© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.4.1.6 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 (Hct_tube) 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:

{Eqn. 9.63}

where a = 0.196, b = -0.117, and d_tube is expressed in microns. Given a normal human male hematocrit of Hct = 46%, in smaller vessels this falls to Hct_tube = 36% at d_tube = 100 microns, 25% at 30 microns, and 13% at 8 microns. Surveying the literature, Gaehtgens¹³²⁹ concludes that minimum hematocrit Hct_tube generally occurs at d_tube ~ 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 d_tube <~ 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 9.4.1.5). The simplest model is the stacked-coins model discussed by Whitmore,¹³¹⁵ wherein the nanorobot velocity v_nano is given by:

{Eqn. 9.64}

Taking d_tube = 8 microns and v_flow = 1 mm/sec for a typical capillary (Table 8.2), a nanorobot with diameter D_nano = 2 microns has v_nano = 1.88 mm/sec, which is faster than v_flow but is slower than v_max = 2 mm/sec.

Last updated on 21 February 2003