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
6.4.2 Inductive and Radiofrequency Power Transmission
Electrically-powered nanorobots may tap natural electric fields already present in the body (Section 4.7.1) or may seek to acquire electromagnetic power from external sources. Transdermal magnetic induction and radiofrequency (rf) energy transfer has been employed in radio tracking and biomedical telemetry since at least the 1920s,634,635,637,638,3510 and commercially available miniaturized implantable transmitters are now commonplace in laboratory work,639 but using this technique to power submillimeter devices is a relatively recent concept.630
The biological effects of radio waves, microwaves, and infrared rays are usually equivalent to the effects of heating, although nonthermal rf-induced vasodilation, possibly due to Ca++ flow manipulation, apparently has been observed in frogs.3328 Radio waves mainly induce thermal agitation of molecules and excitation of molecular rotations, while infrared rays excite vibrational modes of large molecules and may release fluorescent emission as well as heat. Both types of radiation are preferentially absorbed by unsaturated fats. In the United States the maximum permissible continuous occupational exposure level to microwave radiation has been 50 watts/m2 for the testes and 100 watts/m2 for the whole body -- essentially double the thermal radiance of a 100-watt (~2000 Kcal/day) ~2 m2 human body, e.g., ~50 watts/m2 across the skin, or roughly the intensity of direct sunlight on the skin (Section 4.9.4). Figure 6.12 compares several generally accepted international occupational and population exposure limits that have been adopted.824 Michaelson823 carried out extensive investigations and found no evidence for hazard at 100 watts/m2, though there is conclusive evidence of potentially hazardous effects at levels above 1000 watts/m2.
Single exposures to levels up to ~100 times these values may be briefly tolerated without injury, as for example photosetting dental fillings which require ~20 sec exposures to visible intensities of ~105 watts/m2. Optical tweezers also demonstrate that monochromatic exposures of ~1011 watts/m2 are tolerated by biological macromolecules immersed in an optically transparent aqueous medium due to fast thermal equilibrium at the micron scale.1630,1631 On the other hand, the threshold of pain for ink-blackened human skin exposed to a radiant heat stimulus is ~10,000 watts/m2 for 3-second exposures.585
An electromagnetic wave passing through the human body declines in intensity as it heats tissues and is attenuated approximately according to:
where I = power per unit area transmitted through the tissue, I0 < 100 watts/m2 (maximum safe incident intensity), dx is depth of tissue penetration (meters), and aE (meter-1) is the total attenuation factor including scattering and absorption, the inverse of the mean free path. For radio frequency and microwave radiation, aE = ae nE1/2, where nE is incident frequency (Hz) and ae ranges from 2 x 10-3 sec1/2 m-1 for muscle to 10 x 10-3 sec1/2 m-1 for vitreous humor but averages ~5 x 10-3 sec1/2 m-1 for soft tissue.635 At 100 MHz, 99% of incident power is removed in a 5-cm path length of soft tissue; at 1000 MHz (microwaves), 99% attenuation occurs within ~15 mm; at 106 MHz (far infrared), ~0.5 mm of tissue removes 99% of the energy. On the other hand, 53% of the incident energy at 0.1 MHz passes through a 20-cm thick human body unscattered and unabsorbed, thus remains available for utilization by medical nanodevices seeking electrical power. The dependence of aE on nE varies significantly across the electromagnetic spectrum;509,567,727 additionally, aE for different tissues may deviate by up to a factor of 10 from the average values shown in Figure 6.13, especially in the IR-UV region.
