THE CLEARANCEOF BILIRUBIN FROMTHE PLASMA. A MEASUREOF THE EXCRETINGPOWEROF THE LIVER

By A. A. WEECH,DOROTHEAVANN, AND ROSEA. GRILLO(From the Department of Pediatrics, College of Physicians and Surgeons, Columbia University,

and the Babies Hospital, New York)

(Received for publication January 20, 1941)

The clearance of bilirubin from the plasma fol-lowing intravenous injection was first used tomeasure the excretory function of the liver byEilbott (1) and Von Bergmann (2) in Germanyin 1927. In the United States the method wasintroduced by Harrop and Barron (3) in 1931.Additional experiences,-by Soffer (4, 5, 6, 7, 8)and by others (9, 10, 11, 12) have establishedthe value of the test. Aside from the theoreticaldesirability of using a physiologic material (bili-rubin) rather than a dye (bromsulphalein or rosebengal) to assess hepatic excretory function, it isgenerally agreed that the bilirubin test is unusuallysensitive in demonstrating disturbed functionwhen the degree of liver damage is relativelyslight. The usefulness of the test and a desire toextend the range of clinical disorders to which itcan be applied have prompted the present study.

As now used, the test involves determination of thepercentage of injected bilirubin remaining in the circula-tion after a standard time period, usually 4 hours. Threesamples of plasma are required. An initial sample a isobtained to determine the natural level of bilirubin in thepatient's plasma. Pure bilirubin-1 mgm. per kilogramof body weight dissolved in a small volume of 0.1 Msodium carbonate solution-is injected intravenously. Af-ter allowing 4 to 5 minutes for mixing in the blood stream,a second sample of plasma b is secured. The final samplec is collected 4 hours later. If Ba, Bb and Bo representthe bilirubin concentrations in each of the three plasmasamples, the percentage retention equals 100 (Bc-Ba)

(Bb -Ba). Reported results indicate that in manynormal subjects there is no retention of pigment at the endof the 4-hour period. Soffer (7) considers retention inexcess of 5 per cent to be evidence of impaired liverfunction.

It will be observed that the above method whichutilizes percentage retention as the measure ofhepatic function is based on the assumption thatrate of excretion is not influenced by the basallevel of bilirubin in the plasma. The value forthis level is simply subtracted from each of theother levels before the retention is computed. It

will appear presently that the assumption is notjustified. However, since most authors state thatthe test should not be applied when the basal levelis above 1 mgm. per cent, and since the result isusually interpreted simply as normal or abnormal,and not as a quantitative measure of excretoryfunction, it has in general served its purpose satis-factorily. Occasional attempts (13, 14 1) to uti-lize the test when the basal concentration was ele-vated have yielded results which are difficult tointerpret.

In extending the range of disorders to whichthe bilirubin excretion test can be applied, it isnecessary to recognize that probably no test of ex-cretory function can yield meaningful resultswhen the plasma van den Bergh reaction is direct.The direct reaction is generally assumed to meanthat bile is regurgitating from the biliary tract intothe blood; if the assumption is true, a part of thematerial excreted by the liver is returned to theblood and estimations of blood level cannot be ex-pected to measure excretion alone. In hemolyticdisease the reaction is indirect, there is no evi-dence for regurgitation, and it should be possibleto assess excretory function even though the basalconcentration is high. The theory to be describedprovides a rational basis for interpreting the testin this type of case; the estimate of liver functionwhich it yields is quantitative and independent ofthe basal concentration of bilirubin in the plasma.

THEORY

Three assumptions are required in developingthe theory of bilirubin clearance. Two of these

1 These investigators studied the liver function of apatient with chronic hyperbilirubinemia, moderate spleno-megaly and hepatomegaly, and march hemoglobinuria.The conventional bilirubin excretion test showed no re-tention of injected pigment after 3 hours, that is, plasmabilirubin concentration had returned to its previous equi-librium level of 3.0 mgm. per cent. Later, a bilirubinclearance test performed by the method of this paper dis-closed marked impairment of hepatic excretory function.

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A. A. WEECH, DOROTHEAVANN, AND ROSE A. GRILLO

are entirely reasonable; the third is an approxi-mation. The first assumption states that the levelof bilirubin normally circulating in the plasma isthe result of an equilibrium between the rate offormation and the rate of excretion. Accord-ingly, in the equations which follow the basalbilirubin concentration will be represented by thesymbol Leq. which is to be read " level at equi-librium." The rates of formation and excretionwill be expressed by the letters F and E, respect-ively. The second assumption is that the rate ofbilirubin formation will not change significantlyduring the several hours when a test is being run.F is therefore a mathematical constant. The thirdassumption states that the velocity of bilirubin ex-cretion is at any moment proportional to the squareof its concentration in the plasma. If the chang-ing concentrations after an intravenous injectionare represented by the symbol L and the constantof proportionality by K, it follows that instan-taneous excretion equals KL2. These assump-tions will now be used for a mathematical state-ment of the theory; at a later place their validitywill be examined more closely.

