C.J. Voesenek

Automated reconstruction of three-dimensional fish motion, forces, and torques

Fish can move freely through the water column and make complex three-dimensional motions to explore their environment, escape or feed. Nevertheless, the majority of swimming studies is currently limited to two-dimensional analyses. Accurate experimental quantification of changes in body shape, position and orientation (swimming kinematics) in three dimensions is therefore essential to advance biomechanical research of fish swimming. Here, we present a validated method that automatically tracks a swimming fish in three dimensions from multi-camera high-speed video. We use an optimisation procedure to fit a parameterised, morphology-based fish model to each set of video images. This results in a time sequence of position, orientation and body curvature. We post-process this data to derive additional kinematic parameters (e.g. velocities, accelerations) and propose an inverse-dynamics method to compute the resultant forces and torques during swimming. The presented method for quantifying 3D fish motion paves the way for future analyses of swimming biomechanics.

How body torque and Strouhal number change with swimming speed and developmental stage in larval zebrafish.

Small undulatory swimmers such as larval zebrafish experience both inertial and viscous forces, the relative importance of which is indicated by the Reynolds number (Re). Re is proportional to swimming speed (vswim) and body length; faster swimming reduces the relative effect of viscous forces. Compared with adults, larval fish experience relatively high (mainly viscous) drag during cyclic swimming. To enhance thrust to an equally high level, they must employ a high product of tail-beat frequency and (peak-to-peak) amplitude fAtail, resulting in a relatively high fAtail/vswim ratio (Strouhal number, St), and implying relatively high lateral momentum shedding and low propulsive efficiency. Using kinematic and inverse-dynamics analyses, we studied cyclic swimming of larval zebrafish aged 2–5 days post-fertilization (dpf). Larvae at 4–5 dpf reach higher f (95 Hz) and Atail (2.4 mm) than at 2 dpf (80 Hz, 1.8 mm), increasing swimming speed and Re, indicating increasing muscle powers. As Re increases (60 → 1400), St (2.5 → 0.72) decreases nonlinearly towards values of large swimmers (0.2–0.6), indicating increased propulsive efficiency with vswim and age. Swimming at high St is associated with high-amplitude body torques and rotations. Low propulsive efficiencies and large yawing amplitudes are unavoidable physical constraints for small undulatory swimmers.

Biomechanics of swimming in developing larval fish

ABSTRACT Most larvae of bony fish are able to swim almost immediately after hatching. Their locomotory system supports several vital functions: fish larvae make fast manoeuvres to escape from predators, aim accurately during suction feeding and may migrate towards suitable future habitats. Owing to their small size and low swimming speed, larval fish operate in the intermediate hydrodynamic regime, which connects the viscous and inertial flow regimes. They experience relatively strong viscous effects at low swimming speeds, and relatively strong inertial effects at their highest speeds. As the larvae grow and increase swimming speed, a shift occurs towards the inertial flow regime. To compensate for size-related limitations on swimming speed, fish larvae exploit high tail beat frequencies at their highest speeds, made possible by their low body inertia and fast neuromuscular system. The shifts in flow regime and body inertia lead to changing functional demands on the locomotory system during larval growth. To reach the reproductive adult stage, the developing larvae need to adjust to and perform the functions necessary for survival. Just after hatching, many fish larvae rely on yolk and need to develop their feeding systems before the yolk is exhausted. Furthermore, the larvae need to develop and continuously adjust their sensory, neural and muscular systems to catch prey and avoid predation. This Review discusses the hydrodynamics of swimming in the intermediate flow regime, the changing functional demands on the locomotory system of the growing and developing larval fish, and the solutions that have evolved to accommodate these demands. Summary: This Review discusses the solutions that developing larval fish have evolved to the challenges of swimming in the intermediate Reynolds number regime.

Three-dimensional analysis of the fast-start escape response of the least killifish, Heterandria formosa

ABSTRACT Fish make C-starts to evade predator strikes. Double-bend (DB) C-starts consist of three stages: Stage 1, in which the fish rapidly bends into a C-shape; Stage 2, in which the fish bends in the opposite direction; and a variable Stage 3. In single-bend (SB) C-starts, the fish immediately straightens after Stage 1. Despite fish moving in three-dimensional (3D) space, fast-start responses of adult fish have mainly been studied in a horizontal plane. Using automated 3D tracking of multi-camera high-speed video sequences, we show that both SB and DB fast-starts by adult female least killifish (Heterandria formosa) often contain a significant vertical velocity component, and large changes in pitch (DB up to 43 deg) and roll (DB up to 77 deg) angles. Upwards and downwards elevation changes are correlated with changes in pitch angle of the head; movement in the horizontal plane is correlated with changes in yaw angle of the head. With respect to the stimulus, escape heading correlates with the elevation of the fish at the onset of motion. Irrespective of the initial orientation, fish can escape in any horizontal direction. In many cases, the centre of mass barely accelerates during Stage 1. However, it does accelerate in the final direction of the escape in other instances, indicating that Stage 1 can serve a propulsive role in addition to its preparatory role for Stage 2. Our findings highlight the importance of large-scale 3D analyses of fast-start manoeuvres of adult fish in uncovering the versatility of fish escape repertoire. Summary: The fast-start response of the least killifish entails a rich three-dimensional kinematic repertoire including complex combinations of roll, pitch and yaw motions.