Nanomedicine, Volume I: Basic Capabilities

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

4.9.1.6 Environmental Sources

Can in vivo nanodevices directly detect sounds emanating from the environment outside of the body, such as other people talking in the same room or a door slamming? The waves from an external acoustic source of power PR watts travel through the air and, upon arriving at the air/skin interface a distance xR from the source with amplitude Aincident, are transmitted through the interface with amplitude Atransmit. For a specular reflector -- interface dimensions (human body ~ 2 m) > acoustic wavelength (~0.03-3.0 m for typical audible sounds in air) -- with acoustic impedance Z1 and Z2 on either side of the interface and perpendicular incidence,506,628

{Eqn. 4.54}

Acoustic impedance, like the speed of sound, is essentially frequency-independent over the nanomedically-relevant range of ultrasonic frequencies. For Zair = 400 kg/m2-sec and assuming Zskin ~ 1.6 x 106 kg/m2-sec from Table 4.3, then Atransmit = (5 x 10-4) Aincident. In other words, there is ~99.95% reflection from the air-skin interface, which is why coupling mediums like gels and oils are commonly employed in ultrasound imaging. If an immediately subdermal nanodevice can detect a minimum Atransmit ~ 10-6 atm, then from Eqn. 4.53 and simple geometry:

{Eqn. 4.55}

For STP (1 atm, 0°C) air, r = 1.29 kg/m3 and vsound = 331 m/sec. If the minimum detectable pressure ~10-6 atm (Section 4.5.1) ~Atransmit, then at a distance of xR = 2 meters the acoustic source must have a power of ~2000 watts, far exceeding the ~1 milliwatt output of a person loudly shouting. To hear normal conversation at xR = 2 m, minimum nanodevice detector sensitivity falls to 7 x 10-11 atm requiring a subdermal pressure nanosensor ~(17 micron)3 in size (Eqn. 4.29), roughly the dimensions of a single human cell; other methods may prove more efficient (Sections 4.9.5 and 7.4.6.3).

Of course, an ex vivo acoustic nanosensor may receive sound that has passed through no interface, hence may detect pressure waves ~3 orders of magnitude lower in amplitude. Assuming Atransmit = Aincident, PR ~ 600 microwatts, so ex vivo nanorobots with a 0.3 micron3 sensor could hear people shouting at xR = 2 meters. To hear talking (~10 microwatt source) requires a 2.4 micron3 ex vivo pressure sensor (limit ~10-7 atm), from Eqn. 4.29.

Optimally positioned and calibrated nanomedical pressure sensors could directly measure changes in the ambient barometric pressure to within ± 10-6 atm. Normal atmospheric variation due to weather ranges from 0.94-1.05 atm; such slow moving changes are readily monitored. Very near the Earth's surface, the air pressure P at altitude h above sea level is approximated by P = e-kp h (atm), where kp = 1.16 x 10-4 m-1 at 20°C; at sea level, a 10-6 atm change in pressure reflects a change in altitude of only ~1 cm. However, the opening or closing of a door inside a (~5 m)3 room that displaces >125 cm3 of air also causes a minimally detectable >10-6 atm pressure pulse. Other sources of environmental pressure variation such as infrasonic (~0.2 Hz) microbaroms from offshore ocean storms,1526 wind entering through open windows, forced-air currents from central heating or A/C systems, or even the movements of nearby people and pets may be detectable and thus may further confuse the measurement, reducing absolute accuracy unless suitable corrections are made.

Last updated on 17 February 2003