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Research Papers

# Computational Parametric Analysis of the Mechanical Response of Structurally Varying Pacinian Corpuscles

[+] Author and Article Information
Julia C. Quindlen, Victor H. Barocas

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455

Burak Güçlü

Institute of Biomedical Engineering,
Boğaziçi University,
Istanbul 34335, Turkey

Eric A. Schepis

Institute for Sensory Research,
Syracuse University,
Syracuse, NY 13244

Manuscript received December 12, 2016; final manuscript received April 26, 2017; published online June 6, 2017. Assoc. Editor: Eric A Kennedy.

J Biomech Eng 139(7), 071012 (Jun 06, 2017) (9 pages) Paper No: BIO-16-1512; doi: 10.1115/1.4036603 History: Received December 12, 2016; Revised April 26, 2017

## Abstract

The Pacinian corpuscle (PC) is a cutaneous mechanoreceptor that senses low-amplitude, high-frequency vibrations. The PC contains a nerve fiber surrounded by alternating layers of solid lamellae and interlamellar fluid, and this structure is hypothesized to contribute to the PC's role as a band-pass filter for vibrations. In this study, we sought to evaluate the relationship between the PC's material and geometric parameters and its response to vibration. We used a spherical finite element mechanical model based on shell theory and lubrication theory to model the PC's outer core. Specifically, we analyzed the effect of the following structural properties on the PC's frequency sensitivity: lamellar modulus (E), lamellar thickness (h), fluid viscosity (μ), PC outer radius (Ro), and number of lamellae (N). The frequency of peak strain amplification (henceforth “peak frequency”) and frequency range over which strain amplification occurred (henceforth “bandwidth”) increased with lamellar modulus or lamellar thickness and decreased with an increase in fluid viscosity or radius. All five structural parameters were combined into expressions for the relationship between the parameters and peak frequency, $ωpeak=1.605×10−6N3.475(Eh/μRo)$, or bandwidth, $B=1.747×10−6N3.951(Eh/μRo)$. Although further work is needed to understand how mechanical variability contributes to functional variability in PCs and how factors such as PC eccentricity also affect PC behavior, this study provides two simple expressions that can be used to predict the impact of structural or material changes with aging or disease on the frequency response of the PC.

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## Figures

Fig. 1

Histological and model PCs. (a) Image of a single PC in a thick human skin slice. Image obtained from thick human skin after H&E staining and provided by Dr. Christopher Honda from the University of Minnesota. The PC was sectioned perpendicular to the long axis of the receptor. Lamellae can be seen as concentric lines in the cross section. (b) Representation of the PC outer core in the multilayer (Stage 1) model. The thick, solid lines represent lamellae and the shaded regions between lines represent the interlamellar fluid. The shaded pink area in the lower left corner represents the inner core (modeled in Stage 2).

Fig. 2

Ratio of inner to outer shell strain at various lamellar moduli. The ratio is plotted for simulations run with lamellar moduli of 100 Pa (left), 1 kPa (center), and 10 kPa (right). Each modulus was run for PCs with 2–30 shells, with increasing shell number indicated by the arrows.

Fig. 3

Peak frequency and bandwidth for various ratios of lamellar modulus to fluid viscosity (E/μ). (a) The peak frequency was the frequency at which the highest ratio of inner to outer shell strain occurred, which is the frequency of peak strain amplification. The bandwidth was the frequency range over which the ratio of inner to outer shell strain was greater than 1 (dashed line), indicating strain amplification through the PC capsule. (b) The peak frequency was calculated for different values of E/μ. The peak frequency at E/μ is plotted for 12–30 shells, with increasing shell number indicated by the arrow and shading. (c) The bandwidth was calculated for different values of E/μ, with increasing shell number indicated by the arrow and shading.

Fig. 4

Peak frequency plotted for various average lamellar thicknesses (h) and radii (Ro). (a) The peak frequency was calculated for simulations run at different values of h with 12–30 shells. The square and circle icons represent where the PCs shown in (c) and (d) would fall on this graph. Increasing shell number is indicated by the arrow and shading. (b) The peak frequency was calculated for simulations run at various Ro. (c) 12 shell PC run at parameters indicated by the filled square in (a). Black indicates solid lamellae, white indicates fluid-filled spaces, and grey indicates the inner core. (d) 20 shell PC run at parameters indicated by the filled circle in (a).

Fig. 5

Peak frequency and bandwidth vs. h/Ro. (a) Peak frequency calculated for various values of h/Ro at 12–30 shells with increasing shell number indicated by the arrow and hotter color. (b) Bandwidth calculated for various values of h/Ro at 12–30 shells with increasing shell number indicated by the arrow and shading.

Fig. 6

Peak frequency and bandwidth vs. Eh/μRo. (a) Peak frequency calculated from simulations run at various values of Eh/μRo for 12–30 shells, with increasing shell number indicated by the arrow and shading. (b) Bandwidth calculated from simulations run at various values of Eh/μRo, with increasing shell number indicated by the arrow and shading.

Fig. 7

Relationship between the five structural parameters (E, h, μ, Ro, N) and the peak frequency (ω) and bandwidth (B). (a) The value ωμRo/Eh was plotted against the number of shells (N) in a log-log plot for all data points from the simulations. A power-law fit gave an exponent of 3.475, with the best-fit line plotted as a solid red line through the data points. A zoomed-in view of individual data points is shown. Each simulation is marked with a horizontal line in the zoomed-in view. (b) Comparison between the peak frequency measured in all computer simulations and the calculated value N3.475 × Eh/μRo using the parameters input into the simulations. A zoomed-in view of individual data points is shown. Each simulation is marked with a vertical line in the zoomed-in view. (c) The value BμRo/Eh was plotted against N in a log-log plot for all data points from the simulations. A power-law fit gave an exponent of 3.591, with the best-fit line plotted as a solid red line through the data points. (d) Comparison between the bandwidth measured in all computer simulations and the calculated value N3.591 × Eh/μRo using the parameters input into the simulations.

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