Difference in Geometry of Young and Old
Human Erythrocytes Explained
by a Filtering Mechanism
By Peter B. Canham
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ABSTRACT
A mechanism for the geometric difference between young and old human red
blood cells is proposed. It is assumed that the bone marrow produces a
population of cells with a range of sizes and shapes, but only those cells which
can pass through a theoretical 3.65//, cylindrical channel survive in the
circulation. The important geometric parameters of an erythrocyte are the area
and the volume. We suggest that as cells age they have a constant area but
swell in proportion to their original volume. This hypothesis of aging was tested
on 1,016 normal cells using the IBM 7040 computer. When the cells were
theoretically swelled by approximately 15%, the population of cells which could
still pass through the filter had a smaller mean area and volume and were more
osmotically fragile than the same cells before swelling. Young and old cells
were separated by centrifugation. The heaviest 10% of the cells (old cells) had
a lower diameter, area, and volume and higher sphericity index than the
lightest 20% (young cells). The calculated minimum filter diameter was not
significantly different. The good agreement between the predicted and
observed changes in cellular geometry between young and old cells provides
supporting evidence that a cylindrical filter exists in the circulation and may
play a role in determining the life span of the erythrocyte.
ADDITIONAL KEY WORDS
minimum cylindrical diameter
• For years many investigators have been
inquiring about the destruction of red blood
cells. Theories to describe the early stages of
red cell breakdown range from cellular
fragmentation to physical trapping. Canham
and Burton (1) recently demonstrated that
the linear relation between the area and
volume of single erythrocytes in a population
of cells was evidence for a filtering network in
the circulation. Their results indicated that
somewhere in the circulation the red cell is
required to squeeze through very narrow
cylindrical channels. If the cell increased in
volume so much that it could no longer get
through these hypothetical channels, it would
From the Department of Biophysics, Medical
School, University of Western Ontario, London,
Ontario, Canada.
This investigation was supported by a grant from
the Life Insurance Medical Research Fund.
Received February 27, 1969. Accepted for publication May 15, 1969.
Circulation Research, Vol. XXV, July 1969
area and volume
theoretical aging
centrifugation
get trapped and eventually hemolyze. The
hot-dog shape is the most suitable shape for
the flexible red cell to adopt when it is
required to navigate narrow channels (less
than 4(JL). Canham and Burton suggested that
the filter was located in the spleen. The
importance of the spleen in removing defective cells is well established (2, 3), but the
function of the spleen in removing normal
senescent cells is poorly understood (4). Ham
(5) suggested that the spleen functions like a
filter and the present paper provides a
plausible explanation of this function. However, the evidence here does not directly assess
splenic function.
The filtering experiments by Prothero and
Burton (6) and Gregerson et al. (7) provide
supporting evidence for the value of the
calculated mean filter diameter of 3.33/^ (1).
The abrupt increase in viscosity for small
tubes, reported by Dintenfass and Read (8),
also suggests that the minimum cylindrical
39
40
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diameter is an important dimension. The present paper will show how the relation of the
geometry of the erythrocyte to a cylindrical
filter can play an important role in determining the survival of red cells in the circulation.
Young and old cells1 can be separated
according to their differences in osmotic
fragility (9) or by their differences in density
(10). Old cells are both osmotically more
fragile and more dense. A review of the data
regarding the geometry of young and old cells
reveals .that old cells are smaller in area,
volume, and diameter and are more spherocytic (more osmotically fragile) (11, 12).
Prankerd (13) reported that old cells contain
15% less lipid, possibly accounting for the
increased density associated with age.
We are proposing a biophysical mechanism
for red cell aging in which the cells swell as
they age, in proportion to their original
volume. This implies a contradiction because
old cells are smaller than young cells.
However, a theoretical narrow cylindrical
filter imposes a restriction on the circulating
cells in such a way that the larger cells are
selectively removed earlier, thus explaining
the seeming paradox. The gradual increase in
volume might result from an increased membrane permeability or to a decreased active
transport. Tosteson and Hoffman (14) demonstrated that sheep cells with either high or
low potassium content swell when the active
transport mechanism is blocked. A change in
either the membrane permeability or the
active transport mechanism would lead to a
new equilibrium volume (15). Zajicek (16)
also made the assumption of a constant area
with increasing volume as cells age. However,
in his hypothesis each cell would be eliminated when it reached a constant critical
volume, and not a volume dependent on the
cell's original volume as we propose. Ponder
(17) conjectured that young cells were thin
cells and gradually swelled with age, but he
did not enlarge upon this hypothesis.
