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

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

7.4.6.5 Ocular Outmessaging

Nanorobots may send messages to the patient by emitting photons directly into the eye (Fig. 7.5), generating an artificial visual stimulus. Retinal displays could be broadcast by photoemissive nanodevices located:

1. in the palpebral conjunctiva (inner mucosal surface) of the eyelid, where access to nutrients from the capillary bloodflow is still available in muscular tissue below the fibrous plates;

2. on the exterior surface of the cornea, when nanorobots may obtain power from transcorneal-diffused glucose and other sugars in the lacrimal fluids at c_ligand ~ 2.9 x 10^-4 molecules/nm³ (~10% blood plasma concentration);⁵⁸⁵

3. on the interior corneal or exterior lens surface (c_ligand = 1.6-3.7 x 10^-3 molecules/nm³ for glucose in the aqueous humor, ~plasma concentration),^585,3284 or in the anterior chamber in front of the lens (implanting an artificial lens in the anterior chamber was considered an experimental vision correction procedure in 1998);

4. inside the lens which is 68% water (c_ligand = 0.8-2.0 x 10^-3 molecules/nm³ for glucose,⁵⁸⁵ ~50% plasma concentration);

5. the interior lens or retinal surface with access to glucose in the vitreous humor (~same concentration as aqueous humor); or

6. within the individual rod (dim light, monochromatic) and cone (bright light, color-sensitive) cells retinal glucose is stored in glial Muller cells and is supplied upon demand.³²⁶⁰

Oxygen is available at ~5% of normal plasma concentration via solvation in the lacrimal fluids and diffusion into the aqueous humor; CO₂ and lactate exit by the same route. Formation of potentially signal-blocking scar tissue is avoided by using mobile nanorobots with active, biocompatible exterior surfaces³²³⁴ (Chapter 15).

We shall now consider four different methods for ocular outmessaging:

A. Extraretinal Projection -- Photoemissive nanodevices must generate a photon flux intensity sufficient to equal or exceed ambient background illumination levels. With the eyelid lightly closed, normal indoor illumination transmitted through this thin muscular fibrous tissue produces a background retinal flux of at least I_min ~ 10^-2 watts/m². With eyes open in a normally lighted room, the background flux may be ~1 watt/m² or even higher (Section 4.9.4).

Normally the lens of the eye can accommodate viewing distances no closer than X_min ~ 10 cm (measured from posterior lens surface) in adults. Photons emitted from nanodevices located in the eyelid (X_object ~ 8.6 mm), exterior corneal surface (X_object ~ 7.3 mm), interior corneal surface (X_object ~ 6.2 mm), or exterior lens surface (X_object ~ 3.8 mm) cannot be brought to focus inside the eye unless they are tightly collimated. A cylindrical emitter of length h_e = 25 microns and radius r_e = 0.5 micron can produce a collimated beam with an axial divergence angle j_e = 0.5 tan^-1 (2 r_e / h_e) ~ 1° (2° full-width divergence), which is geometrically equivalent to rays passing through a pupil aperture d_pupil = 5-6 mm after emanating from an object located at a distance X_object = d_pupil / 2 tan (j_e) = 12-15 cm which is >~X_min, hence is focusable. One major difficulty with eyelid projection is that tight flexing of the corrugator supercilii muscle (which draws the eyebrow downward and inward) causes the eyelid tissue to ripple and fold, potentially producing significant optical distortions. A large projector suspended in the anterior chamber might offer greater spatial stability. These devices are probably small enough to avoid stimulating lid edema or blepharitis.

Present-day micron-scale LEDs emit up to ~1 watt/m² (Section 5.3.7), so extraretinal displays from such emitters are comfortably read by patients. If the emitters overwrite 10% of the visual field, then total optical power input through the lens is P_out ~ 0.03-3.0 microwatts. Assuming a very conservative energy conversion efficiency of e% ~ 0.01(1%) for LEDs (Section 5.3.7), the emitters consume a total input power (and radiate waste heat) of P_in = P_out / e% = 3-300 microwatts, well below the conservative 2000 microwatt maximum for 0.1 cm³ of eyelid tissue (Eqn. 6.54). Emitter power density ranges from ~0.4 megawatts/m³ at 10^-2 watts/m² intensity up to ~40 megawatts/m³ at 1 watt/m² intensity.

