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 Continuous Stationary Source in Nonstationary Medium

A nonstationary transporting medium does more than just move message molecules in the direction of flow -- it also may create turbulence in the medium, adding a component of turbulent diffusivity that overwhelms simple Brownian diffusion, giving a total diffusivity that is more a property of the flow structure of the medium and the boundary surfaces than of the substance of the medium, a complex analytical problem. Consider a continuous point source emitting a constant 'Qmessage (molecules/sec) from a fixed position near the luminal surface of a blood vessel of radius Rvasc. From the relations given in703 and as a crude approximation assuming plume width << boundary wall separation, 'Qmessage ~ (0.0396) vvasc cminXfadeout7/4 to create an ellipsoidal message molecule plume of maximum detectable length Xfadeout in a medium flowing along the x-axis with fluid velocity vvasc. The widest part of the plume occurs at Xmax ~ (3.57) F4/7, Ymax ~ (0.686) F1/2, and Zmax ~ (0.341) F1/2, where F = 'Qmessage / vvasc cmin. Message receipt time trec ~ Xfadeout / vvasc.

Thus a simple message (Imessage = 100 bits, cmin ~ 10-9 molecules/nm3 for tsensor = 1 sec) broadcast from the luminal surface of the common carotid artery (vvasc ~ 0.2 m/sec, Rvasc ~ 3 mm; Table 8.2) with a desired plume length Xfadeout = 100 microns requires at least 'Qmessage ~ 109 molecules/sec, producing a very narrow plume with Ymax ~ 40 microns, Zmax ~ 20 microns (the radial direction), and trec ~ 0.5 millisec ('I ~ 100 bits/sec, limited by tsensor = 1 sec). For a complex message (Imessage = 109 bits, cmin ~ 9 x 10-11 molecules/nm3 for tsensor = 1 sec), 'Qmessage ~ 7 x 107 molecules/sec at trec ~ 0.5 millisec ('I ~ 109 bits/sec, limited by tsensor = 1 sec).


Last updated on 18 February 2003