It is axiomatic to say that any change in the amountof bilirubin in each 100 cc. of plasma during a giventime period will equal the difference between bilirubinadded to and bilirubin taken away from the 100 cc. ofplasma. Briefly, change = formation -excretion. Sincethe equality holds no matter how brief the time interval,the change in the plasma level can be replaced by itsderivative with respect to time; that is,

1. dL= F - E.

It has been assumed that the instantaneous velocity ofexcretion is equal to KL'; accordingly, the equationtakes the form:

2.dL KL2.

The constant K in this equation can be evaluated to

express for each 100 cc. of plasma the rate of excretionof bilirubin in milligrams per minute per milligram-squared of concentration in the plasma. Accordingly,"the velocity constant " is a measure of the excretorypower of the liver. The higher the value of K, thegreater is the ability of the liver to excrete bilirubin.

Equation 2 can be used to derive the relationship whichdescribes the path of bilirubin concentration in theplasma following an intravenous injection. The deriva-tion is essential to test the reliability of the theory andto compute the velocity constant. We first observe thatthe rate of change in concentration, dL/dt, is zero whenequilibrium has been reached between formation and ex-

cretion. It follows from equation 2 that F = KLeq.'.Substitution in equation 2 yields

3. dL = KLeq.2 _KL2 = -K(L2-Leq.2).Transposition of terms leads to

4. dL Kdt.L2-Leq.2 K

Equation 4 is in a form which can be integrated. Whenthis step has been performed and the constant of inte-gration evaluated by introducing a value L. which repre-sents the bilirubin concentration when time is zero, thatis, the first measurement after the injection, the follow-ing relationship emerges:

.lg (L)= log (Lo+ Leq. +KL6qe

Equation 5 expresses the variations in plasma bilirubinlevel L with respect to time t which is convenientlymeasured in minutes after the first post-injection sampleis withdrawn. The value 1.1513 is a constant whichenters in the conversion of natural to ordinary log-arithms. It will be observed that values for the left-hand term of the equation can be computed readily fromanalyses at different time intervals and that these valuesare linear with respect to time. When multiple serialmeasurements have been made, the procedure for ob-taining the velocity constant is to prepare a graph onwhich these values are plotted as ordinates against timeas abscissas. A straight line is then drawn as closelyas possible through the consecutive points. The slopem of the line will then correspond to the coefficient of t;that is,

M KLeq.1.1513and6. 1.1513 X mK= Le.When K has been determined, equation 5 can be used tocalculate theoretical values of L for a number of valuesof t. Plotting these data with L as ordinate and t asabscissa yields the theoretical curve of clearance; directcomparison between theoretical and observed concentra-tions is then possible. Equation 5, as given, presupposesthat one of the observational points, namely L,, will lieexactly on the theoretical curve. Often a better fit toall of the data can be obtained if this limitation is notimposed. If the equation for the straight line yieldedby the logarithmic plot is written in the form y = m t+ b, it is clear that values of y computed for differentvalues of t will correspond to the left-hand term ofequation 5 for the same values of t. The theoreticalconcentrations L can then be obtained. If a equals thenumber whose logarithm is y, then

L + Leq.'L - Leq.

and7. L = ( ° ) L.

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BILIRUBIN CLEARANCEFROMTHE PLASMA

The reader should note that the equations ofthis section are concerned with the developmentof a theory and with putting the data in suchform that the agreement between theory and ob-servation can be tested. Later it will be shownthat the velocity constant, which is the measureof hepatic function, can be calculated in a simpleway from observational data without recourse tographic methods.

Agreement between observation and theoryThe theory outlined above intimates that the

quantitative appraisal of hepatic excretory func-tion given by the velocity constant is independentboth of the amount of bilirubin injected and ofthe exact time intervals at which samples arewithdrawn. However, practical considerationssuggest that sufficient bilirubin be injected andsamples be taken over long enough time intervalsso that the consecutive concentrations cover arange well outside the limits of analytical error.In the observations to be described, the amountof bilirubin injected was 5 mgm. per kilo. Aninjection of this size has never given rise to toxicmanifestations.

According to the size of the patient (children), thebilirubin was dissolved in from 5 to 10 cc. of a 0.1 Msolution of sodium carbonate. Solution was hastened bywarming over a flame; after cooling to body temperatureit was injected without further sterilization. A bloodsample was taken before injection to determine the valueof L.q.; after injection 5 to 7 minutes were allowed formixing in the circulation; then, a number of sampleswere obtained over a period of 4 hours. Analyses weremade on serum rather than plasma to eliminate theosmotic action of the ordinary anticoagulants.

