Biokinetic model for the calculation of dose coefficients for oral and intravenous administration of 14C labeled drugs

A. Krins; J. Fidorra; U. Pleiß; P. Sahre; T. Schönmuth

doi:10.1515/kern-2003-0083

Published by De Gruyter March 16, 2022

Biokinetic model for the calculation of dose coefficients for oral and intravenous administration of ¹⁴C labeled drugs

Biokinetisches Modell zur Berechnung von Dosiskoeffizienten für orale und intravenöse Zufuhr von ¹⁴C markierten Pharmawirkstoffen

A. Krins , J. Fidorra , U. Pleiß , P. Sahre and T. Schönmuth

From the journal Kerntechnik

https://doi.org/10.1515/kern-2003-0083

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Abstract

A first order biokinetic model is presented for the calculation of dose coefficients from human activity excretion data after intravenous and oral administration of ¹⁴C labeled drugs. It is intended for the dose estimation in human studies in drug research, where the number of measurements is low and their uncertainty rather high. The model depends on only 6 parameters that are to be adjusted with the help of the measurement data. A comparison of measured and calculated activities in excreta of four human studies on ¹⁴C labeled drugs revealed considerable agreement, although some limitations have to be accepted. In contrast to the biokinetic model for ¹⁴C in organic compounds recommended by the International Commission on Radiological Protection (ICRP) the present model does not assume a fixed biological half-life of 40 days, but follows the experimental data. In consequence, the resulting dose coefficients differ from the ICRP value. For experimental data tested and assuming uniform activity distribution, the committed effective doses amount between one twenty-fifth to one fiftieth of the values calculated from the ICRP model. The uncertainty of the derived dose coefficients is estimated to be about ± 50%.

Abstract

Die vorliegende Arbeit beschreibt ein biokinetisches Modell erster Ordnung für die Berechnung von Dosiskoeffizienten anhand von Messwerten der Aktivitätsausscheidung nach intravenöser und oraler Zufuhr von ¹⁴C markierten Pharmawirkstoffen. Es ist für die Dosisbestimmung bei Humanstudien in der Pharmaforschung vorgesehen, wo die Anzahl an Messwerten gering und ihre Unsicherheit relativ hoch ist. Das Modell hängt von nur 6 Parametern ab, die mit Hilfe der Messwerte adjustiert werden müssen. Gemessene und berechnete Aktivitäten in den Ausscheidungen bei vier Humanstudien mit ¹⁴C markierten Pharmawirkstoffen zeigen eine bemerkenswerte Übereinstimmung, wenngleich bestimmte Beschränkungen hingenommen werden müssen. Im Gegensatz zum biokinetischen Modell der ICRP für ¹⁴C in organischen Verbindungen geht das vorliegende Modell nicht von einer festen biologischen Halbwertszeit von 40 Tagen aus, sondern wird an die experimentellen Daten angepasst. Daher unterscheiden sich die resultierenden Dosiskoeffizienten von dem Wert nach ICRP. In den Beispielen betragen die effektiven Folgedosen ± bei homogener Aktivitätsverteilung im Körper ± zwischen einem Fünfundzwanzigstel und einem Fünfzigstel der nach ICRP berechneten Werte. Die Unsicherheit der berechneten Dosiskoeffizienten beträgt rund ± 50%.

Acknowledgement

Part of this work was carried out by order of the German Federal Ministry for Environment, Nature Conservation and Nuclear Safety (Contract StSch4224). The responsibility for the content of this publication is with the authors.

