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
7.2.3 Electromagnetic Broadcast Communication
The receipt of externally-generated radiofrequency (rf) power signals up to ~MHz frequencies by nanorobot antennas has already been considered in Section 6.4.2. Such signals are readily adapted to communication and may carry ~MHz signals into the human body, allowing information transfers to in vivo nanorobots of up to ~106 bits/sec from an external signal intensity of >~0.1 watts/m2. Eqn. 6.32 suggests that rf signals pass through soft tissue with negligible absorption, leaving most of the signal energy available for detection by nanorobot receivers. (See also Section 4.7.1.)
While externally-generated rf signals may be detectable by nanorobots, onboard submicron-scale broadcast antennas probably cannot generate rf signals of sufficient power for meaningful device-to-device communications. For example, low-frequency electromagnetic waves of wavelength lrf and frequency nrf customarily are generated using a simple electric dipole of length dE << lrf / 2 p, or using a magnetic dipole loop antenna of diameter dM << lrf / 2 p. If the current carried by either antenna is Idipole, then the average transmitted power for each radiator is given by727:
where m0 = 1.26 x 10-6 henry/m (permeability constant), and c = 3 x 108 m/sec (speed of light). For nrf = 1 KHz and dE = dM = 1 micron, PE / PM ~ 109 and the electric dipole is strongly preferred over the magnetic dipole radiator; at high frequencies, the relative power emission of the electric dipole is even greater.
An electric dipole antenna of length 1 micron and cross-section 1 micron2 carrying a fairly aggressive current density of ~108 amp/m2 consumes ~200 pW to produce an rf output power of only PE ~ 10-11 pW. Not only is this extremely energy-inefficient, but the signal is too weak for detection by neighboring nanorobots. The 430-nm electret pendulum antenna described by Eqn. 6.34 has a theoretical minimum incident power detection limit of ~0.01 pW at 0.7 MHz; a limit of kT eSNR = 30 zJ/cycle for a 10-11 pW signal implies a maximum operating frequency of ~0.0003 Hz, too low to convey any meaningful information. (Here, signal-to-noise ratio SNR = 2 (20 dB); error-corrected digital signals can provide virtually perfect communications even below 10 dB.) Furthermore, simple scaling predicts nanoelectric antennas will have nondirectional radiation patterns, since antenna gain G ~ A / l; for A = 1 micron2 antenna surface, then l >~ 1 micron (3 x 1014 Hz) to achieve G >~ 1.
The reciprocity theorem in electromagnetic field theory predicts that the radiation pattern of an antenna will have the same shape as the response of that antenna when used as a receiver. W. Ware points out that a group of antennas tuned to a given resonant frequency, if illuminated by an external source at that frequency, will reradiate at that frequency, essentially echoing the signal. Thus a ~1 watt external source may induce 109 micron-scale antennas (one antenna per nanorobot, with a billion nanorobots reporting) to reradiate a total of ~0.01 pW at the same frequency, in theory detectable by a single nanorobot rf receiver and certainly detectable by macroscale instruments situated external to the body. (For comparison, television signals entering home TV antennas typically provide ~10-10,000 pW to the receiver). Near-coherence of the echo is virtually assured because the external rf interrogation signal passes through 30 cm of tissue in ~10-9 sec, so ~MHz antennas located anywhere in the body will lie at worst ~0.1% from perfect coherence. Interrogation pulses at many different rf frequencies may simultaneously poll echoing nanorobots programmed to monitor various internal phenomena of interest (and to adjust their antenna resonances accordingly prior to interrogation) in order to establish spatial distributions of those phenomena -- which may include temperature, pressure, biochemical concentrations, bloodflow velocities, detection of specific cell types or metabolic processes. In 1999, the 250-micron microtransponders under development by PharmaSeq3432 were expected to be interrogated at a throughput rate of >~1000/sec.
