Viscoelastic Characterization of the Primate Finger Pad In Vivo by Microstep Indentation and Three-Dimensional Finite Element Models for Tactile Sensation Studies

Tactile information in humans and primates is encoded in the response of thousands of peripheral nerve endings embedded in the skin. A load applied on the surface of the finger pad is transmitted to mechanoreceptor locations within the skin. The resulting mechanical state (stress/strain) around the mechanoreceptor causes it to “fire,” generating a train of neural impulses sent to the central nervous system and enabling us to interpret touch. These neural impulses, generated by the spatial distribution of responding mechanoreceptors, are in the form of a temporal sequence of action potentials and tactile information is encoded in the frequency of the generated action potentials. The neural response of mechanoreceptors in humans and primates to a “step” stimulus (a step force or step displacement applied on the finger pad with a blunt probe) has been characterized in the literatures [1–5]. For SA-1 mechanoreceptors (Sec. 4.1), there are two distinct phases of neural response to a step indentation on the finger pad: a dynamic phase and a static steady-state phase. The dynamic phase is observed immediately following stimulation, where the firing frequency of mechanoreceptors is initially high followed by a gradual reduction. This firing frequency reduces and eventually settles into a steady-state value. Most models in literature describing the primate finger pad mechanoreceptor neural behavior [6–9] try to relate the incident loading and resulting mechanical state at the mechanoreceptor to the steady-state firing rate or average firing rate (in a chosen time window) of the mechanoreceptor. Recent studies include Gerling et al. [10], where a finite element model of a human distal phalange was developed along with a receptor model to predict the average firing rate in the dynamic phase and static phase and to match available primate empirical data [1]. The average firing rates in the dynamic phase were calculated based on the inverse of the average interspike intervals on the dynamic phase (30–50 ms which includes the highest firing frequency poststimulation), while the average static firing rate was based on spikes observed in a larger time window, 650–950 ms [10]. To the best of our knowledge, limited literature is available that characterizes the transient firing rate of the mechanoreceptor on stimulation during the dynamic phase (i.e., characterizing the change in firing rate with time in the dynamic phase before steady-state). This paper characterizes the viscoelastic behavior of the skin tissue and studies its relationship to the dynamic firing rate of SA-1 mechanoreceptors. To develop a quantitative understanding of how spatiotemporal loads imposed on the surface of the skin are transmitted to mechanoreceptor locations within the skin, it is imperative to fully understand and characterize the geometry as well as mechanical properties of skin and its underlying tissues. One of the interesting problems in tactile sensation is to identify what stress/strain state around the mechanoreceptor causes it to respond. To understand this, we must try to relate the mechanical state around the mechanoreceptor due to an imposed load to the neural impulses that result from the stimulation. The experimental challenges in obtaining mechanoreceptor responses to mechanical stimuli in humans warrant the use of other model organisms to study tactile sensation. The wealth of tactile neural data available in primates [1,2] along with the similarity of the structure of the primate fingertip to that of humans makes it a popular model to study touch in humans. There has been considerable progress in the development of accurate elastic biomechanical models of the primate and human finger pad. Early models idealized the finger pad [3] as an incompressible, homogenous, isotropic linearly elastic half-space. The “waterbed model” [11] assumed the finger pad to be an elastic membrane under pressure and was successful in accurately predicting human and monkey finger pad surface deflection to line loads. However, this model could not explain the transduction of mechanical signals into neural codes. To answer this, two-dimensional [6,7,12] and three-dimensional finite element models [8,13] of the human and monkey fingertips with realistic external geometry and internal layered structure of the skin and subcutaneous tissues were developed, to gage the role of skin biomechanics in tactile response. The models developed by Dandekar et al. [8] used a linear elastic model for the skin tissue where a Poisson's ratio of 0.48 was used (considering the tissue to be almost incompressible). The elastic moduli of the different layers were obtained by matching numerical experiments with available empirical data. Using these models, the strain energy density at the mechanoreceptor locations was shown to be the likely strain measure encoded by the mechanoreceptors. 1.1. Viscoelastic Characterization of Primate Skin Tissue. The work cited in the previous section assumed the mechanical behavior of human and primate skin tissue to be linearly elastic. However, skin is well known to be viscoelastic and anisotropic in nature. We are interested in determining the mechanical state at mechanoreceptor locations at the advent of mechanoreceptor stimulation taking into account the viscoelastic nature of skin tissue. The advent of mechanoreceptor stimulation occurs at small strains [2] and thus there is a need to accurately characterize viscoelastic behavior of skin tissue at these small deformation ranges. There has been progress in the development of viscoelastic models of the human fingertip to study its response to a variety of dynamic mechanical stimuli [14–17]. However, to the best of our knowledge there is limited literature on empirically validated viscoelastic models of the monkey fingertip. Due to the difficulty in isolating biological tissue specimens along with the challenges in preserving mechanical integrity of tissues in vitro, it becomes necessary to characterize material properties using in vivo methods. In this paper, we present a method to estimate mechanistic viscoelastic parameters of primate skin tissue in vivo for small strains by studying the stress relaxation behavior of the finger pad of a primate using a combination of single point indentation experiments and numerical simulation. We characterize the viscoelastic behavior of the finger pad in response to precise microstep indentation using a calibrated system with position resolution of 1 μm and force resolution of 0.3 mN and study the variation of this behavior across different fingers of an anesthetized primate. To avoid noise in the data due to motion artifacts during the experiments, we studied the viscoelastic response of the finger pads of different fingers of an anesthetized primate. To check the variability of our observed data, we model the empirical force–time response using a Maxwell–Weichert element and compare the fitted model parameters. In order to determine more mechanistic viscoelastic parameters, we develop two 3D multilayer finite element models of the primate fingertip: (a) a homogeneous viscoelastic model where all the tissues are modeled with a two term Prony series and (b) a multilayer model where the epidermis is modeled using an incompressible (Poisson's ratio = 0.48) linearly elastic material, and the dermis and inner tissues are modeled with a two term Prony series. We build these models with realistic geometry from previously published data [8] and use them to simulate two sets of indentation experiments: (a) indentation with a cylindrical indenter and (b) indentation with a line load. Both the models are calibrated by matching the force–time response curves of our simulation with our experimental data (step indentation with a cylindrical indenter). In order to validate the models, surface deflection profiles of the model to line loads are matched with data available in the literature [11]. Using these methods, we calibrate and compare a homogeneous viscoelastic model and a multilayer elastic viscoelastic model described in Sec. 4. Finally, we indent the calibrated and validated model with a flat plate and compare the strain energy density versus time with available neurophysiological data in the literature [2]. Results are presented in Sec. 4.1 and reveal that the rate of adaptation of slowly adapting (SA) mechanoreceptors may be linked to the viscoelastic relaxation of the surrounding skin tissue.