Data obtained with A. S., a Jewish boy, aged12 years, are presented in graphic form in Figure1. This patient entered the hospital with spleno-megaly resulting from fibrosis and obstruction ofthe larger branches of the splenic vein. The caseis selected for illustration because at operation(splenectomy) a biopsy specimen was securedfrom the liver. The liver tissue was normal.The bilirubin clearance test was carried out inthe manner outlined above. The upper chart inFigure 1 is a plot of the logarithms of (L + L.q,.)

(L - Leq.) against the time at which the sam-ples were taken. The straight line through theplotted points was fitted by eye and its equationwritten in the form shown. By equation 6 the

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k= 5.28 x 103mg.perzmin.perrng2Leq. = 0. 5i mgj. per 1O0 cc

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0 30 60 90 12 150 180210 240Time in Minutes

FIG. 1. BILIRUBIN CLEARANCEIN A BoY WITH NORMALLIVER FuNCrION

The upper chart illustrates the graphic method of fit-ting a straight line to the observations. In the lowerchart the 'line joining the open circles depicts the theo-retical curve of clearance; the black dots refer to ana-lytical data and show the agreement between observationand theory.

velocity constant of excretion was calculated tobe 5.28 X 1O- mgm. units.2 Then values of y

2 For the sake of brevity the expression " milligramunits " will be used throughout the rest of this paperrather than the more exact " milligrams per minute permilligram-squared of concentration in the plasma."

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325

A. A. WEECH, DOROTHEAVANN, AND ROSE A. GRILLO

were computed for a number of values of t; byequation 7 the theoretical bilirubin concentrationscorresponding to the time intervals were deter-mined. The lower curve of Figure 1, plottedfrom these data, shows the theoretical curve ofclearance; the black dots along the general pathof the curve depict the observed concentrations.It is clear in this case that the theory describes thefindings with close approximation. Inspection ofthe logarithmic graph in Figure 1 shows that thevalues of the ordinate for low values of t havebeen fitted closely to the straight line, whereaswith higher values of t the fit is less close; never-theless the clearance curve lies near to all of thedata. This circumstance results from the natureof the function and indicates a general principleto be followed in obtaining the theoretical curve;the logarithmic values corresponding to high con-centrations and low time intervals must be fittedclosely by the line, whereas with the later valuesfrom lower concentrations considerable latitude ispermissible.

In Figure 2 are presented' data obtained withL. H., a white girl, aged 9 years. An enlarged,firm liver, an abnormal galactose tolerance test,and a history of an acute illness 2%2 years earlierwith jaundice which persisted several months sug-gested a diagnosis of cirrhosis. The findings inthe bilirubin clearance test illustrate the applica-tion of the theory to a case in which liver functionwas impaired without elevation of the equilibriumlevel. The agreement between observation andtheory is adequate, though less close than in mostother cases.

Figure 3 presents data given by R. R., aged 6years, a boy of Italian parentage suffering fromchronic erythroblastic anemia. In this case thebasal bilirubin concentration in the serum waselevated to 2.45 mgm. per 100 cc. and there waschronic jaundice. The agreement between ob-servation and theory is good. The velocity con-stant, 1.23 X 10-8 mgm. units indicates markedimpairment in the excretory function of the liver.

Validity of the basic assumptions

The illustrative cases of the preceding sectionshow that the theory of bilirubin excretion is ableto chart the path of clearance from the plasmawith approximate accuracy. The illustrations are

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Time in MinulbsFIG. 2. BILIRUBIN CLEARANCEIN A GIRL WITH IM-

PAIRED LIviER FUNCTION IN THE PRESENCEOF A NORMALBASAL CONCENTRATIONOF BILIRUBIN IN THE PLASMA

The upper and lower charts have the same meaning asin the previous figure.

average ones; in a number of instances the good-ness of fit between observation and theory hasbeen closer than in any of the cases presented.It does not necessarily follow that the assumptionsunderlying the theory are justified; if they are not,the quantitative estimate of liver function can beunreliable. It is therefore important to examinethe assumptions in greater detail.

The first assumption was that the normal levelof bilirubin in the plasma results from an equi-librium between the rates of formation and ex-cretion. The alternate possibility is that the liverestablishes a threshold level above which bilirubinis excreted and below which it is not. The widerange of normal levels encountered in different

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326

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BILIRUBIN CLEARANCEFROMTHE PLASMA

patients, and the fact that high levels in hemolyticdisease are invariably associated with demonstrablyslow excretion of injected bilirubin, speak againsta threshold mechanism as being the only factor inmaintaining equilibrium values. Moreover, it is

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possible to show that an increase in the rate atwhich bilirubin is added to the circulation willresult in a new and elevated level of equilibrium.An experiment of this type performed on a dogwhich weighed 20 kilos is illustrated in Figure 4.

