Head width influences flow sensing by the lateral line canal system in fishes

The lateral line system is used to sense water motion (Dijkgraaf, 1963). This mechanoreceptive organ is critical for performing tasks such as: detecting predators and prey, navigating turbulent flow and orienting to flow (Coombs et al., 2001; Liao et al., 2003a,b; Montgomery et al., 1997; Pohlmann et al., 2001, 2004; Stewart et al., 2014). The lateral line system is composed of bundles of flow-sensitive hair cells called neuromasts. There are two types of neuromasts: superficial neuromasts, which lie directly on top of the skin of the fish; and canal neuromasts, which are recessed within open-pored canals running just under the surface of the body and head of the fish. Superficial neuromasts are sensitive to flow velocity while canal neuromasts are sensitive to acceleration around the fish and, by extension of Bernoulli's principle, to the pressure differences between adjacent canal pores (Coombs et al., 1988, 1996; Coombs and Janssen, 1990; Haehnel-Taguchi et al., 2014; Kroese and Schellart, 1992).

Fishes exhibit a large anatomical diversity in their lateral line canal; canal diameters, pore spacing and neuromast shapes vary between species (Carton and Montgomery, 2004; Coombs et al., 1988; Montgomery et al., 1994; van Netten, 2006; Webb, 2013). Canals can also possess features such as membranous pore coverings, branching canal patterns or localized constrictions within canals, all of which can affect the lateral line's sensitivity to hydrodynamic stimuli (Carton and Montgomery, 2004; Denton and Gray, 1983, 1988; Janssen, 1997, 2004; Montgomery et al., 1994; Webb, 1989, 2013). Additionally, fishes exhibit a large diversity of trunk lateral line canal architecture. Many fish have a single, continuous trunk canal on their mid-body. However, depending on the ecology and behavior of a species, the trunk canal architecture may vary. Some fish exhibit a canal line that curves around the pectoral fins, possibly to reduce the hydrodynamic noise generated by the motions of the pectoral fins during swimming (Webb, 1989). Fishes that seek refuge within tubes or holes may have incomplete canals that run only halfway along their bodies. Others that occupy habitats just below the surface of the water or bury themselves in sediment may have ventrally or dorsally located trunk canals, respectively (Webb, 2013).

While relatively little is known about the anatomical diversity of the cephalic lateral line canal across species, the general architecture of the cephalic lateral line canal is highly conserved; it usually consists of three rows: one located above the eye (supraorbital), one below (infraorbital) and one along the lower mandible (mandibular) (Coombs et al., 1988; Webb, 1989, 2013). This conserved architecture becomes particularly interesting when considering the large diversity of fish head morphologies (Alexander and Adams, 2004; Boglino et al., 2013; Bouton et al., 2002; Cabuy et al., 1999; Clabaut et al., 2007; Geerinckx et al., 2007; Kajiura, 2001; Lowry et al., 2007; Tedman, 1980; Wyckmans et al., 2007). When fish swim, flow is induced across the head. How flow interacts with the head depends greatly on its shape and thus fish heads may receive different sensory inputs depending on their morphological variation (Chambers et al., 2014; Herzog et al., 2017). Furthermore, because the fish head is the platform upon which the lateral line lies, any differences in head shape alter the spatial position of the lateral line relative to the flow. In this way, the alteration of flow and the difference in spatial positioning of the lateral line induced by head morphology may have important consequences for the ability of fish to sense their aquatic environment.

To begin exploring how head morphology affects flow detection by the lateral line canal system, we focused initially on one common aspect that is known to vary across species and ontogeny: head width. While it is possible to directly record from lateral line afferent nerve fibers to evaluate the sensory performance of fish (Chagnaud et al., 2007; Tricas and Highstein, 1991), it is not trivial to single out the contributions of head width. Instead, in this study, we used pressure sensors embedded in 3D-printed models with varying head widths to measure pressure gradients. We systematically examined how hydrodynamic information varies as a function of head width and how this may affect the sensing ability of fishes. In particular, we focused on detecting and characterizing two types of flow that fish regularly encounter in their natural environment: steady and vortical flow.

