Bending moment dynamics during swimming of developing zebrafish larvae

Zebrafish larvae are able to swim immediately after hatching,
making effective escape manoeuvres at two days post fertilization
(dpf). From 2 to 5 dpf, larval zebrafish improve swimming
performance by increasing their tail-beat frequency and amplitude
(Van Leeuwen et al. (2015) J. R. Soc. Interface 12: 20150479). During
these first days of development, the larvae’s muscle system changes
rapidly, while it continues functioning to power swimming. This
requires them to use their muscles differently across development.
A first step towards understanding how the larvae achieve this
and how they change their performance, is by computing the
time-dependent internal bending moment distributions along
the body during swimming. This allows us to assess the changes
in local bending power as the fish grows. We developed a combined
experimental and computational approach for reconstructing timeresolved
bending moment distributions from high-speed videos of
free-swimming larvae (2-12 dpf). First, we reconstruct the threedimensional
position, orientation and body curvature from these
images. We feed these reconstructions into a computational fluiddynamics
solver in order to calculate the flow field and the fluid
forces along the fish’s body. Finally, we combine the motion of the
longitudinal body axis and the external fluid forces as input for an
optimization procedure to calculate the best fitting time-dependent
bending moment distribution. The dynamics of these bending
moments provide novel insight in the developmental mechanics of
swimming across the first stages of zebrafish.
A1.3 HOW TAIL-BEAT FREQUENCY AND
BODY CURVATURE AFFECT SWIMMING
PERFORMANCE IN LARVAL ZEBRAFISH
TUESDAY 5 JULY, 2016 14:30
GEN LI (CHIBA UNIVERSITY, JAPAN), ULRIKE K MÜLLER
(CALIFORNIA STATE UNIVERSITY FRESNO, UNITED STATES),
HAO LIU (CHIBA UNIVERSITY, JAPAN), JOHAN L VAN LEEUWEN
(WAGENINGEN UNIVERSITY, NETHERLANDS)
GENLI@CHIBA-U.JP
Small undulatory swimmers such as larval zebrafish operate in
the intermediate Reynolds regime and experience relatively high
drag during cyclic swimming. Experimental observations (J. R.
Soc. Interface 12: 20150479) demonstrated (a) that larval zebrafish
tend to increase both tail-beat frequency and amplitude with
swimming speed and (b) a negative power relationship between
Strouhal number and Reynolds number during cyclic swimming.
To elucidate the underlying mechanisms, we developed an
integrated 3D computational approach of hydrodynamics and
free-swimming body dynamics that couples the Navier-Stokes
(NS) equations to the equations of undulating body motion. A
numerical approach is required to analyze the highly non-linear
nature of the dynamics of large-amplitude undulatory swimming
in the intermediate Reynolds regime. Using the model, we explored
how tail-beat frequency and amplitude of lateral curvature along
the body affect swimming performance (in terms of speed, fluid
dynamic efficiency and cost of transport). The explored parameter
space extends beyond the experimentally observed frequencyamplitude
combinations in larval zebrafish.
Our computations predict that increasing both frequency and
amplitude to swim faster improves swimming performance, which
agrees with previous experimental observations. This suggests
that fish larvae adjust their body kinematics to optimize swimming
performance. In addition, a robust negative power relationship
between Re and St was predicted, again in line with experimental
observations, and irrespective of the employed combinations of
frequency and curvature amplitude. The coupling between Re and
St is not an effect of kinematic optimization, but results from fluid
dynamic constraints.