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Continuous Intrvinoux Infusionwith

Sdtffion of Diirubin50 mg. perhour

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Minutes AfterBegiing hfusionFIG. 4. AN EXPERIMENTWITH A DoG WHICHDEM-

ONSTRATESTHAT THE CONTINUOUSINTRAVENOUS INFU-SION OF BILIRUBIN LEADs TO A NEWEQUILIBRIUM CON-CENTRATION IN THE SERUMAT AN ELEVATED LEVEL

At the start the bilirubin concentration in theII II I I I I plasma was 0.13 mgm. per 100 cc. During the

next 4 hours the dog received a continuous in-

3travenous infusion of bilirubin solution; by means

k=L.23xiO03mg.per min.permg2 of special apparatus the rate of flow was main-Leq.= 2.45 mg. per 1OOcc. tained constant at 13 cc., containing 50 mgm. bili-

rubin, per hour. Serial determinations showedan initially rapid, then progressively slower, risein serum bilirubin concentration until a new equi-librium was reached at 1.13 mgm. per 100 cc.Experiments of this kind provide additionalgrounds for believing that the equilibrium level isaffected by the rate of bilirubin formation. Theydo not, however, exclude the possibility of a basalthreshold level which would be reached, but notpassed, if all formation stopped. On anatomicalgrounds it appears unlikely that the liver canfunction as an excretory threshold organ and weknow of no other evidence to indicate that it can.

3I -60 90 I IO I0 I21 , Proof that it cannot is, however, lacking and the306090 120 150 180 21024 first proposition underlying the theory must re-Timmein Mirnules

BILIRUBIN CLEARANCEIN A BoY WITH CHRONIC main a reasonable assumption.ERYTHROBLASTICANEMIA The second assumption that the rate of bili-

ndings illustrate application of the theory when rubin formation will remain constant during theiction is impaired and when the basal serum bili- period of the test rests on the observation thatncentration is elevated. individual subjects tend to maintain the same

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327

4

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1.

A. A. WEECH, DOROTHEAVANN, AND ROSE A. GRILLO

plasma concentrations when studied serially overa number of days and on the fact that high con-centrations such as are encountered in hemolyticdisease do not affect the stability of the equi-.librium level. It is reasonable, then, to supposethat even greater constancy will exist during thelimited 4-hour period of a test. Presumably, therate of bilirubin formation is related closely tothe rate of blood destruction; the latter appears toproceed at a uniform rate both in normal subjectsand in patients with hemolytic disease. In occa-sional conditions, as in the early neonatal period,the rate of blood destruction may be changingrapidly; under such circumstances, the theory de-veloped in this paper would have to be appliedwith great caution.

The third asumption that the rate of excretionis proportional to the square of the concentrationin the plasma is admittedly an approximation.Inspection of the graphs presented in this paper,as well as of similar data charted by Eilbott (1)and by Harrop and Barron (3), leaves no doubtof a direct relationship between concentrationand rate of excretion; after intravenous injectionthe rate of disappearance of bilirubin from theplasma always decreases as the concentration de-clines. Unless velocity of excretion increasedwith rising concentration, no equilibrium could bereached in experiments of the type illustrated inFigure 4. It is clear, then, that E, the excretoryrate, can be represented by some mathematicalfunction of L, the plasma concentration. Thereis no proof, however, that the function will be thesame for all subjects; at the outset it is possiblethat the nature of the function may be altered inthe presence of liver disease. The function rep-resented by the equation, E = KL2, was arrivedat after experimenting with a number of otherrelationships. In particular it was found that thesimpler expression, E= KL, is not adequate todescribe observational findings. On the contrary,the expression, E- KL2, has led to theoreticalclearance curves which agree satisfactorily withobservation in a wide variety of patients and indogs. Cumulative experience, however, stressesthe approximate nature of the relationship. Ex-amination of the average findings in a series ofpatients indicates that somewhat better agreementwith theory would result if, in the general ex-

pression, E = KLn, n were assigned a value some-what greater than 2. The difficulty of handlingsuch expressions mathematically has preventedfurther exploration along this line. Because therelationship used in the theory is only a goodapproximation, it follows that the measure ofliver function K will not, for any one patient, beentirely independent of the amount of bilirubininjected nor of the time interval over which sam-ples are collected. With intervals ranging from2 to 4 hours, the variations in K are small but itis probably inadvisable to rely on velocity con-stants computed from data covering a shorterperiod than 2 hours. Wedo not have experiencewith smaller injections than 5 mgm. per kilo.

