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Three-compartment pharmacokinetic models of radiotracers used in the GFR-determination — estimation of their parameters using the time-concentration curves
Affiliations- Department of Nuclear Medicine, Citomed, Toruń, Poland
- Department of Nuclear Medicine, Aalborg University Hospital, Denmark
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Abstract
BACKGROUND: In GFR measurements with radiotracers, there is evidence that a two-compartment model is unable to describe the full plasma curve, including early time points, but analyses generally focus on two-compartment models.
AIMS: To analyze both the mammillary and catenary three-compartment model and to determine empirical relations between model constants and the overall GFR and ECV (extra-cellular volume).
MATERIAL AND METHODS: Mathematical analysis of the three-compartment model. Full-curve patient data from 32 adults and 7 children were used to relate model parameters to GFR and ECV.
RESULTS: Model volumes were found to be roughly proportional to ECV. In both models, the central (plasma) volume was V1 = 0.24 × ECV and elimination rate from V1 was k10 = 4.2 × GFR/ECV. In the mammillary model, the two parallel volumes were V2 = 0.28 × ECV, V3 = 0.48 × ECV, and intercompartmental clearances were Cl12 [mL/min] = 0.0058 × ECV [mL], Cl13 = 0.042 × ECV. In the catenary model, the serial volumes were V2 = 0.60 × ECV, V3 = 0.16 × ECV, with clearances Cl12 = 0.048 × ECV, Cl23 = 0.0036 × ECV.
CONCLUSION: Insight into the three-compartment model was achieved, and empirical relations to ECV and GFR/ECV were determined.
Abstract
BACKGROUND: In GFR measurements with radiotracers, there is evidence that a two-compartment model is unable to describe the full plasma curve, including early time points, but analyses generally focus on two-compartment models.
AIMS: To analyze both the mammillary and catenary three-compartment model and to determine empirical relations between model constants and the overall GFR and ECV (extra-cellular volume).
MATERIAL AND METHODS: Mathematical analysis of the three-compartment model. Full-curve patient data from 32 adults and 7 children were used to relate model parameters to GFR and ECV.
RESULTS: Model volumes were found to be roughly proportional to ECV. In both models, the central (plasma) volume was V1 = 0.24 × ECV and elimination rate from V1 was k10 = 4.2 × GFR/ECV. In the mammillary model, the two parallel volumes were V2 = 0.28 × ECV, V3 = 0.48 × ECV, and intercompartmental clearances were Cl12 [mL/min] = 0.0058 × ECV [mL], Cl13 = 0.042 × ECV. In the catenary model, the serial volumes were V2 = 0.60 × ECV, V3 = 0.16 × ECV, with clearances Cl12 = 0.048 × ECV, Cl23 = 0.0036 × ECV.
CONCLUSION: Insight into the three-compartment model was achieved, and empirical relations to ECV and GFR/ECV were determined.
Keywords
GFR-determination; pharmacokinetics; compartment model; Tc-99m-DTPA
About this articleTitle
Three-compartment pharmacokinetic models of radiotracers used in the GFR-determination — estimation of their parameters using the time-concentration curves
Journal
Issue
Article type
Research paper
Pages
60-68
Published online
2019-06-05
Page views
726
Article views/downloads
909
DOI
10.5603/NMR.a2019.0014
Pubmed
Bibliographic record
Nucl. Med. Rev 2019;22(2):60-68.
Keywords
GFR-determination
pharmacokinetics
compartment model
Tc-99m-DTPA
Authors
Cyprian Świętaszczyk
Lars Jødal
References (18)- Murray AW, Barnfield MC, Waller ML, et al. Assessment of glomerular filtration rate measurement with plasma sampling: a technical review. J Nucl Med Technol. 2013; 41(2): 67–75.
- Rehling M, Møller ML, Thamdrup B, et al. Simultaneous measurement of renal clearance and plasma clearance of 99mTc-labelled diethylenetriaminepenta-acetate, 51Cr-labelled ethylenediaminetetra-acetate and inulin in man. Clin Sci (Lond). 1984; 66(5): 613–619.
- Fleming JS, Wilkinson J, Oliver RM, et al. Comparison of radionuclide estimation of glomerular filtration rate using technetium 99m diethylenetriaminepentaacetic acid and chromium 51 ethylenediaminetetraacetic acid. European Journal of Nuclear Medicine. 1991; 18(6): 391–395.
- Biggi A, Viglietti A, Farinelli MC, et al. Estimation of glomerular filtration rate using chromium-51 ethylene diamine tetra-acetic acid and technetium-99m diethylene triamine penta-acetic acid. Eur J Nucl Med. 1995; 22(6): 532–536.
- Fleming JS, Zivanovic MA, Blake GM, et al. British Nuclear Medicine Society. Guidelines for the measurement of glomerular filtration rate using plasma sampling. Nucl Med Commun. 2004; 25(8): 759–769.
- Fleming JS. An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation. Nucl Med Commun. 2007; 28(4): 315–320.
- Bröchner-Mortensen J. A simple method for the determination of glomerular filtration rate. Scand J Clin Lab Invest. 1972; 30(3): 271–274.
- Jødal L, Brøchner-Mortensen J. Simplified methods for assessment of renal function as the ratio of glomerular filtration rate to extracellular fluid volume. Nucl Med Commun. 2012; 33(12): 1243–1253.
- Dunne A. An iterative curve stripping technique for pharmacokinetic parameter estimation. J Pharm Pharmacol. 1986; 38(2): 97–101.
- Jødal L, Brøchner-Mortensen J. Reassessment of a classical single injection 51Cr-EDTA clearance method for determination of renal function in children and adults. Part I: Analytically correct relationship between total and one-pool clearance. Scand J Clin Lab Invest. 2009; 69(3): 305–313.
- Brøchner-Mortensen J, Jødal L. Reassessment of a classical single injection 51Cr-EDTA clearance method for determination of renal function in children and adults. Part II: Empirically determined relationships between total and one-pool clearance. Scand J Clin Lab Invest. 2009; 69(3): 314–322.
- Plusquellec Y. Analytical study of three-compartment pharmacokinetic models: concentration, area under curves, mean residence time. J Biomed Eng. 1989; 11(4): 345–351.
- Plusquellec Y, Houin G. Analytical study of open four compartment pharmacokinetic models: concentrations, area under curves, mean residence times. J Biomed Eng. 1990; 12(4): 358–364.
- Biasi Jde. Four open mammillary and catenary compartment models for pharmacokinetics studies. Journal of Biomedical Engineering. 1989; 11(6): 467–470.
- Upton RN. Calculating the hybrid (macro) rate constants of a three-compartment mamillary pharmacokinetic model from known micro-rate constants. J Pharmacol Toxicol Methods. 2004; 49(1): 65–68.
- Dubois A, Bertrand J, Mentré F. Mathematical expressions of the pharmacokinetic and pharmacodynamic models implemented in the PFIM software. INSERM, University Paris Diderot 2011 (UMR738); accessible: http://www.pfim.biostat.fr/PFIM_PKPD_library.pdf.
- Fisher D, Shafer S. Fisher/Shafer NONMEM Workshop Pharmacokinetic and Pharmacodynamic Analysis with NONMEM. Het Pand, Ghent, Belgium 2007. https://wiki.ucl.ac.uk/download/attachments/23206987/Shafer%20NONMEM.pdf.
- Rescigno A. Foundations of pharmacokinetics. Kluwer Academic Publishers. 2004.
