Tikhonov adaptively regularized gamma variate fitting to assess plasma clearance of inert renal markers

Journal of Pharmacokinetics and Pharmacodynamics

Volumn 37, Issue 5, 2010, Pages 435-474

  Wesolowski, Carl A ^a   Puetter, Richard C ^b   Ling, Lin ^a   Babyn, Paul S ^c  

^a General Hospital   (Canada)

^b PixonImaging LLC   (United States)

^c HOSPITAL FOR SICK CHILDREN   (Canada)

Author keywords

Clearance curves; Gamma variate; Minimization of errors; Renal function; Tikhonov regularization

Indexed keywords

EDETATE CHROMIUM CR 51; PENTETATE TECHNETIUM TC 99M; PENTETATE YTTERBIUM YB 169;

ACCURACY; ALGORITHM; ANALYTICAL ERROR; AREA UNDER THE CURVE; ARTICLE; ARTIFACT REDUCTION; BLOOD SAMPLING; CONTINUOUS INFUSION; CURVE FITTING; DIAGNOSTIC ACCURACY; DRUG BLOOD LEVEL; DRUG CLEARANCE; DRUG DISTRIBUTION; DRUG ELIMINATION; GLOMERULUS FILTRATION RATE; HUMAN; INTERMETHOD COMPARISON; ISOTOPE ANALYSIS; KIDNEY FUNCTION; MATHEMATICAL COMPUTING; ORDINARY LEAST SQUARE; ORDINARY LEAST SQUARE GAMMA VARIATE MODEL; PHARMACODYNAMICS; PLASMA CLEARANCE; PRIORITY JOURNAL; PROCESS MODEL; QUALITY CONTROL; STATISTICAL ANALYSIS; STATISTICAL MODEL; SUM OF EXPONENTIAL TERM MODEL; TIKHONOV REGULARIZATION GAMMA VARIATE MODEL;

AREA UNDER CURVE; BIOLOGICAL MARKERS; COMPUTER SIMULATION; GLOMERULAR FILTRATION RATE; HUMANS; INULIN; KIDNEY; LEAST-SQUARES ANALYSIS; METABOLIC CLEARANCE RATE; MODELS, BIOLOGICAL; PENTETIC ACID; RADIOPHARMACEUTICALS; TECHNETIUM TC 99M PENTETATE;

EID: 78049352235     PISSN: 1567567X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10928-010-9167-z     Document Type: Article

References (75)

