The Medium of Haptic Perception: A Tensegrity Hypothesis

ABSTRACT

For any given animal, the sources of mechanical disturbances inducing tissue deformation define environment from the perspective of the animal's haptic perceptual system. The system's achievements include perceiving the body, attachments to the body, and the surfaces and substances adjacent to the body. Among the perceptual systems, it stands alone in having no defined medium. There is no articulated functional equivalent to air and water, the media that make possible the energy transmissions and diffusions underpinning the other perceptual systems. To identify the haptic system's medium the authors focus on connective tissue and the conjunction of muscular, connective tissue net, and skeletal (MCS) as the body's proper characterization. The challenge is a biophysical formulation of MCS as a continuum that, similar to air and water, is homogeneous and isotropic. The authors hypothesized a multifractal tensegrity (MFT) with the shape and stability of the constituents of each scale, from individual cell to whole body, derivative of continuous tension and discontinuous compression. Each component tensegrity of MFT is an adjustive-receptive unit, and the array of tensions in MFT is information about MCS. The authors extend the MFT hypothesis to body-brain linkages, and to limb perception phenomena attendant to amputation, vibration, anesthesia, neuropathy, and microgravity.

Keywords:

• haptic system
• fascia
• connective tissue
• multifractal tensegrity
• ecological approach

ACKNOWLEDGMENTS

The authors would like to acknowledge the intellectual contributions of Paula Silva, Daniela Vaz, Claire Michaels, and Stephen Levin. A very special thanks is given to Claudia Carello for her many contributions, artistic and conceptual.

Notes

1. Internal politics in the USSR conspired against its publication.

2. To anticipate, we identify a particular mechanical characterization of the body (a multifractal tensegrity) as medium, and identify a multiscaled adjustive-receptive architecture as organ.

3. This further comment should be considered in light of a commonality between human and fibroblast locomotion. Human runners adjust the stiffness of their stance leg to accommodate surface stiffness during steady state running (Ferris, Louie, & Farley, 1998). This adjustment allows runners to maintain similar center of mass movement (e.g., ground contact time and stride frequency) regardless of surface stiffness. There are indications that given abrupt transitions in surface stiffness, leg stiffness adjustments occur rapidly enough to minimize disruption of the running mechanics.

4. Although our emphasis is on perception, we should note similarities between the dynamical principles of tensegrity and the Equilibrium Point Hypothesis of motor control (e.g., Feldman & Levin, 1995). Among the similarities identified by Silva, Fonseca, and Turvey (2010) is the “very unusual property” (Skelton & de Oliveira, 2009, p. 23) that tensegrity stiffness can be changed without changing external tensegrity shape, and conversely, tensegrity shape can be changed without changing tensegrity stiffness. Central to the Equilibrium Point Hypothesis are the c and r commands: the former changes joint stiffness but not joint equilibrium; the latter changes joint equilibrium but not joint stiffness.

5. It should be noted that the literature recognizes two broadly distinguished types of tensegrity systems, one structural and one energetic. Defined structurally, a tensegrity system is a system in which prestress (in the form of tensioned components) is balanced predominantly by internal struts (compressed components). Defined energetically, a tensegrity system is a system in which equilibrium of the tensioned and compressed elements arises from minimizing the stored elastic energy (Connelly & Back, 1998). The two definitions differ in how prestress is balanced (Wang et al., 2001)—strictly by internal components in the structural case, and by external as well as internal components in the energetic case. Although structural tensegrity is the most studied, current modeling of the cell emphasizes energetic tensegrity. The contributions of microtubules to the cell's compression are aided and abetted by the external attachments of the cytoskeleton to ECM and neighboring cells (Stamenovic, Mijailovich, Tolic-Norrelykke, Chen, & Wang, 2002; Wang & Suo, 2005). The tent metaphor (Figure 4) applies to the energetic variant of tensegrity system, not the structural.

6. There is evidence of circumstances in which perception of limb position is conditional on efference as well as afference (e.g., Proske & Gandevia, 2009). It could be asked whether it is consistent with an underlying adjustive-receptive architecture at all scales.

7. As an important aside, this myofascial force transmission is evident in organisms with very different body architecture, such as insects. Active and passive forces at the ventral origin and the dorsal insertion of the flight muscle of the migrating locust prove to be significantly different (Meijer, 2007).

8. A mechanism of the flow of forces is provided by Gao, Wineman, and Waas (2009).

9. It should be underscored that for Snelson and Levin there is only one class, only one tensegrity kind (Stephen Levin, personal communication).

10. Bernstein (1996) suggested that the rare occasions in which the level of tonus assumes leadership is in situations when a human is similar to a fish in water, that is, in equilibrium with the environment, without the apparent action of gravity.

11. Windhorst (2008) suggests that Kokkorogiannis's concerns are too insular. Muscle spindles’ function and contribution to haptic perception pose explanatory challenges beyond their number and distribution. For Windhorst, these challenges arise from the multifunctional nature of spindles.

12. In order for a truss with pin-connected members to be stable, it must be composed entirely of triangles. This principle generalizes to tensegrity systems as follows: given flexible joints, the only stable polygons are those that are fully triangulated (namely, the four-sided tetrahedron, the eight-sided octahedron, and the 20-sided icosahedron; see Levin, 2002, 2006).

13. See http://tensegrity.wikispaces.com/Icosahedron for contrasting views of the icosahedron as the basis of biological tensegrity.

14. Figure 5 complements Figure 18 through examples of nested and deforming prestressed icosahedra.

15. In terms of the physical principles that would give rise to MFT, look to constructal theory (Bejan, 2000, 2005), a theory dismissive of fractal theory but seemingly well suited to mutifractality. In terms of constructal theory, the hypothesized MFT is a geometric structure that, for any point source of force, is optimal for conducting that force across all of its scales at the maximal possible speed.

16. The currently popular instantiation of abduction is Bayesian inference.