To help design fish head models, we first collected data from fish species known to have narrow, intermediate and wide heads. Preserved whole fish specimens were acquired from the Florida Museum of Natural History Ichthyology Collection at University of Florida. All morphometric data was measured using dial calipers. Head length was measured as the distance from the tip of the upper jaw to the posterior margin of the operculum. Head width was measured at the point of maximum width across the head. We normalized head width to head length by calculating aspect ratio (AR=width/length) in order to account for the fact that the head width can span a large range based on the size of the fish. Low and high AR heads would correspond to narrow and wide heads, respectively.

We were interested in understanding the effects of head shape in the anterior–posterior axis. We approximated the curvature of the model heads along this axis as half ellipses using Rhinoceros v5 (Robert McNeel & Associates, Seattle, WA, USA). We fabricated three models with head widths 2, 6 and 10 cm (Fig. 1A). The length of the models was kept constant at 10 cm. We refer to these models by their AR as narrow (AR=0.2), intermediate (AR=0.6) and wide heads (AR=1.0). The ARs of the models fell within and spanned the naturally occurring range of fish head ARs (Table 1). Each head was elongated an additional 5.5 cm posterior to the last canal pore to reduce potential effects of having a sharp trailing edge too close to the sensors. This elongation also enabled attachment of the head to a strut located away from the canal pores that positioned the model in the flow tank. In addition, we designed the models to be relatively tall (i.e. 15 cm) to minimize any 3D flow effects that may arise on the dorso-ventral axis. To simulate the lateral line canal, heads were designed with pores arranged in a single horizontal line (Fig. 1B). There was a single pore at the snout and six pores along the sides. Each pore was 3 mm in diameter and pores were spaced 1 cm apart along the curvature of the head. Thus, sensor position corresponds closely to arc length of the head (cm) in our study. Model heads were then 3D printed with acrylonitrile butadiene styrene (ABS) plastic using a Makerbot Replicator 2X (MakerBot^® Industries LLC, Brooklyn, NY, USA).

We embedded seven Mikrotip pressure catheters (Millar Instruments, Houston, TX, USA) into the model heads, one in the snout pore and six on the left side. The sensors were flush with the surface to minimize sensor–fluid interactions. Pressure sensors were calibrated at 1 mm below the surface of still water to estimate the value unit conversion to pascals. Pressure recordings were transmitted via PCU-2000 control units (Millar Instruments, Houston, TX, USA) and recorded with a sampling rate of 1000 Hz using LabChart (ADInstruments, Dunedin, New Zealand). Experiments were performed in our 175 l recirculating flow tank. We tested the model heads in steady and vortical flows. Vortical flow (a Kármán vortex street) was generated by placing a stationary cylinder in steady flow (Fig. 1C). The working section of the flow tank (25×26×87 cm height×width×length) was outfitted with an 80/20 aluminium frame (80/20 Inc.) custom designed to mount heads and cylinders in the working section. To enable repeated positioning of the head in the same region of the flow tank across experiments, heads were secured to the frame from above with a strut. Both heads and cylinders rested against the bottom of the flow tank to prevent self-oscillation.

For steady flow trials, heads were secured to the center of the working area with no cylinder. Pressure was then measured prior to any flow to record mean hydrostatic pressure for all seven sensors simultaneously for 20 s. Steady flow was then initiated, after which pressure was recorded for 30 s. Hydrostatic pressure was also recorded for 30 s after flow was stopped to account for potential drift in our sensors. The mean hydrostatic pressure was then subtracted from the steady flow pressure recordings. Because the lateral line canal neuromasts are sensitive to pressure differences between canal pores, we calculated the pressure difference between adjacent sensors for our analyses. Furthermore, because pressure difference is dependent on the distance between pores (van Netten, 2006), we normalized it to the spatial distance between pores for our steady flow measurements. Hereinafter, we refer to this normalized pressure difference as the pressure gradient. To assess sensory performance of each head for different sized vortices, we used three different cylinder diameters (1.3, 2.5, 5 cm). The diameter of shed vortices is dictated by cylinder diameter (Liao et al., 2003a), so by using different cylinder sizes we were able to generate vortices that we refer to as small, medium and large for this study. We additionally tested head performance for each vortex size at four flow speeds (26, 52, 79, 105 cm s⁻¹) and seven distances from the cylinder (ranging from 3 to 9 cylinder diameters downstream). Pressure was recorded for 60 s for all vortical flow trials. All data analyses were performed using custom-written scripts in MATLAB 2013b, and all values are shown as means±s.e.m., unless stated otherwise.