1. LA Stevens J Coresh T Greene AS Levey 2006 Assessing kidney function-measured and estimated glomerular filtration rate N Engl J Med 354 2473 2483 10.1056/NEJMra054415 16760447 1:CAS:528:DC%2BD28XlsVaiurk%3D (Pubitemid 43855050)
2. AH Calvert MJ Egorin 2002 Carboplatin dosing formulae: gender bias and the use of creatinine-based methodologies Eur J Cancer 38 11 16 10.1016/S0959-8049(01)00340-9 11750834 1:CAS:528:DC%2BD3MXpt1aitrc%3D (Pubitemid 34031819)
3. GT Schumock MG Butler PD Meek LC Vermeulen BV Arondekar JL Bauman 2003 Evidence of the economic benefit of clinical pharmacy services: 1996-2000 Pharmacotherapy 23 113 132 10.1592/phco.23.1.113.31910 12523470 (Pubitemid 36077375)
4. Wesolowski CA, Puetter RC, Babyn PS (2010) The inappropriateness of the sum of exponential terms for modelling plasma concentrations of bolus-injected, radiolabeled DTPA. J Nucl Med 51 (Supplement 2):No.429
5. Wesolowski CA, Puetter RC, Babyn PS, Ling L (2010) Limitations of ordinary least squares fitting of gamma variate functions to plasma-clearance curves. J Nucl Med 51 (Supplement 2):No.1674
6. Wesolowski C, Puetter R, Ling L, Babyn P (2010) Tikhonov regularized gamma variate fits to radiochelated-DTPA bolus dilution curves with minimum plasma-clearance relative error. J Nucl Med 51 (Supplement 2):No.1677
7. Wesolowski CA, Puetter RC, Babyn PS (Filed May 29, 2009) Method for evaluating renal functifon. U.S. Provisional Patent Application No. 61/182,676
8. Trutna L, Spagon P, del Castillo E, Moore T, Hartley S, Hurwitz A (2009) NIST/SEMATECH e-handbook of statistical methods 5.5.9.9.2. Motivation: How do we construct a goodness-of-fit metric for a model? U.S. Commerce Department's Technology Administration. http://www.itl.nist.gov/div898/handbook/pri/section5/ pri5992.htm
9. DG Levitt 2003 The pharmacokinetics of the interstitial space in humans BMC Clin Pharmacol 3 3 10.1186/1472-6904-3-3 12890292 (Pubitemid 38751346)
10. Piepsz A, Colarinha P, Gordon I, Hahn K, Olivier P, Sixt R, van Velzen J (2001) Guidelines for glomerular filtration rate determination in children. Eur J Nucl Med 28:BP31-BP36
11. JS Fleming MA Zivanovic GM Blake M Burniston PS Cosgriff 2004 Guidelines for the measurement of glomerular filtration rate using plasma sampling Nucl Med Commun 25 759 769 10.1097/01.mnm.0000136715.71820.4a 15266169 (Pubitemid 39099987)
12. RE Smith MF Morales 1944 On the theory of blood-tissue exchanges: I. Fundamental equations Bull Math Biol 6 125 131
13. R Smith M Morales 1944 On the theory of blood-tissue exchanges: II. Applications Bull Math Biol 6 133 139
14. GW Schmidt 1952 A mathematical theory of capillary exchange as a function of tissue structure Bull Math Biol 14 229 263 1:CAS:528:DyaG3sXivFalug%3D%3D
15. N Metropolis S Ulam 1949 The Monte Carlo method J Am Stat Assoc 44 335 341 10.2307/2280232 18139350 1:STN:280:DyaH1M%2FktV2htQ%3D%3D
16. B Efron 1979 Bootstrap methods: another look at the jackknife Ann Stat 7 1 26 10.1214/aos/1176344552
17. PR Schloerb 1960 Total body water distribution of creatinine and urea in nephrectomized dogs Am J Physiol 199 661 665 13747834 1:CAS:528: DyaF3MXhvVyntw%3D%3D
18. Larson KB, Cox JR Jr (eds) (1974) Computer processing of dynamic images from an Anger scintillation camera: the proceedings of a workshop. Society of Nuclear Medicine, New York
19. 131I] hippuran clearance Scand J Clin Lab Invest 37 49 51 616026 1:CAS:528: DyaE1cXkvVKksLo%3D
20. ME Wise 1985 Negative power functions of time in pharmacokinetics and their implications J Pharmacokinet Biopharm 13 309 346 10.1007/BF01065658 4087166 1:STN:280:DyaL287hsVygsg%3D%3D (Pubitemid 16194627)