References

1 International Commission on Radiological Protection (ICRP): Limits for Intakes of Radionuclides by Workers. ICRP Publication 30, Part 3. Annals of the ICRP 6 (2/3), 198110.1016/0146-6453(81)90126-3Search in Google Scholar

2 International Commission on Radiological Protection (ICRP): Age-dependent Doses to Members of the Public from Intake of Radio-nuclides: Part 1. ICRP Publication 56. Annals of the ICRP 20 (2), 1990Search in Google Scholar

3 International Commission on Radiological Protection (ICRP): Radiation Doses to Patients from Radiopharmaceuticals. ICRP Publication 80. Annals of the ICRP 28 (3), 199810.1016/S0146-6435(98)00006-1Search in Google Scholar

4 Richardson, R. B.; Dunford, D.W.: Review of the ICRP Tritium and ¹⁴C Internal Dosimetry Models and their Implementation in the Genmod-PC Code. Health Phys. 81 (2001) 289–30110.1097/00004032-200109000-00010Search in Google Scholar

5 International Commission on Radiological Protection (ICRP): Age Dependent Doses to Members of the Public from Intake of Radionuclides: Part 2. Ingestion Dose Coefficients. ICRP Publication 67. Annals of the ICRP 23 (3/4), 1993Search in Google Scholar

6 Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B.P.: Numerical Recipes in C++. 2^nd Edition, Cambridge University Press 2001. ISBN 0-521-75033-4.Search in Google Scholar

7 International Commission on Radiological Protection (ICRP): 1990 Recommendations of the International Commission on Radiological Protection. ICRP Publication 60. Annals of the ICRP 21 (1–3), 1991Search in Google Scholar

8 International Commission on Radiological Protection (ICRP): Limits for Intakes of Radionuclides by Workers. ICRP Publication 30, Part 1. Annals of the ICRP 2 (3/4), 198110.1016/0146-6453(80)90046-9Search in Google Scholar

9 Noßke, D.; Karcher, K.: personal communication 2002Search in Google Scholar

10 Cristy, M.; Eckerman, K. F.: SEECAL: Program to calculate age-dependent specific effective energies. ORNL/TM-12351. Oak Ridge National Laboratory, Oak Ridge, Tennessee 199310.2172/10119219Search in Google Scholar

11 Pleiss, U.: personal communication 2002Search in Google Scholar

12 International Commission on Radiological Protection (ICRP): Age-dependent Doses to Members of the Public from Intake of Radionuclides: Part 4 Inhalation Dose Coefficients. ICRP Publication 71. Annals of the ICRP 25 (3–4), 199510.1016/S0146-6453(00)80008-1Search in Google Scholar

Appendix 1

Solution of the system of differential equations (1)

Obviously, the original functions of the homogenous differential equations are exponentials. The special solutions of the non-homogeneous differential equations are obtained from sums of exponentials with the rate constants equal to those of the non-homogeneities. The integration constants are fixed by the boundary conditions. Different experimental conditions are studied as specializations of the general solutions.

The following solutions are obtained:

(A1) A1(t)=A0⋅e−k1t

(A2) A2(t)=k1,2⋅A0k2−k1⋅(e−k1t−e−k2t)

(A3) A3(t)=k2,3⋅k1,2⋅A0k2−k1⋅(1k3−k1(e−k1t−e−k3t)−1k3−k2(e−k2t−e−k3t))

(A4) A4(t)=k3,4⋅k2,3⋅k1,2⋅A0k2−k1⋅{ 1k3⋅(1k3−k1−1k3−k2)⋅(e−k3t−1) +1k2⋅1k3−k2⋅(e−k2t−1)−1k1⋅1k3−k1⋅(e−k1t−1) }

(A5) A5(t)=k3,5⋅k2,3⋅k1,2⋅A0k2−k1⋅{ 1k5−k3⋅(1k3−k2−1k3−k1)⋅(e−k3t−e−k5t) −1k5−k2⋅1k3−k2⋅(e−k2t−e−k5t)+1k5−k1⋅1k3−k1⋅(e−k1t−e−k5t) }+k1,5⋅A0k5−k1⋅(e−k1t−e−k5t)

(A6) A6(t)=α⋅{ 1k5⋅( 1k3−k2⋅(1k5−k3−1k5−k2) +1k3−k1⋅(1k5−k1−1k5−k3) )⋅(e−k5t−1) −1k3⋅1k5−k3⋅(1k3−k2−1k3−k1)⋅(e−k3t−1) +1k2⋅1k5−k2⋅1k3−k2⋅(e−k2t−1) −1k1⋅1k5−k1⋅1k3−k1⋅(e−k1t−1) } +k5,6⋅k1,5⋅A0k5−k1⋅(1k5(e−k5t−1)−1k1(e−k1t−1)) With α=k5,6⋅k3,5⋅k2,3⋅k1,2⋅A0k2−k1