To examine how well a model head could theoretically detect changes in flow speed, we define sensitivity as the change in pressure gradient induced by a unit change in flow speed. Thus, the larger the change in pressure gradient, the higher the sensitivity. During steady and vortical flows, we observed that the pressure gradient at each point along the head increased linearly with flow speed. Therefore, we calculated sensitivity from the slope of the linear fit between pressure gradient and flow (Fig. 2C). We also evaluated the goodness of the linear fit using the coefficient of determination (R² value). In addition, to identify how sensitivity varies along the head, we first selected the data points with R²>0.8, and then fitted an exponential curve (y=ae^bx+c). The parameters of the exponential curve (a, b and c) were estimated using least-square methods.

We evaluated the ability of model heads to detect the periodicity of the vortical flow (i.e. vortex shedding frequency). We first obtained the frequency spectrum of pressure measurements using fast-Fourier transform and identified the frequency with maximum amplitude (i.e. dominant frequency). After confirming that the dominant frequency matched the expected vortex shedding frequency (i.e. desired signal), we calculated the SNR by dividing the amplitude of the desired signal by the noise amplitude (i.e. amplitudes of other frequencies). We estimated the noise amplitude as described in a previous study (Miersch et al., 2011). For each model head at a given trial, we compared the SNR values along the head and chose the maximum one. To determine the effects of head width, vortex size, flow speed and cylinder position on maximum SNR, we used a four-way ANOVA at an α-level of 0.05 (and subsequent Tukey's multiple comparison post hoc test).

Pressure gradient increased with flow speed and maximum pressure gradients were concentrated at the front of the model heads (Fig. 2A). The maximum pressure gradient experienced by the narrow head was higher than those experienced by the wider heads. However, the region of maximum pressure gradient was substantially smaller in the narrow head than in the wider heads. For example, in the narrow head the pressure gradient dropped from maximum to minimum at P2–P3 (Fig. 2Ai), whereas in the intermediate and wide heads the pressure gradient dropped to minima at P3–P4 and P6–P7, respectively (Fig. 2Aii,iii). Our results show that C_p profiles along the narrow and intermediate head did not change with flow speed, and they closely matched the theoretical predictions (Fig. 2Bi,ii). The mean absolute error between measured and predicted C_p was 0.04 and 0.06 for the narrow and intermediate heads, respectively. In contrast, we found that the C_p profile along the wide head changed with flow speed, and there was a larger difference between measured and predicted C_p with mean absolute error 0.12 (Fig. 2Biii). This may have been due to the fluid–structure interactions caused by the more constricted environment inherent to the wide head in a flow tank of finite width relative to narrow and intermediate heads. We found that the sensitivity profiles of the heads closely reflected their pressure gradient and C_p profiles (Fig. 2C). Sensitivity along all heads decreased across sensor position exponentially (y=ae^bx+c) with the following parameters: narrow a=1626×10⁶, b=−12.69, c=−0.15; intermediate a=40.05, b=−1.13, c=0.18; and wide a=951.8, b=−0.0005, c=−947.8. The maximum sensitivity experienced by the narrow head was higher but limited to a smaller anterior region than those experienced by the wider heads. The sensitivity of the narrow, intermediate and wide heads dropped below 20% of the maximum sensitivity measured at 9.6%, 25.1% and 49.0% of head arc length, respectively. Pressure measurements in steady flow did not experience any fluctuation, indicating that if any vortices were shed from the trailing edge of the models, they still had no influence on the pressure gradient along the head (Bearman, 1984).

