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
18.104.22.168 Hematocrit Reduction in Narrow Vessels
Fahraeus1313 found that when blood of a constant hematocrit Hct is allowed to flow from a large feed reservoir into a small tube, hematocrit in the tube (Hcttube) decreases as the tube diameter decreases; Fahraeus and Lindqvist1323 found a decrease in apparent viscosity when tube diameter is reduced to below 300 microns (Fig. 9.17). Barbee and Cokelet1324 crudely approximated the experimental data using the following (slightly modified) empirical formula:
where a = 0.196, b = -0.117, and dtube is expressed in microns. Given a normal human male hematocrit of Hct = 46%, in smaller vessels this falls to Hcttube = 36% at dtube = 100 microns, 25% at 30 microns, and 13% at 8 microns. Surveying the literature, Gaehtgens1329 concludes that minimum hematocrit Hcttube generally occurs at dtube ~ 15-20 microns, which Cokelet1327 suggests marks the transition from multi-file flow to single-file flow among the red cells. Gaehtgens1330 also showed that the relative viscosity of human RBC suspensions reaches a minimum at about 5-7 microns.
Hematocrit decreases in small blood vessels for several reasons. First, a cell-free layer approximately equal to RBC radius exists near the wall, so the smaller the vessel, the larger the fraction of volume occupied by this layer, hence the lower the hematocrit.362 Second, a vessel side branch that draws mainly from the cell-free layer produces a lower hematocrit in that side branch (an effect called plasma skimming.1326) Third, red cells are elongated and oriented along the direction of shear flow, making it less likely that they will enter a side branch aligned perpendicular to the direction of flow (an effect at dtube <~ 29 microns,1327 sometimes called screening or steric hindrance.1328) All three factors should be less important for near-spherical rigid nanorobots that are smaller than RBCs, hence any reduction in nanocrit during passage through narrow blood vessels should be quite modest.
The velocity of a cell or nanorobot located on the axis of a small vessel is greater than the mean velocity of the suspending fluid,1328 but is always slightly less than the fluid in the immediate vicinity on the axis (Section 22.214.171.124). The simplest model is the stacked-coins model discussed by Whitmore,1315 wherein the nanorobot velocity vnano is given by:
Taking dtube = 8 microns and vflow = 1 mm/sec for a typical capillary (Table 8.2), a nanorobot with diameter Dnano = 2 microns has vnano = 1.88 mm/sec, which is faster than vflow but is slower than vmax = 2 mm/sec.
Last updated on 21 February 2003