Plasma and Blood Coagulation Time Detector Based on the Flow Sensitivity of Self-Heated Thermistors William D. Bostick' and Peter W. Car+ Department of Chemistry, University of Georgia, Athens, Ga, 30602
The physical principles of a self-heated thermistor used to detect the time at which plasma forms a clot have been developed. A gently vibrated self-heated thermistor is very sensitive to bulk fluid flow. When placed in human plasma which is coagulated by the addition of thromboplastin and calcium, a very distinct signal is invariably obtained, coincident with clot formation. We have shown that the end point is not calorimetric in origin nor is it due to a change in the thermal conductivity of the media. The observed signal is due to a "freezing-out" of fluid flow by clot formation. Optimum resuits in normal plasma (Le., a fibrinogin level of 200-400 mg/dl) are obtained with small thermistors (radius 0.05-0.13 cm) which are vibrated at 60 Hz with an amplitude of 0.05 cm. Various diffusion models have been tested, and it appears that the time dependence of the phenomenon is functionally similar to slow spherical diffusion in a quiescent fluid. The results have been verified by measuring the thermal diffusivity of several organic solvents using water as a calibrant.
Prothrombin time and related hematological tests in which the time required for blood or plasma to clot under the aegis of one or more added catalysts are among the most frequently requested clinical measurements. Their significance is related to the diagnosis of the diseases of the hemeostatic regulatory system ( I ) and to the control of dosage rates in anticoagulation therapy ( 2 ) . The latter accounts for the largest proportion of all coagulation testing since oral anticoagulants (2) (such as coumarin and indanedione derivatives) are used to diminish the possibility of internal thrombus formation in patients with ischemic vascular diseases. The one stage prothrombin time test (which is sensitive to plasma levels of protein clotting factors 11, V, VII, and X) ( I ) is used to control therapy with the anticoagulant drugs (which depress the biosynthesis of factors 11,VII, IX, and X) ( 3 ) . In uiuo coagulation is an extremely complex series of transformations. Most texts (4, 5 ) recognize at least twelve clotting factors; however, recent work, particularly that of Seegers ( 6 ) , indicates that the complete mechanism is even more complex. Fortunately, the various coagulation time measurements are principally concerned with the last stages of the in vitro process, which are summa-
rized below ( 4 ) , and therefore the entire process is not of direct analytical importance. Thrombogenesis: Thromboplastin, Ca2+
Prothrombin
c Factor V Factor VI1 Factor X (Thrombin)
-+ -
Thrombin
(1)
Thrombin
Fibrinogen
f
nf
\
m fn
peptides
fn
clot
(2) (3) (4)
In reaction 1 above, protein coagulation factors V, VII, and X accelerate the conversion of prothrombin into thrombin. In this reaction, thrombin is autocatalytic; there is an induction period during which a critical level of thrombin builds up prior to a rapid turnover of prothrombin to thrombin. Reaction 2 is a proteolytic reaction in which the protein substrate fibrinogen is cleaved by thrombin into f, "activated fibrinogen" or fibrin monomer (soluble), plus low molecular weight fibrinopeptides. These monomers (f) form an intermediate end-to-end polymer fn, (reaction 3) and finally a cross-linked gelatinous polymer (reaction 4) (7, 8). Since the appearance of the clot is the only readily observable phenomenon in the entire sequence of reactions, the time required for clot formation is a very common clinical measurement. Blood and plasma coagulation testing may be considered in the category of variable-time kinetic analysis (9, 10) and, in contrast to virtually all other enzymatic assays, such tests are inherently not amenable to the constant-time, variable concentration approach to kinetic analysis. Since the reaction sequence given above is rather complex, we will formulate prothrombin time measurements as a variable-time analysis in terms of the generalized reaction below in which R, a reactant or substrate (fibrinogen), is converted to P, a product (clot), by means of C, a catalyst and/or reaction initiator (some combination of coagulation factors).
