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Mechanical filtering by the boundary layer and fluid–structure interaction in the superficial neuromast of the fish lateral line system

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Abstract

A great diversity of aquatic animals detects water flow with ciliated mechanoreceptors on the body’s surface. In order to understand how these receptors mechanically filter signals, we developed a theoretical model of the superficial neuromast in the fish lateral line system. The cupula of the neuromast was modeled as a cylindrical beam that deflects in response to an oscillating flow field. Its accuracy was verified by comparison with prior measurements of cupular deflection in larval zebrafish (Danio rerio). The model predicts that the boundary layer of flow over the body attenuates low-frequency stimuli. The fluid–structure interaction between this flow and the cupula attenuates high-frequency stimuli. The number and height of hair cell kinocilia and the dimensions of the cupular matrix determine the range of intermediate frequencies to which a neuromast is sensitive. By articulating the individual mechanical contributions of the boundary layer and the components of cupular morphology, this model provides the theoretical framework for understanding how a hydrodynamic receptor filters flow signals.

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Abbreviations

a :

radius of cupula at base

a s :

radius of a sphere

b m :

force coefficient for cupular material

b w :

force coefficient for fluid

c :

speed of sound in water

C :

integration constant

E m :

Young’s modulus of cupular matrix

F :

stimulus frequency

F b :

buoyant force

F e :

elastic force

F m :

inertial force

F a :

acceleration reaction

F u :

viscous drag

h h :

height of hair bundle

h c :

height of cupula

h k :

height of kinocilia

I :

second moment of area

k :

viscous drag coefficient

L :

hydrodynamic force coefficient

M :

bending moment

N :

number of hair cells

p :

distance between center of sphere and flat plate

q l :

linear spring bundle stiffness

q t :

torsion spring bundle stiffness

r :

distance from center of sphere

Re :

Reynolds number

S h :

sensitivity of cupula to local flow

S b :

sensitivity of local flow to freestream flow

S f :

sensitivity of cupula to freestream flow

S l :

Sensitivity of local flow to an oscillating sphere

S s :

sensitivity of cupula to oscillating sphere

St :

Strouhal number

t :

time

U :

flow velocity

U ∞ :

freestream velocity

U s :

flow velocity generated by an oscillating sphere

U s,lin :

linearized flow velocity generated by vibrating sphere

W :

sphere velocity

\( \hat{\user2{x}} \) :

unit vector along body

z :

position along height

\( \hat{\user2{z}} \) :

unit vector along height

β :

boundary layer flow velocity gradient

δ :

boundary layer thickness

μ:

dynamic viscosity of water

ν:

cupula deflection

νs :

cupula deflection by vibrating sphere

ρm :

density of cupular material

ρw :

density of fluid

ω:

angular rate of oscillation

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Acknowledgments

This research was supported by National Science Foundation grants to MJM (IOS-0723288 and IOB-0509740). Although no experiments were performed for this work, we have complied with the “Principles of animal care”, publication no. 86-23, revised 1985 of the National Institute of Health, and also with the current laws of the USA and The Netherlands.

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Authors and Affiliations

  1. Department of Ecology and Evolution, University of California, 5205 McGaugh Hall, Irvine, CA, 92697, USA

    Matthew J. McHenry & James A. Strother

  2. Department of Neurobiophysics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

    Sietse M. van Netten

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  1. Matthew J. McHenry
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  2. James A. Strother
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  3. Sietse M. van Netten
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Correspondence to Matthew J. McHenry.

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McHenry, M.J., Strother, J.A. & van Netten, S.M. Mechanical filtering by the boundary layer and fluid–structure interaction in the superficial neuromast of the fish lateral line system. J Comp Physiol A 194, 795–810 (2008). https://doi.org/10.1007/s00359-008-0350-2

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  • DOI: https://doi.org/10.1007/s00359-008-0350-2

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