Specialization: intravenous bolus injection

A bolus injection to the blood is simulated by k₁ = k_1,2 → ∞ and k₁;₅ = 0. It follows that

(A7) A2,iV(t)=A0⋅e−k2t

(A8) A3,iv(t)=k2,3⋅A0k3−k2⋅(e−k2t−e−k3t)

(A9) A4,iv(t)=k3,4⋅k2,3⋅A0k3−k2⋅(1k3⋅(e−k3t−1)−1k2⋅(e−k2t−1))

(A10) A5,lv(t)=k3,5⋅k2,3⋅A0k3−k2⋅(1k5−k3⋅(e−k5t−e−k3t)−1k5−k2⋅(e−k5t−e−k2t))

(A11) A6,iv(t)=k5,6⋅k3,5⋅k2,3⋅A0k3−k2⋅{ 1k5⋅(1k5−k2−1k5−k3)⋅(e−k5t−1) +1k3⋅1k5−k3⋅(e−k3t−1)−1k2⋅1k5−k2⋅(e−k2t−1) }

The activity in urine is given by A₄ðtÞ, that in feces by A₆ðtÞ. f₃;₄ determines the fraction of activity reaching the urine and the fraction reaching the feces, all other constants only determine the kinetics. This can be seen from the equations in thelimit t!1using k₂;₃ = k₂:

(A12) A4,iv(∞)=k3,4⋅k2,3⋅A0k3−k2⋅(1k2−1k3)=k3,4⋅k2,3⋅A0k2⋅k3=A0⋅f3,4

Often, this ratio is easily determined from the experimental data and need not to be numerically estimated. This is a great advantage in view of the low number of measurement data.

Specialization: complete resorption to blood

This case is described by the model taking k₁ = k_1;2 and k_1;5 = 0. In the limit t→ ∞ the same expression for the activity in urine as above follows

(A13) A4,vR(∞)=k3,4⋅k2,3⋅k1,2⋅A0k2−k1 ×(1k3⋅1k3−k2−1k3⋅1k3−k1−1k2⋅1k3−k2+1k1⋅1k3−k1) =k3,4⋅k2,3⋅k1,2⋅A0k2−k1⋅( 1k3−k2⋅(1k3−1k2) +1k3−k1⋅(1k1−1k3) ) =k3,4⋅k2,3⋅k1,2⋅A0k2−k1⋅(1k1⋅k3−1k2⋅k3) =A0⋅f3,4

Appendix 2: Measurement data of four human studies with ¹⁴C labeled drugs

Substance A, intravenous administration

6 male healthy volunteers (mean age 24 years, mean weight 75 kg). Intravenous bolus injection of 10 ml solution.

Substance A, oral administration

6 male healthy volunteers (mean age 24 years, mean weight 75 kg). Oral administration of 259 mg substance in 13 ml solution.

Substance B, oral administration

6 male healthy volunteers (mean age 33 years, mean weight 78 kg). Oral administration of 20 mg substance in 10 ml solution.

Substance C, oral administration

4 male healthy volunteers (mean age 54 years, mean weight 75 kg). Oral administration of 400 μg substance.

Substance D, oral administration

4 male healthy volunteers (mean age 48 years, mean weight 79 kg). Oral administration of 33 mg substance.

