{Eqn. 9.83}
Nanomedicine, Volume I: Basic Capabilities
© 1999 Robert A. Freitas Jr. All Rights Reserved.
Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999
9.5.2 Epidermal Locomotion
The epidermis is a modified cellular surface, so most of the techniques described for cytoambulation (Section 9.4.3) are applicable to epidermal locomotion as well. There are so many special situations and obstacles to motility on skin that we can only mention a few of them here:
A. Flaky Corneum -- Desiccated stratified epidermal cells crack, chip, or flake off entirely when rubbed or jostled with too much force. Nanorobots traversing a dead cell could find themselves flaked off into the air or onto the floor, especially if the surface is rubbed by the patient.
B. Steep Topography -- Many physical features of the skin are huge in scale compared to a micron-size nanorobot and thus must be carefully circumnavigated. Dermal fingerprint ridges are ~500 microns wide and 20-50 microns deep. Hair follicle shafts are 50-100 microns in diameter. Scent-secreting apocrine glands are ~200 microns in diameter; eccrine (sweat) glands are only 20 microns wide. Skin-dwelling fungi (e.g., athlete's foot) grow into irregular globs 5-20 microns in size. The tongue surface includes taste buds ~150 microns wide and tiny papillae measuring 30 microns wide and 80 microns long. Other surface features are described in Section 8.6.1. At the micron scale, the topmost layer of the epidermis is littered with obstacles and protrusions, with electron micrographs showing a surface that closely resembles a flaky puff pastry in appearance.1571
C. Constant Motion -- The skin is almost always in motion at size scales up to ~1000 microns, folding and unfolding, stretching and tightening, twisting and curving, with normally distant surfaces being brought into and out of contact as the patient moves about normally.
D. Dust Mites and Bacteria -- In eyelashes and eyebrows, the hairs of the upper lip, in the ears, and elsewhere on the body, dust mites measuring 150 microns x 300 microns survive by chewing up dead skin cells. Epidermal-walking nanorobots must be able to identify mite surfaces, and avoid climbing aboard them by mistake. Everyone inhales a few mites now and then; mite excrement (to which some patients are allergic) is concentrated into fecal packets so small and light that they float in the air and may settle back onto the skin. Many other surface-dwelling ectoparasites and microfauna similarly must be avoided.3253 Bacterial density over most of the body surface is quite low, ~103/cm2; the count ranges from ~102/cm2 on the palms and dorsa of the hands, up to 104-105/cm2 on the hairy axilla, scalp, perineal regions, and beneath the distal end of the nail plate.360
E. Obstructions -- The skin may be covered with dirt, or grease, or cooking oils and fats, or sebaceous gland oils, which may be many tens or even hundreds of microns thick. Another potential obstacle is the sweat wash -- the skin can pour out up to 2 liters/hour of perspiration. Nanorobots can easily crawl underneath the tightest-fitting clothing or rubber gloves, although a patch of superglue stuck to the skin could provide a formidable obstacle requiring overpassage.
F. Itching/Crawling Sensations -- Tickling sensations attributable to isolated nanorobots traversing the skin are unlikely. Skin-crawling ~2 mm ants are readily detected; ~100-micron mites are not. Absolute epidermal pressure stimulus thresholds, as measured by a laboratory esthesiometer, range from a low of 2000 N/m2 at the tongue- and finger-tip, up to 12,000 N/m2 on the back of the hand, 26,000 N/m2 on abdomen, 48,000 N/m2 on the loin, and a high of 250,000 N/m2 on the thickest part of the sole of the foot.773 By comparison, the weight of a (100 micron)3 nanorobot, if distributed across a (100 micron)2 contact surface, is only ~1 N/m2, quite undetectable on the skin. At a velocity of 1 cm/sec, the inertial force required to propel a 100-micron nanorobot is ~1 nN (Section 9.4.2.1). This additional force, if distributed over 10 footpads each of area 100 micron2, gives a shear pressure of ~1 N/m2 across all contact surfaces, also undetectable; the sensible threshold velocity for such a nanorobot is ~45 cm/sec. Skin sensor frequency response is << KHz (Table 7.3), whereas skin walkers <~10 microns in size may employ nleg >~ KHz leg motions; the weight of a 1 micron3 nanorobot produces only ~0.01 N/m2 of contact pressure.