The part played by the changing geometry
'The age of an erythrocyte has been used to mean
the time elapsed after the cell's introduction into the
circulation.
CANHAM
would complement the biochemical and biophysical changes reported in the literature for
senescent erythrocytes (18-20) and might also
explain some of the changes in cellular life
span in disease.
Methods and Materials
1. The minimum cylindrical diameter is twice
the radius, r, which satisfies the following
equation: V = Ar/2 - 2TTT3/3 (equation 1) (1).
Both the volume, V, and area, A, are parameters
of the equation. For each A and V there is a
different r, found by Newton's method. (Although there are three real solutions to this cubic
equation for the range of values of A and V, only
one is meaningful.)
2. A large number (1,016) of single erythrocytes from seven healthy subjects have already
been photographed and measured to obtain the
areas, volumes, and other geometric parameters
(1). The areas and volumes were obtained by the
theorem of Pappus. Although the mean volume is
higher than that reported by the method oi:
centrifugation, the importance of the data is the
knowledge of the area and volume of individual
cells rather than the averages of populations.
3. The 1,016 cells were considered to be one
population of cells representing the full range of
cellular ages. Each cell was allowed to swell
theoretically by a percentage of its initial volume.
The minimum cylindrical diameter' was then
recalculated from the new volume and the old
area, using equation 1. If the cell was then too
large to pass through a 3.65/JL channel without
stretching its membrane, then the cell was
eliminated from the population. At each degree of
swelling, the means of the areas and volumes of
the cells which could still pass through the 3.65|u.
channel were determined. The size of the
population diminished as the degree of theoretical
swelling was increased. At 18% swelling the
population was reduced from 1,016 to 14.
Numerical calculations and statistical routines
were done on the IBM 7040 at this university.
Graphic results were obtained from a Calcomp
plotter, model 563.
4. It is important to compare the effect of the
theoretical aging process on erythrocytes with the
changes in geometry measured experimentally.
For this the geometry of young and old cells was
studied using the hanging-drop technique described in detail previously (1, 21). Cells from
one subject (male, age 26) were analyzed. Approximately 50 cells, from both the young and the
old fractions of cells, were photographed on edge
and measured. The two fractions were separated
according to the method outlined by Danon and
Marikovsky (10); a mixture of phthalate esters
Circulation Research, Vol. XXV, July 1969
41
GEOMETRY OF YOUNG AND OLD RED BLOOD CELLS
220
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70
90
110
130
150
170
190
CELLULAR VOLUME
FIGURE 1
T/ie computer plot of area versus volume for 1,016 red blood cells from seven normal subjects,
aged 5 to 71. The straight line is for the 95% cut-off diameter, 3.65/i, determined by equation
1 in the text.
(immiscible with water) of known density was
put with the whole blood in a microhematocrit
tube. Cells were spun at approximately ll,000g
for 30 minutes in a microhematocrit centrifuge in
a cold room at 10°C. Slightly different mixtures
of the esters were needed than were reported by
Danon and Marikovsky, (10), probably because
we used human blood and centrifuged the cells in
the cold room. (They studied the red cells of
rabbits.) The old cells in the heavy fraction were
hypersensitive to glass; they became crenated
upon approaching glass and reverted to the biconcave away from the coverglass. Neither the use of
sealing putty nor flaming the tip to seal the end
altered this phenomenon. For this reason plastic
coverslips were used and the problem was
avoided. The young cells were not nearly as
sensitive to the coverglass. The specific gravities
of the mixed esters were approximately 1.090 and
1.102, which separated a young and old fraction
representing approximately 20% and 10%, respectively, of the cell column.
Results
1. Figure 1 demonstrates clearly the linear
area-volume relation. The normal areas and
volumes were plotted by computer plotter and
the 95% cut-off line (3.65/i) was drawn. (The
Circulation Research, Vol. XXV,
July 1969
same data were plotted differently before [1]
because the plotter was not available at that
time.) The unexpected linearity of the areavolume plot forms the fundamental evidence
for the cylindrical filtering mechanism which
is proposed. It must be emphasized that the
diameter of the cylindrical filtering network
fixes not only the slope but also the intercept
of the straight-line relation of area and
volume. In addition, there is the special
significance of the 95% cut-off line, which
coincides with the straight right margin of the
data on the area-volume diagram. The left
edge is not as linear.
