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

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

7.3.1 Fiber Networks

Fiber networks may employ fixed-topology data-conducting cables (Section 7.2.5) of virtually any description, including electrical, optical, acoustical, mechanical, or chemical. A complete design analysis of each of these network classes is beyond the scope of this book. The following discussion focuses on high-frequency electrical and optical cables, which most clearly exemplify the salient characteristics of fiber networks.

Suppose that a simple three-dimensional hierarchical Cartesian grid of electromagnetic communication fibers of radius r_fiber is embedded in a block of tissue of volume V_tiss (m³) with a mean separation between adjacent parallel fibers of x_fiber1 in the rectangular grid. This defines a total of V_tiss / x_fiber1 ³ = N_node1 intersection nodes and an equal number of cubic voxels, each of volume x_fiber1³ (m³) and bounded by N_seg1 = 3 N_node1 fiber segments each of length x_fiber1.* Total fiber volume is V_fiber1 = 3 p r_fiber² V_tiss / x_fiber² and total fiber length L_fiber1 = 3 V_tiss / x_fiber1². Allowing a maximum power budget of P_net1 (watts) for the network, then each internodal fiber segment may dissipate up to P_seg1 = P_net1 x_fiber1³ / 3 V_tiss. A cable energy dissipation of E_bit1 (joules/bit) implies a maximum data traffic of 'I = P_seg1 / E_bit1 on each segment between nodes.

* This network design, with each node having 6 connecting fibers, may be unduly redundant, resulting in excess fiber usage. Single nodes may need no more than 4 connecting fibers, forming a tetrahedral grid.

For whole-body installation in a human being, V_tiss ~ 0.1 m³. For the first subnetwork, x_fiber1 = 100 microns, r_fiber = 0.5 microns, and P_net1 = 1 watt, giving total fiber length L_fiber1 = 3 x 10⁷ meters, fiber volume V_fiber1 = 24 cm³, and N_seg1 = 3 x 10¹¹ internodal fiber segments defining N_node1 = 10¹¹ communications voxels. This network may be emplaced by ~10¹¹ installer nanorobots (Chapter 19) of size ~1000 micron³ that travel through tissue at 1-100 microns/sec (Section 9.4.4). Each installer unspools ~300 microns of internally stored fiber (~240 micron³) in 3-300 sec while consuming <<1 pW of motive power (Section 9.4.4.2), then briefly conjugates (Section 9.4.4.4) with other installers to make the nodal connections. Using GHz nanocoax (diameter ~1 micron) with E_bit1 ~ 3 zJ/bit, internodal traffic has a capacity of 'I₁ ~ 10⁹ bits/sec (~1 GHz). Cable power density is ~40,000 W/m³; power intensity is ~4 W/m².

Three additional subnetworks are interleaved with the first, each passing messages to the others through appropriate nodal junctions:

In subnetwork #2, x_fiber2 = 1 mm, giving total fiber length L_fiber2 = 3 x 10⁵ meters and 10⁸ communications voxels. For P_net2 = 1 watt and using a single IR line or a bundle of ten 100 GHz lines (diameter ~3.6 microns) with E_bit2 ~ 3 zJ/bit, 'I₂ ~ 10¹² bits/sec.

In subnetwork #3, x_fiber3 = 1 cm, giving total fiber length L_fiber3 = 3 x 10³ meters and 10⁵ communications voxels. For P_net3 = 1 watt and using a bundle of ten 10-THz optical cables (Section 7.2.5.2; bundle diameter ~3.6 microns) with E_bit3 ~ 10 zJ/bit, 'I₃ ~ 10¹⁵ bits/sec.

In subnetwork #4, x_fiber4 = 10 cm, giving total fiber length L_fiber4 = 30 meters and 100 communications voxels. For P_net4 = 1 watt and using a bundle of 100,000 10-THz optical cables (bundle diameter ~360 microns) with E_bit4 ~ 10 zJ/bit, 'I₄ ~ 10¹⁸ bits/sec, and power intensity ~10⁵ W/m², the maximum deemed safe for in vivo applications (Section 6.4.3.2).

Assuming 5 zJ/bit switching losses at each node, total power dissipation of all nodes in each subnetwork is ~0.5 watts, or ~2 watts for nodes at all four levels. Combining the four subnetworks into a single well-linked network gives the ability to transfer 10⁹ billion-bit (e.g., "genome packet") messages per second across the entire installation volume -- providing ~10¹⁸ bits/sec along the optical backbone with a 6-watt power budget. By comparison, in 1997 the Internet backbone (admittedly much larger in physical extent) could transfer only ~10¹⁰ bits/sec, average global communications traffic was ~10¹² bits/sec, total worldwide Ethernet capacity was ~10¹³ bits/sec, and worldwide data storage in all movies, recordings, corporate and government databases, and personal files was informally estimated by Michael Dertouzos,⁹⁸³ Philip Morrison,¹⁶⁴⁹ and Michael Lesk³¹³⁰ as ~10¹⁹ bits.