Table A2.1

Arithmetic mean and standard deviation of ¹⁴C activity in urine after intravenous administration of substance A (in % of intake).

	collection period [h]
	0–2	2–4	4–8	8–12	12–24	24–48	48–72	72–96	96–120
mean	33.94	13.44	12.42	5.78	6.52	2.05	0.45	0.23	0.12
s.d.	3.50	1.38	0.48	1.84	2.58	0.99	0.16	0.07	0.03

Table A2.2

Arithmetic mean and standard deviation of ¹⁴C activity in feces after intravenous administration of substance A (in % of intake).

	collection period [h]
	0–24	24–48	48–72	72–96	96–120
mean	3.44	5.54	5.61	1.34	0.95
s.d.	4.00	3.99	3.74	1.53	1.67

Table A2.3

Arithmetic mean and standard deviation of ¹⁴C activity in urine after oral administration of substance A (in % of intake).

	collection period [h]
	0–2	2–4	4–8	8–12	12–24	24–48	48–72	72–96	96–120
mean	23.18	11.55	8.72	5.31	4.96	1.17	0.30	0.10	0.10
s.d.	3.40	1.90	2.62	2.56	1.33	0.36	0.13	0.04	0.03

Table A2.4

Arithmetic mean and standard deviation of ¹⁴C activity in feces after oral administration of substance A (in % of intake).

	collection period [h]
	0–24	24–48	48–72	72–96	96–120
mean	3,91	26,15	11,57	0,42	0,99
s.d.	4,66	9,35	12,71	0,21	2,04

Table A2.5

Arithmetic mean of ¹⁴C activity in urine after oral administration of substance B (in % of intake).

	collection period [h]
	0–4	4–8	8–12	12–16	16–24	24–48	48–72	72–96
mean	0.51	1.94	3.87	6.38	9.78	11.18	1.32	0.32

Table A2.6

Arithmetic mean of ¹⁴C activity in feces after oral administration of substance B (in % of intake).

	collection period [h]
	0–24	24–48	48–72	72–96
mean	0.49	17.91	25.15	7.74

Table A2.7

Arithmetic mean of ¹⁴C activity in urine after oral administration of substance C (in % of intake).

	collection period [h]
	0–4	4–8	8–16	16–24	24–48	48–72	72–96	96–120	120–144
mean	2.3	7.4	9.9	2.9	0.8	0.3	0.1	0.1	0.0

Table A2.8

Arithmetic mean of ¹⁴C activity in feces after oral administration of substance C (in % of intake).

	collection period[h]
	0–24	24–48	48–72	72–96	96–144
mean	38.0	19.6	8.2	2.7	1.3

Table A2.9

Arithmetic mean and standard deviation of ¹⁴C activity in urine after oral administration of substance D (in % of intake).

	collection period [h]
	0–4	4–8	8–24	24–48	48–72	72–96	96–120	120–144	120–144
mean	2.47	0.88	1.09	0.30	0.084	0.037	0.024	0.013	0.008
s.d.	0.67	0.42	0.42	0.10	0.037	0.019	0.011	0.007	0.007

Table A2.10

Arithmetic mean of ¹⁴C activity in feces after oral administration of substance D (in % of intake).

	collection period [h]
	0–24	24–48	48–72	72–96	96–144
mean	26.2	44.8	5.2	15.5	0.2

Received: 2003-05-06

Published Online: 2022-03-16

Biokinetic model for the calculation of dose coefficients for oral and intravenous administration of ¹⁴C labeled drugs

Abstract

Abstract

Acknowledgement

References

Solution of the system of differential equations (1)

Specialization: intravenous bolus injection

Specialization: complete resorption to blood

Appendix 2: Measurement data of four human studies with ¹⁴C labeled drugs

Substance A, intravenous administration

Substance A, oral administration

Substance B, oral administration

Substance C, oral administration

Substance D, oral administration

Journal and Issue

Articles in the same Issue

Biokinetic model for the calculation of dose coefficients for oral and intravenous administration of 14C labeled drugs

Abstract

Abstract

Acknowledgement

References

Solution of the system of differential equations (1)

Specialization: intravenous bolus injection

Specialization: complete resorption to blood

Appendix 2: Measurement data of four human studies with 14C labeled drugs

Substance A, intravenous administration

Substance A, oral administration

Substance B, oral administration

Substance C, oral administration

Substance D, oral administration

Journal and Issue

Articles in the same Issue

Biokinetic model for the calculation of dose coefficients for oral and intravenous administration of ¹⁴C labeled drugs

Appendix 2: Measurement data of four human studies with ¹⁴C labeled drugs