p. L. BLACKSHEAR AND R. J. FORSTROM 
529 
30 cc. SYRINGE 
TP 
-10 cc. Blood 
Mole Leur Lok 
Fitting 
20 Gauge Needle 
(Inserts to Ice. in syringe) 
Female Leur Lok 
Fittings 
'01 ID. 
M 
_Mole Leur Lok 
Fitting 
yOn - Oil Valve 
NEEDLE ASSEMBLY 
ADAPTER 
=^=1 To Saline Supply 
STAINLESS STEEL 
SALINE SYRINGE 
-O- Ring Seal 
-0.95 
Exhaust 
Valve 
Return Plenum, 
2 Liters 
Supp ly 
Valve 
=(g)=> To Air Supply 
Pressure 
Regulator 
0.3 cm Micromeler 
"Needle Valve 
Supply 
Valve 
JUL 
HYDRAULIC CYLINDER 
4cm Bore and 15cm Stroke 
Activation Valve 
Oil 
Exhaust 
Valve 
Inlet Plenum, 
16 Liters 
LlJ 
zL 
Micro Switches for 
Velocity Measurement 
Timer 
Figure 8. — Schematic representation of jet fragility test 
facility. 
volume and area of the undistorted cell. In such 
a flow, we propose the criteria for lysis is tA = 
2 ttRo-, where A is cell area, R is cylinder radius, 
and o- is the membrane tension in dynes/cm. 
For all RBC, we expect A and V of the de- 
formed cell to equal the static values.^^ Letting 
L' be the length of the cylindrical portion of 
the cell, A = 2 ttRL' + 4 ttR^ and V = ttR^L' + 
4/3 ttRs. 
We have plotted Chien's data of cell area and 
volume for different species (Table I) and 
noted a surprising relationship (see Figure 11) . 
Even for the nucleated non-mammalian RBC, a 
unique relation, A = 3.9V*'-^\ adequately de- 
scribes the data. For comparison purposes, the 
relation A = 4, 84 V^/^ describes a sphere. The 
equation A = 1.6V can describe four of the five 
mammalian cells. (The sphericity index, ^ pro- 
portional to V^/^/A, may also be used to describe 
the data. Letting AccV, the index is propor- 
tional to V2/3-n_ The exponent, n, is greater than 
2/3, so the sphericity index increases monot- 
onically as cell volume decreases.) By using the 
area-volume relation and solving for R and L', 
we find R is virtually a constant and has a value 
of about 1.2/x. for all mammalian cells. This 
finding is not unexpected in reviewing the RBC 
transmission through sieves in Figure 5. 
Our force balance becomes cr = r A/ (27rR) oc 
tAoctV", where exponent n is about 1.0. We 
recall the jet result that tV = constant and thus 
cr = constant. To our knowledge, this is the 
first demonstration that all mammalian species 
may be endowed with RBC of the identical 
strength. 
The cylindrical model of the deformed cell 
aids in the clarification of other jet fragility 
results. RBC were tested in various tonicities 
and the results are shown in Figure 12. Ordi- 
nate t' is the ratio of hemolytic turbulent stress 
to the stress at tonicity 1.0. Note that the RBC 
in an isotonic environment are the most sus- 
ceptible to fluid stresses. 
Assuming (1) the cell area is 152ju,- and is 
independent of tonicity, (2) the isotonic volume 
is 90/>i'\ and (3) the osmotic volume change re- 
lation is V = 90 [(0.6/T) + 0.4], then R and 
total deformed length L = L' + 2R may be 
calculated. These dimensions are shown in Fig- 
ure 13 relative to the values at tonicity 1.0. 
In cases for which the areas is constant, 
o-ocr/R. Figures 12 and 13 are combined in Fig- 
ure 14 to examine this relation. Lethal mem- 
brane tension appears to be constant in osmotic 
swelling. However, the lethal tension increases 
with shrinking. The isotonic suspension appears 
to separate the two states of the RBC. It is un- 