Direct computation of the constant of bilirubinexcretion

The illustrative data which have been presentedso far and the method of computing the velocityconstant, have been given in order to establish thevalidity of a theory. Actually, the assessment ofhepatic excretory function can be accomplishedwhen only three samples of serum are analyzed.

The level in the circulation before injecting bilirubin,Leq., must be measured first. When sufficient time haselapsed after the injection for thorough mixing, a secondsample, L1, is obtained. Finally, after 2 to 4 hours, thethird sample, L2, is secured. If t, and t2 represent thetime in minutes corresponding to the samples L1 and L3,which express concentration in milligrams per 100 cc.serum, the value of the velocity constant K can be com-puted from the equation:

8. K= 1.1513o

(L2 +Leq.) (L -Leq.)Leq.(h- ti) (L, - L .) (Li + Leq.)

Error of measurementIn the bilirubin tests carried out in the Babies

Hospital a fairly large number of samples hasbeen analyzed with each patient in order to chartthe path of the clearance curve. By use ofequation 8 such data permit several independentcalculations of the velocity constant. Since an ap-proximation is involved in the theory, the agree-ment to be expected among the several values willdepend to some extent on the time periods usedin their computation. Wehave already stated thedesirability of a time interval of at least 2 hours.In most of our cases three samples, L1, L2 and L8,were obtained during the first 30 minutes after in-jection of bilirubin; subsequent samples L4, L,

328

BILIRUBIN CLEARANCEFROMTHE PLASMA

and L,,, were taken at 120 minutes, at 180 minutesand at 240 minutes, respectively. Illustrative val-ues of K computed from L1 and L, L, and L,LB and L6f, are recorded in Table I. If the func-

TABLE I

Agreement among three independently calculatedvalues of the velocity constant

The figures in column A were computed from samplestaken at 0 and 120 minutes, in B from samples at 15 and180 minutes, in C from samples at 30 and 240 minutes.The illustrative cases were selected to sample the range ofaverage values which have been encountered.

K X 10' mgm. per minute per mgm.2Patient

A B C Average

N.R . ..........26.226.9 20.4 24.5D.C............ 9.1 9.9 8.5 9.2E.R......... ..7.5 8.0 7.4 7.6D.S... 5.9 6.4 6.1 6.1W.C..... . 4.9 6.2 4.8 5.3S.F ......... ..4.4 5.2 4.5 4.7M.K.. 3.8 3.5 2.8 3.4H.S......... ..2.3 2.4 2.3 2.4R.R......... ..1.2 1.4 1.1 1.2A.L.. 1.3 1.1 0.9 1.1

tion of the liver is to be assessed from the mini-mumnumber of analyses, and if the two sampleswhich follow the injection are separated by an in-terval of at least 2 hours, data like those in TableI can be used to determine the error of the assess-

ment. Examination of the separate K valuesyielded by the 35 patients studied so far showsthat, although the error becomes larger as thevalue of K rises, the percentage error is approxi-mately constant for all values of K. This error

(coefficient of variation) is + 13.6 per cent.When several independently determined values are

averaged, the error will be reduced. Since therange of K encountered in different subjects, bothdiseased and healthy, has been from 1.09 X 10-to 24.5 X 108 mgm. units, the 13.6 per cent error

will not in most instances interfere with ade-quately accurate appraisal of liver function. Onlyin those cases where function is within or near thezone which separates normal from abnormal isgreater accuracy desirable and in such cases a

larger number of samples should be taken.

Clinical findingsThe measures of liver function, that is, K values,

to be reported were determined by the method ofaveraging several independent estimates. In most

instances three, in a few only two, such estimateswere utilized. Experience shows that these aver-age values yield theoretical clearance curves whichagree with observation as well as, and often betterthan, the values obtained by the graphic method.The agreement between values determined by thetwo methods has always been close.

The 35 patients whose excretory liver functionhas been measured were selected from the wardsof the Babies Hospital. They ranged in age from8 months to 15 years. Since within these limitsthere is no evidence that function varies with age,this factor will not be considered further. Nosingle group of the patients can be set aside asrepresenting normal healthy controls since suchsubjects do not constitute the population of a hos-pital. In the majority of instances, however,there was no reason to suspect the presence ofimpaired liver function; a few patients were stud-ied because of chronic hemolytic jaundice, a fewbecause of known cirrhosis of the liver, and in afew the status of the liver was in doubt. Noneof the patients had fever when the tests were done.

With 17 of the 35 patients the velocity constantwas above 5.0 X 10- mgm. units; in none of thesecases was there reason to suspect impaired liverfunction and the K values are clearly within therange of normal. The highest excretory rate inthe group, 24.5 X 10- mgm. units, was recordedin a colored boy, aged 11 years, who presented acardiac murmur and a story of recurrent arthralgiaover a number of years. There was no past epi-sode of cardiac decompensation and the possiblediagnosis of rheumatic fever was never clearlyestablished.