Similar to the pressure gradient profiles in steady flow, the maximum pressure fluctuation points were concentrated at the front of the model heads in vortical flow, and the maximum pressure fluctuation experienced by the narrow head was higher than that experienced by the wider heads (Fig. 3A). This was true regardless of the flow speed or cylinder size (i.e. vortex size) (Fig. 3A,B). In the narrow and intermediate heads, pressure fluctuation at P1–P2 increased with vortex size but remained constant in the wide head (Fig. 3B). At 26 cm s⁻¹, C_p profiles along the narrow and intermediate heads were consistently higher than C_p of other flow speeds (Fig. 3C). We found that the sensitivity of the model heads was significantly lower in vortical flow than in steady flow (i.e. up to 1000 times less at the front of the head). Similar to the finding in steady flow, the sensitivity profiles of the heads closely reflected their pressure and C_p profiles (Fig. 3D). Sensitivity along all heads decreased across sensor position exponentially with the following parameters: narrow a=23.90, b=−1.517, c=0.4672; intermediate a=9.902, b=−1.175, c=0.5474; and wide a=3.269, b=−1.198, c=1.089. The maximum sensitivity experienced by the narrow head was higher but limited to a smaller anterior region than that experienced by the wider heads. The sensitivity of the narrow and intermediate heads dropped below 20% of the maximum sensitivity at 36.1% and 49.0% of head arc length, respectively. The sensitivity of the wide head never dropped below 20% of the maximum sensitivity measured for vortical flow.

To calculate the flow parameters, we averaged the pressure gradient and pressure fluctuation from the regions with sensitivities higher than 20% of the maximum sensitivity for steady and vortical flow, respectively (see Figs 2C and 3D). In steady flow, this corresponded to P1–P2 for the narrow head, and to P1–P2 and P2–P3 for the intermediate and wide heads (Fig. 2C). In vortical flow, this corresponded to P1–P2 for the narrow head, to P1–P2, P2–P3 and P3–P4 for the intermediate head and to P1–P2, P2–P3, P3–P4, P4–P5, P5–P6 and P6–P7 for the wide head (Fig. 3C). Our results show that all heads could accurately identify the vortex shedding frequency with a prediction error less than 10%, regardless of the flow speed or cylinder size (Fig. 4A). The model heads could also be successfully used to estimate the flow speed in both flow regimes (Fig. 4B,C). The prediction error for steady flow was less than 20%. The prediction error for vortical flow was less than 15% except at the lowest flow speed (26 cm s⁻¹), which had prediction errors between 10% and 30%. After estimating the vortex shedding frequency and flow speed, we recovered the cylinder diameter using Eqn 5 with a prediction error less than 15% except for the lowest flow speed (Fig. 4D). At the lowest flow speed, the model heads yielded prediction errors between 20% and 65%, likely due to the high error associated with estimating that particular flow speed.

In all model heads, SNR was maximum at the front part of the head (i.e. P1–P2) and decreased gradually across sensor position (Fig. 5A). This trend was independent from the flow speed and vortex sizes tested. On average, SNR was higher for medium and large vortices than for small vortices. We found that SNR was highest at intermediate flow speeds (i.e. 52 and 79 cm s⁻¹; Fig. 5B). SNR varied greatly with distance but did not follow any predictable pattern (Fig. 5C). Considering the overall performance of each model head, we found that sensitivity for a given vortex size varied with head width (Fig. 6). For small vortices, the narrow head had the highest SNR (15.10±0.24 dB) followed by the intermediate head (13.8±0.24 dB) and then the wide head (11.1±0.23 dB). For medium vortices, the narrow and intermediate heads had the highest SNR (20.7±0.30 and 20.4±0.21 dB, respectively), whereas the wide head had the lowest SNR (14.68±0.24 dB). For large vortices, the intermediate head had the highest SNR (21.57±0.19 dB), followed by the narrow head (19.68±0.41 dB) and then the wide head (17.78±0.34 dB).