Aside from the environmental sources of electrical noise already described in Section 4.7.1, two additional potential sources deserve brief mention. First, radio, television, radar and other broadcast sources in developed countries produce a frequency-dependent broadband background (e.g., a carrier-frequency spike for each source) across a 0.01-1000 MHz spectrum up to ~10-11 watts/m2-Hz which at <~MHz frequencies passes through the human body largely unattenuated (Section 6.4.2). However, a ~1 micron2 antenna employing a ~1 MHz channel receives at most ~10-5 pW of this rf broadcast energy, only ~0.002 kT/cycle which is almost certainly undetectable. In other words, micronscale nanorobots probably cannot directly receive commercial TV, radio, or satellite broadcasts or GPS signals unless mediated by a macroscale communication organ (Section 7.3.4) or assemblage. Hence such broadcasts should generate no detectable noise at these frequencies.
Second, electrical discharges associated with muscular and neural action throughout the body cause electrical potentials to appear at the skin3508 which are typically detected in a medical context during electrocardiographs (ECG or EKG, ~10-3 volt), electroencephalographs (EEG, ~10-4 volt), and biofeedback monitoring with frequencies ranging from 1-40 Hz. These surface waves also may reach ~10-11 watts/m2-Hz, producing an undetectable 10-9 pW signal in a ~1 micron2 antenna using a 100-Hz channel -- although an electric field strength of >10-2 volts/m is in principle detectable by living cells (Section 4.7.1). Thus, micron-scale nanorobots can sense individual neural discharges nearby but probably cannot directly monitor global brainwave, ECG, gastroelectric or intestinal electrical wave patterns (which require a macroscale electrosensory organ or, possibly, cellular eavesdropping).
Electromagnetic modulations nrf >> 10-100 MHz (which must be imposed upon microwave, infrared, or optical carrier waves) may be difficult to generate, control and detect using submicron nanorobot components if those components are limited to mechanical ~GHz motions (Section 10.1.2.2); electronic components may cycle faster. Such carrier waves are 99% absorbed by soft tissue for path lengths ranging from ~10 cm for 100 MHz waves, to ~1 mm for infrared, or ~40 microns for optical photons. Energetic carriers also face a sharply declining count rate at the receiver due to the increasingly particle-like nature of the nondirectional transmission carrier at higher frequencies. For example, while micron-scale solid-state lasers are available, from simple geometry, an omnidirectional 1-micron2 optical photon (~1014 Hz) emitter with a 1-pW power budget producing 107 photons/sec transmits only ~103 photons/sec to a 1-micron2 receiver located 100 microns away (~maximum mean free path in tissue; Section 4.9.4). This limits information transfer to ~103 bits/sec at an energy cost of ~106 zJ/bit. Short bursts at much higher bit rates also satisfy the stated power budget; using this strategy, photon intensity must still be held below ~100 watts/m2 (Section 6.4.2) at the source, so for a 1 micron2 transmitter the maximum transfer rate is ~105 bits/sec in a ~0.01 second burst, with bursts repeatable only once per second.
Relatively slow modulations impressed on high-frequency electromagnetic waves might provide another useful communications channel. For example, nanorobots may detect each other's heat signatures, so modulations of those signatures can be used to transmit messages. Consider a nanorobot immersed in a medium of thermal conductivity Kt and heat capacity CV, producing Pn watts of thermal power at a distance Rdetect from a second nanorobot equipped with a thermal sensor of temperature sensitivity DTmin. The maximum detection range is
For Kt = 0.623 watts/mK for water at 310 K, DTmin = 10-6 K (Section 4.6), and Pn = 10-1000 pW, then Rdetect ~ 1-100 microns. If Pn is pulsed on and off to send a message, the thermal time constant tthermal = 4 p Rdetect CV / Kt = 0.0001-1 sec for CV = 4.19 x 106 watts/m3-K in water at 310 K. Assuming single-channel bandwidth ~ 1 / tthermal, then detectable signals range from ~10 KHz (~104 bits/sec) at a distance Rdetect = 1 micron from a 10-pW modulated heat signature down to 1 Hz (~1 bit/sec) at a distance Rdetect = 100 microns from a 1000-pW modulated heat signature.
Last updated on 19 February 2003