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
4.8.2 Transcellular Acoustic Microscopy
Acoustic microscopy is another noninvasive scanning technique that can provide nanomedically useful spatial resolutions. Frequencies are in the GHz range, far exceeding the relaxation time of the protoplasm. A cryogenic acoustic microscope operated at 8 GHz has demonstrated 20 nm lateral resolution in liquid helium.482 By 1998, the best resolution achieved with water as the coupling fluid has been 240 nm at a frequency of 4.4 GHz.488 Operated in water at 310 K, a nanomechanical 1.5 GHz acoustic microscope would achieve a far-field minimum lateral resolution l/2 ~ 500 nm, ~105 voxels per human cell, sufficient to locate and count all major organelles and a few intermediate-scale structures. Scanning acoustic microscopes (SAM) operated at 2 GHz in reflection mode (which allows detection of interference effects) achieve 30-50 nm resolution in the direction of the acoustical axis, and the Subtraction SAM approach reveals topographical deviations of 7.5 nm at 1 GHz.483 It has been proposed that picosecond ultrasonics could be used to obtain an image of the cytoskeleton with detail comparable to that of conventional X-ray images of a human skeleton.1022
Power requirements are a significant constraint on acoustic reflection microscopy (echolocation). In the simplest case, consider an acoustic emitter of radius rE which converts an input power of Pin into acoustic power of intensity IE < Imax = 1000 watts/m2 (Section 6.4.1) with efficiency e%, conservatively taken here to be 0.50 (50%). The emitter produces a train of omnidirectional pressure pulses of amplitude Ap = (2 r vsound IE)1/2 (N/m2) (Eqn. 4.53) and frequency n which travels a distance Xpath to a target of radius rT. As the signal reaches the target, its amplitude has been reduced by (rE / Xpath) due to the 1/r2 dependence of intensity in spherical waves (Section 126.96.36.199) and by e-atiss n Xpath by attenuation (Eqn. 4.52) with atiss = 8.3 x 10-6 sec/m for soft tissue.
Upon reaching the target, a fraction freflect of the signal is reflected as a point source echo; if the target surface has an acoustic impedance similar to liver tissue and the medium is similar to water, then from Eqn. 4.54 and Table 4.3, freflect ~ 0.05 (5%). The echo then travels a distance Xpath back to a receiver (which may or may not be located near the emitter), the amplitude again losing (rT / Xpath) by geometry and e-atiss n Xpath by attenuation. The echo is finally detected by the receiver which can measure a pulse of minimum pressure amplitude DPmin ~ 10-6 atm (Section 4.5.1).
Combining these relations gives the following result:
To scan the entire interior of a (20 micron)3 cell, whether from within or without, requires Xpath >~ 20 microns. A frequency of n = 1.5 GHz allows vsound/n ~ 1 micron spatial resolution. The fastest possible pulse repetition time is Xpath/vsound ~ 13 nanosec. Assuming rE = rT = 0.5 micron, Pin ~ 7 pW or ~5 watts/m2, well within the safe intensity range for acoustic radiation (Section 6.4.1). At maximum safe transmitter intensity Imax, the longest scannable path length at 1.5 GHz is Xpath ~ 46 microns.
Power constraints are somewhat less severe in the case of acoustic transmission microscopy (acoustic tomography), a technique which requires a minimum of two physically separated components (e.g., a transmitter and a receiver). Consider an acoustic emitter radiating a series of omnidirectional pressure pulses of frequency n which travel across a tissue cell of width Xpath, to be detected by a receiver on the other side after a signal transit time tcell ~ Xpath / vcell, where vcell is the speed of sound in the cytosol. In the simplest case, assume that the cytosol is clear except for one target of interest along the path (e.g., an organelle) in which the speed of sound is vtarget # vcell. The minimum detectable difference in travel times between a signal that passes through the target and one that does not is Dt (~10-9 sec for diamondoid systems), so the minimum resolvable target size is rmin ~ vtarget vcell Dt / 2 abs(vtarget - vcell) when rmin >~ vcell / n. For soft tissue targets in water at 1.5 GHz, rmin ~ 30 microns; for tooth enamel in water (see Table 6.7), rmin ~ 1 micron. However, the use of sampling gates will permit the detection of phase shifts that are much less than the characteristic time constant of the system in incoming waves, hence the minimum thickness of objects in theory detectable by acoustic tomography can be far smaller than the values for rmin estimated above.
Computing acoustic tomographic power requirement Pin in a similar manner as for echolocation, except that the transmitted signal rather than the echo is detected and assuming the signals are of approximately equal strength regardless of the path taken, gives:
Using the same values as the previous example, Pin = 1 pW for Xpath ~ 45 microns; for Xpath ~ 140 microns, Pin = 1000 pW, near Imax.
In either mode of operation, data gathering is accelerated by positioning more than one receiver around the target. Sensitivity is boosted by increasing emitter size, taking multiple measurements, or by illuminating the target with some large external source located elsewhere in the tissue or even outside of the organ. However, cells and body tissues are mesoscopic "junkyards" -- highly heterogeneous media which may produce large numbers of nontarget scattering events, thus increasing the difficulty of extracting signal from noise. Additional complications arise due to:
1. scattering on rough surfaces;
2. rapid pressure variations with range in the Fresnel zone or near field of the transmitted signal;
3. cytoplasmic viscosity inhomogeneities due to the asymmetric arrangement of cytoskeletal structure, granules, vacuoles, and the endomembrane system; and
4. variation in cytoplasmic Young's modulus due to time-varying tensions in semirandomly-distributed cytosolic fibrillar elements (e.g., a relaxed or contracted state) which alter elasticity and thus the local speed of sound.
Last updated on 17 February 2003