Zebrafish swimming in the flow: a particle image velocimetry study

Abstract

Zebrafish is emerging as a species of choice for the study of a number of biomechanics problems, including balance development, schooling, and neuromuscular transmission. The precise quantification of the flow physics around swimming zebrafish is critical toward a mechanistic understanding of the complex swimming style of this fresh-water species. Although previous studies have elucidated the vortical structures in the wake of zebrafish swimming in placid water, the flow physics of zebrafish swimming against a water current remains unexplored. In an effort to illuminate zebrafish swimming in a dynamic environment reminiscent of its natural habitat, we experimentally investigated the locomotion and hydrodynamics of a single zebrafish swimming in a miniature water tunnel using particle image velocimetry. Our results on zebrafish locomotion detail the role of flow speed on tail beat undulations, heading direction, and swimming speed. Our findings on zebrafish hydrodynamics offer a precise quantification of vortex shedding during zebrafish swimming and demonstrate that locomotory patterns play a central role on the flow physics. This knowledge may help clarify the evolutionary advantage of burst and cruise swimming movements in zebrafish.

Keywords: Flow physics; PIV; Strouhal number; Swimming; Vortex; Zebrafish.

Figure 1. Experimental setup.

(A) Assembled model of swim tunnel (top) and exploded view (bottom) of the parts, including a 3D printed funnel (1) to inject water flow with a small cylindrical hall frame serving as door frame, a 3D printed cap serving as a door (2), a 3D printed door locker (3), plastic collimators (4) and (5) placed on each side of the acrylic tube (6) in order to sustain laminar flow, and a second 3D printed funnel (7) to output the water flow. (B) Experimental setup for the study of zebrafish swimming against a water current. The camera is connected to an external computer to store the picture frames for subsequent analysis. (C) Flow velocity magnitude along the diameter (red dashed line) of the swim tunnel measured in the absence of the fish at three different flow rates.

Figure 2. Illustration of zebrafish locomotion.

(A) Schematics of fish body shape undergoing burst and cruise. (B) Schematics of a swimming fish in the water tunnel. The central line of the body is represented by the red dashed line. A fixed point (O) on the fish body is chosen as 1/3 of the body length from the head. The heading direction (x_f) of the fish is determined by a line connecting point O and the tip of the head. A coordinate system attached to the fish body with origin at O is indicated by the blue arrows. The fish tail beating amplitude (A) is tracked in the body frame.

Figure 3. Measured locomotory indicators of zebrafish swimming.

Comparison of (A) fish swimming velocity, (B) tail beat amplitude, (C) tail beat frequency, and (D) change in heading angle for both burst and cruise at three flow speeds (U = 26, 39, 52 mm/s). Label ^∗ indicates significant difference between burst and cruise at p < 0.05, and ^∗∗ is for significance at p < 0.01. Error bars represent ± standard errors.

Figure 4. Nondimensional numbers associated with zebrafish locomotion.

Correlation between the Strouhal number St and the Reynold number Re for (A) burst and (B) cruise and correlation between fish change in heading angle (Δθ) and St for (C) burst and (D) cruise. Dashed black lines in the figure indicate estimated linear regression fit of Δθ = 0.819 St − 0.002, with p = 0.002. The dashed black line in (D) is a linear regression fit of Δθ = 0.487 St − 0.025, with p < 0.001.

Figure 5. Velocity and vorticity fields around a bursting zebrafish.

Time sequence (A–F) of the velocity (arrow) and vorticity (color) fields in the vicinity of the fish body during a burst against a laminar flow with speed U = 39 mm/s. The time interval between consecutive snapshots is 1/32 s. For visualization purposes, one velocity vector is plotted every three rows and columns.

Figure 6. Velocity and vorticity fields around a cruising zebrafish.

Time sequence (A–F) of the velocity (arrow) and vorticity (color) fields in the vicinity of the fish body during a cruise against a flow with speed U = 26 mm/s. The time interval between consecutive snapshots is 1/32 s. For visualization purposes, one velocity vector is plotted every three rows and columns.

Figure 7. Fluid pressure around a bursting zebrafish.

Fluid pressure fields (A–F) correspond to the velocity fields shown in Figs. 5A–5F.

Figure 8. Fluid pressure around a cruising zebrafish.

Fluid pressure fields (A–F) correspond to the velocity fields shown in Figs. 6A–6F.

Figure 9. Measurements from individual zebrafish burst and cruise movements.

(A) Normalized circulation as a function of the relative Strouhal number. Dashed line is a linear fit to the data points, Γ∕LV = 0.11St + 0.10, with p = 0.078. Triangles represent cruise movements while circles represent burst movements. Each data point is obtained based on one movement of burst or cruise. Data from different fish are plotted in different colors. (B) St as a function of Re for the same movement presented in (A). (C) Δθ as a function of St for the same instances presented in (A). Dashed line is a linear fit to the data points, Δθ = 1.61St − 0.346, with p = 0.003.