THYROID FUNCTIONASSAYWITH RADIOIODINE. II. ROUTINECALCULATIONOF THYROIDAL AND

RENALRATE FACTORS1

By T. H. ODDIE,2 I. MIESCHAN, AND J. WORTHAMI(Froni the Department of Radiology and Department of MIedicine,

University of Arkansas, Little Rock, Ark.)

(Su-bmitted for puiblication May 7, 1954; accepted August 30, 1954)

In the preceding paper (1) mathematical equa-tions and numerical data were presented describ-ing the early movement of a test dose of radio-iodine in the human body. The informationgiven can be used directly to calculate thyroidaluptake and renal excretion rate factors (or clear-ance rates) from observed values of the fractionsof the net dose in the neck, N, and urine E,without the need for any blood samples, but theprocess is rather too tedious for routine use.However, the procedure can be greatly simplifiedby making suitable charts relating N and E tothe thyroidal, ki, and renal, k2, rate factors forselectedfixed times t after injecting the test dose.Fixed time schedules are necessary because other-wise a large number of charts is required. Forconvenience the pertinent equations from thepreceding paper (1) are repeated below:

k = k1 +k2 (1)

k1k=N - NoV./V + ENoV./V (2ki/k N - NoVX/V + E (2)

kot = ItiI - NoV/V (3)

All the symbols used are as defined in the preceding paper(1), namely:

E = The fraction of the original dose excreted by thekidneys up to time t minutes after injection.

k min.-' = The average combined (thyroid plus kidneys)fractional rate of removal of radio-iodide from the iodidespace during the time interval t = 0 to 30 minutes;that is, an average fraction k of the circulating iodidepool is removed each minute.

k1 min.-' = The average fractional rate of uptake by thethyroid from t = 0 to 30 minutes.

k2 min.- = The average fractional rate of renal excretionfrom t = 0 to 30 minutes.

N = The fraction of the original dose observed in theneck by external counting at time t, including boththyroid and extra-thyroid tissues.

1 University of Arkansas Research Series No. 1007.Assisted by Grants numbers C-1866 and H-1702, from theNational Institute of Health, Dixvision of Research Grants.

2 Fulbright Fellow.

N0 = rhe iniitial value of N at time t = 0 assuminig in-stantaneous mixing of the dose with the circulatinigplasma.

t mim. = The time from inijection of the test dose.V ml. = The volume of the total effective iodide space at

time t.VnNo ml. = The apparent volume of iodide space, at time

t, that is "observed" in the extra-thyroid neck tissuesby the external counter.= The average value of 1/V up to time t expressed as afraction of the average Up to t = 30 minutes.

The above three equations are all that are needed forthe development of simple routine methods and charts,as will be shown in the following sections.

EXTRA-THYROIDAL RADIOIODINE CONTENTOF

NECK TISSUES OBSERVEDBY

EXTERNALCOUNTER

The term NoNV/N' in equations (2) and (3) isderived from the fraction of the net dose observedin the extra-thvroidal neck tissues at time t,which has been shown (1) to be given byNoVn,e-koI0VXe . It has also been shown that VI/'\Vvaries with time, but average smoothed valuesof this ratio have been tabulated in the form

VAr -where the denominator represents the

value of V/ at exactlIy two minutes afterinjection.

If then, No0Vn/\ (at any particular time t)can be treated as a constant for all patients,equations (1), (2) and (3) can be represented ononly one pair of charts connecting k1 and k2 withN and E for each selected time t; but if NoVn/Vvaries too widely from patient to patient, a largenumber of pairs of charts must be constructed tocover the range of variation of this factor. More-over, there is the additional advantage that ifNoVn/V is known with sufficient accuracy for allpatients, there will usually be no need to makean initial in vivo count over the neck immediatelyafter injection.

Obviously variations from patient to patient106

CALCULATION OF THYROIDAL AND RENAL IODINE CLEARANCE

.05 .1 .2 3 .4 .5 6 .7NV-.P

FIG. 1. CHARTFORTHYROIDAL RATE k1 MEASUREDAT ONEHOUR(t = 60)

become less troublesome when the extra-thyroidaltissue contribution NOVn/V is kept small by care-ful collimation of the external counter; to providesome data on this point we have measured thevalue of No(Vn/V)2--that is the extra-thyroidalneck tissue fraction two minutes after injection-in the same athyroid patient with four different

counting arrangements with the results presentedin Table I.