Messages are transmitted acoustically from in vivo nanorobots present within a (100 micron)³ communications voxel to the nearest local network node. These nonoptical links are the principal bottleneck in the system. In the worst case, a nanorobot lies at most L_n / 2 = (3^1/2 / 2) x_fiber1 from the nearest local node (Section 5.2.1 (F)). From Eqn. 7.9, taking n = 100 MHz, f_duty = 1%, r = 1 micron and X_path = 87 microns, then P_in = 550 pW per voxel. Each communications voxel contains up to ~100 (20 micron)³ tissue cells, so one nanorobot per cell communicating continuously on a 10⁴ bit/sec channel produces 10⁶ bits/sec of message traffic, just 0.1% of rated capacity of each local node. At this maximum bit rate, local acoustic power dissipation totals ~55 watts, giving a total of ~60 watts for the network. If nanorobots can physically dock at a node, the need for acoustic links is eliminated; bit rate per channel rises to ~10⁷ bits/sec and network power draw falls to ~6 watts.

Assigning one nanorobot in each tissue cell (~10¹³ nanorobots) a unique address requires each message packet to contain a log₂ (10¹³) = 44-bit sender identifier plus a 44-bit recipient identifier, mandating a ~100-bit header allowing 12 check bits, the absolute minimum message packet size for a comprehensive cell-addressible network. At a 1 MHz acoustic nodal access rate, a simple 200-bit message takes ~0.2 millisec to upload or download, plus ~2 meters / ~c = ~10^-8 sec to pass through the network at ~0.67c, where c = 3 x 10⁸ m/sec (speed of light). Nodal read/write functions should operate at 10-10,000 MHz (Section 7.2.6) and optical switching may be even faster, so signal passage through at least the local nodes should impose no significant additional delays. Hence simple messages may be passed between any two specific nanorobots in ~0.4 millisec; a complex 10⁹-bit message requires ~1000 sec. By comparison, simple adjacent internodal Internet "pinging" takes ~10 millisec. (Again, node-docked nanorobots with no acoustic intermediaries can exchange messages several orders of magnitude faster.)

Communication with bloodborne nanorobots is most convenient during capillary passage (once every ~60 sec), when nanorobots should remain within the operating range of local nodes during the entire transit owing to the narrow width of such vessels (4-15 microns). Capillaries are typically ~1 mm long with flow rates of 0.2-1.5 mm/sec (Table 8.1), so the passing nanorobot has 0.75 sec to upload or download messages. Given the ~0.2 millisec echo time, a nanorobot entering a capillary can announce its position and begin receiving its email before it has traveled more than ~0.2 micron through the narrowest vessels; messages of up to ~5 x 10⁶ bits may be sent or received during each capillary transit.

Communication from the arterioles (average ~100 microns diameter) requires contacting the nearest local node which may be 150 microns away, boosting required nanorobot acoustic transmitter power to ~1600 pW at 100 MHz. Energy costs become prohibitive in the arteries and larger veins and other special locations such as the cardiac chambers, the bursae, and the bladder. Simple 200-bit messages might possibly be transacted by nanorobots immediately adjacent to the 25,000-micron diameter aortal wall; maximum flow velocity of ~1 m/sec carries an unanchored nanorobot beyond the 100-micron operational radius of a medial local node in just ~10^-4 sec. Under conditions of bradycardia or cardiostasis, communications improve significantly in the vascular regions because bloodborne nanorobots remain longer in the vicinity of nearby embedded nodes.

Subdermal networks may be useful in some specialized applications, but the skin area (~2 m²) is relatively small in comparison with various internal surfaces such as the vascular network (~300 m²).

Fiber nodes may store considerable quantities of useful data. For instance, in the above example there are 10¹¹ local network nodes. If each node stores just ~2600 bits on hydrofluorocarbon memory tape at 26 bits/nm³ (Section 7.2.1.1) accessible in <10⁵ sec (Section 7.2.6), this cache occupies a volume of ~100 nm³ per node and the entire local nodal network storage capacity is ~3 x 10¹⁴ bits, or ~one Library of Congress.

Last updated on 19 February 2003