Bending moments in swimming fish

Most fish swim with body undulations that result from fluid-structure interactions between the fish's internal tissues and the surrounding water. Gaining insight into these complex fluid structure interactions is essential to understand how fish swim. To this end, we developed a dedicated experimental-numerical inverse dynamics approach to calculate the lateral bending moment distributions for a large-amplitude undulatory swimmer that moves freely in 3D space. We combined automated motion tracking from multiple synchronised high-speed video sequences, computation of fluid-dynamic stresses on the swimmer’s body from computational fluid dynamics, and bending-moment calculations using these stresses as input for a novel beam model of the body. The bending moment, which represent the system’s net actuation, varies over time and along the fish’s central axis due to muscle actions, passive tissues, inertia, and fluid dynamics. Our 3D analysis of 113 swimming events of zebrafish larvae ranging in age from 3 to 12 days after fertilisation shows that these bending moment patterns are not only relatively simple but also strikingly similar throughout early development, and from fast starts to periodic swimming. This suggests that fish larvae may produce and adjust swimming movements relatively simply, yet effectively, while restructuring their neuromuscular control system throughout their rapid development.绝大多数鱼类依靠身体摆动实现游动，这类摆动源于鱼类体内组织与周遭水体之间的流体-结构相互作用（fluid-structure interactions）。深入解析这类复杂的流体-结构相互作用，是理解鱼类游动机制的核心前提。为此，我们开发了一套专属的实验-数值逆动力学方法，用于计算可在三维空间自由游动的大振幅摆动型游泳生物的侧向弯矩分布。我们整合了三项核心技术：来自多组同步高速视频序列的自动化运动追踪、基于计算流体动力学（computational fluid dynamics）的游泳生物体表流体动力应力计算，以及以该应力为输入、针对鱼类身体构建的新型梁模型（beam model）的弯矩计算。作为该系统净驱动力的弯矩，会随时间与鱼类体轴位置发生动态变化，其驱动来源包括肌肉活动、被动组织、惯性效应与流体动力学作用。我们对113段斑马鱼幼体（zebrafish larvae）的游动事件开展了三维分析，这些幼体的日龄覆盖受精后3至12天。分析结果表明，这类弯矩模式不仅相对简洁，而且在早期发育的全阶段，以及从快速逃逸游动到周期性游动的各类游动模式中，均呈现出惊人的一致性。这一发现提示，尽管斑马鱼幼体在快速发育过程中持续重构其神经肌肉控制系统，它们仍可通过相对简洁却高效的方式生成并调整游动动作。