The benefit derived from using a long colli-mator is apparent from the reduced value of thecontribution of the neck tissues. In addition wehave made observations on two series of differentpatients with long and short collimators, finding

107

T. H. ODDIE, I. MESCHAN, AND J. WORTHAM

mean values with standard deviations of theindividual values set out in Table II.

Here again the long collimator gives more con-

cordant results, and by using it for routine up-

take studies No(Vn/V)2 can be taken as 0.071,with a maximum expected variation of about4.027, for all cases except doubtful ones under-

going repeated tests; such cases occur sometimes

when the numerical results of a first test lie close

to the diagnostic borderline values separatingeuthyroid and hyperthy roid groups.

For the latter exceptional cases, or for colli-mators of different shape, it is necessary to de-duce the individual values of NoVW/V from theinitial and final total counts over the neck. Thiscan be done by approximating equation (11) ofthe preceding paper for times t and two minutes,finally obtaining the approximate relation

N0V 'nV = [ t'N\ - 4.3 N]

Et (Vtn/ V)2- 4.3]

Vn/\' (4)

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CALCULATION OF THYROIDAL AND RENAL IODINE CLEARANCE109

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FIG. 3. CHARTFORTHYROIDALRATE k1 MEASUREDAT FOURHOURS(I = 240)

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T. H. ODDIE, I. MIESCHAN, AND J. WORTHAMN

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NFIG. 4. CHARTFOR REN-AL RATE k2 MEASUREDAT FOURHOURS(t = 240)

TABLE I

Estimated areaof neck and

torso observed,including

penumbral ObservedCounting arrangement region No (V,`V),2

Cylindrical Geiger counter intransverse position 15 cm.from skin; open type lead 550 cm.2 .126shield similar to arrangementof Werner, Quimby, andSchmidt (2)End window Geiger counter,15 cm. from skin, in cylin- 250 cm.2 .106drical lead shield of opentype.Scintillation counter, 47 cm.from skin, short collimator 1000 cm.2 .151as described earlier (1)Scintillation counter, 47 cm.from skin, long collimator as 200 cm.2 .073described earlier (1)

or, if the initial count is taken over the period 2to 10 minutes

NON,n/o f = [OtN2, 10 - 8.9 N]I

[95 Vn/V 2- 8.9] (5)Thus, for example, if t = 60 minutes is the

time selected for the second count, the tabu-

TABLE II

Standarddeviation

Number NO(Vn/V)2 of indi-Colli- of vidualmator cases Mean Range readings

Short 17 .146 .074-.272 .047Long 24 .071 .046-.100 .013

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CALCULATION OF THYROIDAL A:

lated values required are found in Table IIIof the preceding'paper as t = 50.8 minutes and

V=l/V - 0.84 so equation (5) reduces to(Vn/V) 2

NOVn/V = 1.05 N2,10 -0.184 N

Similar computations for other times lead tothe coefficients listed in Table III.

In the routine case where N0(Vn/V)2 = 0.071the derived figures for NOVn/V are those in thefourth column of Table III.

CHARTS;ORROUTINE TESTS

Assuming that routine tests can be timed sothat the middle of the period of the uptake ob-

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ND RENAL IODINE CLEARANCE 1l1

servations is at a preselected time, charts arereadily constructed to give k1 and k2 directlyfrom the observed fractions N and E. Suchcharts for our long collimator have been derived

TABLE III

Data for finding NoV5/ V

Time t minutes MeanNoVn/V

First Second Formula for finding with longobser- obser- from two neck counts colli-vation v-ation NoWN/V mator

2 30 1.01 N2 -0.144 N .0622-10 (mean) 30 1.28 N,10-0.38 N .0622-10 60 1.05 N o10-).184 N .0602-10 120 0.91 N 1o-0.093 N .0562-10 240 0.80 N 1o0.048 N .0512-10 1,440 0.56 N21o-0.009 N .037

--- ---- - -------ES - --- ---4 < w ° *.04 .0 40 - .3N

FIG. 5. CHARTFORTHYROIDALRATE k1 MEASUREDAT 24 HOURS(t = 1,440)

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NFIG. 6. CHARTFOR RENAL RATE kQ- MI EASUREDAT 24 HOURS(t = 1,440)

TABLE IV

Corrections for urine collection time *

Actual Correction Acttual CorrectionRequired collection factor for Required collection factor for

tt timet obserxed E tt timet observed E

55 1.15 230 1.0660 1.07 235 1.04

60 65 1.00 240 240 1.02(1 houir) 70 0.94 (4 hours) 245 1.00

75 0.89 250 0.9880 0.84 255 0.96

260 0.95

110 1.12 1,400 1.03115 1.08 1,415 1.02

120 120 1.04 1,440 1,430 1.01(2 hours) 125 1.00 (24 hours) 1,445 1.00

130 0.97 1,460 0.99135 0.94 1,475 0.98140 0.92 1,490 0.97

* Note that 5 minutes' lag is allowed in urine accumulation, so that urine collected at, for example, 65 minutes, isassumed to be that excreted tip to t = 60.

t All times in minutes from injection.