B. Foveal Projection -- The fovea is a small pit in the macula lutea, opposite the visual axis, which is the spot of most distinct vision (Fig. 7.5). There are no rod cells in the fovea and relatively few in the near-foveal region. Foveal cone cells have diameters of 15 microns⁵⁸⁵ (average d_fov ~ 3 microns) with a minimum center-to-center separation of ~2.6 microns (average x_sep ~ 5.2 microns) across the foveal surface of the retina. The retina is arranged "inside out" so that light must pass through nine layers of connecting nerve cells and other tissue to reach the receptors which lie at the deepest level (Fig. 7.6, enlargement of box in Figure 7.5). This covering tissue is x_tiss ~ 130 microns deep across the fovea (the ganglion and bipolar layers are pushed aside, directly above the fovea) and x_tiss ~ 300 microns thick elsewhere on the retina. The foveal and near-foveal region extends ~2° (~0.55 mm²) around the visual axis, comprising ~20,000 cone cells and providing a resolvable visual angle of 0.5-2.3 minutes of arc (sufficient for reading printed text) and creating a 140 x 140 pixel writeable billboard.

Consider a cylindrical emitter of diameter ~1 micron affixed to the retinal surface over the fovea. This emitter produces a collimated beam with an axial divergence angle j_e ~ 1°, which diverges to a width w_beam = x_tiss tan (2 j_e) ~ 5.2 microns after traveling a distance x_tiss = 130 microns into the fovea. Each cylindrical emitter can target one foveal cone cell with no overlap, so ~20,000 photoemissive nanorobots are required for complete control of all foveal cone receptors. A population of 20,000 photoemissive nanodevices ~1 micron in diameter attached to the inner retinal membrane above the foveal surface blocks only ~3% of photons entering the fovea via the lens, an unnoticable diminution of the natural incident intensity that is visible to the patient.*

* J. Logajan points out that if the cylindrical emitter has a photodetector on the end facing the lens, then even the 3% loss could be largely retrieved by amplification; the emitters could also serve as dark-area amplifiers, providing improved night vision or infrared-to-visible light conversion (Chapter 30).

Given that d_fov < w_beam and pr_e² < 1 micron², achieving 0.01-1 watts/m² intensity at the receptor cells to overcome the natural illumination background requires an emitter photonic intensity of 0.04-4 watts/m², already within state-of-the-art in 1998. At a very conservative e% = 0.01(1%) ergophotonic efficiency, P_in ~ 3-300 pW per nanodevice or 0.06-6 microwatts for the entire population, well below the ~0.1 watt recommended thermogenic limit for the eyeball from Eqn. 6.54. If the nanorobot employs an oxyglucose power supply, continuous foveal control consumes ~10¹⁰-10¹² glucose molecules/sec which would exhaust the ~10¹⁹ glucose molecules present in the vitreous humor in ~0.3-30 years but would more quickly exhaust the oxygen supply (Section 6.5.3) in ~0.5-50 days even if there were no diffusive resupply from the surrounding tissues; fortunately, such resupply appears highly likely.

If the photoemissive foveal nanorobot population is extended to cover the rest of the retinal surface (with most devices not emitting photons most of the time), then real-time ocular and cranial positional information provided by kinesthetic macrosensors (Section 4.9.2.1) via the communication network can be used to shift displayed images in synchrony with eye and head movements, allowing displays to appear fixed in the field of view as in normal viewing of external objects. (Information gleaned from the oculomotor, trochlear, trigeminal, abducens, and spinal accessory nerves may assist in this control process.) Accommodation sensors (Section 7.4.2.2) assist in maintaining proper focus. Foveal nanorobots should be designed to avoid stimulation of uveitis or retinitis.

C. Ganglionic Stimulation -- Because of the inverted structure of the retina, neurostimulatory nanorobots attached to the inner retinal membrane can trigger artificial action potentials directly in the axons of afferent ganglia carrying information from rods and cones to the optic (2nd cranial) nerve. It is useful to briefly review the basic structure of the human retina (Fig. 7.6).

Starting with the outermost layer and moving inward toward the vitreous humor that fills the eyeball, the choroid layer (Fig. 7.5) is covered with a very sensitive optically absorbing pigmented epithelium which bleeds and detaches easily from the retina if physically disturbed by overpressures of ~10 mmHg. Above and covering the pigment layer lie about 250 million rod cells and 6 million cone cells. Rod and cone cells communicate by electronic conduction, not by action potentials. Rod and cone receptor cells converge in a complex synaptic network on bipolar and horizontal cells. Bipolar cells are depolarizing (inhibited by rod/cone neurotransmitters) or hyperpolarizing (excited by rod/cone neurotransmitters), allowing the transmission of positive and negative signals to amacrine and ganglion cells. Horizontal cells laterally connect rods and cones to bipolar cells, allowing lateral inhibition in the retina. Amacrine cells connect bipolar cells to ganglion cells. Numerous types of ganglion cells react to contrast borders, intensity changes and color contrasts. Preprocessed visual information flows into ~1 million ganglion cells whose fibers collect into a giant bundle and exit the eyeball under the ~1.5 mm-diameter optic disk or "blind spot", forming the optic nerve. Convergence is maximal at the periphery of the retina -- rods outnumber cones by more than 10:1 in the periphery, and up to 10³-10⁴ rods may report to a single ganglion cell. Convergence is minimal in the fovea, where one cone cell may synapse with a single ganglion cell through a single bipolar cell.

