Analysis and Interpretation of the Impedance
Blood Coagulation Curve
AMIRAM UR, M.D.
Ur, Amiram: Analysis and interpretation of the impedance
blood coagulation curve. Am J Clin Pathol 67: 470-476,
1977. The impedance coagulation curve represents the relationship between the changing impedance of a clotting blood
sample and the impedance of a heparinized control sample.
The impedance method is independent of the conventional
technics for coagulation studies and offers, therefore, new
perspective into the study of the coagulation process. The technic provides accurate measures of the whole-blood clotting time
and clot retraction time and has higher diagnostic power
than current methods for whole-blood clotting time determination. The purpose of this study was to reveal the mechanism
of the impedance changes and to explore the curve for additional information relevant to clinical or theoretical problems.
It is established that before clotting the curve reflects
"lag" and "activation" phases that strongly suggest a
"cascade mechanism" of coagulation activation. The mechanisms of other parts of the curve are explained and their
possible relevances to the coagulation process are discussed.
(Key words: Blood coagulation; Clotting time; Clot retraction; Blood sedimentation.)
THE IMPEDANCE METHOD of monitoring blood
coagulation continuously compares the electrical impedance of a c|otting blood sample with the impedance
of another part of the sample that is heparinized to
prevent clotting. 8_, ° Compared with other methods of
whole-blood clotting time determination, the impedance method is more reproducible 5 and has a higher
sensitivity to detect bleeding disorders. 1 These features
are due to the accurate standardization of the measuring cells, the graphic clearly defined end points,
and the elimination of mechanical movement, which is
a major cause of irreproducibility in other technics.
The test yields a curve relating to the entire coagulation process. Clotting and clot retraction are two
details of the curve that may contain additional valuable information. The interpretation of the complete
curve requires analysis of the mechanism of its production by monitoring the absolute impedance changes in
the clotting and control samples and relating these
changes to the coagulation curve as normally perReceived March 25, 1976; accepted for publication April 22,
1976.
Address reprints to Dr. Ur.
Division of Bioengineering,
Clinical Research Centre, Watford Road,
Harrow, Middlesex HA1 3UJ, England
formed, on the one hand, and to known biologic
and physical phenomena on the other. However, in
measuring absolute impedance the advantages of the
comparative impedance measurements in cancelling
out noise and drift are lost, and it is essential,
therefore, to eliminate or reduce such noise and drift
and carefully assess any residue. Moreover, since the
analysis requires comparison of curves, it is necessary
also to standardize the measurements as if they were
obtained simultaneously using one machine. This required solving many technical difficulties, which
caused the delay between the first publication in 19708
and the present work.
Materials and Methods
Two coagulometers, each having three independent
channels (Fig. I), were used. The conductivity
cells in matched pairs were incorporated in plastic
cassettes (Fig. 2) that had conduits for filling with
blood and air escape. One of the cells in each cassette
was preheparinized and served as control. During the
test the cassette, placed in a temperature-controlled
holder, was maintained at 37 C with stability better
than 0.01 C. The amplified and rectified output from
the measuring bridge was recorded on a multichannel
chart recorder and stored also in a data-logging device.
The absolute impedance of the conductivity cells could
be determined at any time by substituting them with
resistor boxes through external sockets.
Blood was collected from the antecubital veins of
healthy donors using a 2-ml plastic syringe and 19gauge needle. The precautions necessary in collecting
blood for coagulation studies were carefully observed. 12 The time the syringe was withdrawn was
marked on the recorder as time zero. After discarding
the needle and expelling a few drops, the syringe was
gently tilted six to eight times to ensure even distribu-
470
Vol. 67 • No. 5
471
ANALYSIS OF COAGULATION CURVE
FIG. 1. The three-channel
Blood Coagulometer.
tion of the blood cells. The conductivity cells in the
six holders were then filled directly from the syringe.
The coagulation curve, as normally performed, was
recorded on channels I and 2, each presenting continuous comparison of the impedances of the clotting
and unclotting samples. Soon after filling of the conductivity cells, the bridge was rebalanced to correct
forany residual minordifferences between the matched
cells and then offset by a predetermined value so that
the curves would be recorded on one side of the zero
line. In channels 3 and 5 the impedance of each
clotting sample was monitored in absolute values by
substituting the control cell with a resistor box. The
bridge was balanced by adjusting the box at the beginning of the test and was not offset as the results
were expected to be on one side of the zero line.