..41f. J*..AI

112

CALCULATION OF THYROIDAL AND RENAL IODINE CLEARANCE1

TABLE V

Solution of equation (3) for k at preselected times

10'k minl1 -NoVD/V1-N-E

1.001.051.101.151.201.251.301.351.401.451.501.551.601.651.701.751.801.851.901.952.002.12.22.32.42.52.62.72.82.93.03.13.23.33.43.53.63.73.83.94.04.24.44.64.85.05.56.06.57.08.09.0

10.01214161820

} hourt -30

0.001.633.184.76.17.48.7

10.011.212.413.514.615.716.717.718.619.620.521.422.323.124.726.327.829.230.531.933.134.335.536.637.738.839.84142434444454648495152545760626569737783889296

100

1 hour60

0.000.961.882.753.594.45.25.96.67.38.08.69.39.9

10.411.011.612.112.613.213.614.615.516.417.218.018.819.620.321.021.622.322.923.524.124.725.225.826.326.827.328.329.230.130.931.733.635.336.938.34143454952555759

2 hours120

0.000.561.101.612.102.563.023.453.874.34.75.05.45.86.16.46.87.17.47.78.08.59.19.6

10.110.511.011.411.812.212.613.013.413.714.114.414.715.015.315.615.916.517.017.518.018.519.620.621.522.423.925.326.528.630.331.933.234.4

4 hours240

0.000.330.640.941.231.511.772.032.272.512.742.963.173.383.583.783.974.24.34.54.75.05.35.65.96.26.46.77.07.27.47.67.98.18.38.58.68.89.09.29.49.7

10.010.310.610.911.512.112.613.114.014.815.616.817.818.719.520.2

24 hours1,440

0.000.090.170.250.320.390.460.530.590.660.720.770.830.890.940.991.041.091.131.181.231.311.391.471.551.621.691.761.821.881.942.002.062.112.162.212.262.312.362.412.452.542.622.702.772.843.013.173.313.443.683.884.14.44.74.95.15.3

from equations (1), (2), and (3) using the mean

NoV./V from Table III; they are shown in Fig-ures 1 through 6, which give k1 and k2 for uptaketimes of 1, 4, and 24 hours (t = 60, 240 and1440 minutes).

In using the charts it is assumed that the neckcontent N is measured over the ten-minuteperiod from t - 5 to t + 5 minutes, and that Eis measured with urine produced up to t butcollected from the bladder at t + 5. If the urineis not collected at exactly this time a correctionshould be applied from Table IV.

NON-ROUTINETESTS

In non-routine tests where previous resultshave been doubtful or where there is reason tosuspect that NoV./V may be well away from theexpected average value, it is advisable to makeinitial counts over the neck during the periodt = 0 to 10 minutes. This should always bedone, if the final count is to be at 30 minutesbecause the average NoV./V may not be preciseenough for this short time of uptake.

Having found N, E, and N1or N2,lo, Table IIIenables NoV./V to be calculated, qt is foundfrom the figures tabulated earlier (1) so thatequation (3) gives k, equation (2) gives ki andfinally equation (1) gives k2.

To save time if t is kept to one of the selectedvalues (2, 1, 2, 4, or 24 hours), the solution ofequation (3) for the value of k may be foundfrom Table V. These methods will become clearfrom the following examples.

EXAMPLESOF CALCULATIONS

Routine case at t = 60 minutesLet the observed neck fraction, measured with the long

collimator from t = 55 to 65 minutes, be N = .235, andthe urine fraction collected at t = 73 minutes be .063.

From Table IV the corrected excretion fraction must beE = .063 X .91 = .057.

With these values of N and E, Figures 1 and 2 givek1 = 4.2 X 10-t minute1k2 = 1.3 X 10-3 minute-1

Non-routine case at t - 240 minutesLet N2 lo, measured over the period t = 2 to 10 minutes,

have an average value of .095; N, observed from t = 235to 245 minutes, be .106; and E, collected at t = 250 min-utes, be .134.