R A P
(5)
The reaction rate may be written in differential form as: Present address, C h e m i c a l Technology Division, O a k Ridge N a t i o n a l Laboratory, O a k Ridge, T e n n . 37830. T o w h o m requests for r e p r i n t s should be addressed. A. J. Quick, "Hemorrhagic Diseases and Thrombosis," Lea and Febiger, Philadelphia, Pa., 1966. G. Goldstein, L. Aronow, and S. Kalman, "Principles of Drug Action,'' Harper and Row,New York, N.Y., 1968, pp 412-13. A. Goth, "Medical Pharmacology." C. V . Mosby, St. Louis, Mo.. 1972, pp 396-404. J. B. Miale, "Laboratory Medicine-Hematology,'' 3rd ed., C. V . Mosby Co., St. Louis, Mo., 1967, pp 999-1 115. M. M. Wintrobe, "Clinical Hematology," Lea and Febiger, Philadelphia, Pa., 1962, pp 288-95. W. H. Seegers, L. McCoy, and E. Marciniak, Ciin. Chem.. 1 4 , 98 (1968).
h [ R 3 = - - =4'p1 4t
At
-k [R] [C]
In a variable time assay, the time interval required for [R]
(7) J. M. Sturtevant, M. Laskowsky, Jr., T . H. Donally, and H. A . Scheraga, J . Amer. Chem. SOC.. 77, 6168 (1955). (8) R. L. Searcy, "Diagnostic Biochemistry," McGraw-Hill, New York, N.Y.,1969, pp 212-22. (9) H. V. Malmstadt, C. J. Delaney, and E. A . Cordos, Crif. Rev. A n a / . Chem.. 2, 559 (1972). (10) W. J. Blaedel and G. P. Hicks, Advan A n a / . Chem Instrum.. 3, 105-142 (1964).
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 8, J U L Y 1974
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or [PI to change between two pre-determined fixed levels is measured. It is equally valid to determine the time interval required for some transducer signal to change between the two predetermined levels. A very significant advantage of variable-time methods is that the relationship between transducer output (10) and concentration need not be linear-e.g., two sample optical transmittances or electrode potentials could serve to establish the time interval. Provided that reaction 5 is carried out under pseudo zero order conditions in concentration of R, the concentration of catalyst may be expressed as:
where f ( S t ) denotes some functional relationship between concentration and the transducer signal. Combining all the terms on the right of Equation 7 which are fixed or constant, the concentration of catalyst may be related to the time interval A t = t 2 - t l .
Prothrombin time is taken as the time from the initiation of the clotting process ([PI = 0) to the first detectable sign of a clot. The second level is very much dependent upon the mode of detection and the success of a given end-point detector depends upon its ability to produce a distinct signal some time close to the instant of clot formation. Recently, Uldall ( 2 1 ) has evaluated several empirical mathematical models relating coagulation time, A t , to the relative concentration of some combination of coagulation factors (11, VII, X, abbreviated here as C) in blood or plasma. One of the best fits for the experimental data was the model proposed by Biggs and MacFarlane (12):
et
=
A,,
+ A,/[%]
(9)
where A0 and A I are constants. This equation is similar to the generalized Equation 8. A relationship analogous to Equation 8 may be derived to relate clotting time to substrate concentration, [R], provided [C] is a true catalyst or is present in great excess.
[R]
k"
= -
At
Shinowara (13) has shown that the reaction between thrombin and fibrinogen follows first-order kinetics a t low fibrinogen levels and that clotting time is inversely related to fibrinogen concentration when a constant initial concentration of thrombin is added. When plasma is diluted sufficiently ( e . g . , lho to l/20) fibrinogen becomes the limiting factor in clotting time upon addition of excess thrombin, and the reciprocal relationship between clotting time and substrate concentration has been utilized for a semiautomated micromethod for the determination of plasma fibrinogen (14) [which is elevated or depressed as a complication in a number of disease states ( 8 ) ] . Manual determination of clotting time involves a highly subjective decision by the analyst as to the precise moment of clot formation, which is normally only 10-15 seconds and is therefore very imprecise. Several automatic and semi-automatic instrumental detection systems have
(11) A . Uldall, R . Dybkaer, M. Lauritzen, and K. Rolighed, Scand. J Ciin. Lab. i n v e s t , 29, 417 (1972). (12) R. Biggs and R . G. McFarlane, in "Blood Coagulation," Blackwell Scientific Publications, Oxford, 1953, p 50. (13) G. Y . Shinowara, Blochim. Biophys. Acta.. 13, 359 (1966). (14) E. E. Morse, S. Panek. and R. Menga. Amer. J . Clin. Pathol.. 5 5 , 671 (1971).