The proposed aging process involves cellular swelling with no change in area. The
location of a swelling cell on the area-volume
graph moves to the right parallel to the
volume axis. When it reaches the 95% line, the
cell is eliminated from the circulation. This
principle is presented schematically in Figure
2. Two groups of cells of different volumes are
shown before and after swelling. The larger
cells would move further toward the elimina-
42
CANHAM
200
160
9 5 % cut-ail
line
120
•
young
O after
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80
60
100
Volume
cells
swelling 10 %
140
180
FIGURE 2
A schematic interpretation of how the cylindrical
filter can account for the decrease in area and volume
when each cell swells. Theoretically any cell is eliminated from the circulation if its location on the graph
falls to the right of the line.
tion point if each group of cells underwent the
same degree of swelling. In this example, 10%
swelling has eliminated two large cells and
only one small cell. The outcome is a reduced
mean cell area and volume, even though the
volume of each cell increased. The purpose of
this research was to test the validity of this
hypothesis by imposing the aging process on
the data for normal cells.
2. Table 1 presents the computed results of
swelling the 1,016 normal cells by 18% in 2%
increments. The first line in the table indicates
the normal values before filtration. The second
line shows the result of theoretical filtration
without swelling. As the swelling increased,
the mean area decreased, clearly indicating
the preferential elimination of the larger cells.
After an initially slight increase, the mean
volume of the surviving population became
less also. The sphericity index increased,
meaning that the surviving population had an
increased osmotic fragility. (The sphericity
index has values from zero to unity and is a
quantitative index of thickness or thinness
[1].)
3. The results of the hypothetical aging
mechanism are consistent with the study of the
geometry of young and old erythrocytes.
Table 2 provides the data for the geometrical
parameters of young and old cells separated
by the phthalate ester method of Danon and
Marikovsky (10). The young cells (top 2d% of
the hematocrit tube) are larger with respect to
diameter, area, and volume and are less
TABLE 1
Mean Areas and Volumes of a Normal Population of Red Cells after Varying Degrees of Swelling subsequent Passage through a Theoretical Cylindrical Filtering System (Tube Diameter
3.654?)
Volume
Sphericity*
index
Population
size
138.2 ± 17.8
105.8 ± 17.5
.782 ± .023
1010
137.5
136.9
135.6
134.4
133.1
131.7
128.7
126.8
124.6
121.0
104.6
105.6
105.8
105.8
105.4
104.7
102.4
101.2
99.5
96.0
.781
.790
.798
.805
.812
.817
.824
.829
.835
.840
Area
Percent swelling
Before filtration
After filtration
ot
2
4
0
8
10
12
14
16
18t
±
±
±
±
±
±
±
±
±
±
16.9
16.3
15.4
15.1
15.1
15.4
15.8
16.4
16.0
17.3
±
±
±
±
±
±
±
±
±
±
16.1
15.6
14.7
14.2
14.1
14.4
14.6
15.0
14.4
14.8
±
±
±
±
±
±
±
±
±
±
.027
.020
.025
.024
.024
.024
.026
.027
.028
.033
900
900
801
655
489
317
180
98
46
14
Values are means ± SD.
*4.84X Vol 2/3 /Area. t Only 95% of the 1,016 cells can pass the filter since 3.05M is the
95 percent cut-off point. J One cell became a sphere.
Circulation Research, Vol. XXV,
July 1969
43
GEOMETRY OF YOUNG AND OLD RED BLOOD CELLS
TABLE 2
Geometric Parameters of Young and Old Cells Separated by Ultracentrifugation
Sample
Sample size
Diameter Ou)
Coeff. of variation
Area (M2)
Coeff. of variation
Volume (M3)
Coeff. of variation
Sphericity index
Coeff. of variation
Minimum cylindrical diam. (M)
05% Cut-off (M)
Top 20% of cells
Bottom 10% of cells
55
52
8.35 ± 0.48
±5.7%
14S.0 ± 15.9
±10.7%
112.9 ± 10.0
±14.1%
0.75S ± 0.019
±2.0%
3.27 ± 0.14
3.550
7.8G ± 0.51
±G.G%
133.1 ± 10.2
±12.2%
9S.S ± M.S
±14.9%
0.777 ± 0.020
±3.3%
3.23 ±0.13
3.493
P value
< 0.001
<0.00l
<0.001
<0.001
<0.2
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Values are means ± SD. P value derived by /-test of significance between the means. Subject
was a 2G-year-old male.