21. K Zierler 1981 A critique of compartmental analysis Annu Rev Biophys Bioeng 10 531 562 10.1146/annurev.bb.10.060181.002531 7259129 1:CAS:528:DyaL3MXltFShsrk%3D
22. D Baird 1983 The Fisher/Pearson Chi-squared controversy: a turning point for inductive inference Br J Philos Sci 34 105 118 10.1093/bjps/34.2.105
23. JE Hall AC Guyton BM Farr 1977 A single-injection method for measuring glomerular filtration rate Am J Physiol Renal Physiol 232 72 76
24. 51Cr-EDTA overestimate true renal clearance by 10 percent Eur J Nucl Med Mol Imaging 30 4 8 10.1007/s00259-002-1007-y 12483403 1:CAS:528:DC%2BD38XpsV2iurk%3D (Pubitemid 36692886)
25. HK Thompson Jr CF Starmer RE Whalen HD McIntosh 1964 Indicator transit time considered as a gamma variate Circ Res 14 502 14169969
26. JM Bogaard SJ Smith A Versprille ME Wise F Hagemeijer 1984 Physiological interpretation of the skewness of indicator-dilution curves; theoretical considerations and a practical application Basic Res Cardiol 79 479 493 10.1007/BF01908149 6385958 1:STN:280:DyaL2M%2Fit1ektA%3D%3D
27. O Carlsen O Hedegaard 1987 Evaluation of regional cerebral circulation based on absolute mean transit times in radionuclide cerebral angiography Phys Med Biol 32 1457 1467 10.1088/0031-9155/32/11/007 3423115 1:STN:280: DyaL1c%2FpslOjtw%3D%3D
28. CA Wesolowski P Hogendoorn R Vandierendonck AA Driedger 1988 Bolus injections of measured amounts of radioactivity J Nucl Med Technol 16 1 4
29. RK Millard 1997 Indicator-dilution dispersion models and cardiac output computing methods Am J Physiol 272 H2004 H2012 9139989 1:CAS:528: DyaK2sXivF2qtbY%3D
30. JT Kuikka E Lansimies 1999 A fractal approach for evaluation of pulmonary circulation in man at rest and during exercise Clin Physiol 2 107 110 10.1046/j.1365-2281.1999.00153.x (Pubitemid 29137596)
31. P Macheras 1996 A fractal approach to heterogeneous drug distribution: calcium pharmacokinetics Pharm Res 13 663 670 10.1023/A:1016031129053 8860420 1:CAS:528:DyaK28XivFaqurs%3D (Pubitemid 26156216)
32. AS Perkinson CJ Evans MT Burniston SW Smye 2010 The effect of improved modelling of plasma clearance in paediatric patients with expanded body spaces on estimation of the glomerular filtration rate Physiol Meas 31 183 10.1088/0967-3334/31/2/005 20016117 1:STN:280:DC%2BC3c%2FktFyjuw%3D%3D
33. 99mTc chelates Med Phys 14 1032 1041 10.1118/1.596117 3696068 1:CAS:528:DyaL1cXntFCitw%3D%3D (Pubitemid 18025958)
34. 99mTc-DTPA for measurement of glomerular filtration rate J Nucl Med 17 317 320 1255261 1:CAS:528: DyaE28XhslGru78%3D
35. 51Cr-labelled ethylenediaminetetra- acetate and inulin in man Clin Sci 66 613 619 6423339 1:CAS:528: DyaL2cXkt1SisLg%3D
36. 99mTc-labelled diethylenetriaminepenta-acetic acid exchange Clin Sci (Lond) 93 471 477 1:CAS:528:DyaK2sXnvFahu78%3D
37. 99mTc-DTPA and inulin Eur J Nucl Med 23 49 54 10.1007/BF01736989 8586101 1:CAS:528:DyaK28XhsFKgu7c%3D (Pubitemid 26013615)
38. 169Yb-DTPA compounds in brain sarcoma and kidneys of mice J Nucl Med 13 205 5058238 1:CAS:528:DyaE38XktVSmt7k%3D
39. KW Florijn JNM Barendregt EGW Lentjes W Van Dam W Prodjosudjadi JL van Saase LA van Es PC Chang 1994 Glomerular filtration rate measurement by "single-shot" injection of inulin Kidney Int 46 252 10.1038/ki.1994.267 7933844 1:STN:280:DyaK2M%2FhvFCntg%3D%3D
40. A Siebenhofer A Meinitzer J Brandmair J Plank TR Pieber 2001 Variability of glomerular filtration rate estimation using single injection methods in Type 1 diabetic patients Diabet Med 18 464 10.1046/j.1464-5491.2001.00508.x 11472465 1:STN:280:DC%2BD3MvisFWqsw%3D%3D (Pubitemid 32738695)
