© 2003 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume IIA: Biocompatibility, Landes Bioscience, Georgetown, TX, 2003

15.5.2.3 Nanorobot Convoy Formation

All else equal, mechanical damage during histopenetration by medical nanorobots is proportional to the volume of disturbed tissue. The tissue volume required to be displaced by a given population of passing nanorobots is minimized if transit tunnel volumes are reused by successive nanorobots – that is, if nanorobots histopenetrate in linear convoys. More quantitatively, if a population of N_bot cube-shaped nanorobots each of edge d moves at velocity v_bot through a cubic tissue block of volume L³ using c_tunnel separate histopenetration tunnels each of length L and cross-sectional area d², then the tissue holing fraction is f_hole = c_tunnel d² / L², the length of each convoy is L_convoy = d N_bot/c_tunnel, and the transit time for the fleet is t_transit = (L + (d N_bot / c_tunnel)) / v_bot.

For N_bot = 10⁹ nanorobots, L = 1 cm, d = 1 micron, and v_bot = 100 microns/sec (Sections 9.4.4.2 and 15.3.6.5), then randomized single-nanorobot histopenetration (c_tunnel ~ N_bot) gives f_hole = 1000% and the block of tissue is entirely holed ten times by the passing nanorobot fleet, a massively intrusive event. However, if f_hole = 1% is regarded as an acceptable and fully biocompatible maximum degree of tissue intrusion (Section 15.6.3), then c_tunnel = 10⁶, giving t_transit = 110 sec and L_convoy = 1 mm. (See also Section 15.3.6.5.)

Last updated on 30 April 2004