Heetderks630 has analyzed the feasibility of transmitting electrical power into the body using submillimeter receiver coils -- a magnetic transcutaneous link, which is preferred when large power-transfer rates are required. In one of several designs, Heetderks starts with a 14-cm diameter transmitter coil (~diameter of the neck) with 11 turns (~40 microhenries inductance) and a 10 volt peak driving voltage at a frequency of 2 MHz delivering 4 watts RMS into the coil, a high but probably acceptable incident intensity of ~260 watts/m2 at the skin. Inside the body, Heetderks uses a 400 micron diameter ferrite-core receiver coil with 60 turns spaced 50 microns apart, making a total receiver solenoid length of 3000 microns with ~0.89 microhenries inductance and Q = 40 for both transmitter and receiver, giving a fractional energy loss per cycle of 2p / Q ~ 16%. The receiver produces 1.1 volts and 320 microwatts in the ideal case where the receiver lies coplanar within the circumference of the transmitter coil. Large noncoplanar displacements may produce significant performance declines.
Each of Heetderks' receivers develops a power density of ~106 watts/m3. Up to 600 receivers may be present within the volume of operation of each transmitter, collectively drawing up to 10% of unloaded transmitter coil power consistent with maintaining Q ~40. In a nanomedical application, each receiver could act as a microscopic power station, absorbing the externally supplied electromagnetic energy and then transducing it into other forms of energy which may more directly be tapped by in vivo medical nanorobots. In theory, a 100 watt/m2 flux imposed on the entire ~2 m2 human body surface should allow the transdermal importation of ~20 watts, enough to support a population of ~1012 10-pW nanorobots assuming 50% energy transduction efficiency among the widely dispersed "power stations".
How much smaller could Heetderk's receivers be made? A detailed design analysis is beyond the scope of this book, but a simple scaling estimate may be made as follows. For a receiver coil of magnetic inductance Lm (henries), resistance Rc (ohms), and rf waves of angular frequency wE (rad/sec), a coupling coefficient (kcoupling) between transmitter and receiver coils may be crudely approximated as the ratio of the power stored in the magnetic field of the LR oscillator to the total power delivered to the receiver coil by the transmitter, or (dividing out the terms for current) kcoupling ~ wE Lm / (Rc + wE Lm). For nE = wE / 2p, m0 = 1.26 x 10-6 henry/m, mf ~5 (a self-inductance factor when the receiver coil of Ncoil loops contains a ferrite core630), rwire = wire resistivity (~3 x 10-8 ohm-m), and L is the characteristic size of the receiver (meters), then Lm ~ m0 mf Ncoil2 L3, R ~ rwire Ncoil2 / L, and
where km = rwire / 2p m0 mf ~ 10-3. For discrete-component (macroscopic) radios that receive broadcast signals, L ~ 1 cm and nE = 1-100 MHz, giving kcoupling = 0.9-0.999, which is very good. For Heetderks' submillimeter receiver designs, kcoupling = 10-3 - 10-5; for example, the receiver described above has L ~ 700 microns, nE = 2 MHz, giving kcoupling ~ 5 x 10-4, which is very poor. With such poor coupling, very large transmitter intensities are required to induce very small receiver power levels. Troyk and Schwan636 have suggested that printed thin-film coils integrated directly with sensor circuitry driven by a special transmitter coil topology could provide adequate amounts of power to implanted coils having coupling coefficients up to two orders of magnitude lower than Heetderks' designs. However, even kcoupling ~ 10-7 at 2 MHz only reduces receiver size to L ~ 500 microns, which is not much improvement. The L4 scaling of kcoupling suggests that magnetic transcutaneous power receivers smaller than ~500 microns may be impractical, given the negligible amounts of magnetic field energy that can be stored in nanoscale volumes (Section 6.2.4) and the likelihood that small AC circuits will be heavily damped.10 (See also Section 7.2.3.)