Similarly, the impedance of each respective control
cell was monitored on channels 4 and 6. The cells to
be compared (the two cells in channel 1, the two
cells in channel 2, the cells each in channel 3 and 5,
and channel 4 and 6) were matched in their physical
characteristics so that their impedances when filled
with standard solution (0.25% NaCI in water) at 37 C
differed by less than 0.2%. Similarly, the temperatures
of the cell holders in the channels to be compared
(3 against 5 and 4 against 6) were adjusted to within
0.05 C of each other.
The effect of blood sedimentation was determined in
a test in which the absolute impedances of six clotting
samples and six unclotting samples were monitored.
At predetermined intervals consecutive cells were ro-
tated by one-half turn to reverse the direction of blood
sedimentation. As this also disturbed the temperature
stability, control tests in which the procedure was
followed without rotating the cells were performed.
The conductance of the heparin in the preheparinized
control cells was determined by measuring the cells'
impedance using the standard solution and repeating
the measurement after washing the cells. The drift
caused by the heparin was assessed also by obtaining curves from tests where the cassettes were filled
with the standard solution.
The effect of evaporation of water from the conductivity cells was assessed by monitoring the absolute
km
FIG. 2. The cassette of conductivity cells. The cell marked H is
preheparinized. The cells are glass capillaries with the electrodes
plated at each end of the lumen (shaded area). The plating
on the external surface extends over the edge of the capillary and is
continuous with the inner electrodes; it serves as electrical contact with the bridge circuit.
472
UR
FIG. 3. Six simultaneous curves obtained from parts of the same
blood sample. The ordinate represents the amplified and rectified
bridge output. Curves a and b are coagulation curves as normally performed where the bridge output represents the relationship
between the changing impedance of the clotting and the unclotting
samples. In curves c and e the output reflects the absolute
impedance changes of the clotting samples and in d a n d / of the
unclotting samples.
impedances of cells filled with the standard solution,
which has a specific impedance similar to that of blood.
After allowing 10 minutes for temperature equilibration, the impedance changes were related to evaporation.
A.J.C.P. • May 1977
mum of curves a and b the clotting samples were about
230 (1 lower than the unclotting samples.
The impedance of the unclotting samples declined
exponentially with time to a limit in about two
hours. However, when the cells containing these samples were rotated to reverse the blood sedimentation,
the impedance immediately increased and then gradually decreased (Fig. 4). When the rotation was early
in the test (at 7 minutes), the impedance increased to
its level at the beginning of the test. When the rotation
was later in the test, the impedance increase was even
higher, but it did not reach the cell's initial impedance.
Following the sharp increase on rotation, the impedance
declined as at the beginning of the test, but the decline
was faster when the rotation was later in the test.
Although the impedance of the clotting sample also
declined with time, the process was not homogeneous,
and distinct changes of the rate of decline were obvious
(Fig. 3, c and e). Rotation of such cells caused a
much smaller increase in impedance (Fig. 5) than that
observed with the unclotting samples, even when the
rotation was as early as at the fifth minute. The
effect was the same during the entire test and was
also obtained when the procedure was repeated without
actually rotating the cell, indicating that it was caused
mainly by temperature changes.
To complete the analysis, the different sources of
drift and noise were carefully evaluated:
Results
In each of the main experiments, six tests were
performed simultaneously using samples from a single
blood collection. Curves a and b in Fig. 3 are coagulation curves as usually obtained, where the machine
output, in volts, changes with the relationship between
the impedances of the clotting sample and the unclotting control. In curves c and e the output relates
directly to the changing absolute impedances of the
clotting samples and in curves d and/to the impedance
changes of the unclotting control samples. Curves a
and b start at about 1.5 volts because of the deliberate
offsetting of the bridge. This was not necessary with
curves c, d, <?, and/, which are monotonic and were
therefore started at zero.
At the setting of the test the impedance of each of
the samples c, d, e, and/was around 10,300 fl(±0.4%).
After 40 minutes, the impedances of the clotting
samples had dropped to 7,900 O and of the unclotting
samples to 8,640 Q, (±0.5%). At the time of the mini-
6
S
10
15
20
25 Mimitis
FIG. 4. The effect of blood sedimentation on the impedance of
unclotting samples is demonstrated in the four superimposed curves
where each cell in turn was rotated {arrow) to reverse the sedimentation. During the first 10 minutes the initial cell impedance
could be so restored. The dotted line shows the effect of temperature disturbances as the cell was replaced without rotation.
ANALYSIS OF COAGULATION CURVE
Vol. 67 • No. 5
The conductance of the dissolving heparin was 2.4
x 10~fi mhos; this decreased the impedance of a
10,300-fl control cell by about 70 fi and caused a drift
of 220 mV in the first 2-3 minutes (Fig. 6, h).
