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Interpolation of nonlinear quench correction curves for a liquid scintillation counter using an olivetti 101 calculator
ANALYTICAL
BIOCHEMISTRY
Interpolation for
53, 2!%%%8 (1973)
of Nonlinear Quench Correction a Liquid Scintillation Counter Using an Olivetti
101
Curves
Calculator
The external standard ratio (ESR)l method of measuring radioactivity using a liquid scintillation counter is widely used at the moment. Our scintillation counter gives a nonlinear relationship when the ESR is plotted against counting efficiency (Fig. 1) for W. It was found that the equation ax3 + bX3 + cx + d = 0
(1)
did not accurately describe the variation of efficiency with ESR as was suggested by the manufacturer of the scintillation counter and led to
EXTERNAL FIG. divided
1. Counting efficiency into five straight-line
STANDARD
RATIO
as a function of external standard sections for the purpose of calculation.
ratio.
Curve
is
calculation errors at intermediate and low counting efficiencies. The following program has been designed to interpolate such a curve given the observed ESR using an Olivetti 101 calculator in the program mode and making full use of the potential of a rather small memory core. * Abbreviations: disintegrations Copyright All rights
ESR = external per minute.
standard
@ 1973 by Academic Press, of reproduction in any form
ratio,
295 Inc. reserved.
cpm
= counts
per minute,
dpm
=
296
SHORT
The efficiency curve (Fig. lines :
COMMUNICATIONS
1)
can be estimated
by a series of straight
Y=mX+b,
(2)
where Y = counting efficiency, m = slope, X = ESR, b = Y-intercept. A set of straight lines is superimposed on a quench-correction curve to best approximate that curve (Fig. 1). An auxiliary program (Fig. 3) is then used to calculate rn and b values for sections 1-5 of the curve. Enter in order: X,, X,, Y,, and Y,. After the last entry, the compound number mlbl-XZ will be printed automatically. A similar calculation is done for sections 2-5. The main program (Fig. 2) employs compound numbers stored as constants in the memory to calculate dpm. The co-ordinate X, is stored with m and b for section 1 of the calibration curve as a compound number m,b,-X, in register B of the memory. Similarly, registers B/, C, C/ and AV B& 1:
/t II/: 4
D/Z & F X Sl E/f C/V z B/V 01 L 1% DI: c FX E/ C/W Z B/W Cd
FX E/C/Y Z 61 Y c/r it -s o/t & FX A: E/ D/Y Z E/Y 04 I+ Y
s s AY D/Z AZ Fd F X ‘0,: D/I W s s S S AW IS
E/X III/t FX FX II/+ S2 : L_ RY s s S S S FY I= X
-FX D/q At 0 F+ F/S F + A20 RZ 10 s v
Fro. 2. Program for the calculation of dpm. External stop S1 and cpm is entered at stop S,. Other stops are that both numerical values and program steps can be At G, dpm is printed while at A? dpm corrected by printed.
standard ratio is entered at included in the program so stored in the same register. the factor in register F/ is
SHORT
297
COMMUNICATIONS
D of the memory contain the compound numbers mzbz-X, to m5b6-X6, respectively. The slope, m, may have three or four digits, b and X must each have three digits. A constant, 10, is stored in register F. When a correction factor is desired for dilutions or other manipulations, a value up to four digits in length may be stored in F/. At the user’s option, one may either place 1.0 in F/ or omit the second and third last steps of the program (FJ divide, A print) if no correction factor is needed. A routine calculation is done using the program in Fig. 2 by entering the ESR and the observed cpm value. The calculator then prints dpm. The program has the advantage that a set of straight lines can be quickly superimposed on a quench-correction curve. This curve-fitting procedure requires a minimum of mathematical knowledge. When stored on a magnetic card, the same program can be used for several scintillation counting fluids by placing in the memory the appropriate set of compound number constants. Other curves which have linear and nonlinear portions and are thus difficult to approximate with Eq. (1) may also be interpolated using this program. AV Sl
cl/ ? SZ D?
C’ 04 c x CX /a -
s3 E/t
ci
s, Et D/+ Cl D/t E/k ED./ f 0% B 4 OX E! Ea/! A/+ R/S 04
c+ C+ D : B/d C X ‘/: w: Bh CX CX it cx CX Cx cl+
Dt 814 c/v A/t E/ 4 c/t
X D+ c/x 10 Ai 0 IQ v w v El+ /Q
A2Q /Q V
FIG. 3. Program for the calculation of the slope and Y-intercept of a straight line. Enter in order at stops S,, S,, SJ, and S, co-ordinates X,, X,+1, Y., and Y,,. A compound number m,,bn*X,+l is printed at A, or Az.
SHORT
COMMUNICATIONS
ACKNOWLEDGMENTS The author thanks Dr. Ronald MacPherson, Defense Research Establishment Valcartier and Drs. Claude Willemot and Andre Comeau, Canada Dept. of Agriculture, Ste-Foy for helpful discussions.