In this study, sensitivity, pressure fluctuation and SNR were greatest at the snout regardless of head width or flow condition. Pressure gradient in steady flow was also greatest at the snout for narrow and intermediate heads and just behind the snout for wide heads. Thus, when a fish is oriented upstream in both steady and vortical flows, the most flow information for the lateral line canal is available at the anterior head region (directly at the snout or just behind) in steady flow. Previous experimental and computational studies in steady flow revealed similar pressure distributions (Akanyeti et al., 2013; Ristroph et al., 2015; Herzog et al., 2017). Moreover, flow imaging and modeling studies show that gliding fishes, which our study most closely approximates, experience the largest pressure gradient at the anterior region of the head during obstacle avoidance and wall-following behaviors (Windsor et al., 2010a,b). During steady swimming, fish continuously heave and yaw their head, which also has the potential to alter the pressure profile along the head (Lighthill, 1993; Akanyeti et al., 2016). It is remarkable, then, that across the different conditions of flow and swimming behaviors, the distribution of pressure stimuli along the fish head remains similar in that the snout is the most sensitive to external stimuli (Dubois et al., 1974; Akanyeti et al., 2016). These results suggest that the anterior region of the head has access to a rich area of hydrodynamic information for the lateral line canal. It would be of great interest in future studies to examine the anatomy of anterior canals in more detail to see whether any anatomical specializations were selected for in regions where hydrodynamic information is greatest (Coombs et al., 1988; Webb, 1989, 2013; Ristroph et al., 2015; Windsor et al., 2010a).

Fish hold station behind objects to take refuge from fast flows (Johansen et al., 2008; Liao et al., 2003a; Krause et al., 1998; Sutterlin and Waddy, 1975). To do so, fish can adjust their swimming gait to slalom between vortices shed by a stationary object in flow (i.e. Kármán gait), allowing them to significantly reduce the cost of locomotion (Liao et al., 2003a,b; Taguchi and Liao, 2011). Trout are able to Kármán gait across several different flow speeds and cylinder sizes, but prefer certain conditions (Akanyeti and Liao, 2013; Liao et al., 2003a; Liao, 2006). This preference across flow speeds may be mediated by the lateral line as, in the absence of vision, trout will still Kármán gait (Liao, 2006).

We found that SNR for vortices was highest at intermediate flow speeds, regardless of head width. These speeds correlate with the flow speeds at which rainbow trout are most likely to Kármán gait (Akanyeti and Liao, 2013). Intermediate flow speeds likely have higher SNR due to the shedding of stronger, more coherent vortices with less noise. This is in comparison to lower and higher flow speeds, which have weaker vortices and more turbulence, respectively (Blevins, 1990). The correlation between the likelihood of Kármán gaiting and a high SNR suggests that active sensing could play a role in Kármán gaiting (Liao et al., 2003a,b; Liao, 2006). Furthermore, fish will only Kármán gait behind an appropriately sized cylinder (Liao et al., 2003b; Akanyeti and Liao, 2013). We found that the width of the head optimizes the detection of vortices by the canal system, whereby wide heads are more sensitive to detecting larger vortices than smaller vortices, and narrow heads are more sensitive to detecting smaller vortices than larger vortices. Within species, there is evidence that the ratio of head width to body length does not vary much across development (Ceas and Page, 1996; Randall and Page, 2012; Wright and Page, 2008). Thus, as an individual fish grows, it may continue to passively optimize the detection of vortices from which it can best take refuge. Across species, we suggest that fish with wider heads will detect vortical flows with larger vortices and those with narrower heads will detect vortical flows with smaller vortices. This may lead to preferences in refuging locations and thus have implications for differential habitat utilization between species of different head widths. The inability to record neural activity from the lateral line cephalic canal system makes it challenging to understand what flow information is actually detected by the head of a fish during swimming. However, this study provides a fundamental advance in our understanding by simply describing what information is available to the canal system along the fish head. While we know that fish can detect and exploit vortices in nature, this study is the first to show how the amount of hydrodynamic information available to fish is shaped by the head in different flow conditions.

Animals that undulate in water generate vortex wakes that the lateral line can sense (Gardiner and Atema, 2007; Hanke and Bleckmann, 2004; Pohlmann et al., 2001, 2004). These thrust wakes (as opposed to drag wakes) contain information such as tailbeat frequency and amplitude of the swimming prey, which can be used to estimate the animal's swimming speed and size (Blickhan et al., 1992; Hanke et al., 2000; Hanke and Bleckmann, 2004; Müller et al., 1997). Our study suggests that in addition to facilitating the ability to seek optimal flow refuges, the natural tuning to specific vortex sizes could allow fish to passively size-select optimal prey even in low-light environments, which could maximize energy gains (Kislalioglu and Gibson, 1976; Prejs et al., 1990). Furthermore, we provide evidence that the lateral line canal can be used to identify cylinder sizes and flow speeds, which suggests that it is possible in theory for fish to actively differentiate between prey size and identify swimming speeds. However, verification of this ability awaits experiments on live fish.

