© 1999 Robert A. Freitas Jr. All Rights Reserved.

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

6.4.1 Acoustic Power Transmission

Acoustically powered medical nanorobots may derive their energy either from sources indigenous to the human body (Section 6.3.3 and Table 6.3) or from artificial sources placed in or on the human body. Large arrays of microscale acoustic radiators could create focused coherent sonic beams. Such artificial sources are likely to involve ultrasonic frequencies designed to minimize any aural discomfort to the user. According to the official statement issued by the American Institute of Ultrasound in Medicine (AIUM) in 1978,⁶²⁶ no significant biological effects have been reliably observed in mammalian tissues exposed in vivo to unfocused ~MHz ultrasound with intensities of 1000 watts/m² or less, although the onset of continuous-wave ultrasound-induced lysis of human erythrocytes has occasionally been detected experimentally at intensities as low as 60 watts/m² at 1.6 MHz when micron-size gas bubbles are also present.³⁰⁴³ There are also no significant biological effects observed after continuous exposures exceeding 1 second in duration for total energy transfers of 500 kilojoule/m² or less. (The comparable hazard threshold for UV excimer laser light is ~0.5 kilojoule/m².⁶⁴⁵) Exposures of any duration >500 kilowatts/m² may cause cavitation and other harmful effects in biological tissue (see below). On the basis of additional experimental results, the AIUM in 1988 slightly revised its statement⁶²⁷ to allow intensities as high as 10,000 watts/m² for exposures to highly focused sound beams, which is about the highest that human volunteers can tolerate.⁵⁰⁵ (In 1985 the FDA allowed ultrasound intensities up to 7300 watts/m² for cardiac use, 15,000 watts/m² for peripheral vessels, and 1800 watts/m² for fetal, abdominal, intraoperative, pediatric, cephalic, and small-organ (breast, thyroid, testes) imaging.⁶²⁸) Figure 6.8 summarizes current standards in simplified graphical form.

Deleterious biological effects may occur in at least five ways:

1. Transient Cavitation -- Transient bubbles which implode produce temperature increases of ~10³ K and pressure spikes of ~10³ atm localized in regions of a few microns in radius. Normal or transient cavitation requires ~10⁵ watts/m² (~5.4 atm) at 30 KHz or ~10⁶ watts/m² (~17 atm) at 1 MHz to form in water.⁶²⁸ Intensities less than ~10⁴ watts/m² will not produce transient cavitation in any tissue.⁶²⁹

2. Stable Cavitation -- Small pre-existing bubbles surrounded by water resonate in synchrony with the acoustic field, with the liquid acting as the oscillating mass and the gas serving as the compliant component. For an air bubble of radius r_bubble (meters) in water, resonant frequency n_res ~ 3 / r_bubble (Hz) for hard-shell-less bubbles up to ~1 MHz;⁶⁴⁷ thus a 6-micron bubble resonates at ~600 KHz. Resonating bubbles have been reported in therapeutic beams at power intensities as low as 6800 watts/m² at 750 KHz.⁶²⁸

3. Heating -- Dissipation of vibrational energy can initially heat tissues ~1 K/minute if applied at, say, 50,000 watts/m² at 3 MHz, in the hazard zone of Figure 6.8. Continuous exposure to 2000-6000 watts/m² at 0.1-10 MHz raises human tissue temperature by 1 K at equilibrium, which is considered safe.⁶²⁹ Ultrasound intensities of ~2 x 10⁷ watts/m² at the point of action are used to cauterize liver tissue after surgery.¹⁵⁸

4. Acoustic Torque and Fluid Streaming -- Physical fluid motions are driven by ultrasonic radiation pressure, typically ~0.001 N/watt, or ~1 pN/micron² at 1000 watts/m². Forces of this magnitude or larger can cause damaging shear stresses in molecules or cells and may give rise to small voltages in bone via the piezoelectric effect.⁶²⁸

