**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

**8.3.5 Macrotransponder
Networks**

It has been proposed^{888}
that a macroscopic acoustic signal source could be used by individual medical
nanorobots to determine their location within the body, much as handheld radio
receivers can use satellite transmissions (e.g., the 24-satellite Global Positioning
System or GPS)^{1310} to determine
their position on Earth's surface. Such a system might involve externally generated
signals from beacons placed at fixed positions outside the skin, or could employ
dedicated internally-installed emitter organs. As described in the microtransponder
example (Section 8.3.3), at least four beacon signals
must be detectable simultaneously to allow a fix to be determined in three-dimensional
space. Macrotransponder networks may be useful in some applications, but also
have several important drawbacks as described below.

Since in a macrotransponder system the nanorobots determine
their positions by direct detection of beacon range signals rather than by polling
their neighbors, accuracy may be solely a function of the total range measurement
uncertainty DX_{min}. As before (Section
8.3.3), given a typical signal path length X_{path} ~ 15 cm and
a mean v_{sound} ~ 1540 m/sec, signal travel time (t
~ 97,400 nanosec) is known to an accuracy of Dt ~
1 nanosec if beacon clocks and nanorobot clocks are stable and synchronized,
adding (v_{sound} Dt) ~ 1.5 microns of range
uncertainty.

However, by far the greatest source of uncertainty in a macrotransponder
system is the variation in the speed of sound along the randomly chosen linear
paths through the human body which the beacon signals must follow. The speed
of sound is reasonably uniform within specific tissues or local regions, but
an arbitrary 15-cm path through the body may plausibly involve sound velocities
ranging from 630 m/sec for a path entirely through the lungs up to ~4090 m/sec
for a path entirely through the densest skull bone (Table
6.7). This implies a velocity uncertainty range of Dv_{sound}
~ 3460 m/sec and thus a maximum range uncertainty of Dv_{sound}
t ~ 33.7 cm -- approximately the anteroposterior
thickness of the human body. There is also some variation in v_{sound}
as a function of temperature (Section 10.5.5) and other
factors.

While local (~100 micron range) sound speed may be measured
on site by one or a small number of nanorobots (Section
8.3.3), the net sound speed along an arbitrary ~15 cm path cannot be similarly
assessed without a comprehensive survey effort. Pathwise uncertainty in sound
velocity is somewhat reduced by completing a whole-body survey of v_{sound}
as a function of position, then loading this map into each nanorobot using the
navigational system.* In some cases, standardized maps with modest customization
will suffice. A whole-body v_{sound} map to ~(100 micron)^{3}
resolution, giving Dv_{sound} ~ 25 m/sec,
would require ~1 terabit of onboard storage, a minimum 38 micron^{3}
memory tape volume inside a (~4 micron)^{3} memory mechanism. Assuming
a more reasonable ~1 micron^{3} tape volume allows a ~0.026 terabit
velocity map to be stored onboard, providing ~(340 micron)^{3} resolution
and giving Dv_{sound} ~ 84 m/sec. Unfortunately,
a measurement uncertainty of ~84 m/sec in the local speed of sound still adds
(Dv_{sound} t)
~ 8 mm of positional uncertainty to each ~15 cm range measurement, a ~5% error.
Shortening the average beacon-nanorobot distance to X_{path} ~ 1 cm
(e.g., by installing ~60,000 internal emitter organs, which may be unduly intrusive)
reduces positional uncertainty to ~500 microns, possibly sufficient in some
applications.

* This suggests some interesting open problems requiring further computer science research. For instance, how might individual nanorobots know which section of the map is relevant for them, before they are able to determine their position?

Adequately stable surfaces on the skin or even inside the body may be difficult to find for large macroscopic transmitters, causing significant source movement and degrading the positional accuracy of the beacons as system monuments. This problem is partially overcome by using acceleration compensators (e.g., gimbals and gyros to "float" transmitters), thus neutralizing the effects of minor body motions. However, because of the minimum ~8 mm range uncertainty noted above, it will be difficult for beacons to mutually recalibrate their own positions to high accuracy, so there will be unavoidable unmonitorable monument movements especially during rapid joint rotations and limb flexures. And macroscopic transmitters are physically more responsive to the small random centrifugal and gravitational forces normally experienced by the body than are microtransmitters, adding to their moment-by-moment positional uncertainty.

By now, the alert reader will be wondering if measurements of just the angular positions of at least three externally located macroscopic acoustic beacons, taken without regard to range measurements, can suffice for accurate navigation. The answer is that an angles-only system is quite possible, but unfortunately offers little improvement. (GPS uses 4 satellites so that inexpensive handheld receivers don't need accurate clocks and thus can avoid ranging errors. Orbiting satellites do have atomic clocks and transit time codes, but the ground-based receiver need only compare time differences between received signals.)

Consider an acoustic sensor pair with x_{sensor} =
1.54 micron, giving the minimum possible angular measurement error Dq
~ 3° (Section 8.3.3). The positional uncertainty Dx
of the nanorobot is then

_{}
{Eqn. 8.4}

where X_{path} is the average distance between beacon
and nanorobot and N_{beacon} is the number of noncollinear beacons sampled
during each measurement cycle. Assuming an epidermal beacon network with X_{path}
= 15 cm, Dx ~ 8 mm for N = 3 beacons; Dx
~ 400 microns for N = 1000 beacons.

Beacon signals will also travel many adjacent pathways with sound speeds that differ only very slightly, producing a multiplicity of received pulses and a smearing effect, further degrading signal quality. Signals suffer refraction over such lengthy courses, causing the beam to bend significantly from its original path in unknown amounts. By contrast, the acoustic energy received from a pulse traversing a ~100 micron path lies close to the sensor detection limit; these signals are rapidly attenuated by the medium beyond this limit, and thus produce no confusing detectable signal at the next navicyte station located ~200 microns from the transmitter. Another problem with macrobeacons is that they must use lower frequencies (~100 KHz; Section 6.4.1) due to the long path lengths their signals must traverse unamplified, hence maximum data flow rate may be up to ~1000 times slower than for the microtransponder system. Finally, macrobeacons permit only a one-way flow of navigational information, a major limitation.

Last updated on 19 February 2003