Findings with the 18 patients who exhibitedconstants below 5.0 X 1i0-1 mgm. units are re-corded in Table II. Inspection of the diagnosesfor the first 6 patients, with constants rangingfrom 4.88 to 3.63 X 10-8 mgm. units, suggeststhat these values must likewise be regarded as nor-mal. The seventh patient, R. H., yielded a con-stant of 3.36 X 10- units; he had suffered forsome years with cirrhosis of the liver, proven bybiopsy. There was chronic ascites for which ab-dominal paracentesis had been performed on nu-merous occasions. However, the history failed toreveal any episode of jaundice, the basal level ofbilirubin in his plasma was relatively low, and itseems likely that hepatic excretorv function was

329

A. A. WEECH, DOROTHEAVANN, AND ROSE A. GRILLO

TABLE ll

Findings wuith 18 patients in whom the velocity constant ofbilirubin clearance, K, was less than 5.0 X 10-3 mgm. perminute per milligram-squared of concentration in the plasma

Patient Age Leq. K Diagnosis

mgm. mgm.years per units

100 cc. X 10-81. S.F ....... 2 0.86 4.88 Bronchitis2. D.S....... 1 0.50 4.69 Intracranial angioma3. S.D....... 1 0.72 4.54 Behavior disorder4. A.R...... 4 0.73 4.50 Epilepsy5. A.C....... 6 0.52 3.90 Nephritis6. F.B....... 7 0.73 3.63 Nephritis7. R.H...... 11 0.36 3.36 Cirrhosis8. R. ....... 11 0.99 3.35 Nephrosis9. M.K...... 7 0.59 3.35 Diabetes

10. H.R...... 9 0.92 2.62 Intestinal parasites11. H.S....... 12 0.76 2.36 Osteodystrophy12. A.G ....... h 1.80 2.33 Erythroblastic anemia13. R.C ...... 2 0.69 1.92 Cirrhosis14. B.S ....... 9 0.86 1.45 Cirrhosis15. W.B...... 13 1.84 1.39 Sickle cell anemia16. L.H ....... 9 0.55 1.38 Cirrhosis17. R.R...... 6 2.45 1.23 Erythroblastic anemia18. A.L....... 15 1.40 1.09 Hemolytic anemia (un-

classified)

not greatly impaired. Patients 8, 9, and 10, withconstants from 3.35 to 2.62 X 10- mgm. units,presented no other finding to suggest hepatic de-fect. Patient 11 exhibited the peculiar syndromeof asymmetrical osteodystrophy with areas of pig-mented skin which has been described by McCune(15) and by Albright (16). She herself showedno sign definitely attributable to liver malfunction;however, other patients with the same syndrome(15, 17) have given a story of severe and pro-tracted neonatal icterus. The last seven cases inthe table represent instances either of chronichemolytic anemia and hyperbilirubinemia or ofcirrhosis. In all of these there is reason to thinkthat excretory hepatic function was impaired.

Review of all of the findings indicates first thatexcretory liver function exhibits in different sub-jects variations through a fairly wide range beforeit can be designated as impaired. It follows thatsome patients may as the result of disease sufferconsiderable loss of this power and still retainmore adequate function than other normal sub-jects. The range of excretory power in individ-uals with functionally adequate livers aids in anunderstanding of the wide range of serum bili-rubin levels encountered in normal subjects. Inour experience these levels have varied from 0.21to 0.99 mgm. per 100 cc. The findings also sug-gest that values for the excretory constant below2.0 X 10-a mgm. units must be regarded as evi-dence of impaired function. With values between2.0 and 2.5 X 10-3 mgm. units, it is probable thatfunction has been damaged. With constants

above 2.5 X 103 mgm. units, the significance ofindividual findings is less clear. If all of the con-stants above 2.5 X 10-3 mgm. units, with the ex-ception of the finding in the cirrhotic patient (R.H.), are accepted as apt to be encountered in theabsence of hepatic defect, there are 26 records todetermine the range and distribution of normalvalues. In mgm. units X 10-8 these records dis-close: 2.5 to 4.0, 5 cases; 4.0 to 5.5, 8 cases; 5.5to 7.0, 5 cases; 7.0 to 8.5, 4 cases; 8.5 to 10.0, 1case; above 10.0, 3 cases.

SUMMARY

The rate of removal from the circulation ofintravenously injected bilirubin can be evaluated asa " velocity constant of excretion " which providesa measure of the excretory function of the liver.The measure is not affected, as is the older typeof bilirubin excretion test, by elevation of the basalplasma concentration.

