Thesis subject

Summary of the thesis: How fish larvae swim - from motion to mechanics

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Most of the world’s 34,000 known fish species are undulatory swimmers. Their body undulations are produced by fluid-structure interaction between water and the body of the fish, powered by its muscle system. Despite these complex physics, just-hatched fish larvae can already produce effective swimming motion. How they do this is not yet fully understood. With this thesis, we aim to contribute to answering this question by examining the biomechanics of swimming of early-development larval zebrafish. With novel experimental and computational techniques, we reconstructed the dynamics of the larvae from high-speed video. These analyses highlight the challenges that larval fish face during swimming, and how the larvae have evolved to solve these challenges.

In chapter 2 we reviewed the mechanics of swimming of larval fish. We examined the functional demands on the locomotory system of fish larvae: immediately after hatching, fish need to escape predators, search and hunt for food, and migrate and disperse. These demands need to be fulfilled by the larvae while undergoing large changes in their bodies, both internal and external. Furthermore, the swimming speed and size of many larvae causes them to be in the intermediate flow regime, where the nature of the flow changes considerably with changes in size or speed. In this chapter, we integrated previous literature to gain insight into how these functional demands on the locomotory system are met with the advantages and limitations of their developing bodies and the changing hydrodynamic regime.

In chapter 3, we analysed near-periodic swimming of zebrafish larvae with two-dimensional inverse dynamics from motion that was manually tracked from high-speed video images. We used these data to show how the intermediate flow regime affects the swimming dynamics of fish larvae. We used the Reynolds number, which indicates the relative importance of viscous forces to inertial forces, to characterise the flow regime that the larvae swim in. Furthermore, we applied the Strouhal number, a measure of the ratio of the approximate lateral tail speed to the forward swimming speed, to express changes in swimming kinematics. We found that the Strouhal number depends inversely on the Reynolds number. Fish swimming at low Reynolds numbers tend to use relatively high Strouhal numbers, indicating that their tail-beat amplitude and frequency are high. Even the larvae swimming at the highest Reynolds numbers still use relatively high Strouhal numbers (around 0.72) compared to adult fish (typically 0.2–0.3). Swimming at intermediate Reynolds numbers is associated with high drag, requiring the larvae to use high tail-beat amplitudes and frequencies (and therefore Strouhal number) to produce sufficient thrust. This mode of swimming requires relatively high-amplitude yaw torques, resulting in large angular amplitudes and an expected high energetic cost of transport: the small size of the larvae is a burden to their swimming.

Most of the previous research on fish swimming, including our chapter 3, has been done two-dimensionally. However, fish can perform complex, three-dimensional motions to escape predators, search or hunt for food, or manoeuvre through the environment. To expand our analyses to the third dimension, we developed a method to reconstruct the 3D motion of fish from multi-camera high-speed video, described in chapter 4. With an optimisation algorithm we find the 3D position, orientation, and body curvature that best fits the high-speed video frames. We demonstrated that the method allows us to reconstruct the swimming kinematics with high accuracy, while requiring minimal manual work. In addition, we developed a novel method to calculate resultant hydrodynamic forces and torques from the reconstructed motion. The described method is a valuable tool for analysing the biomechanics of swimming, providing data for future analyses of fish swimming.

In chapter 5, we apply this automated tracking method to analyse fast starts of zebrafish larvae five days after fertilisation. To be able to escape predators, the main functional demands on a fast start are producing sufficient speed within a narrow time frame and being able to generate a wide range of escape directions. To investigate how these demands are met, we used a five-camera high-speed video of fast-starting zebrafish larvae with unprecedented spatiotemporal resolution. From these videos, we reconstructed the 3D motion of the larvae and the resultant hydrodynamic forces and torques. Due to their undulatory swimming style, the larvae first need to bend into a C-shape before being able to produce a propulsive tail beat. For this reason, the first stage of the start is often considered ‘preparatory’. Based on the reconstructed forces and torques, we show that the first stage of the start, in addition to its preparatory role, also serves to provide most of the reorientation of the start. After this stage, the larvae unfold their bodies, moving their tails at high speeds and thus producing large propulsive forces. The turn angle produced during a start mostly depends on the amount of body curvature in the first stage, while the escape speed mainly depends on the duration of the start. This suggests that larvae are able to independently adjust the direction and speed of their escape.

Fish larvae are able to produce these escape responses and the subsequent swimming bout immediately after hatching, despite their bodies and brains still undergoing development. To understand how this is possible, we use an advanced inverse-dynamics approach, with computational fluid dynamics and a large-amplitude beam model, to reconstruct internal mechanics from the motion of the fish in chapter 6. We compute the internal bending moments from more than 100 3D-recordings of swimming over a range of developmental stages. We show that larvae use similar bending moment patterns across development, speeds and accelerations. By varying the amplitude and duration of this pattern, the larvae can adjust their swimming speed and/or acceleration. This similarity suggests that their muscle activation patterns are also similar, which would help to explain how just-hatched larvae with limited neural capacity can produce effective swimming motion across a range of speeds and accelerations.

In this thesis, we demonstrated that larval fish swim in a challenging hydrodynamic regime. Despite the relatively high drag, they can produce effective swimming motions to
help them survive to adulthood. We developed novel methods to quantify this motion in 3D, and from it reconstructed the external and internal mechanics. With these inverse-dynamics approaches, we show that fish larvae can likely adjust their swimming in a relatively simple way, for both fast starts and continuous swimming. Thus, complex physics do not obstruct developing larvae from swimming effectively.