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been devised in an effort to improve precision (15, 16). Such devices fall into two distinct categories: end-point instruments which merely stop a clock when a clot has been detected and provide no other information about the sample, and those instruments which record some physical property of the sample throughout the entire clotting process. The electromechanical fibrin switch has been the most successful of the end-point devices. In this device, a reciprocating armature shorts an electrical timer when a fibrin strand is picked up from solution. The limitations of this instrument include lack of a continuous permanent record of the experiment, absence of qualitative or quantitative information concerning the fibrinogen content of the sample, and a precision limited to a range of 0.5 sec-ie., the instrument's cycle time. The great advantage of the instrument is its documented excellent correlation with manual clotting time determinations for both normal and abnormal samples ( I 7, 18). The most frequently utilized property for continuous monitoring of the coagulation process has been the change in light transmittance or increase in light scattering upon clotting (19, 20). The optical techniques are subject to error when lipemic, icteric, or hemolyzed plasmas are tested (20), frequently do not correlate well with the electromechanical fibrin switch method (nor, by implication, with manual testing) in the therapeutic prothrombin time (15-30 sec) range (20) and cannot be employed a t all on whole blood. Optical methods may be used to provide a continuous permanent record of the clotting process, thus yielding some information as to the nature of the fibrin clot formed in addition to a measurement of the clotting time (21). Recently, we introduced a novel coagulation timer based on a thermometric detection system which has overcome some of the limitations of existing techniques (21). The system has demonstrated an excellent correlation with the electromechanical fibrin switch (r = 0.98 a t greater than the 99.9% confidence interval) for the determination of both normal and abnormal prothrombin times. In addition, the system inherently monitors the temperature of the test solution prior to coagulation, automatically indicates the addition of reaction initiating reagents, continuously records a property of the sample before and after coagulation, and provides a distinct and precise indication of clotting time independent of any optical property of the sample (22). The method described here evolved from an attempt to locate the prothrombin time end point calorimetrically based on the heat evolved upon the conversion of fibrinogen to fibrin. Sturtevant (7) has determined the reaction enthalpy of the formation of intermediate fibrin polymers from fibrin monomers (reaction 3 above) to be -44.5 kcal/ mole of fibrin monomer a t 25 "C,pH 6.88 in 1M sodium bromide. Similarly, Laki (23) has measured an enthalpy of -44 kcal/mole for the clotting of fibrinogen by thrombin in phosphate buffers over the pH range 6 to 8.5. From these values, one estimates that the total heat available from 1 ml of normal plasma, containing 2 to 4 mg of fi(15) K. N. von Kaulla. in "Progress in Hematology." L. M . Tocantins, Ed., Vol. 111. Grune and Stratton, New York, N.Y., 1962, pp 21843. (16) G .M. Brittin and G. Biecher, ibid.. Vol. V I I , 1971, pp326-9. (17) J. B. Miale, Amer. J . Clin. Pathol.. 43, 475 (1965). (18) F. G. Fewell, A. Cundy. and G. C. Jenkins, Med. Lab. Techno/.. 29, 147 (1972) (19) C. Sibley and J. W. Singer, Amer. J. Clin. Pathoi.. 57, 369 (1972) (20) A. G. Jacobs and J. A. Freer, Brit. Med. J . , 2, 978 (1963). (21) H. F. Deutsch, J . Clin. invest., 25, 37 (1946). (22) W. D. Bostick and P. W. Carr, Amer. J . Clin. Pathol.. 60, 330 (1973). (23) K. Laki and C. Kitzinger, Nature (London), 178, 985 (1956).
8
ROT S I MREHT I (
LEADS -GLASS -EPOXY TUBING
GLfZ;ELOPE-A SEMICONDUCTOR
-TEFLON DISC IMPELLER
L- THERMISTOR BEAD
a
b
Figure 2. Detail of thermometric clot detector Curve a. Schematic of bead. Curve b. Construction of probe unit
0.2 -
,
I
I
1
I
I
1
ology may be useful in other areas, such as polymer chemistry, and as a simple dynamic method for the measurement of the thermal diffusivity of liquids.