Evaluation of the velocity constant is based onthe assumption that normally circulating bilirubindepends on an equilibrium between the rate offormation, which is constant, and the rate of ex-cretion, which has been observed to be approxi-mately proportional at any moment to the squareof the concentration in the plasma.

The velocity constant is computed in milligramunits which express the rate of excretion fromeach 100 cc. of plasma in milligrams per minuteper milligram-squared of concentration in the cir-culating plasma. A minimum of three determina-tions of serum bilirubin concentration is requiredfor the calculation. The level before injectingbilirubin, Leq. is measured first. The injection, 5mgm. per kilogram of body weight, is then given.After a lapse of 5 to 7 minutes for mixing in thecirculation, a second sample, L,, is obtained. Fi-nally, when from 2 to 4 hours have elapsed, thethird sample, L2, is withdrawn. If t1 and t2 repre-sent the time in minutes corresponding to the sam-ples L1 and L2, which express concentration inmilligrams per 100 cc. serum, the value of thevelocity constant, K, can be computed from theequation:

1.1513 1 (L2 + Leq.)(L1 -Lq.)RLeq.(t2- 11) (L2- Le.)(L1 + Le,.)

A study of 35 patients with normal and de-fective livers revealed variations in the velocityconstant from 1.09 to 24.5 X 108 mgm. units.

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For the present, values above 2.5 X 10-8 mgm.units must be interpreted as evidence of normalhepatic function, although low constants withinthe normal range may for some patients be in-dicative of loss of excretory power. Values be-tween 2.0 and 2.5 X 10-3 mgm. units provide pre-sumptive evidence of damaged hepatic functionand values below 2.0 X 103 mgm. units are posi-tive evidence that function is impaired.

APPENDIX-METHODOF ANALYSIS

The assessment of hepatic function by means of bili-rubin clearance depends upon accuracy in determiningbilirubin in serum or plasma. In common with otherinvestigators (1, 3) we have found that the requisite pre-cision is not obtainable through measurement of the colordeveloped in the van den Bergh reaction. This is trueeven when the azobilirubin is estimated photoelectricallyby the excellent method of Malloy and Evelyn (18).Accordingly, we have followed the suggestions of Ernstand F6rster (19) and of Eilbott (1) in using acetone toprecipitate serum protein so that the yellow color of bili-rubin itself can be measured in the filtrate. The sensi-tivity of the method and the accuracy of the results havebeen increased significantly by use of a selective colorfilter and photoelectric analysis. Previous investigatorswho have used the method for measuring bilirubin excre-tion have not been concerned with the error due to theyellow color of lipochromes; such carotenoid pigmentspresumably do not vary throughout the test and theirabsolute magnitude was unimportant since only incre-ments in bilirubin concentration above the basal level wereused in computing percentage retention. Measurement ofthe velocity of bilirubin clearance, however, depends uponthe absolute concentration of bilirubin at all times duringthe test. Accordingly, carotenoid pigments have been es-timated separately after extracting the serum with petro-leum ether; a correction is then applied in the measure-ment of bilirubin.

Estimation of total yellow color (bilirubin plwu lipo-chrome). Two and five-tenths cc. of distilled water, 0.5cc. of the serum, and 10 cc. of redistilled acetone arepipetted in the order mentioned into a 15 cc. centrifugetube. The contents are mixed thoroughly with a stirringrod which is subsequently discarded so that the tube canbe closed with a rubber cap. It is then placed in theicebox for 15 minutes or until well chilled. Throughoutthese and later manipulations every effort is made tominimize exposure to light. We have routinely storedsamples and tubes in a covered can, removing them onlyin subdued light for essential steps in the procedure.Centrifugation of the chilled tubes is carried out for 15minutes in 300 cc. bronze cups which are filled withcracked ice before the tubes are inserted. Immediatelyafterwards the supernatant fluid is transferred to anothertube which is stoppered and allowed to come to roomtemperature. The purpose of chilling during this phaseof the procedure is to obtain a solution free from any

trace of turbidity. When chilling is neglected the fluidwill become warm while in the centrifuge and, eventhough clear when first removed, may later develop aslight cloudiness as the temperature falls. The final stepinvolves the photoelectric reading.

Estimation of the yellow of lipochrome. Since it isassumed that the amount of carotenoid pigment in theserum does not vary during the test, the portions of theserial samples which remain after the estimation of totalyellow color are mixed to provide a single sample onwhich lipochrome is measured. In principle the analysisfollows the procedure of Stoner (20). Two cc. of theserum is transferred to a test tube; anhydrous calciumsulphate is added and by means of a glass spatula thor-oughly mixed with the serum until a dry paste results.Two cc. of 95 per cent alcohol is stirred thoroughly withthe paste. Then, exactly 8 cc. of petroleum ether isadded; the tube is stoppered and the contents shakenvigorously for several minutes. Upon settling, a portionof the petroleum ether layer, which now contains thecarotenoid pigments, is removed for measurement ofcolor intensity in the photoelectric instrument.

