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
184.108.40.206 Free-Tissue Acoustic Channel Capacity
Figure 7.1 (with blood pressure variations compared; Section 220.127.116.11) 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 Xpath from a transmitter of like size must receive at least kT eSNR ~ 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% = Pout/Pin (Eqn. 7.7), receiver duty cycle is fduty, and acoustic attenuation in the medium is given by Eqns. 4.52 and 4.53 with atiss = 8.3 x 10-6 sec/m for soft tissue (Table 4.2), then to satisfy the above criterion requires that
For fduty = 10%, r = 1 micron, Xpath = 100 microns, taking n = 10 MHz gives e% ~ 0.05 (5%), Pin ~ 6000 pW continuous, and 'I ~ 106 bits/sec. Increasing n to 100 MHz improves e% to at least ~50% and 'I = fduty n ~ 107 bits/sec without increasing Pin, giving a maximum safe acoustic power intensity of ~e% Pin / pr2 ~ 1000 watts/m2 (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