Low-level signal processing aided by amacrine and horizontal cells in the bipolar layer thus reduces the optic data traffic from 256 million to only 1 million channels at the ganglionic axons which lie closest to the nanorobots attached to the inner retinal membrane. The ganglia are spaced from ~3 microns apart bordering the fovea to ~100 microns apart at the farthest periphery of the retina, averaging ~30 microns. For simplicity, if we regard each ganglion as carrying the equivalent of a single pixel of data in a 1000 x 1000 pixel visual field, then a comprehensive retinal ganglionic management system comprising ~10⁶ neurostimulatory devices installed within each eyeball allows complete control of the entire human visual field with a refresh rate close to the flicker frequency for rods of ~15 Hz,⁵⁸⁵ with ocular data transfer near ~10⁷ bits/sec which is near the practical upper limit for in vivo mobile communication networks (Section 7.3.2). Assuming up to P_in ~ 30 pW for each neurostimulatory nanorobot (Section 7.4.5.6) a continuously operated retinal ganglionic control system consumes at most ~30 microwatts, comparable to ocular projection systems described in (A) and (B), so energy supply and heat generation are not significant design limitations.

As of 1998, prototype retinal implant components had been installed and tested in rabbits. These test devices delivered ~10 microamps per electrode directly to ganglion cells and produced measurable activity in the visual cortex of the animals' brains.¹⁰⁴⁴ Other retinal implant devices were under investigation by Rolf Eckmiller at Universitat Bonn, by a Harvard Medical School/MIT collaboration, and by a Japanese group at Nagoya University;^1887-1890 Eckmiller expects the first implant in a human volunteer by 2001. Direct electrical stimulation of the human visual cortex was first attempted in 1968 using 100 Hz pulses applied in 200 microsec bursts via an array of 81 electrodes implanted in a blind person's brain, with poor results.¹⁷¹³

D. Direct Photoreceptor Stimulation -- A single photoemissive nanorobot may be carefully stationed in each of the 256 million rod and cone cells of the human eye. If the nanorobot is positioned in the pigment-rich apical region of the cell,* (e.g., the ~9-nm thick double-membranous lamellae, or planar structures, of the outer segment of the rod cell; Figure 7.6) its emitted photon is likely to be detected even without collimation. Assuming a very conservative 1% energy conversion efficiency to generate optical photons, 10% absorption efficiency of optical photons within the cell, and a 25 Hz image refresh rate, power consumption is only ~0.01 pW per nanorobot for continuous transmission and ~2.5 microwatts for complete control of the human visual apparatus. Outmessaging rates are limited by the peak capacity of the external communications link, ~10⁷ bits/sec for a mobile network using n ~ 100 MHz and f_duty = 10% (Section 7.3.2).

* The tips of rod cells are renewed at the end of each night, the tips of cone cells at the end of each day, as regulated by the diurnal circadian clock (Section 10.1.1).¹⁶⁶⁴ Resident nanorobots should avoid being sloughed off during this process.

Chemical or mechanochemical stimulation may also be used in place of photons. For example, such means could induce the 11-cis to 11-trans torsional isomerization of the retinal chromophore in rhodopsin, the first step in photoreceptor stimulation, which occurs naturally in ~0.2 picosec.¹⁶⁹² This conformational change opens a calcium channel in the rod cell membrane; the rapid calcium ion influx triggers a nerve impulse, and light is perceived by the brain.⁹⁹⁶ (Each rod rises1-2 microkelvins in temperature during the heat burst following a light flash causing 180-1800 rhodopsin photoisomerizations per rod.³⁴⁷⁰) Direct nanorobot modulation of intracellular concentrations of a-transducin, the G-protein that transduces the light signal in retinal cells, or directly opening an artificial transmembrane Ca⁺⁺ channel allowing a Ca⁺⁺ influx (mediated by a membrane-spanning nanorobot) may be even more efficient.

Last updated on 19 February 2003