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
4.9.4 Optical Macrosensing
In vivo medical nanodevices can gather little useful optical information from the external environment. Here's why.
In biological soft tissues, scattering dominates absorption except in the pigmented layers of the epidermis and stratum corneum. Thus the propagation of light in tissues may be regarded as occurring in two steps.509,510
In the first step, optical photons of intensity I0 falling perpendicularly on skin are transmitted according to Beer's law through tissue to a depth z with a transmitted intensity of
where rsp = specular reflection coefficient for visible light (Fresnel reflection at the air-tissue surface) ~ 4%-7%,508 or 0% if the original light source lies within the body; and the transmission coefficient st = sa (absorption coefficient ~ 300 m-1) + ss (scattering coefficient ~30,000 m-1) for various human soft tissues at optical wavelengths.510 (Coefficient values for the most heavily pigmented skin layers may be 5-7 times higher.)508 Typical values for st ~ 10,000-100,000 m-1, average ~30,000 m-1 for soft tissue, although exceptionally clear tissues with st = 1000 m-1 have been reported.510,729 Thus the mean free path of an optical photon in human soft tissue is 10-100 microns, average ~ 30 microns (~1.5 tissue cell-widths), up to an extreme maximum of ~1 mm for the most transparent tissues known. For st ~ 30,000 m-1, at z = 150 microns, Iz / I0 ~ 0.01 and ~99% of all photons have been scattered at least once from their initial path.
In the second step, in an unbounded medium the patch of fully scattered photons continues to propagate through the tissue via diffusion until all photons are absorbed. The complicated governing diffusion equation has not yet been been completely solved analytically,510 but the asymptotic diffusive fluence is given roughly by
where sd is the diffusion exponent or effective attenuation coefficient (averaging ~900 m-1 for typical soft tissues but with an extremely wide range reported over the ultraviolet, visible, and near-infrared wavelengths, from 10-1,000,000 m-1.)729 As a crude approximation, the initial intensity of the fully scattered photon patch Ii ~ I0 (1 - rsp) ascat, where ascat = ss / (ss + sa) ~ 0.987 is the albedo for single particle scattering.
Over the optical band from 400-700 nm, incident intensity I0 = 100-400 watts/m2 when standing in direct sunlight; artificial lighting in homes and offices is typically 0.1-10 watts/m2; moonlight provides only I0 ~ 10-4 watts/m2; and the absolute threshold for human vision is ~10-8 watts/m2.585 For sd ~ 900 m-1, the intensity ratio of transmitted/incident visible light falls to Id / I0 = 0.1 at z = 2.5 mm depth (~eyelids), ~10-4 at z = 1 cm depth, and ~10-11 at z = 2.8 cm -- a depth at which the tissue would be completely dark to the human eye even under direct sunlight illumination at the outermost skin surface.
An optical nanosensor with Nsensor receiver elements, with each receiver element having an area Ae = 1 nm2 and capable of single-photon detection, requires an integration time for reliable detection of eSNR photons given by
where h = 6.63 x 10-34 joule-sec and n = 4.3-7.5 x 1014 Hz for optical photons. Let us assume that a patient is standing in I0 ~ 400 watt/m2 direct unfiltered sunlight, and that tmeas = 1 sec, SNR = 2, Nsensor = 25,000 elements giving a nanorobot eyespot of Ae Nsensor = 0.025 micron2, and that sd = 900 m-1. Then from Eqns. 4.58 and 4.59 the maximum tissue depth for optical photon detection is zmax ~ 17 mm (Id ~ 10-4 watt/m2) which includes a volume of tissue comprising up to ~30% of total body volume. Changes in illumination at the minimum indoor artificial level of ~0.1 watts/m2 are visible to zmax ~ 7 mm depth. This eyespot, if exposed to air on the outermost surface of the skin, is just sensitive enough to detect full moonlight.
Our general conclusion is that variations in normal indoor lighting may be directly measurable by nanorobots stationed within the outermost ~1 cm of body tissues. Imaging, as opposed to the simple illumination detection system described here, is a much more difficult design challenge (Chapter 30). Direct stimulation of retina-resident nanosensors is described in Section 184.108.40.206 (D).
Last updated on 17 February 2003