THEORY
brinogen (mol wt 340,000) (24), upon complete conversion of fibrinogen to fibrin would be of the order of -0.5 millicalorie or -0.5 m"C. Although it is possible to determine a thermochemical event of this magnitude (23), further complication is that, at the classical clotting end point, only a small fraction [e.g., 20% conversion after 20 minutes, ( 2 5 ) ] of the total fibrinogen has been converted to the active form and has found its way into the structural fibrin web (25, 26). Our preliminary investigations were carried out in primitive adiabatic cells utilizing crude sensing equipment. Based on previous experience, it should not have been possible to measure the heat of reactions 2-4 because of insufficient temperature sensitivity and the very small quantity of heat actually liberated a t the moment of clot formation. Nevertheless, a small but discernible "thermometric event" was observed when a fibrinogen solution was clotted by addition of thrombin. This "event" was coincident with the increase in turbidity associated with the formation of a fibrin web. The objective of subsequent work was to exaggerate this end-point signal, make it repeatable, and develop a coagulation time detector. The results of this work have been reported elsewhere (23). The purpose of the present work was to explore the physical process responsible for the end-point signal and ultimately to choose the optimum analytical conditions for the measurement of coagulation time by this technique. As will be shown (uide infra), the process responsible for the distinct prothrombin-time end point (see Figure 1) is the rather substantial change in the rate of heat transfer from a self-heated thermistor upon transforming the test plasma to a highly viscous gel. In this regard, the physical principle is related to such diverse applications of thermistors as: anemometers, flowmeters, fluid-velocity meters, manometers, gas phase thermal conductivity cells and liquid level sensors (27). We believe that the current application is the first reported use of the flow sensitivity of thermistors for the determination of a liquid phase concentration (or enzyme activity). In addition, the method(24) E. B. Smith, C. s. Barnes. and P. W. Carr, Anal. Chem.. 44, 1663 (1972). (25) D. F. Waugh and M. J, Patch, J . Phys. Chem.. 5 7 , 377 (1953). (26) K. Laki, in "Blood Clotting and Allied Problems," Carles. Macy and Co., Inc.. New York, N.Y., 1951, pp 226-9. (27) F. J. Hyde, "Thermistors," iliffe Books, London, 1971, pp 115-41.
Since the proposed explanation of the end-point phenomena is predicated on the change in the heat transfer characteristics of a thermistor in motion with respect to the surrounding media, an approximate mathematical model is presented, in order to form a basis for comparison with the observed experimental results. The model is illustrated in Figure 2 . Due to the passage of electrical current ( i r ) through the thermistor the semiconductor bead is inevitably heated to some temperature ( T T )above that of the surrounding bulk fluid ( T O )Heat . will be transferred away from the semiconductor bead through the electrical leads of the thermistor and uia the protective glass envelope to the surrounding fluid. The efficiency of heat transfer via the surrounding media will be dependent upon the thermal conductivity of the media and its motion relative to the thermistor. The dissipation constant ( 6 ) of a thermistor is generally defined (26) as the ratio of the power ( P T )applied to the thermistor to the temperature difference between the thermistor (7'7) and the fluid in which it is immersed ( T O )The . dissipation constant is determined both by the construction of the thermistor and its environment; it is dependent upon the thermistor's geometry and mounting, and the thermal conductivity and relative rate of motion of the surrounding media (27). In this work, we attempt to relate the magnitude of 6 and the time dependence of the thermistor's internal temperature to various perturbations including changes in the applied power level ( P T ) ,the velocity of the probe, and the temperature of the solution. In order to avoid the presentation of detailed mathematical derivations it is useful to consider the analogy between the situation described above and electrolysis with constant current at a microelectrode. We have developed the topic by analogy to the related electrochemical situation since this is more familiar to analytical chemists. This is, of course, the reverse of the historical development of diffusion theory-i. e. heat transfer was developed prior to mass transfer (28). In the chronopotentiometric experiment, the current flux a t the electrode surface is constant. In the thermometric experiment, it is the power dissipated in the thermistor (PT) which is esentially constant, and thus the heat flux a t the surface of the thermistor ( q c ) may under certain circumstances be considered constant:
''
=
P,
4.184A
where qc is the heat flux (cal/sec cm2), PT the power dissipated (watts) and A is the surface area (cm2) of the bead from which heat is transferred to fluid media. In (28) L. L. Bircumshaw and A. C. Riddiford. Quart. Rev. ( L o n d o n ) , 6, 157 ( 1 952).
