Fingertip Models and Finite Element Analysis

We have performed linear and nonlinear finite element analysis of a series of mechanistic models of the fingerpad under a variety of mechanical stimuli (Srinivasan and Dandekar, 1992; 1996; Dandekar and Srinivasan, 1994; 1995; Dandekar and Srinivasan, 1996). The models range from a semi-infinite medium to a 3D model based on the actual finger geometry, and composed of a homogeneous elastic material, a thick elastic shell containing a fluid or a multilayered medium. Simulations of the mechanistic aspects of neurophysiological experiments involving mapping of receptive fields with single point loads, determination of spatial resolution of two-point stimuli, and indentations by single bars as well as periodic and aperiodic gratings have been carried out for the 2D and 3D models. We have also solved the nonlinear contact problem of indentations by cylindrical objects and sinusoidal step shapes. The large number of numerical calculations needed even for the linear two dimensional models necessitated the use of the Cray-C90 at the NSF Pittsburgh Supercomputer Center.

The results show that the model geometry has a significant influence on the spatial distribution of the mechanical signals, and that the elastic medium acts like a low-pass filter in causing blurring of the mechanical signals imposed at the surface. Multilayered 3D models of monkey and human fingertips accurately predicted the surface deformations under a line load, experimentally observed by Srinivasan (1989). The same models predicted the experimentally observed surface deformations under cylindrical indentors as well. These 3D finite element models were used to simulate neurophysiological experiments involving indentation by rectangular bars, aperiodic gratings, cylindrical indentors and step shapes. Several strain measures at typical mechanoreceptor locations were matched with previously obtained neurophysiological data, so as to determine the relevant mechanical signal that causes the receptors to respond. In all the simulations, the strain energy density at the receptor location was found to be directly related to the static discharge rate of the Slowly Adapting afferents. In addition, strain energy density is a scalar that is invariant with respect to receptor orientations and is a direct measure of the distortion of the receptor caused by loads imposed on the skin. We have therefore hypothesized that the strain energy density at the receptor site is the relevant stimulus to the slowly adapting receptors.