Fig 1.
Pacinian corpuscle removed from a human cadaveric hand. Tick marks on the ruler correspond to 0.5 mm. Sample was obtained from cadaveric tissue provided, with approval, by the University of Minnesota Anatomy Bequest Program.
Fig 2.
The multiscale model of the PC includes a macroscale finite-element mesh with representative volume elements (RVEs) of microscale fiber networks and neo-Hookean matrix.
Fig 3.
Finite-element meshes and representative networks.
(A) The isolated PC model was populated with circumferentially-aligned Delaunay networks and indented with an indenter of diameter 250μm. (B) The epidermis and dermis PC models were populated with circumferentially-aligned Delaunay networks in the PC elements (red) and transversely isotropic Delaunay networks in the skin elements (gold). Single nodes on the surface of the meshes were indented.
Fig 4.
Comparison between model and experiments [7].
(A) Rapid, nonlinear drop in displacement with distance from the indenter site observed experimentally (green circles, from Güçlü) is matched by the current model (red triangles, solid line) but not by a linear elastic model (blue squares, dotted line; from Güçlü). (B) To visualize the nonlinearity, lines were drawn to represent the initial (first column) and final (second column) of the nodes in the indentation experiment. The multiscale model (third column) matched the experimental data much better than the linear elastic model (fourth column). These results confirm Güçlü’s observation that a linear elastic model cannot capture the response of the PC and demonstrate the ability of a structurally-motivated anisotropic model to do so.
Fig 5.
Von Mises stress in isotropic and aligned network cases.
Von Mises stress along the top (surface layer) of the PC after 10 μm indentations (in the +z direction) with a 250μm diameter indenter for simulations run with isotropic networks (left) or circumferentially-aligned networks (right). The isotropic network case shows higher stress around the indenter than that shown in the aligned network case.
Fig 6.
Long-axis strain in isotropic and aligned network cases.
The strain along the long axis of the PC was calculated after 25 steps of 1 μm indentation. The cases of circumferentially-aligned (red squares) network and isotropic (blue circles) networks are shown. While the long-axis strain increases monotonically with indentation into the PC in both network cases, the isotropic network case showed higher strain than the aligned network case.
Fig 7.
PC long-axis strain resulting from surface indentation at various nodes.
Surface indentation sensitivity plot showing the long-axis strain along the PC resulting from 10 μm indentation at various nodes along the surface of the epidermis (left) and dermis (right) models. The dotted black line indicates the position of a quarter of the PC beneath the surface of the skin. The solid black line on the epidermis plot indicates the contour line for zero strain, which is the strain value below which the neurite would not be expected to respond to indentation.
Fig 8.
Von Mises strain resulting from surface indentation at different locations.
The Von Mises strain (millistrain) at each element in the epidermis (top) and dermis (bottom) cases calculated after 10 μm indentation at three different locations on the surface (750 μm down the short axis of the PC, directly above the center of the PC, 750 μm down the long axis of the PC). The green arrows indicate the location of indentation. The large-strain region around the indenter reaches the epidermally-located PC but does not penetrate to the depth of the dermally-located PC. Only one quarter of the embedded PC mesh is shown due to symmetry.
Fig 9.
PC long-axis strain for horizontal and vertical PC alignment in skin mesh.
Surface indentation sensitivity plot showing the long-axis strain along the PC resulting from 10 μm indentation at various nodes along the surface of the skin in a PC oriented with its long axis parallel to the surface of the skin (left, Horizontal) and its long axis perpendicular to the surface of the skin (right, Vertical). Both models contain a dermally-embedded PC. The dotted black line indicates the position of a quarter of the PC beneath the surface of the skin. The scale bars indicate the long-axis strain values for each model.
Fig 10.
Comparison between long-axis strain and area strain.
The long-axis strain of the PC (blue circles) and the area strain of the PC (red squares) were calculated for 25 steps of 1 μm indentation. Both long-axis strain and area change increase monotonically as the PC is indented.