However, efficient micron-scale MHz-frequency rf antennas may still be feasible for individual nanorobots, as suggested by the following simplistic analysis. Consider a simple spring pendulum with a bob of mass mbob, density r (~diamondoid), thickness hbob, and face area L2, with nq charges and total charge Qbob = nq qe = L2 Cq (coul) permanently embedded on the bob surface, where Cq is bob surface charge density. An oscillating rf field of strength Ee (volts/m) and frequency nE drives the charges with a force F = Ee Qbob = mbob abob at an acceleration abob (m/sec2). The bob mass accelerates for a half-cycle of duration t = (2 nE)-1, periodically displacing a distance xbob = (1/2) a t2 = Qbob Ee/ 8 mbob nE2 and traveling at a mean velocity vbob ~ 2 xbob nE. The local energy density produced by the transmitter field is DE = (1/2) ke e0 Ee2 (joules/m3) (variables defined in Section 4.7.1, for water), with transmitter power intensity It = c DE / n (watts/m2) where c = 3 x 108 m/sec (speed of light) and n = ke1/2 is the refractive index for a nonmagnetic material at low frequency; hence Ee = (2 It / ke1/2 e0 c)1/2 (volts/m). At the end of each half-cycle the bob receives an energy E1/2 = (1/2) mbob vbob2. Assuming mechanical rectification, a lever arm connected to the charged bob in the receiver transmits to the nanorobot a received power of Pn ~ 2 E1/2 nE (watts); making the appropriate substitutions we have:
An additional constraint is that bob travel xbob must not exceed the space available within a receiver housing of depth Ltrav. The bob travels slower but farther at lower rf frequencies, and the lowest possible operating frequency minimizes attenuation in tissues. Taking xbob <~ n# hbob = Ltrav as a limit establishes a minimum operating frequency that will not peg the bob against its stops, given by:
We require a high charge density and thus assume Cq = 0.1 coul/m2 (~0.6 charge/nm2), somewhat less than the ~0.16 coul/m2 for charged amino acid molecules and the ~0.3 coul/m2 for a "fully ionized surface",1149 but well above the 0.005-0.02 coul/m2 recorded experimentally for SiO2 on mica,1154 the 2 x 10-3 coul/m2 for the electrodes in the electrostatic motor (Section 6.3.5) designed by Drexler,10 and the 2 x 10-4 coul/m2 figure given by Lowell and Rose-Innes1151 cited as typical for "highly charged surfaces." For a water-immersed bob, the DC surface field from this 0.1 coul/m2 charge density is a sustainable EDC = Cq / 2 ke e0 = 76 megavolts/meter.
Signal attenuation is minimal below ~1 MHz (Eqn. 6.32). Taking It = 100 watts/m2, L = 1 micron, r = 2000 kg/m3, hbob = 20 nm, n# = Ltrav / hbob = 50 for Ltrav = L, ke = 74.31 for 310 K water, and e0 = 8.85 x 10-12 farad/m, then minimum nE = 0.17 MHz giving Pn ~ 0.8 pW delivered to the nanorobot producing a power density within the housing of Dn = Pn / Ltrav L2 ~ 106 watts/m3. In a practical system, these receivers must be aligned precisely with the incident field to maximize energy coupling, possibly requiring dynamic orientation control of each onboard receiver. Resonating beam structures 8-30 microns in size that can serve as rf filtering and oscillator elements have been demonstrated experimentally at ~15 MHz.879 High-frequency submicron electrometers with charge per unit bandwidth sensitivity of ~0.1 electron/Hz1/2 have been demonstrated,2926 and submicron rf mechanical resonators have been discussed by Cleland and Roukes.2927
In 1999, Pharma Seq3432 was developing laser-photon-powered cubic ~250-micron rf microtransponders for use with oligonucleotide probes in DNA assays; suspended in slurry, each device had an integrated circuit storing the sequence of the oligo attached to it, and emitted a coded signal (the probe's serial number) to a nearby receiver when a fluorophore-labeled target DNA molecule binded to a complementary probe. However, direct visible-spectrum photonic powering of medical nanorobots in vivo is not promising except within a few millimeters of the unclothed epidermis and only in the presence of direct sunlight or strong artificial sources of illumination (>10-100 watts/m2) near maximum safe exposure limits, due to the poor detection efficiency (low photon count rate sec-1 m-2) and rapid attenuation of photons in human tissue (Section 4.9.4).
Last updated on 18 February 2003