soherocytic than the old cells (bottom 10% of
the tube). The shift of mean sphericity from
07T58 to 0.777 corresponds to a shift in osmotic
fragility of 0.02% NaCl. Although this is only a
slight change, it is significant and is similar to
the change reported by Prankerd (13).
The one parameter which did not change
significantly between the young and old cells
was the minimum cylindrical diameter. An
examination of the area-volume graphs for the
young and old cells (Fig. 3) reveals the same
linearity of the right edge of the data as
Figure 1. Although there are only 50 cells in
each age group, it seems enough to provide
good supporting evidence for the cylindricalchannel filtering theory.
Discussion
The experimental results of the geometric
difference between young and senescent erythrocytes agree with those of other investigators (11, 12) and also with the results of the
proposed aging mechanism. In the experimental study, the difference between the two age
groups was approximately 15% with respect to
both area and volume. There are three
possible explanations for the discrepancy
between the model and experiment. Firstly,
the mechanism of aging was imposed on
normal cells of all ages and should have been
imposed on young cells only. (Unfortunately,
we do not have enough data to do this.)
Circulation Research, Vol. XXV,
July 1969
Secondly, the geometric difference between
young and old cells was determined for only
one subject and using one technique. Thirdly,
other mechanisms operating at the same time
might affect the geometry of aging erythrocytes. For example, we did not consider the
effect of the stiffness of the membrane.
Because a large cell must undergo relatively
greater shape changes than a small cell when
navigating the circulation one might envisage
the large cell to be more mechanically fragile
and hence more susceptible to damage and
lysis. In this way also, large cells would be
preferentially eliminated from the circulation.
From this experiment it is possible to approximate the swelling an average cell can tolerate
before its own corpulence results in its being
trapped and removed. We feel that between
10% and 20% swelling could explain the
geometric differences between young and old
cells.
Zajicek's proposed model (16) for the aging
of red cells was based also on the cell's
constant area with an increasing volume.
However, he considered that a cell would
reach a critical volume independent of the
cell's original volume. By his mechanism there
is no way of selectively removing the larger
cells, and thereby accounting for the decreased cellular area and volume with age. We
proposed that the cell's area determines what
that critical volume will be and is therefore
44
CANHAM
200
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80
100
120
140
i60
mo
160
CELLULHR VOLUME
200
80
100
120
that, therefore, the cellular density could be
replaced by cellular age. Other investigators,
using radioactive tags and various density
gradient techniques, have suggested the linear
density-age relation but the scatter is very
great (22). Therefore, a particular fraction
separated by centrifugation is representative
of a similar age fraction but is probably
contaminated with cells of many other ages.
The proposed filtering mechanism might
assist in the understanding of hereditary
spherocytosis, a disease of the blood characterized by small, spherocytic red cells. The
bone marrow might produce a normally sized
population which has the defect of cells with
leaky membranes (23) causing an equilibrium
volume higher than normal. Only the smaller
cells which can tolerate a greater percent of
swelling could still pass the cylindrical filter
(probably located in the spleen). The success
of splenectomy in such cases might be
explained by the removal of the filter. The
remaining filtering system (the reticuloendothelial system outside the spleen) might not
have such a narrow filter and therefore permit
the circulation of a greater percent of the cells
produced. We have just begun the study of
the geometries of cells for subjects with and
without hereditary spherocytosis, with and
without splenectomies.
CELLULRR VOLUME
References
FIGURE 3
The area-volume graph for the young and old human
red blood cells separated hy the method of Danon
and Marikovsky (6). Although the old cells are
significantly smaller with respect to area and volume,
both the young and old cells have the same 95% cutoff line.
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Difference in Geometry of Young and Old Human Erythrocytes Explained by a Filtering
Mechanism
PETER B. CONHAM
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Circ Res. 1969;25:39-45
doi: 10.1161/01.RES.25.1.39
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