536 
HEMODYNAMICS 
clear as to why hypertonic suspensions in- 
crease the apparent lethal tension. At isotonic 
conditions the fluid shear stress of short (less 
than 1 sec) duration that any mammalian red 
cell can withstand can be estimated from rV = 
constant 7 X 10-^ dyne-microns (10-^ 
dynes/cm- X microns^). For stress of long du- 
ration (>15 sec) the lethal stress should be 
half the above value.* 
For cell failure where the lethal membrane 
tension is required (e.g. trapped cells, filter 
lysis, etc.) a lethal membrane tension of cr = 
80 dynes/cm for short duration (t <1 sec) and 
15 dynes/cm for long duration (t >15 sec) can 
be used for all mammalian species. 
MASS TRANSPORT AUGMENTATION BY 
RED BLOOD CELL MOTION 
Diffusion augmentation of oxygen by red 
blood cell motion in a velocity gradient has been 
reported by Keller." Augmentation of platelets, 
white cells and other plasma solutes also depend 
on RBC motion.i*' " Predictions based on model 
studies for diffusion augmentation have been 
published by Collmgham.^ Figure 15 from his 
thesis permits an estimate of the range of im- 
portance of this effect. Simply read up from 
molecular diffusion coeflScient (or particle 
weight of solute) to the local shear rate. If the 
intersection occurs above the 10% augmenta- 
tion line an effect should be realized. 
In this section we wish to speculate on the in- 
fluence of species differences on this effect. Col- 
lingham's data» show that in model studies 
diffusion augmentation varies roughly as par- 
ticle diameter. Thus, if the red blood cells were 
all rigid, species differences in augmentation 
would be large. In the limit that the cells dis- 
tort into cylindrical shapes nearly parallel to 
the wall, the effect would depend on cylinder 
radius. We have seen in the section above that 
this radius is roughly the same for all mammals 
(about 1.2jLi) . Thus, augmented diffusion would 
be the same for all species at high shear rates 
where distortion can be expected. 
Until this diffusion phenomenon is studied 
experimentally (it is much too diflicult to treat 
analytically now) it would seem that model 
experiments at very high wall shear rates may 
predict diffusion augmentation for humans that 
would be the same or in proportion to cell size. 
In any event, to the extent that diffusion aug- 
mentation by red cell motion is understood at 
present it appears likely that the species dif- 
ferences if they exist will correlate with cell 
size. 
CELL CONCENTRATION NEAR WALLS 
Bugliarello, et al ^^'^^ show that the mean dis- 
tance in microns of the nearest cell to the vessel 
wall can be represented by 100/Hct for human 
cells. Goldsmith shows that cells in dilute cell 
suspensions are repelled from the wall strongly 
and move to the tube axis; hardened cells are 
less strongly repelled. Thus, it is inferred that 
the cell depleted layer near walls is determined 
by a balance of forces, repulsion due to a wall 
effect and dispersion due to cell-cell interactions 
in a velocity gradient. 
Brenner predicts the wall repulsion force to 
be proportional to velocity gradient squared.^'' 
Voss confirms this experimentally (see ref. 19) . 
Brenner also predicts wall repulsion varies di- 
rectly with deformability and as diameter to a 
power greater than 2. Physical arguments sug- 
gest that dispersion forces should decrease 
with increased deformability and be independ- 
ent of cell diameter. As we have seen deform- 
ability is related to cell size so that all the fac- 
tors that influence skimming layer depend upon 
size. 
All -these effects conspire to reduce the cell 
depleted layer as cell volume decreases. The 
increased cell wall interaction and enhanced 
mass transfer that results may be of significance 
in model experiments. 
RELATION OF MODEL EXPERIMENTS TO 
HUMAN BLOOD 
The red blood cell of man is one of the largest 
mammalian cells. In relation to the research 
animals — goat, sheep, cow, rabbit, and dog, the 
human RBC is the largest. The following dis- 
cussions, thus, will assume the RBC of all model 
experiments is smaller than the human RBC. 
At shear rates exceeding 50 sec"^, the viscos- 
ity of the model and human blood is about the 
same at normal species hematocrit. At low 
