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

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

8.3.2 Cartotaxis

Another positional navigation technique is simple landmark-centered map-following, or cartotaxis. Consider a nanorobot that wishes to crawl to a specific 1 micron² patch on the subvilliary mucosal surface of the small intestine. Ignoring the villi and microvilli but including the circular folds, the mucosal surface of the small intestine is ~1 m² (Section 8.2.3), at worst requiring a map of ~8 terabits to achieve 1 micron² resolution using 8-bit pixels.

A more compact map might include only the positions, sizes and shapes each of the ~100 million 50-micron-wide intestinal glands dotting the surface of the small intestine at least ~100 microns apart. These dots form a pattern unique to each person that changes slowly over time. After defining a two-dimensional intestinocentric coordinate system, two coordinates of log₂ (10⁶) ~ 20 bits each can specify a location to 1-micron accuracy on a 1 m² surface. Using 20 bits each for the two surface coordinates, 20 bits each for the major and minor elliptical axes framing the gland aperture, and another 920 bits to record unique topographic features of each hole, a complete small intestinal gland map requires at most ~1000 bits/gland or ~0.1 terabits.

This data storage requirement may be significantly further reduced by recognizing that on its way to its destination, an efficient ~10 micron³ surface-walking nanorobot need pass over at most 0.002% of the 1 m² of small intestinal surface recorded on the map described in the previous paragraph, even assuming a maximum-length 4-meter whole-intestine traverse, passing at most a total of 4 m / 100 microns = 40,000 identified glands each requiring ~1000 bits to describe. Hence the minimum intestinoglandular map required for this longest traverse could in theory contain as few as ~40 megabits of data for a perfectly navigating nanorobot using a perfectly compiled and absolutely stable map. As a practical matter, to ensure reliability the onboard map conservatively should contain complete intermediate annular ring segment recalibration maplets at least ~500 microns in length along the tube axis and spaced ~2 cm apart, to be sequentially encountered axially while traveling down the tube. Nanorobots use dead reckoning to navigate between these guide rings until the ring closest to the destination is reached, analogous to the mid-course correction areas employed by cruise missiles. Having arrived at this nearest ring, the nanorobot follows a final map swath ~500 microns wide leading directly to the three glands lying closest to the destination patch; the final 1 micron² target patch is reached by interpolation and dead reckoning between these last three glands. Reliability and efficiency are enhanced by using large numbers of intercommunicating nanorobots simultaneously (Sections 7.3.2 and 8.3.3). This ~1 gigabit "practical map" contains complete descriptions of ~1 million individual intestinal glands and may be stored in a ~0.1 micron³ onboard data spool using hydrofluorocarbon memory tape (Section 7.2.1.1).

The above scenario describes the ideal case. In actual living systems, biological surfaces are constantly in motion, are coated with slime, and are frequently being remodeled. Some mucosal surfaces may replace their entire luminal cell population every ~10⁵ sec (~1 day).* Thus the precise shapes and features of individual intestinal glands are constantly changing, although their larger structures and the pore pattern may remain intact for considerably longer periods of time. Intestinal glands are easily located by moving in the direction of rising concentration of enzyme-loaded intestinal juice, a basic chemonavigational technique (Section 8.4.3), and villiary trunks are available to provide additional cartographic guidance. But cartotaxic nanorobots will achieve the best results by using only the most recently prepared maps.

* In the fundus, the cell turnover cycle is ~5 days, while in the body of the stomach the whole cycle takes ~1 day. The time required for complete renewal of intestinal epithelium is ~2.3 days for the duodenum and ~2.8 days for the ileum.³⁵⁹ At the other extreme is the lens of the eye -- one of the few structures containing cells that is preserved without turnover.⁵³¹

Last updated on 19 February 2003