© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.5.1 Dental Walking

The exposed surfaces of natural dentition consist of a ~500 micron thick layer of enamel coating the exposed crown of each tooth inside the mouth. Enamel is a composite structure containing ~96% inorganic material similar to hydroxyapatite, a dense bone mineral, embedded in an organic matrix of glycoprotein and a keratin-like protein. The mineral forms crystallites oriented into hexagonal cylinders with a horseshoe-shaped cross-section wrapping around the dentin, forming enamel prisms ~5 microns in diameter stacked in parallel congeries.^646,854,1571 These prismatic columns are directed vertically at the summit of the crown and horizontally along the sides of the tooth, pursuing a generally wavy course. There are no nutritive channels permeating the enamel and leading into the dentinal layer below, although dentinal tubules (nutritive channels) do extend from the pulp chamber into the dentin which may get extremely close to the occlusal (enamel) surface of the tooth, and may be exposed by receding gums. However, ~0.4-micron-wide fissures separating enamel prisms are filled with an interprismatic substance of much higher organic content. The entire enamel surface is pockmarked by numerous micropores of irregular but generally oval shape, ranging from 0.1-2.0 microns (average ~0.5 micron) in diameter and spaced ~1-2 microns apart. Thus a dental-walking micron-size nanorobot encounters a spongelike topography with holes and fissures comparable in size to the nanorobot diameter, and with gently rolling hills ~2 device diameters in height and ~5 diameters across. (There is also a thin layer of salivary proteins coating the tooth enamel surface.)^3669,3670

Nanorobots may traverse tooth enamel using ambulatory techniques previously described in other contexts (Section 9.4), including legged walking, rolling, or amoeboid locomotion using footpads for anchorage. Teeth may be clenched with a force up to 300-500 N,^{1296,3671-3673} although forces of ~50 N are more common during normal mastication of soft foods. Assuming ~1 cm² of dental contact surface, shear forces at that surface during chewing or clenching are 0.5-5 x 10⁶ N/m², close to the limit for noncovalent anchorage (Section 9.4.3.3). Nanorobots seeking further refuge from shear forces may congregate in the valleys between enamel prisms or can seat themselves in the irregular micropores. E. Reifman notes that ~90% of U.S. adults have multiple occlusal surface restorations composed of many different materials such as resin composites of various hardness coefficients, porcelain or gold crowns, amalgam fillings, composites, and the relatively newer but very popular glass polymer crowns, representing a substantial percentage of all exposed dental surfaces with which oral nanodevices must cope; yield strength of these materials at 0.1% strain deformation typically ranges from 110-10,000 atm.³²⁷¹

Are the forces of dental grinding sufficient to crush medical nanodevices? Tests of sized jeweler's grinding powders by the author confirm that even irregularly-shaped diamondoid particles ~3 microns and smaller apparently roll smoothly out of the way when ground between the teeth, whereas particles larger than ~3 microns cannot roll sufficiently and retain a sensible grittiness. In the case of a trapped nanorobot-size diamond block slowly being squeezed between opposed enamel surfaces (static force), the Young's moduli for enamel and diamond are 7.5 x 10¹⁰ N/m² and 1.05 x 10¹² N/m², respectively (Table 9.3), so the enamel deforms ~14 times more than the diamond. Crystalline diamond can deform at least ~5% before fracturing, diamond composites (Chapter 11) much more; a 50% strain in each enamel surface (an indentation equal to the entire diamond block radius, probably causing the enamel to fail) produces a 3.6% deformation across the diameter of the block, slightly below the conservative tolerance limit for diamondoid fracture strain. In the case of a 50-gram jaw moving at the maximum 0.1 m/sec clenching velocity that is suddenly brought to a halt via enamel deformation to a depth equal to a ~1 micron nanorobot radius across a 1 cm² enamel contact area, the jaw decelerates at ~1000 g's producing a kinetic force of ~500 N and a contact force of 5 x 10⁶ N/m² (~50 atm), well below the ~10¹¹ N/m² failure strength of solid diamond.

However, nanorobot crushing strength is an explicit design parameter which is normally significantly lower than for solid diamond if the device has large unbraced internal voids or diameters that are weak in compression. Such nanorobots may not be regarded as solid diamond structures as assumed above. For example, the Euler buckling force for a solid cylindrical rod of outer radius R is proportional to R⁴ (Eqn. 9.44), but for a hollow cylinder with inner radius r the buckling force is proportional instead to (R⁴ - r⁴) during axial compressions.³⁶⁴ Hence a trapped, thin-walled cylindrical nanorobot of radius R with r/R = 0.90 buckles at only ~34% of the force needed to buckle a solid rod of radius R, and thus could probably be crushed by static compression of the teeth. The oral cavity appears to be the only place in the human body where thin-walled medical nanorobots might plausibly be destroyed by mechanical grinding. Such destruction is avoided by nanorobots with composite diamondoid shells >~10% R thick at a maximum allowable strain <~10%, or by nanodevices possessing maps of mastication contact spots that actively avoid those spots during nanorobotic perambulations.

Last updated on 22 February 2003