ANALYTICAL C H E M I S T R Y , VOL. 46, NO. 8 , J U L Y 1974
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chronopotentiometry, one is concerned with the rate of change in concentration, dcldt, a t the electrode surface; in the thermometric experiment, the rate of change of temperature, dT/dt, a t the transducer surface is of interest. The change in temperature a t the surface of a selfheated thermistor may be initiated by a change in the applied power or by a change in velocity of the surrounding media. The latter condition might be achieved in an essentially step-functional manner by stopping the vibratory motion of the probe in a free-flowing fluid, or as postulated, by rapid formation of a highly viscous gel a t the thermistor surface and throughout the entire sample. Under these conditions, the rate of heat transfer from the thermistor will be controlled by thermal diffusion. To a first approximation (see Figure 2a) the thermistor bead appears to have spherical geometry. Heat transfer controlled by spherical diffusion may be treated in a manner similar to that previously described for mass transfer controlled by spherical diffusion (29). The equation for semi-infinite spherical heat diffusion in the absence of a velocity field is
where r is the radial distance (cm) from the surface of the sphere and D is the thermal diffusion coefficient (cm2/ sec) of the media. At r = ro, the thermistor surface, the boundary condition for constant flux is taken to be
where A is the thermal conductivity (cal/”C.sec.cm) of the surrounding fluid. In the equation above it is assumed that the heat flux at the thermistor surface ( q c ) is transmitted entirely to the media. At r = m , an effective infinite distance from the thermistor surface, the following boundary conditions are assumed:
(W
T(m,t) = To
That is, a t a sufficient distance from the thermistor, the temperature is constant and equal to the bulk temperature of the fluid (To). Equation 13 may be solved by conventional techniques (29). The temperature at r = ro (the thermistor surface) is given by:
T(r,,t) = To - qcro[l - exp(8)’ erfc(0)I where 0 is a dimensionless parameter.
,(17)
In the special case of small t or large ro (27), Equation 17 reduces to a expression for semi-infinite planar heat diffusion:
A reasonable alternative to spherical diffusion is cylindrical heat transfer. The dimensionless cylindrical correction factor I?(€)), most completely derived by Dornfeld and Evans (30) for correction of chronopotentiometric transition time, is also valid in this case when applied to the expression for semi-infinite heat diffusion (Equation 19):
(29) P Delahay, C C Mattox, and T Berzins, J Amer Chem SOC 76, 5319 (1954) ( 3 0 ) D I Dornfeld and D H Evans, J Elechanal Chem 20, 341 (1969) 1098
* ANALYTICAL CHEMISTRY, VOL. 46, NO.
8, JULY 1974
EXPERIMENTAL Apparatus. The essential apparatus for the thermometric clot detector has been described elsewhere (22). The sensing element, is illustrated in Figure 2b, is a 2000 il glass probe thermistor (Victory Engineering) which is fitted with a Teflon (DuPont) disk impeller near the tip of the sensor. The unit is mounted in the chuck of a vibratory mixer (Chemapec VIBRO-mixer E-1) and the thermistor probe forms one arm of an equal arm Wheatstone bridge. The bridge disbalance is monitored by use of an X-Y recorder (Hewlett-Packard Model 7001A) with the X-axis in the time-sweep mode. Experiments were conducted in a water bath regulated to *0.05 “C at mean temperatures of 37.0 “C and 25.0 “C by use of a temperature controller (YSI Thermistemp, Model 71). It was found vide infra that the amplitude of vibration of the probe is one of the most critical parameters in obtaining a sharp and distinct clotting end point. The amplitude of the (60 Hz) vibrator was controlled by use of a variable transformer (Powerstat type 116, Superior Electric Co.). The amplitude of displacement at various transformer settings was observed by synchronization with a stroboscope and was calibrated by use of a cathetometer (Griffin and George, Ltd.) to the nearest 10 micrometers. Reagents. Simplastin (General Diagnostics Division, Warner-Chilcott Corp.) is the thromboplastin reagent used in the prothrombin time studies. Normal plasma samples were obtained from local hospitals. For the data in the study of end-point magnitude us. fibrinogen content, citrated normal plasma (lot No. CNP52, Dade Division, American Hospital Supply Corp.) was used. This product is a fibrinogen control, and is certified to contain 265 mg/dl of fibrinogen after reconstitution. The fibrinogen used in preparation of the diluent in this study is purified fibrinogen, free of prothrombin complex and accessory factors (lot No. 246811, General Diagnostics Division, Warner-Chilcott Corp.). This product is certified to contain 300 mg/dl fibrinogen and 0.85% saline after reconstitution, The clottable protein in the fibrinogen preparation was checked by biuret test after coagulation with dilute purified thrombin, and was in good agreement with the certified value. The solvents used in the thermal diffusion studies were ACS reagent grade and were used with no further purification. Procedure. The procedure used for the one-stage prothrombin time test has been given elsewhere (22) and is in accord with that recommended by the supplier of the thromboplastin reagent. The transition magnitudes reported in this work are referenced to a 10-Q resistance change in order to correct for variation in bridge sensitivity with temperature and voltage. The resistance change is expressed in temperature units (“C) via the temperature coefficient of the thermistor, assuming a typical value of -0.04fl/Q.°C. RESULTS AND DISCUSSION Variable-Time Kinetic Analysis. Many laboratories routinely present coagulation time measurements in terms of “percent of normal activity” as determined by comparison of the clotting time of the test sample US. that of a suitably diluted normal sample. In a previous publication (22), we have presented data for such a “dilution curve” for the one-stage prothrombin time test. Barium sulfate adsorbed normal plasma, with coagulation factors I1 (prothrombin), VII, and X substantially reduced while main-
o.q
/
0.08
I
0’
/
Lo O.O+ d
11
I I
I
I
1
,
, TIME L5ecI
20 40 60 80 100 Yo OF NORMAL CONCENTRATION, FACTORS ( I1+ VI1 + X i
Figure 4. T h e role of flow-sensitivity in the end-point phenomenon
Figure 3. Calibration curve for the determination of coagulation factors (I1 VI1 X ) . Normal plasma is diluted with barium
+
.