Nanorobots of large size can also step over most of the obstacles described above. Consider an Rnano = 50 micron walking nanorobot with Nleg = 10, Lleg = 100 microns, Rleg = 15 microns, and vleg = 1 cm/sec as defined for Eqn. 9.82, with nleg ~ vleg / 2 Lleg ~ 50 Hz. From Eqn. 9.75, the viscous force per leg is Fleg ~ FnanoN ~ 5 nN in a 20°C water bath, 0.1 nN in 20°C air. From Eqn. 9.73, Fnano ~9 nN in water, 0.2 nN in air. Thus the total driving force Ftotal = 59 nN in water, 1.2 nN in air, assuming a still medium.
Another way to avoid obstacles is to hop over them in the manner of a jumping flea, an insect that subjects itself to an acceleration of ~200 g's while leaping ~130 times its own dimension.739 Diamondoid saltators could tolerate much higher accelerations, although it is important not to disturb the takeoff surface; also, airborne ex vivo trajectories may be only poorly controlled. The approach is interesting1982,2385,2386 but will not be considered further in this book.
What about dislodgement forces? Assuming a headwind of v ~ 1 m/sec and a d ~ 10 micron boundary layer, then from Eqn. 9.58 the shear stress (and shear force) on a 100-micron wide nanorobot is F/A ~ 100 N/m2 (1000 nN) in water, 2 N/m2 (20 nN) in air. A single 10 micron2 footpad with a conservative adhesive pressure of 105 N/m2 (Section 9.4.3.3) provides a 1000 nN anchorage force, allowing the nanorobot to remain adhered to the skin even in the strongest water currents (e.g., white water rapids, showers, or spas at ~1 m/sec per anchored footpad used) and air currents (e.g., up to ~50 m/sec (~110 mph) winds per anchored footpad used). A finger rubbed hard against the skin with the objective of dislodging adhered epidermal-resident nanorobots may apply up to 10 N of force over a ~1 cm2 area, giving a ~105 N/m2 shear force (~1,000,000 nN) which may be resisted by ten 100 micron2 footpads each having a maximum adhesive pressure of ~106 N/m2 (Section 9.4.3.3).
What about epidermal penetration? Complex and subtle low-speed methods are readily imagined (Section 9.4.4), but let us consider here a simple brute-force approach. Failure strength of human skin is ~107 N/m2 (Table 9.3), so a 1 micron2 rod may be driven through the skin with a force of ~10,000 nN. A 100-micron long telescoping manipulator arm with stiffness ~25,000 nN/nm can apply 10,000 nN to the rod at 1 cm/sec producing an elastic deflection in the arm of less than 1 nm, drawing ~100,000 pW of power (manipulator arm power density ~106 watts/m3) at the moment of penetration (Section 9.3.1.4). Bruising and other biocompatibility issues related to dermal penetration are deferred to Sections 15.5.1 and 15.5.2.
The surfaces of toenails and fingernails have 2-20 micron features and longitudinal striations with 10-15 micron valleys, and are usually littered with dirt, bits of skin, and other surface debris as small as 1-2 microns in size. The nail surface is heavily keratinized, with a failure strength about 20 times higher than that of skin (Table 9.3). Similar considerations apply as with the skin, in regard to nanorobot locomotion.
What happens if the nanorobot falls off, or is otherwise removed from, the epidermal surface? Solem1982 has analyzed the case of nanorobots walking on walls and ceilings. Setting the electrostatic image force (Eqn. 9.11) equal to the gravity force rnano Lnano3 g for a cubical conducting-surface nanorobot of edge Lnano, the voltage required to cling to the ceiling without falling off is:
Taking zsep = 0.5 microns, rnano = 2000 kg/m3, g = 9.81 m/sec2, e0 = 8.85 x 10-12 farad/m, ke = 1, and Lnano = 10 microns, then Vplate ~ 0.1 volt. Similarly, the largest nanorobot that can cling to the ceiling using an adhesive contact surface of strength S has a characteristic dimension:1982
For S = 10-100 N/m2 (typical for weak adhesives such as Post-It notes), then Lmax ~ 500-5000 microns. By wetting the contact area with water having surface tension g ~ 73 x 10-3 N/m at room temperature (Section 9.2.3), a cubical nanorobot clinging to the ceiling may have a maximum characteristic dimension of:1982
Last updated on 16 April 2004
{Eqn. 9.84}
{Eqn. 9.85}