With both analyses, total yellow color and lipochrome,the galvanometer readings are calculated to express inmilligrams per 100 cc. of serum the quantity of bilirubinwhich would have yielded the same readings. Bilirubinis then computed as total yellow color minus the yellowdue to lipochrome. With most subjects the correctionfor lipochrome is small, in the neighborhood of 0.1 or 02mgm. per 100 cc. In one patient only in our series, adiabetic, the correction reached a value of 0.67 mgm. per100 cc.

The photoelectric photometer used for the estimationof color intensity was one which was constructed in ourown laboratory (21); other instruments which utilizeselective color filters should be adaptable to the procedure.Readings were made in optical cells which were either2.5 or 5.0 cm. in length; the shorter cell was used whencolor intensity was high and the longer cell with palersolutions. The filter, which furnishes blue light, wasconstructed of the following components: Corning Num-ber 511, violet glass, thickness 3 mm.; Jena optical filterglass GG-5, thickness 2 mm.; Corning light shade Akloglass Number 396, thickness 2 mm. Solutions of bili-rubin exhibit maximum light absorption at 440mu; thefilter described transmits light from 410 to 490 nv, witha peak transmission at 450m/A.

Calibration presented a problem. Whendifferent stand-ard solutions are prepared by dissolving weighed amountsof bilirubin in chloroform and subsequently diluting eitherwith alcohol or acetone, discrepancies among replicatereadings will be much greater than when multiple meas-urements are made on the same solution. This is espe-cially so when the bilirubin of one manufacturer is com-pared with that of another. We have assumed, then,that part of the difficulty arises from impurities in avail-able samples of bilirubin; another part undoubtedly comesfrom the circumstance that bilirubin in either alcohol oracetone is not in true solution but rather in a state ofcolloidal dispersion. Variation in the size of such col-loidal aggregates is known to influence light absorption

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(22). On the other hand, calibration curves preparedfrom dilutions of solutions showing the same initial colorintensity have always agreed closely; likewise, the agree-ment between duplicate analyses of serum has beenexcellent. Evidently, then, the method is capable of yield-ing results whose relative precision is high; the absoluteaccuracy of the levels is not better than can be obtainedby other good technics. These circumstances determinedthe method of calibration. The relative value of readingson the galvanometer scale was first determined carefully.The absolute concentration of the solutions of bilirubinused for this purpose was not known. Carefully pre-pared dilutions of each solution revealed slight butclearly demonstrable deviation from Beer's law. Thedeviations were calibrated so that color intensity couldbe measured in arbitrary units of bilirubin. Finally, thenumber of milligrams corresponding to each arbitraryunit was determined in the following way: Twenty-foursamples of serum which contained varying amounts ofindirect bilirubin were analyzed by the procedure out-lined above and by the photoelectric method of Malloyand Evelyn (18). The latter method had previously beencalibrated in our own laboratory with pure Hoffmann-La Roche bilirubin. The average findings by the twomethods were then used to determine the milligrams tobe assigned to each unit. An important circumstance inleading us to adopt this comparative method of calibra-tion was the fact that Hoffmann-La Roche bilirubin canno longer be purchased on the market. Malloy andEvelyn have presented reasons for believing this bili-rubin to be of a higher grade of purity than that pro-curable from other sources.

Practically all of our analyses of serum have beenperformed in duplicate. The relative accuracy of thepresent method is indicated by the agreement between theduplicates. With levels of bilirubin below 1.0 mgm. per100 cc., the data reveal a standard error of analysis,S.E.A, of ±0.012 mgm. per 100 cc. With higher con-centrations, the errors per 100 cc. are as follows: 1.0 to2.0 mgm., S.E.A =0.023 mgm.; 2.0 to 5.0 mgm., S.E.A= 0.029 mgm.; above 5.0 mgm., S.E.A = 0.045 mgm. Thevalues yielded by the method do not appear to be affectedby hemolysis in the sample. We have obtained identicalresults in serum analyzed before and after the additionof laked red blood cells. In contrast, such additions havealways decreased the intensity of color in the van denBergh reaction. The method cannot be used to measurebilirubin in the serum of patients with obstructive jaundiceor with icterus due to hepatitis. A part of the bilirubinin these cases gives a direct reaction in the van den Berghtest; direct bilirubin is precipitated by acetone along withthe serum proteins. Under such circumstances the pro-tein precipitate is stained yellow and the fact that theestimate will be unreliable can be recognized at once.

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