**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 r_{fiber} is
embedded in a block of tissue of volume V_{tiss} (m^{3}) 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_{fiber1}^{3} (m^{3}) and bounded
by N_{seg1} = 3 N_{node1} fiber segments each of length x_{fiber1}.*
Total fiber volume is V_{fiber1} = 3 p r_{fiber}^{2}
V_{tiss} / x_{fiber}^{2 }and total fiber length L_{fiber1}
= 3 V_{tiss} / x_{fiber1}^{2}. 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_{fiber1}^{3}
/ 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 m^{3}. 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 10^{7} meters, fiber volume V_{fiber1}
= 24 cm^{3}, and N_{seg1} = 3 x 10^{11} internodal fiber
segments defining N_{node1} = 10^{11} communications voxels.
This network may be emplaced by ~10^{11} installer nanorobots (Chapter
19) of size ~1000 micron^{3} that travel through tissue at 1-100 microns/sec
(Section 9.4.4). Each installer unspools ~300 microns
of internally stored fiber (~240 micron^{3}) 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 'I_{1}
~ 10^{9} bits/sec (~1 GHz). Cable power density is ~40,000 W/m^{3};
power intensity is ~4 W/m^{2}.

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 10^{5} meters and 10^{8}
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, 'I_{2} ~ 10^{12} bits/sec.

In subnetwork #3, x_{fiber3} = 1 cm, giving total
fiber length L_{fiber3} = 3 x 10^{3} meters and 10^{5}
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, 'I_{3} ~ 10^{15}
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, 'I_{4}
~ 10^{18} bits/sec, and power intensity ~10^{5} W/m^{2},
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 10^{9} billion-bit (e.g., "genome
packet") messages per second across the entire installation volume -- providing
~10^{18} 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 ~10^{10 }bits/sec, average global communications
traffic was ~10^{12} bits/sec, total worldwide Ethernet capacity was
~10^{13} 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 Lesk^{3130
}as ~10^{19} 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 10^{4} bit/sec channel produces 10^{6} 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 ~10^{7} bits/sec and network power draw falls to ~6 watts.

Assigning one nanorobot in each tissue cell (~10^{13 }nanorobots)
a unique address requires each message packet to contain a log_{2} (10^{13})
= 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 10^{8} 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 10^{9}-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 10^{6}
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 m^{2}) is relatively small in comparison with
various internal surfaces such as the vascular network (~300 m^{2}).

Fiber nodes may store considerable quantities of useful data.
For instance, in the above example there are 10^{11} local network nodes.
If each node stores just ~2600 bits on hydrofluorocarbon memory tape at 26 bits/nm^{3}
(Section 7.2.1.1) accessible in <10^{5}
sec (Section 7.2.6), this cache occupies a volume of
~100 nm^{3} per node and the entire local nodal network storage capacity
is ~3 x 10^{14} bits, or ~one Library of Congress.

Last updated on 19 February 2003