Temperature equilibration caused drift in the first
3-4 minutes of the test. A sample at 25 C that caused
a drift of 1.5 volts in the first minute caused no
significant drift in the third or fourth minute (Fig.
6, g). In practice, much of this drift is cancelled
out by the opposing cell. Moreover, blood is usually
introduced into the conductivity cells within 1 or 2
minutes of its collection, and is unlikely to cool
below 33 C; hence, the initial drift in the absolute
impedance curve is unlikely to exceed 450 mV in the
first few seconds.
Evaporation of water increases the electrolytic concentration and decreases the impedance by 0.08% per
hour. Its effect on a 10-K.O sample results in a drift
of 250 mV/hour (Fig. 6,j). The rate of evaporation
is fairly constant in the first few hours and the drift
is therefore linear. It has no significant effect on the
coagulation curve as the drifts from the opposing
cells largely cancel out.
The effects of the minute temperature fluctuations
of the cell holder (less than 0.01 C) on the blood
impedance (temperature coefficient of about - 2 % per
degree C), the possible effects of polarization, the
heating from the current through the cell, and the electronic drift of the circuits were each found to be less
than 6 mV per hour and are therefore negligible.
Discussion
The main objective of this work was to monitor and
analyze the absolute impedances of the clotting and
473
FIG. 5. The effect of sedimentation on the clotting sample is
much smaller than that on the unclotting sample (Fig. 4). even as
early as the seventh minute.
control samples and to relate the results to the coagulation curve on the one hand and to known physical
and biologic events on the other. To check the validity
of such analysis, coagulation curves were constructed
from the absolute impedance curves as follows:
G(o — K — [R,D — Cm]
(1)
where G(t) is the constructed coagulation curve (Fig.
7, in and /;), R(l) is the absolute curve of the clotting
sample (Fig. 3, c and e), C(t) is the absolute curve of
the control sample (Fig. 3, d and/) and K is a constant
FIG. 6. The effects of noise and drift compared with a normal coagulation curve a, and
curve from unclotting sample c. Curve h is drift
caused by the dissolving heparin; g is drift
caused by temperature equilibration; j is drift
caused by water evaporation and the cumulative
effect of temperature fluctuations in the cell
holder, and possible effects of polarization,
and drift from the electronic circuit. Most of
the drift represented by curves g and j is cancelled out by a similar drift in the opposing
cell in the circuit.
20 Minutas
474
UR
Volts
2.5 i -
//
2.0 -
15
•
0
/~^\
5
'
\
\\
\ vn
/ /
10
15
20
25
30 Minutes
FIG. 7. Comparison of coagulation curves as normally performed, a and b (as in Fig. 2) and two curves, m and n, constructed
from the absolute impedance curves c; e and d;f (Fig. 2).
representing the initial offset voltage of the bridge.
The curves so constructed (Fig. 7, m and n) are very
similar to the coagulation curves (Fig. 3, a and b) shown
also in Fig. 7 in dotted lines. The minima, which
appeared at 9.7 minutes, were within 0.3 minutes on
all four curves, and the maxima, at 23 minutes, were
within 1 minute on three curves, although on curve b
the maximum was 5 minutes earlier. The curves are
similar also in their amplitudes.
The coagulation curves start 1-2 minutes after blood
collection, which is the time required to fill the cells
and set the machines. The first 3 minutes, counting
from blood collection, are governed by noise and
drift mainly from the heparin solution and temperature
equilibration (Fig. 6, h and g). When the noise subsides, the coagulation curves tend to become horizontal, showing that there is no significant difference
between the impedance changes in the clotting and
the unclotting samples and therefore no obvious specific activity in the clotting sample. This "lag phase,"
which lasts 2 to 3 minutes, was hardly noticeable
in the earliest published experiments in 1970,89 and
it was only with the progress in controlling drift and
noise that it became obvious in 197411 and more so in
1975.5
At about 5-6 minutes, the coagulation curves suddenly start declining towards the minima.
It is obvious that the impedances of both the clotting
and unclotting samples decrease with time throughout
the test (Fig. 3, c, d, e, and / ) . The curve from
the control cell is monotonic and the impedance decline is gradually slowed, to end after about two hours.
When checked graphically, it closely fitted a cumulative log-normal distribution curve. This strongly
suggests that it is dominated by one process, such as
A . J . C . F . • May 1977
blood sedimentation, which leaves increasing layers of
plasma whose conductivity, 30-40 times that of blood
cells,7 short-circuits the upper part of the electrodes
in the conductivity cell. This assumption was confirmed by reversing the direction of sedimentation,
which reversed the impedance change (Fig. 4). At
least until the seventh minute of the test, the initial
impedance could be restored, but later, although the
effect was stronger, the original impedance value could
not be restored, as by that time, instead of discrete
blood cells, aggregates or even layers of cells moved
together, causing a shift of the plasma layer from
the bottom of the conductivity cell to its top. This
also explains the faster rate of these impedance changes
later in the test.
