The semicircular ducts (SCDs) of the vestibular system play an instrumental role in equilibration and rotation perception of vertebrates. The present paper is a review of quantitative approaches and shows how SCDs function. It consists of three parts. First, the biophysical mechanisms of an SCD system composed of three mutually connected ducts, allowing endolymph to flow from one duct into another one, are analysed. The flow is quantified by solving the continuity equations in conjunction with the equations of motion of the SCD hydrodynamics. This leads to mathematical expressions that are suitable for further analytical and numerical analysis. Second, analytical solutions are derived through four simplifying steps while keeping the essentials of the coupled system intact. Some examples of flow distributions for different rotations are given. Third, the focus is on the transducer function of the SCDs. The complex structure of the mechano-electrical transduction apparatus inside the ampullae is described, and the consequences for sensitivity and frequency response are evaluated. Furthermore, both the contributions of the different terms of the equations of motion and the influence of Brownian motion are analysed. Finally, size limitations, allometry and evolutionary aspects are taken into account.

前庭系统的半规管 (SCD) 在脊椎动物的平衡和旋转感知中发挥重要作用。本文是对定量方法的回顾，并展示了 SCD 的功能。它由三部分组成。首先，分析了由三个相互连接的管道组成的 SCD 系统的生物物理机制，允许内淋巴从一个管道流入另一个管道。通过结合 SCD 流体动力学的运动方程求解连续性方程来量化流动。这导致了适用于进一步分析和数值分析的数学表达式。其次，通过四个简化步骤推导出解析解，同时保持耦合系统的基本要素完好无损。给出了不同旋转的流量分布的一些示例。第三，重点是 SCD 的换能器功能。描述了壶腹内机电转换装置的复杂结构，并对灵敏度和频率响应的影响进行了评估。此外，分析了运动方程的不同项的贡献和布朗运动的影响。最后，考虑了尺寸限制、异速生长和进化方面。