+
sulfate-absorbed plasma (factor deficient) taining other factors (including fibrinogen) a t near-normal levels ( 4 ) , was used as the diluent in order to mimic the action of oral anticoagulant drugs (2). In Figure 3, the data are considered in terms of Equation 8 for a variable time assay. The abscissa of the figure represents the concentration of a combination of coagulation factors (I1 VI1 + X) relative to that of the undiluted 100% normal plasma. The ordinate is the reciprocal of the clotting time as determined thermometrically. At low relative concentrations, the predicted linear relation (Equation 8) is observed (correlation coefficient = 0.997, p < 0.005). The positive y-intercept corresponds closely to the clotting time of the diluent ( - 105 sec). At concentraX tions greater than -40% of normal, factors I1 + VII are observed to be no longer rate-limiting; perhaps fibrin formation (Equations 2-4) rather than thrombogenesis (reaction 1) here controls the rate of clot formation. It should be possible in principle to selectively analyze for the relative plasma level of any coagulation factor, individually or in combination (as above) by use of the appropriate factor-deficient plasma as a diluent, provided that the coagulation test used is sufficiently sensitive to that factor or factors. In the above example, the sample could be diluted to 30% (v/v) with adsorbed plasma and referenced to the corresponding dilution of the normal sample as “100% activity.” The Role of Flow-Sensitivity in the End-Point Phenomenon. A typical prothrombin time clotting curve for a normal plasma specimen is shown in Figure 4 , curve a. The entire curve consists of three distinct regions. Prior to point A the reagents (thromboplastin and calcium) contained in a test tube are thermally equilibrated with the incubation bath. The temperature-time curve prior to point A constitutes a base line which indicates when the test temperature (generally 37 “C) has been attained. At point A, a test plasma is rapidly injected into the reagents; mixing is brought about by both injection and by the vibratory motion of the thermistor probe. The distinct indicator of the start of the reaction is most expediently provided by deliberately not matching the temperature of the injected plasma and the reagents. Between points A and B, the temperature change is due to thermal re-equilibration of the sample with the water bath. At point B, the recorder indicates a sharp deflection which invariably coincides with clot formation. The time of clotting is proportional to the distance C. Since the steady state temperature excursion is established rather slowly, the magnitude of the end-point phenomenon was measured as the distance D at some pre-determined time interval (usually 30 sec) after the end point. In order to determine what brings about the end-point
+
+
Curve a. Prothrombin time test for a normal plasma sample; 0.076-cm probe: vibration amplitude, 0.05 c m , PT u 25 mW. Curve b. Termination of t h e vibration of t h e probe in water; 0.076-cm probe; initial vibration 25 m W amplitude, 0.05 c m , PT
transition, a number of qualitative tests were carried out. We found that the clotting curve after point B (Figure 4 , curve a ) is remarkably similar to the temperature transition which occurs when the vibratory motion of the selfheated probe is suddenly turned off (see Figure 4 , curve b ) in the absence of a clot. This similarity suggests that the end point is due to the termination of relative bulk flow around the thermistor and not to a change in the thermal conductivity of the plasma upon conversion to a gel nor to a change in the temperature of the test solution. In order to verify this conclusion the vibratory mixer was turned off (similar to point E in curve a of Figure 4) after a clot was formed. Only a very small temperature change is observed, provided that the fibrinogen level is in the normal range. Under the experimental conditions