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Research Papers

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

[+] Author and Article Information
Siddarth Kumar

Laboratory for Human and Machine Haptics
(MIT Touch Lab),
Research Laboratory of Electronics,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mails: siddarth@mit.edu;
siddarthk@gmail.com

Gang Liu

Department of Chemistry,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: gangliu@mit.edu

David W. Schloerb

Laboratory for Human and Machine Haptics
(MIT Touch Lab),
Research Laboratory of Electronics,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: schloerb@mit.edu

Mandayam A. Srinivasan

Laboratory for Human and Machine Haptics
(MIT Touch Lab),
Research Laboratory of Electronics
and Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: srini@mit.edu

1Corresponding author.

Manuscript received September 21, 2014; final manuscript received March 1, 2015; published online March 18, 2015. Assoc. Editor: David Corr.

J Biomech Eng 137(6), 061002 (Jun 01, 2015) (10 pages) Paper No: BIO-14-1469; doi: 10.1115/1.4029985 History: Received September 21, 2014; Revised March 01, 2015; Online March 18, 2015

When we touch an object, surface loads imposed on the skin are transmitted to thousands of specialized nerve endings (mechanoreceptors) embedded within the skin. These mechanoreceptors transduce the mechanical signals imposed on them into a neural code of the incident stimuli, enabling us to feel the object. To understand the mechanisms of tactile sensation, it is critical to understand the relationship between the applied surface loads, mechanical state at the mechanoreceptor locations, and transduced neural codes. In this paper, we characterize the bulk viscoelastic properties of the primate finger pad and show its relationship to the dynamic firing rate of SA-1 mechanoreceptors. Two three-dimensional (3D) finite element viscoelastic models, a homogeneous and a multilayer model, of the primate fingertip are developed and calibrated with data from a series of force responses to micro-indentation experiments on primate finger pads. We test these models for validation by simulating indentation with a line load and comparing surface deflection with data in the literature (Srinivasan, 1989, “Surface Deflection of Primate Fingertip Under Line Load,” J. Biomech., 22(4), pp. 343–349). We show that a multilayer model with an elastic epidermis and viscoelastic core predicts both the spatial and temporal biomechanical response of the primate finger pad. Finally, to show the utility of the model, ramp and hold indentation with a flat plate is simulated. The multilayer model predicts the strain energy density at a mechanoreceptor location would decay at the same rate as the average dynamic firing rate of SA-1 mechanoreceptors in response to flat plate indentation (previously observed by Srinivasan and LaMotte, 1991 “Encoding of Shape in the Responses of Cutaneous Mechanoreceptors,” Information Processing in the Somatosensory System (Wenner-Gren International Symposium Series), O. Franzen and J. Westman, eds., Macmillan Press, London, UK), suggesting that the rate of adaptation of SA-1 mechanoreceptors is governed by the viscoelastic nature of its surrounding tissue.

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References

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Figures

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Fig. 1

Block diagram of the indentation apparatus used for characterizing the viscoelastic properties of the primate finger pad. The inset image shows the Delrin probe tip used for the indentation experiments. The diameter of the flat end of the cylindrical indenter is 0.5 mm. A typical input displacement stimulus and observed force output (shown qualitatively, not to scale). The indenter was not glued to the primate finger pad during experiments; however, on retraction of the tip from the skin some adhesion was observed.

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Fig. 2

Position calibration of the indenter. (a) The setup used to determine the position calibration constant. Note that the photo does not show the PDMS block that was on top of the micrometer positioning “Z” stage used for calibration. (b) The calibration plot of the measured voltage versus the displacement controlled by adjusting the Z stage.

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Fig. 3

Force calibration of the indenter. (a) Presents a schematic of the inverted indenter tip used to derive the force calibration constant and (b) the calibration plot of the measured voltage versus the applied weight on the indenter.

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Fig. 4

Force response of the primate to static step indentation. (a) Illustrates the repeatability of the measurements by superimposing five independent trials of the force response of the little finger to a static indentation of 0.8 mm. (b)–(f) The force responses of the thumb, index finger, middle finger, ring finger, and little finger in response to step inputs of 0.2 mm, 0.4 mm, 0.6 mm, and 0.8 mm.

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Fig. 5

Model fit. (a) A variation of the Maxwell–Weichert model comprises three elastic springs and two purely viscous dampers. (b) The model fit to the force response of the ring finger pad of the primate in response to a step input (displacement) of depth 0.6 mm.

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Fig. 6

Estimation of model parameters. (a) The two exponential decay parameters for all five fingers and (b) the dimensionless coefficients. Each point represents a mean of n = 19 readings taken across all four indentation depths (except for the index finger which includes only 10 successful trials; see Sec. 2.3). All error bars are ± 1 standard deviation and the finger digits are defined as follows: (1) index finger, (2) middle finger, (3) ring finger, (4) little finger, and (5) thumb. The plots show that for our given indentation ranges (200–800 μm) there is not much finger–finger variation in the model parameters and there are two distinct time regimes. In the short term (∼<3 s), the viscoelastic behavior is like a viscous liquid with fast stress relaxation governed by the smaller time constant. In the longer term (>3 s), unlike a viscous liquid with small time constant, the decay slows and the stress does not entirely reduce to zero instead slows toward an asymptotic value governed by the springs in the model.

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Fig. 7

(a) Cross section of the multilayer viscoelastic model built in adina showing the four layers of tissue, labeled L1–L4, with L4 being the outermost layer. The innermost layer of the model, the bone, is not shown such that the finger appears hollow in the figure. For scale, the monkey fingertip width at the cross section is ∼8 mm. (b) The full 3D model used for simulating the indentation experiments.

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Fig. 8

Line load indentation. (a) The model simulating the line load indentation experiment reported by Srinivasan [11]. (b) The deformed mesh of the primate finger pad indented to 0.5 mm after 3 s. The legend shows displacement in millimeter.

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Fig. 9

(a) The model simulating a step indentation to a cylindrical tipped indenter similar to experiments performed in Sec. 2.3 and (b) the deformed mesh of the primate finger indented to 0.2 mm after 1 s. Effective stress is shown in megapascal.

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Fig. 10

(a) The calibration curve used to estimate the viscoelastic properties of the primate fingertip model. Both the multilayer model as well as the homogeneous viscoelastic model could fit the force response data. (b) The surface deflection profiles of the calibrated multilayer model and homogeneous viscoelastic model showing that only the multilayer model is able to predict the surface deflection due to a line load as observed in experiment (Srinivasan [11]).

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Fig. 11

(a) The temporal sequence of action potentials of SA afferents in response to indentation with a flat plate (data from Srinivasan and LaMotte [2]). Five independent trials are shown where each vertical spike represents an individual action potential: (b) The comparison of the strain energy density at a mechanoreceptor location with the average spike frequency (taken with 70 bins) versus time and (c) the calibrated and validated multilayered model indented with a flat plate. Effective stress is shown in megapascal.

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