From Table IV the corrected urine value isE = .134 X .98 = .131

From Table III, putting in values

NgV,/V .80 X .095 - .048 X .106 = .071

then1 -N0V,/V 1 - .071 1.221-N-E 1-.106-.131 1

113

T. H. ODDIE, I. MESCHAN,AND J. WORTHAm

and Table V gives k - 1.34 X 10- minute-'. Fromequation (2)

so that

106 -07+.11= .9

k- - .265 X 1.34 X 10-8 .35 X 10-3 minute-1and from equation (1)

k2 - (1.34 - .35) X 10- = .99 X 10-8 minute'Non-routine case at I - 190 minutes

Let the measured fractions be N2, lo= .083, N = .317and the urine collected at t = 205, E = .188. Becausethe time of observation, t = 190 minutes, is not covered

by the charts or Table V, much more calculation is neededin this case.

First E is corrected from the presumed time of excretion(200 minutes) to the time of observation (190 minutes)by multiplying by the ratio of the corresponding ot valuestaken from the preceding paper (1). Thus the correctedvalue is

E = .188 X 124/129 = .181Then interpolating between the tabulated data of Table

IIINoV./V - .86 N,io .067 N .050

Equation (2) with these values gives=.317 .050 + .009

.317 050+ .181

and equation (3) gives

k .050 -5.1 X 10-' minute'1124 log 1- 31- .181so that

andki .616 X 5.1 X 10-3 3.1 X 10-8 minute-'

k2 2.0 X 10-1 minute-'

DISCUSSION

The method that has been described for calcu-lating the rate constants k, and k2 can be appliedregardless of the type of measuring equipmentused for uptake observations and urine assay;

the charts (Figures 1 through 6), however, are

only applicable to collimated counting arrange-

ments with a low average factor No(Vn/V)2 ofabout .07. Whenother wide-angle apparatus isemployed it is necessary to observe the initialcounts over the neck (or less preferably over thethigh) to find the correction for extra-thyroidalneck tissue.

Provided that sufficient counts are obtainedfor good statistical accuracy, and that the colli-mator is carefully positioned over the patient'sgland, a fair degree of accuracy can be expectedwith the higher values of kl, if measurements are

made one hour after injection. For low-k hypo-thyroid or cardiac cases, however, there will belittle or no rise in the counts over the neck inone hour and we suggest that the four-hour read-

ings should be selected, and in very low casesan additional set of values should be measuredat 24 hours also.

The fixing of diagnostic limits for the rate con-stants ki and k2 depends upon a number of ques-tions distinct from the more physical problemsdiscussed above; in fixing such limits use can be,made of some of the information already pub-lished by other groups, as will be shown in alater paper describing some of our own clinicalresults.

In the meantime it can be stated, from theinformation given in the preceding paper, thatthe thyroidal rate factor k, minute-' is relatedto the thyroidal clearance rate g ml. per minute,for a 70 Kg. patient, by the relation

ki= 10-' g/16.3This means that, if we take g = 60 ml. per

minute as the approximate diagnostic borderlinebetween euthyroid and hyperthyroid patients,the corresponding borderline value of k, will bearound 3.7 X 10- minute-'. Thus euthyroidvalues of ki will usually lie below this level, andthere will be another not very distinct borderlinebetween hypothyroid and euthyroid groups atabout k, = 2 X 10- minute-'.

SUMMARY

Based on a preceding paper, routine methodsare developed for calculating thyroidal uptakeand renal excretion rate factors from measuredfractions of the dose of radioiodine observed atan early time t after administration.

Charts are included, for selected times t of 1,4, and 24 hours, giving the rate factors directlyfrom the experimental observations when uptakereadings are made with good collimation to keepthe extra-thyroidal neck tissue contribution low.Under these conditions such contribution is takenas a mean value for all patients and an uptakestudy normally requires only one observationover the thyroid gland and one urine assay.

REFERENCES1. Oddie, T. H., Meschan, I., and Wortham, J., Thyroid

function assay with radioiodine. I. Physical basisof study of early phase-- of iodine mepbolism and!iodine uptake. J. Clin. Iavest., 1955, 34, 95*

2. Werner, S. C., Quimby, g. H., and Schmidt, C., Theuse of tracer doses of radioactive iodine, Ix, in thestudy of normal and disordered thyroid function inman. J. Clin. Endocrinol., 1949, 9, 342.

114