employed in this work, the vibratory motion of the thermistor does not have a very significant effect on the thermistor’s dissipation constant. This was demonstrated by repeating the experiment of Figure 4, curve b, in a solution stirred via magnetic mixing. No change in temperature was observed. The very small amplitude of vibration used in this work was mandated by the fragility of the fibrin web. Excessive vibration or mechanical mixing can completely prevent the formation of a clot. Quantitative evidence that the end point phenomenon is not thermochemical in nature is presented in Figure 1. With Wheatstone bridge instrumentation, the recorder deflection is proportional to the change in resistance of the sensor and by the bridge equation (31) to the first power of the bridge voltage provided that an enthalpic transition-ie., change in the temperature of the solution-has occurred. In contrast to this, the transition magnitude (as in curves a and b in Figure 4) is found to be proportional to the second power of the applied bridge potential-ie., to the power delivered to the thermistor (PT) as suggested by Equation 11. Curve b in Figure 1 represents data for the clotting experiment (as in Figure 4a) using a self-heated probe of nominal bead radius 0.055 cm (Veco 32A8). Curves a,c, and d in Figure 1 represent the data as in the experiment of Figure 4 b for probes of nominal bead radii of 0.055 cm (Veco 32A8), 0.076 cm (Veco 32A223), and 0.127 cm (Veco 32All), respectively. The magnitude of the transition can be related to an apparent change in dissipation constant via Equation 11. The slopes in Figure 1, curves a-d, are summarized in Table I. In accord with intuition, the change in dissipation constant increases as the mass of the thermistor becomes smaller. An exact correlation with the equation of (31) P. W. Carr, Crit. Rev. Anal. Chem.. 2, 491 (1971)
ANALYTICAL C H E M I S T R Y , VOL. 46, NO. 8, J U L Y 1974
1099
VARiAC
VOLTAGE,
(
va.c.)
-
I
0.20"C
"
4
1.0-
0.8 -
- 0.6
-
c
-9e-
t=
a 09-
a
0.2 -
I
I
,
1
I
0.02 0.04 Q06 008 0.10 012 PROBE DISPLACEMENT, (CMI
Figure 5. Transition magnitude, AT("C), vs. probe displacement (amplitude)at 60 Hz NORMPL PLASMA
t' Figure 7. Transition magnitude, AT("C), of prothrombin time
DILUTED PLASMA
end point vs. fibrinogen content of test plasma Curve a. Bead radius, 0.076 cm; "I-bars'' indicate standard deviation of triplicate determinations; vibration amplitude, 0.05 cm; PT N 17 mW. Curve b . Bead radius, 0.076 cm; vibration amplitude, 0.04 cm; PT N 17 mW
ao& rn
a05crn
TIME,(w)
Figure 6. Prothrombin time curves for normal plasma and diluted plasma (1:5, 0.9% saline diluent) as a function of probe displacement
Table I. Thermistor Characteristicw Nominal radius, cm
mW/"C
0,055 0.076 0.127
3.0 5.0
...
Apparent change in 6, mW/OCC
12.4 18.0 23.3
S,d
"C/W
42.8 28.7 14.9
All data for experiments as in Figure 46, in small nonadiabatic teat tubes filled with water. Thermistor dissipation constant from manufacturers specifications in still water. From the slope of the appropriate curve in Figure 1. From the slope of the appropriate curve in Figure S and as defined in Equation 21.
'
spherical diffusion is not obtained. It is nonetheless clear that a small thermistor provides a more distinct end point a t a given power level. The magnitude of the thermistor self-heating transition depends upon the change in the thermistor's dissipation constant ( 6 ) . The efficiency with which the thermistor bead can transmit heat to its surrounding media is, within limits, dependent upon the relative velocity of the media with respect to the bead (27, 32). In the system described, the amplitude of the probe displacement a t constant vibrational frequency (60 Hz) is related to the relative fluid velocity. In the experiments whose results are summarized in Figure 5 , the vibration of the probe in water is sudden(32) M. Sapoff and R. M . Oppenheim. Proc Inst. Elec Electron Eng 51, 1291 (1963).