On the other hand, the decreasing impedance in
the clotting sample is accelerated and decelerated
several times during the test (Fig. 3, c and <?)• Between
the fifth and ninth minutes it is obviously faster than in
the control cell (Fig. 3, d and/) and causes the coagulation curve to descend towards the minimum (Fig. 7, in
and n). This acceleration, which is the most intriguing part of the curve, is unlikely to be caused by
faster cell sedimentation; in fact, the results in Fig. 5
show that sedimentation may be slowed even before
the appearance of the clot. The accelerated impedance
decline in the clotting sample must therefore relate
to the biochemical reactions that take place before
the clotting. Although it is impossible to relate it with
certainty to the prevailing theories on blood coagulation, yet the lag phase and the sudden burst of activity,
probably of exponential nature, are very suggestive
of a "cascade mechanism."2 The absence of this acceleration in severe hemophilia1,5 further suggests that
it depends on the activity of factor VIII.
The observation of this acceleration and its independence of the sedimentation process indicates the
possibility of extending the impedance method to
studies of plasma. However, because of the shorter
time scale of the reactions, the results may appear in
the noisier part of the curve. The necessity to add
and mix reagents would certainly increase such noise.
The accelerated impedance decline in the clotting
sample reaches its peak at about the eighth minute
(2 minutes before clotting). This does not necessarily
mean that the specific reactions responsible for it are
completed, as the acceleration may also decrease
as the result of the beginning of another process,
such as an increase in viscosity prior to coagulation,
or decrease in the number of charged particles caused
by polymerization.
From the eighth minute, the rate of the impedance
decline of the clotting sample is slowed to less than
ANALYSIS OF COAGULATION CURVE
Vol. 67 • No. 5
its rate in the control sample. At about the tenth
minute the rates are identical in the two samples
and the minimum in the coagulation curve is produced.
This is the most important point of the curve, as
empirically it was found to correspond to the clotting
time.8-11 In the coagulation curves as normally recorded it is possible to define the minimum to within
6 seconds. Such resolution is superfluous to current
clinical requirements but is instrumental in establishing
the reproducibility of the test and its coefficient of variation, which was 9%.5 By comparison, the coefficient
of variation in the thrombelastographic method of
whole-blood clotting time determination is 14%, and
those for the Lee and White method and its modifications 21 to 24%. Recent data show, however, that
the dispersion in the impedance technic is more likely
to be 6%. The clinical significance of this accuracy
was demonstrated by Arnhold and associates in a study
of 29 patients with known coagulation disorders and
18 normal donors.1 Each subject had his coagulation
time determined by the thrombelastograph and by the
impedance method. All the normal samples and two of
the abnormal samples appeared as normal in both tests.
All the other 27 abnormal samples appeared as abnormal on the impedance test, yet six of them
still appeared as normal on the thrombelastograph.
This accuracy and sensitivity allowed also demonstrating and measuring the hypercoagulability caused by
major surgery.6
It was noticed in previous work that a delay of as
long as 2 minutes between filling the clotting cell and
the control cell did not affect the time of the minimum.
This was puzzling, as such delay certainly disturbs the
synchronicity of processes such as blood sedimentation. This observation is now easily explained by the
present results, which show that between the fifth
and twentieth minutes the control curve is fairly
linear. As at the points of maximum and minimum of
the coagulation curve the first derivative of equation 1
is zero:
G'(t> =
—
R'a> + C'd) = 0
and as at the region of the minimum C(t) is linear, its
first derivative is constant. In the said range, therefore,
the control curve does not affect the timing of the
minimum.
The climb of the coagulation curve after the minimum is caused by the continued slowing of the impedance decrease of the clotting sample compared with
its rate in the control sample.
At about the sixteenth minute, 6 minutes after clotting, the declining impedance of the clotting sample
475
is again accelerating, but only for 1 or 2 minutes.
This acceleration, which does not quite bring it to the
decline rate of the control sample, causes some flattening of the coagulation curve. The reaction reflected
by this second acceleration is obscure; there are not
yet enough data to relate it to activities such as
that of factor XIII.