H. J. Canadu
Department
of Agriculture
Station 2660 Chemin Gamin Quebec IO, Quebec, Canada Research
Received
August
9,197s;
accepted
February
2,197S
HOPE
BIOCHEMISTRY
Interpolation for
53, 2!%%%8 (1973)
of Nonlinear Quench Correction a Liquid Scintillation Counter Using an Olivetti
101
Curves
Calculator
The external standard ratio (ESR)l method of measuring radioactivity using a liquid scintillation counter is widely used at the moment. Our scintillation counter gives a nonlinear relationship when the ESR is plotted against counting efficiency (Fig. 1) for W. It was found that the equation ax3 + bX3 + cx + d = 0
(1)
did not accurately describe the variation of efficiency with ESR as was suggested by the manufacturer of the scintillation counter and led to
EXTERNAL FIG. divided
1. Counting efficiency into five straight-line
STANDARD
RATIO
as a function of external standard sections for the purpose of calculation.
ratio.
Curve
is
calculation errors at intermediate and low counting efficiencies. The following program has been designed to interpolate such a curve given the observed ESR using an Olivetti 101 calculator in the program mode and making full use of the potential of a rather small memory core. * Abbreviations: disintegrations Copyright All rights
ESR = external per minute.
standard
@ 1973 by Academic Press, of reproduction in any form
ratio,
295 Inc. reserved.
cpm
= counts
per minute,
dpm
=
296
SHORT
The efficiency curve (Fig. lines :
COMMUNICATIONS
1)
can be estimated
by a series of straight
Y=mX+b,
(2)
where Y = counting efficiency, m = slope, X = ESR, b = Y-intercept. A set of straight lines is superimposed on a quench-correction curve to best approximate that curve (Fig. 1). An auxiliary program (Fig. 3) is then used to calculate rn and b values for sections 1-5 of the curve. Enter in order: X,, X,, Y,, and Y,. After the last entry, the compound number mlbl-XZ will be printed automatically. A similar calculation is done for sections 2-5. The main program (Fig. 2) employs compound numbers stored as constants in the memory to calculate dpm. The co-ordinate X, is stored with m and b for section 1 of the calibration curve as a compound number m,b,-X, in register B of the memory. Similarly, registers B/, C, C/ and AV B& 1:
/t II/: 4
D/Z & F X Sl E/f C/V z B/V 01 L 1% DI: c FX E/ C/W Z B/W Cd
FX E/C/Y Z 61 Y c/r it -s o/t & FX A: E/ D/Y Z E/Y 04 I+ Y
s s AY D/Z AZ Fd F X ‘0,: D/I W s s S S AW IS
E/X III/t FX FX II/+ S2 : L_ RY s s S S S FY I= X
-FX D/q At 0 F+ F/S F + A20 RZ 10 s v
Fro. 2. Program for the calculation of dpm. External stop S1 and cpm is entered at stop S,. Other stops are that both numerical values and program steps can be At G, dpm is printed while at A? dpm corrected by printed.
standard ratio is entered at included in the program so stored in the same register. the factor in register F/ is
SHORT
297
COMMUNICATIONS
D of the memory contain the compound numbers mzbz-X, to m5b6-X6, respectively. The slope, m, may have three or four digits, b and X must each have three digits. A constant, 10, is stored in register F. When a correction factor is desired for dilutions or other manipulations, a value up to four digits in length may be stored in F/. At the user’s option, one may either place 1.0 in F/ or omit the second and third last steps of the program (FJ divide, A print) if no correction factor is needed. A routine calculation is done using the program in Fig. 2 by entering the ESR and the observed cpm value. The calculator then prints dpm. The program has the advantage that a set of straight lines can be quickly superimposed on a quench-correction curve. This curve-fitting procedure requires a minimum of mathematical knowledge. When stored on a magnetic card, the same program can be used for several scintillation counting fluids by placing in the memory the appropriate set of compound number constants. Other curves which have linear and nonlinear portions and are thus difficult to approximate with Eq. (1) may also be interpolated using this program. AV Sl
cl/ ? SZ D?
C’ 04 c x CX /a -
s3 E/t
ci
s, Et D/+ Cl D/t E/k ED./ f 0% B 4 OX E! Ea/! A/+ R/S 04
c+ C+ D : B/d C X ‘/: w: Bh CX CX it cx CX Cx cl+
Dt 814 c/v A/t E/ 4 c/t
X D+ c/x 10 Ai 0 IQ v w v El+ /Q
A2Q /Q V
FIG. 3. Program for the calculation of the slope and Y-intercept of a straight line. Enter in order at stops S,, S,, SJ, and S, co-ordinates X,, X,+1, Y., and Y,,. A compound number m,,bn*X,+l is printed at A, or Az.
SHORT
COMMUNICATIONS
ACKNOWLEDGMENTS The author thanks Dr. Ronald MacPherson, Defense Research Establishment Valcartier and Drs. Claude Willemot and Andre Comeau, Canada Dept. of Agriculture, Ste-Foy for helpful discussions.
H. J. Canadu
Department
of Agriculture
Station 2660 Chemin Gamin Quebec IO, Quebec, Canada Research
Received
August
9,197s;
accepted
February
2,197S
HOPE