**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

**7.2.2.2 Free-Tissue
Acoustic Channel Capacity**

Figure 7.1 (with blood pressure variations compared; Section 4.9.1.2) and Eqn. 7.7 illustrate the well-known result in acoustics that for a given driving amplitude, micropistons and microspheres are more powerful sound radiators at higher frequencies. That is, input power (driving the radiator) is more efficiently transduced into output power (waves in the medium) both at higher frequencies and at larger radiator sizes. Thus to achieve the highest acoustic channel capacity per unit of input power, the highest practical frequency and the largest possible radiator should be used for nanorobot-to-nanorobot acoustic communications. Of course, at higher frequencies, attenuation becomes more severe and eventually limits the value of ever higher frequencies.

An acoustic sensor of radius r located a distance X_{path}
from a transmitter of like size must receive at least kT e^{SNR} ~ 30
zJ within a n^{-1 }(sec) integration time
in order to receive information at frequency n (bits/sec)
for SNR = 2 (Section 4.5.1). If acoustic energy conversion
efficiency e% = P_{out}/P_{in} (Eqn.
7.7), receiver duty cycle is f_{duty}, and acoustic attenuation
in the medium is given by Eqns. 4.52 and 4.53
with a_{tiss} = 8.3 x 10^{-6} sec/m
for soft tissue (Table
4.2), then to satisfy the above criterion requires that

For f_{duty} = 10%, r = 1 micron, X_{path}
= 100 microns, taking n = 10 MHz gives e% ~ 0.05
(5%), P_{in} ~ 6000 pW continuous, and 'I ~ 10^{6} bits/sec.
Increasing n to 100 MHz improves e% to at least ~50%
and 'I = f_{duty} n ~ 10^{7} bits/sec
without increasing P_{in}, giving a maximum safe acoustic power intensity
of ~e% P_{in} / pr^{2} ~ 1000 watts/m^{2}
(Section 6.4.1) at the transmitter surface. Further
increases in n cause 'I to decline, because e% cannot
improve beyond a maximum of 100%.

These results imply that nanorobot-to-nanorobot acoustic communications will generally take place at ~10-100 MHz frequencies over 10-100 micron path lengths in vivo. Acoustic messaging over longer path lengths require mobile signal amplifiers such as communicytes (Section 7.2.6), dedicated fixed-position communication organs with repeater protocols, or packet routing networks analogous to the Internet (Section 7.3).

Last updated on 19 February 2003