In our previous work, the basilar membrane velocity V(BM) for a gerbil cochlea was calculated and compared with physiological measurements. The calculated V(BM) showed excessive phase excursion and, in the active case, a best-frequency place shift of approximately two fifths of an octave higher. Here we introduce a refined model that uses the time-averaged Lagrangian for the conservative system to resolve the phase excursion issues. To improve the overestimated best-frequency place found in the previous feed-forward active model, we implement in the new model a push-pull mechanism from the outer hair cells and phalangeal process. Using this new model, the V(BM) for the gerbil cochlea was calculated and compared with animal measurements, The results show excellent agreement for mapping the location of the maximum response to frequency, while the agreement for the response at a fixed point as a function of frequency is excellent for the amplitude and good for the phase.

中文翻译：

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在 Corti 器官中使用时间平均拉格朗日函数和推挽机制的耳蜗模型

在我们之前的工作中，计算了沙鼠耳蜗的基底膜速度 V(BM) 并与生理测量值进行了比较。计算出的 V(BM) 显示出过度的相位偏移，在活跃的情况下，最佳频率位置偏移大约高出五分之二八度。在这里，我们引入了一个改进的模型，该模型使用保守系统的时间平均拉格朗日函数来解决相位偏移问题。为了改善先前前馈主动模型中高估的最佳频率位置，我们在新模型中实施了外毛细胞和指骨过程的推拉机制。使用这个新模型，计算了沙鼠耳蜗的 V(BM)，并与动物测量值进行了比较，结果显示出对频率最大响应位置的映射非常一致，