While neural mechanisms such as the particular response properties of afferent neurons may enhance the ability to detect vortices, a hydrodynamic mechanism that could contribute to our observation that head width self-selects for vortex size detection is vortex rebound. Vortex rebound occurs when a vortex contacts, and then rebounds off, a broad surface such as the head (Orlandi, 1990). In the case of Kármán vortex streets where vortices are continually shed into the wake, a vortex could rebound from the head and interfere with the next oncoming vortex. This would diminish the strength and periodicity of the vortex street in the region of the head. Because the wider the head, the more it approximates a straight wall to an inbound vortex (particularly for smaller vortices), we believe that vortex rebound may be responsible for reducing SNR when intermediate and wide heads interact with small vortices generated by a small cylinder. We believe that fluid–structure interactions dictate the patterns in SNR we observed. However, our experimental design could not distinguish whether the differences in SNR were due to fluid interactions or to small differences in the spatial distribution of sensors across different head widths. Further studies into the mechanism underlying vortex size discrimination would benefit from computational models, given that the large size of pressure sensors in experimental studies limits the resolution of spatial sampling of canal pores.

Flows in nature are often much more complex than vortex streets, arising from the fluid–structure interactions of multiple objects. While our analyses focused on characterizing the hydrodynamic information available in unsteady flow induced by a single cylinder, a fertile area for future experiments would be to evaluate how more complex environments may be perceived and how they can be assessed by the pressure-sensing lateral line canal system. For example, two cylinders arranged in tandem can significantly alter the strength and shedding frequency of vortices, which changes when and how fish Kármán gait (Stewart et al., 2016). In this context, it would be interesting to evaluate how pressure sensing plays a role in how fish decide to position themselves around aggregate structures in flow.

Flow sensors provide crucial information for autonomous underwater vehicles (AUVs) seeking to navigate complex and novel environments (Devries et al., 2015; Salumäe and Kruusmaa, 2013; Tan, 2011). Both physical and mathematical models have shown that a linear array of pressure sensors can be used to accurately determine environmental flow speeds, characterize vortex wakes and localize objects (Chambers et al., 2014; Ćurčić-Blake and van Netten, 2006; Franosch et al., 2009; Klein and Bleckmann, 2011; McConney et al., 2009; Pandya et al., 2006; Ren and Mohseni, 2012; Venturelli et al., 2012; Yang et al., 2006, 2010). While all model heads could accurately estimate several steady flow parameters in our study, they used different subsets of sensors to do this. Narrow heads were only able to accurately determine flow speed by using the pressure measurements at the front part of the head. The intermediate and wide heads, in contrast, could most accurately determine flow speed by averaging measurements across a larger region of the head. This suggests that narrow heads need fewer sensors to detect flow speed compared with wider heads. Coupled with the relatively greater sensitivity to change in flow speed towards the snout, a narrow sensor platform appears optimal for velocity detection on an AUV. Furthermore, head width had minimal effect on how accurately vortex shedding frequency, flow speed and cylinder size within a Kármán vortex street could be determined. Taken together, we recommend a narrow sensor platform for use on AUVs to minimize the number of sensors required to detect and characterize both steady and vortical flows.

Our 2D study on head width focused on only one aspect of head morphology. AUV sensor placement must be designed to represent a 3D structure that possesses substantial dorso-ventral curvature. Another rich area of investigation would be the influence of surface topography on flow sensing. Microscopic depressions called epidermal pits observed on the head of ides (Leuciscus idus) have been suggested to increase SNR by 10–30 dB when detecting predators or prey (Herzog et al., 2017). This becomes particularly interesting when considering the large diversity of fish scale morphologies that exist (Agassiz, 1833; Roberts, 1993). Future studies on 3D head morphology and surface topography promise to provide insight on how to enhance the sensitivity and efficiency of AUV sensor platforms.

We would like to thank William Stewart, Lawrence Page, Lawrence Ukeiley and David Blackburn for helpful discussions throughout the project. Comments from two anonymous reviewers improved the manuscript substantially.