*Corresponding author. Tel.: 001 510 231 5720; fax: 001 510 231 5729; e-mail: rempel@itsa.ucsf.edu Journal of Biomechanics 31 (1998) 639 — 646 A structural model of the forced compression of the fingertip pulp Elaine R. Serina, Eric Mockensturm, C.D. Mote Jr., David Rempel * Department of Mechanical Engineering, University of California, Berkeley, USA Ergonomics Program, Department of Medicine, University of California, 1301 South 46th Street, Richmond, CA 94804, USA Received in final form 21 April 1998 Abstract The fingertip pulp modulates the force transmitted to the underlying musculoskeletal system during finger contact on external bodies. A model of the fingertip pulp is needed to represent the transmission of forces to the tendons, muscles, and bone during these contacts. In this study, a structural model of the in vivo human fingertip was developed that incorporates both the material inhomogeneity and geometry. Study objectives were to determine (1) if this fingertip model can predict the force—displacement and force—contact area responses of the in vivo human fingertip during contact with a flat, rigid surface, and (2) if the stresses and strains predicted by this model are consistent with the tactile sensing functionality of the in vivo human fingertip. The in vivo fingertip pulp was modeled as an inflated, ellipsoidal membrane, containing an incompressible fluid, that is quasi-statically compressed against a flat, frictionless surface. The membrane was assigned properties of skin (Veronda and Westmann, 1970) and when inflated, possessed dimensions approximating those of a human fingertip. Finite deformation was allowed. The model was validated by the pulp force—displacement relationship obtained by Serina et al. (1997) and by measurements of the contact area when the fingertip was pressed against a rigid surface with contact forces between 0.25 and 7.0 N. Model predictions represent the experimental data sufficiently well, suggesting that geometry, inhomogeneous material structure, and initial skin tension appear to represent the nonlinear response of the in vivo human fingertip pulp under compression. The predicted response of the fingertip pulp is consistent with its functionality as a tactile sensor.  1998 Elsevier Science Ltd. All rights reserved. Keywords: Fingertip; Pulp; Compression; Model; Finite deformation theory 1. Introduction Humans use the fingertips in the exploration of the external world through the sense of touch and during the motor activities of pinching and grasping. Forces applied at the fingertips are transmitted to the tendons, muscles, and other tissues of the hand and arm. The contact force history is modulated by the fingertip pulp, the soft tissue surrounding the palmar side of the distal phalanx. Criti- cal to understanding how the mechanics of the pulp contribute to our ability to touch and grasp is a model that predicts the response of the human fingertip pulp under externally applied compression. The fingertip pulp is inhomogeneous in structure and includes the skin surrounding the digital extremity to- gether with the underlying fatty tissues. Although skin is a nonlinear, inhomogeneous, anisotropic material (Barbenel et al., 1973; Daly, 1982; Daly, 1966; Gibson and Kenedi, 1970; Kenedi et al., 1965; Manschot and Brak- kee, 1986; Wan Abas, 1994), its in vitro tensile response has been described successfully by isotropic, homogene- ous, and incompressible constitutive relations (Lanir, 1987). The skin contains FA I and SA I mechanorecep- tors which are concentrated in the curved region of the fingertips (Phillips and Johnson, 1981a; Westling and Johansson, 1987). These mechanoreceptors are sensitive to fingertip deformation and stretch of the skin, and they provide afferent information to the central nervous system used to modulate the motor response to contact during fingertip loading (Westling and Johansson, 1987). The subcutaneous tissue is composed of elastic adipose cells enmeshed in a loose fibrous tissue network (Glicenstein and Dardour, 1981). By volume, the subcutaneous tissue matrix is 60 —72% water (Fawcett, 1986). 0021-9290/98/$19.00  1998 Elsevier Science Ltd. All rights reserved. PII S0021-9290(98)00067-0