1100
ANALYTICAL CHEMISTRY, VOL. 46, NO. 8, J U L Y 1974
ly terminated and the magnitude of the resulting selfheating transition is plotted US. the amplitude at which the probe had been previously vibrated. We stated above that the amplitude of vibration of the probe is a critical factor in obtaining distinct coagulation end points. In Figure 6, prothrombin time curves are illustrated, a t several probe vibration amplitudes, for both normal and saline-diluted plasma. Two types of effects are noted, depending upon the dilution of the plasma sample. For a normal plasma ( i e . , one containing the usual level of fibrinogen), the clotting curve becomes more distinct at larger vibration amplitudes because of better initial mixing of reagents and the greater change in rate of power dissipation upon clotting. This is a consequence of the effect observed in Figure 5. However, for a dilute plasma (with little fibrinogen available to form a structurally sound fibrin gel), disruption of the clot may occur a t large vibration amplitude yielding indistinct, ill-defined end points. For our system, vibration of the probe at 60 Hz with an amplitude of 0.05 cm appeared optimum for the fibrinogen content of normal plasma. The effect of fibrinogen content upon prothrombin time end-point magnitude is further examined in Figure 7 a t two near-optimum vibration amplitudes. A dilute normal plasma (1:lO) was used, the diluent being saline with added purified fibrinogen in order to preserve all coagulation factors (except fibrinogen) at a constant low level. At normal (200-400 mg %) and near-normal fibrinogen levels, little effect upon end-point magnitude (determined as in Figure 3, measurement D) was observed. As the fibrinogen level is decreased further, the clot becomes more diffuse and structurally tenuous. Presumably the bulk flow of the media is no longer reduced to zero, and thus the observed transition magnitude is decreased. This is verified by stopping the motion of the probe after the end point (as at point E in Figure 4a); a substantial self-heating change in contrast to point E in Figure 4A occurs. The Thermal Diffusion Model. The above data clearly indicate that the clotting end point is related to heat transfer from the thermistor rather than a result of a temperature change in the test solution. In order to completely characterize the mechanism of the transducer, the time dependence of the end-point signal was considered. Although this is not of primary importance to the work pre-
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Figure 8. Transition magnitude, AT ("C), vs. square-root of
time, (sec'12) All data using small, nonadiabatic vessel; initial vibration amplitude, 0.05 cm. P r 3 8.2 rnW. Curve a. Bead radius, 0.055 crn. Curve b. Bead radius, 0.076 crn. Curve c. Bead radius, 0.127 c m
sented above, we are presently developing applications of the detection system in which the rate of conversion of fibrinogen to fibrin (reactions 2-4) are considerably slower (e.g., plasma recalcification time measurements), and it is of paramount importance to determine whether the transducer or the chemistry establishes the shape of the endpoint response. In the absence of a relative velocity field, thermal diffusion becomes the controlling factor in the transfer of heat from the semiconductor bead to the media. In Figure 8, the transition magnitude ("C) is plotted us. ( t ) l I 2 for the experiment of Figure 3, curve b. In each curve, a linear segment is observed, as predicted by Equation 17. The curves represent data for experiments in the nonadiabatic test-tubes with thermistors of nominal radii of 0.055 cm (curve a ) , 0.076 cm (curve b ) , and 0.127 (curve c ) . Each probe was operated a t an applied power (PT) of 8.2 mW. The clotting curve presented in Figure 46 was obtained using the 0.076-cm probe. When the transition magnitude (measurement D), normalized for PT,is plotted as in Figure 8, the data are nearly superimposable on curve b of Figure 8. The slopes of the linear portions of the curves were 28.7 and 25.2 ("C sec-1'2 W - l ) for the termination of vibratory motion of the probe in water and for the prothrombin time end point, respectively. This indicates that there is very little change in the thermal conductivity of the fluid upon clotting, and the major effect is due to the elimination of bulk flow around the thermistor. Equations 12 and 19 predict that the slope of the linear segment of a plot of A T ~ s . ( t ) l /a~t , constant applied power, will increase as the radius, and therefore the available surface area, of the probe decreases. The data of Table I show this to be the case. The curves in Figure 8 indicate that deviation from linearity becomes more serious and occurs a t shorter time as the thermistor's radius becomes smaller. Both Equation 17 (spherical diffusion) and Equation 20 (cylindrical diffusion) yield a greater deviation from Equation 19 (planar diffusion)-ie., a downward curvature as 8 becomes larger. This is in agreement with the observed results. Experiments in large adiabatic cells, where the boundary conditions given in Equations 15 and 16 are valid (see Figure 9), show that the heat transfer process is more nearly described by spherical diffusion than by cylindrical diffusion. At very short time (
