© 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

{Eqn. 4.57}

where r_sp = 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 s_t = s_a (absorption coefficient ~ 300 m^-1) + s_s (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 s_t ~ 10,000-100,000 m^-1, average ~30,000 m^-1 for soft tissue, although exceptionally clear tissues with s_t = 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 s_t ~ 30,000 m^-1, at z = 150 microns, I_z / 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

{Eqn. 4.58}

where s_d 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 I_i ~ I₀ (1 - r_sp) a_scat, where a_scat = s_s / (s_s + s_a) ~ 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 s_d ~ 900 m^-1, the intensity ratio of transmitted/incident visible light falls to I_d / 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 N_sensor receiver elements, with each receiver element having an area A_e = 1 nm² and capable of single-photon detection, requires an integration time for reliable detection of e^SNR photons given by

{Eqn. 4.59}

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 t_meas = 1 sec, SNR = 2, N_sensor = 25,000 elements giving a nanorobot eyespot of A_e N_sensor = 0.025 micron², and that s_d = 900 m^-1. Then from Eqns. 4.58 and 4.59 the maximum tissue depth for optical photon detection is z_max ~ 17 mm (I_d ~ 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 z_max ~ 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 7.4.6.5 (D).

Last updated on 17 February 2003