5. Shock Wave Formation -- Shock waves most easily form in liquids having low attenuation such as urine in the bladder or amniotic fluid. A 3-MHz 10-atm pulse shows a shock waveform after passing through 5 cm of water.⁶²⁸

Consider a micron-scale nanorobot located somewhere deep within the human body that wishes to receive acoustic power from an artificial external source. A "safe" I_power = 1000 watt/m² source pressed against the skin suffers three major reductions in intensity before its emanations reach the nanorobot. First, the power transferred to the entire body is reduced by a geometrical power reduction factor (PRF) which may be approximated as the ratio of the area of the transmitter in contact with the skin to the largest planar section through the torso, ~1500 cm². Second, after conversion of incident power intensity to pressure amplitude using Eqn. 4.53, transmitted amplitude is reduced by reflection losses (Eqn. 4.54), which may range from a 90% loss for a poorly-coupled source to just 10% loss for a well-coupled transmitter. Third, the pressure amplitude of the power signal is attenuated by absorption, reflection, and scattering as it passes through human tissue, as described by Eqn. 4.52.

Thus attenuated, the power signal finally reaches the nanorobot and is converted to mechanical power using a piston-type transducer as described by Eqn. 6.13. Combining all the above factors gives received power P_n which is a cubic and exponential function of acoustic frequency n_p and an exponential function of acoustic path length X_path, which factors interact to produce an optimum acoustic power transmission frequency for various path lengths as shown in Figure 6.9. P_n is given by Eqn. 6.13, with DV = L³ and DP = (1­R_loss) (2 r v_sound I_power PRF)^1/2 e^{(atiss np Xpath)}, where r = 993.4 kg/m³, v_sound = 1500 m/sec in water at 310 K (Eqn. 4.53), and R_loss = 1 ­ A_transmit/A_incident from Eqn. 4.54.

In operating table scenarios wherein acoustic transmissions from the table may reach all parts of the body within a very short path length (~10-30 cm) and the 1000 watt/m² transmitter may be well-coupled to ~40% of the patient's body surface giving PRF >1.00(100%), the power available to a ~0.3 micron³ nanorobot receiver may be quite large, on the order of ~10⁴ pW or greater even at sub-MHz frequencies at the 1000 watts/m² incidence level. Similar power levels might also be achieved using carefully-designed permanently-implanted acoustic radiator organs which are themselves powered by some external source such as induced emf, backpack batteries or even tethered household electrical current.

The greatest engineering challenge arises when whole-body acoustic power is to be supplied by some small extradermal source the size of a wristwatch, wallet, belt buckle, ankle bracelet, headband*, or amulet worn around the neck. The power curves in Figure 6.9 assume a wristwatch-band-sized radiator (~30 cm²) with a PRF of 2% and a single 0.3 micron³ receiver on the nanorobot. For a conservative design the longest acoustic path length in the human body (~200 cm) would govern the calculation, giving an optimum acoustic power transmission frequency of ~60 KHz, providing >40 pW in this configuration for a path entirely through soft tissue (a_tiss ~ 8.3 x 10^-6 sec/m; Table 4.2). Thus a 10-pW nanorobot may be powered on just a ~25% duty cycle, allowing plenty of "quiet time" for acoustic communications, sensing, and navigational activities. A 1000 watt/m² transmitter with 30 cm² of contact area provides 3 watts of acoustic power, enough to supply ~10¹¹ 10-pW nanorobots; ~10¹³ 10-pW nanorobots could be supported in the operating table scenario. For comparison, typical average power outputs of medical ultrasound scanners are 170 milliwatts at 0.520 MHz.^506,628

* The maximum acoustic threshold of pain for the human ear in air is ~100 watts/m² or ~140 dB, roughly independent of frequency within the audible range, for experienced habituated listeners.^628,1016 Animals may also take notice -- maximum audible frequencies via air conduction are 20 KHz (humans), 33 KHz (monkeys), 40 KHz (dogs, pigs, rats), 45 KHz (cats, katydids), 95 KHz (deer mice), 98 KHz (bats), and up to ~250 KHz (dolphins), while birds and fish are generally limited to <12 KHz.⁵⁸⁵

