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
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 rfiber is embedded in a block of tissue of volume Vtiss (m3) with a mean separation between adjacent parallel fibers of xfiber1 in the rectangular grid. This defines a total of Vtiss / xfiber1 3 = Nnode1 intersection nodes and an equal number of cubic voxels, each of volume xfiber13 (m3) and bounded by Nseg1 = 3 Nnode1 fiber segments each of length xfiber1.* Total fiber volume is Vfiber1 = 3 p rfiber2 Vtiss / xfiber2 and total fiber length Lfiber1 = 3 Vtiss / xfiber12. Allowing a maximum power budget of Pnet1 (watts) for the network, then each internodal fiber segment may dissipate up to Pseg1 = Pnet1 xfiber13 / 3 Vtiss. A cable energy dissipation of Ebit1 (joules/bit) implies a maximum data traffic of 'I = Pseg1 / Ebit1 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, Vtiss ~ 0.1 m3. For the first subnetwork, xfiber1 = 100 microns, rfiber = 0.5 microns, and Pnet1 = 1 watt, giving total fiber length Lfiber1 = 3 x 107 meters, fiber volume Vfiber1 = 24 cm3, and Nseg1 = 3 x 1011 internodal fiber segments defining Nnode1 = 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 22.214.171.124), then briefly conjugates (Section 126.96.36.199) with other installers to make the nodal connections. Using GHz nanocoax (diameter ~1 micron) with Ebit1 ~ 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, xfiber2 = 1 mm, giving total fiber length Lfiber2 = 3 x 105 meters and 108 communications voxels. For Pnet2 = 1 watt and using a single IR line or a bundle of ten 100 GHz lines (diameter ~3.6 microns) with Ebit2 ~ 3 zJ/bit, 'I2 ~ 1012 bits/sec.
In subnetwork #3, xfiber3 = 1 cm, giving total fiber length Lfiber3 = 3 x 103 meters and 105 communications voxels. For Pnet3 = 1 watt and using a bundle of ten 10-THz optical cables (Section 188.8.131.52; bundle diameter ~3.6 microns) with Ebit3 ~ 10 zJ/bit, 'I3 ~ 1015 bits/sec.
In subnetwork #4, xfiber4 = 10 cm, giving total fiber length Lfiber4 = 30 meters and 100 communications voxels. For Pnet4 = 1 watt and using a bundle of 100,000 10-THz optical cables (bundle diameter ~360 microns) with Ebit4 ~ 10 zJ/bit, 'I4 ~ 1018 bits/sec, and power intensity ~105 W/m2, the maximum deemed safe for in vivo applications (Section 184.108.40.206).
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 Ln / 2 = (31/2 / 2) xfiber1 from the nearest local node (Section 5.2.1 (F)). From Eqn. 7.9, taking n = 100 MHz, fduty = 1%, r = 1 micron and Xpath = 87 microns, then Pin = 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 220.127.116.11) 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