响最大的参数是紧张部的杨氏模量、厚度和密度；镫骨环形韧带的杨氏模量；以及锤骨的杨氏模量和密度。当砧骨、镫骨、砧锤关节、砧镫关节和后砧骨韧带的材料属性在基线参数集中的值基础上变化±10%时，鼓膜和锤骨柄的位移以及镫骨的低频位移没有显示出大的变化。