As a practical matter, acoustic power transmission may require slightly higher frequencies (e.g., >110 KHz) to ensure that some patients do not hear an annoying high-pitched noise that would be perceived as being centered in the head. Ultrasonic hearing via bone or body-fluid conduction has been reported at least up to 108 KHz in humans, probably mediated by the saccule, an otolithic organ that normally responds to acceleration and gravity.¹³⁷² Physical discomfort,³⁵³⁶ intra-articular pain,³⁵³⁷ and a lowering of electrical pain sensation threshold³⁵³⁸ due to ultrasound exposure have also been reported in humans.

Figure 6.10 quantifies the effects of transdermal power reflection and receiver size, neither of which significantly influence the choice of optimum acoustic frequency although larger receivers have a steeper frequency cutoff due to rapidly rising piston inertia losses with frequency (Section 6.3.3).

Net power received by medical nanorobots is also strongly influenced by the type of tissue lying across the acoustic path because of the exponential dependence of received power on the absorption coefficient a_tiss (Fig. 6.11). Similarly, Table 6.6 shows that very highly absorbent tissues such as bone, organs containing gas bubbles such as the stomach or bowel, and especially the air-filled lungs efficiently scatter and reflect large amounts of acoustic energy. Nanorobots positioned such that these highly attenuative tissues lie between them and the source should still receive adequate power due to internal acoustic reflection, since 99.95% of the acoustic amplitude reaching the skin-air interface from inside the body is reflected back into the body (Eqn. 4.54).

Available power declines rapidly for nanodevices located inside bone, bowel, or lung tissue, creating an "energy shadow". Fortunately the path lengths are sufficiently short within these regions of the body that such losses should not become severe. For example, a 1 micron³ receiver located 200 cm from a 1000 watt/m² transmitter at 60 KHz with PRF = 2% and reflection loss = 10% at the skin receives 153 pW if the acoustic path passes through soft tissues only, 46 pW if the 200 cm acoustic path includes 1 cm of bone (with a 66% reflection loss at the tissue-bone interface), or 7 pW if the path length includes 5 cm of lung tissue (with an 80% reflection loss at the tissue-lung interface). If two or more acoustic power sources are simultaneously employed, destructive interference might occur within spatially periodic regions of smallest width on the order of one wavelength, or >~v_sound/n_p ~ 1 cm (>>r_nano) for 150 KHz waves in water at 310 K, reducing locally available power.

Energy concentration, the opposite of energy shadowing, can also occur. If all nanorobot activity is confined to a specific organ or other small volume, a concave focusing transducer can shape pulse waves so that they arrive at a specific focal point within the body at high intensity. Spheroidally shaped regions in which the speed of sound is slower than in the surrounding medium (e.g., lower bulk modulus, or higher density or elasticity, as for instance a fat globule inside an organ; Eqn. 4.30 and Table 6.7) will tend to concentrate acoustic energy towards the center by refractive focusing.⁹²⁸ Sound waves also bend toward the cold side of a thermal gradient, the low-pressure side of a pressure gradient, and the low-concentration side of a salinity gradient. Large tubular tissue systems with areal cross-sections >(~l)² can act as acoustic waveguides; e.g., for 60 KHz waves in water, l ~ 2.5 cm, roughly the diameter of the human aorta.

In general, liquids within the body are only weakly absorbing, allowing maximum transmission. Common sonolucent fluids include urine, aqueous humor, vitreous humor, amniotic and cystic fluids. In medical ultrasound, water immersion scanning is commonplace (99.77% transmission at water-tissue interface; Table 6.6) and a full bladder is a standard technique for obtaining an ultrasound window into the uterus. Muscle tissue acoustic absorption is anisotropic; a difference of a factor of 2.5 has been reported between the attenuation across and along its fibers.⁶²⁸

Last updated on 18 February 2003