Around the eighteenth minute, the impedance of the
clotting sample reaches a value that stays constant for 3
to 4 minutes. Probably by that time most of the activities in the clotting sample have ceased, including
any cell sedimentation. It is, of course, possible also
that the impedance stays constant because of dynamic
balance between two or more reactions that have
opposing effects on the impedance, but the likelihood for such balance to sustain over several minutes in
the many different samples checked is small. While
the impedance of the clotting sample remains constant the impedance of the unclotting sample continues
its decline as governed by the sedimentation rate,
and its effect on the coagulation curve, now unopposed
by the clotting sample, is expressed in the increased
steepness of the ascending curve in minutes 18 to 21,
which therefore reflects the blood sedimentation rate.
At about the twenty-second minute, the impedance
of the clotting sample starts decreasing again. Within
a minute or two the rate of impedance decline overtakes that of the unclotting sample and produces
the maximum in the coagulation curve. It is apparent
that a new process has begun, and it was relatively
easy to confirm that this was clot retraction,10 and that
the time of the maximum therefore represented the
clot retraction time. The forces causing the retraction probably develop with the formation of the clot,4
but their development is not reflected in the impedance changes as presently measured. These forces
remain ineffective until they overcome the forces
adhering the clot to the glass surface. The clot retraction forces then tear the clot from the glass surface and release layers of conductive serum that decrease the impedance of the clotting sample. The interplay of these forces causes a stepwise retraction of
the clot, which is expressed as waves in the declining branch of the coagulation curve after the maximum. The process is accelerated with time and, with
the now-slowing sedimentation in the unclotting
sample, causes a steeper decrease in the coagulation
curve. The adherence of the clot to the glass depends
strongly on the properties of the glass surface, and it is
the difficulties in standardizing this surface that cause
the occasional odd timing of a maximum (Fig. 7, b).
Within about an hour, clot retraction ends and the
impedance of the clotting sample reaches a steady
476
value (not shown in the figures). If by this time sedimentation still proceeded in the unclotting sample,
a second minimum would appear in the coagulation
curve; otherwise, the curve would reach a constant
value and would proceed horizontally until clot lysis
began. This was not included in the present study.
From the above analysis it is obvious that the impedance changes observed depend on the configuration
of the conductivity cell.10 This is because the blood
sample, whether clotting or not, is not a homogeneous
conductor. The results depend also on the orientation
of the conductivity cells; had the present cells been
upright instead of horizontal, the sedimentation would
have increased rather than decreased the impedance
because the resistances of the plasma and the sediment would appear in series between the electrodes
rather than in parallel. Statements attributing definite
impedance changes to clotting blood samples are
therefore meaningless unless the measuring system is
carefully defined, and such statements have been
a source of conflicting reports.3 Since the impedance
changes are not standard, the choice of the measuring system and, in particular, of the conductivity cell
should be guided by the aim to manifest characteristics
that can be of value to theoretical and practical
clinical requirements.
A.J.C.R • May 1977
UR
Acknowledgment. Mr. D. G. Norman helped with the experiments.
References
1. Arnhold L, Theiss W, Tiemann J: Messung der elektrischen
Impedanz als Suchmethode in der Diagnostik hamorrhagischer Diathesen. Dtsch Med Wochenschr 33:16571663, 1975
2. Biggs R, Macfarlane RG: Human Blood Coagulation and Its
Disorders. Fourth edition. Oxford, Blackwell, 1972
3. Connelly JA, Buckler MJ: The continuous measurement of
resistivity and permittivity of human blood plasma during
coagulation. Med Biol Eng, July 1975, pp 523-530
4. Hartert H: Die Retraktion des Blutkuchens: Ein gerinnungssynchroner Vorgang. Verh Dtsch Ges Inn Med 66:989-992,
1960
5. Hilgard P, Ur A: The reproducibility of the impedance clotting
time method. IRCS (Research on: Biomedical Technology;
Cardiovascular System: Hematology) 2:1555, 1974
6. Holford C, Ur A: Proceedings of the 2nd International Congress of Bioelectrical Impedance, Lyon, 1976 (in press)
7. Rosenthal L, Tobias W: Measurement of the electrical resistance of human blood. Use in coagulation studies and cell
volume determinations. J Lab Clin Med 33:1110-1122, 1948
8. Ur A: The changes in the electrical impedance of blood during
coagulation. Nature 226:269-270, 1970
9. Ur A: Determination of blood coagulation using impedance
measurements. J Biomed Eng 5:342-345, 1970
10. Ur A: Detection of clot retraction through changes of the
electrical impedance of blood during coagulation. Am J Clin
Pathol 56:713-718, 1971
11. Ur A: The blood coagulation curve of some mammals. Res
Vet Sci 16:204-207, 1974
12. Wintrobe MM: Blood platelets and coagulation. Clinical
Haematology. Sixth edition. London, Kimpton, 1967, pp
326-329