41. 51Cr-EDTA Scand J Clin Lab Invest 23 301 305 10.3109/00365516909081695 4986443
42. N Kampa I Bostrom P Lord U Wennstrom P Ohagen E Maripuu 2003 Day-to-day variability in glomerular filtration rate in normal dogs by scintigraphic technique J Vet Med A 50 37 41 10.1046/j.1439-0442.2003.00494.x 1:STN:280:DC%2BD3s7jsFymtw%3D%3D
43. WF Hamilton JW Moore JM Kinsman RG Spurling 1932 Studies on the circulation IV. Further analysis of the injection method, and of changes in hemodynamics under physiological and pathological conditions Am J Physiol 99 534 551 1:CAS:528:DyaA38Xis1Wjug%3D%3D
44. LA Sapirstein DG Vidt MJ Mandel G Hanusek 1955 Volumes of distribution and clearances of intravenously injected creatinine in the dog Am J Physiol 181 330 336 14376619 1:CAS:528:DyaG2MXmsF2ksw%3D%3D
45. D Ratkowsky 1993 Principles of nonlinear regression modeling J Ind Microbiol Biotechnol 12 195 199
46. L Ingber 1993 Simulated annealing: practice versus theory Math Comput Model 18 29 10.1016/0895-7177(93)90204-C
47. Sheskin D (2004) Handbook of parametric and nonparametric statistical procedures. CRC Press, Boca Raton
48. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge
49. SA Wesolowski CC Fries AM Sabini PN Sawyer 1965 The significance of turbulence in hemic systems and in the distribution of the atherosclerotic lesion Surgery 57 155 162 14242043 1:STN:280:DyaF2M%2Fks1Cktg%3D%3D
50. GR Cokelet HL Goldsmith 1991 Decreased hydrodynamic resistance in the two-phase flow of blood through small vertical tubes at low flow rates Circ Res 68 1 17 1984854 1:STN:280:DyaK3M%2FosV2juw%3D%3D
51. B Rippe B Haraldsson 1994 Transport of macromolecules across microvascular walls: the two-pore theory Physiol Rev 74 163 219 8295933 1:CAS:528:DyaK2cXhvVOktrg%3D
52. R Becker 1991 A derivation of mean residence time Eur J Drug Metab Pharmacokinet Spec No 3 15 16 1820869 1:STN:280:DyaK38zisVWmtw%3D%3D
53. Tikhonov AN (1943) On the stability of inverse problems. In: Presented at the CR (Dokl.) Acad Sci URSS. n. Ser
54. Tikhonov AN, Arsenin VY (1977) Methods for solving ill-posed problems. Wiley, New York
55. Tikhonov AN, Goncharsky AV, Stepanov V, Yagola AG (1990) Numerical methods for solving ill-posed problems. Nauka, Moscow
56. CD Russell PG Bischoff FN Kontzen KL Rowell MV Yester LK Lloyd WN Tauxe EV Dubovsky 1985 Measurement of glomerular filtration rate: single injection plasma clearance method without urine collection J Nucl Med 26 1243 1247 3903074 1:STN:280:DyaL28%2Fjs1Cqtw%3D%3D
57. CD Russell AT Taylor EV Dubovsky 2002 A Bayesian regression model for plasma clearance J Nucl Med 43 762 766 12050320
58. JA Nelder R Mead 1965 A simplex method for function minimization Comput J 7 308 313
59. AE Hoerl RW Kennard 2000 Ridge regression: biased estimation for nonorthogonal problems Technometrics 42 80 86 10.2307/1271436
60. WJ Gutjahr 2002 ACO algorithms with guaranteed convergence to the optimal solution Inf Process Lett 82 145 153 10.1016/S0020-0190(01)00258-7 (Pubitemid 34181987)
61. J Shao CFJ Wu 1989 A general theory for jackknife variance estimation Ann Statist 17 1176 1197 10.1214/aos/1176347263
62. D Du Bois EF Du Bois 1916 A formula to estimate the approximate surface area if height and weight be known Arch Intern Med 17 863 871 1:CAS:528:DyaC28XhtVCnug%3D%3D
63. 99mTc-DTPA, two blood sample, paediatric data Nucl Med Commun 27 963 970 10.1097/01.mnm.0000237988.52572.2c 17088682 (Pubitemid 44706892)
64. 99mTc-DTPA, two blood sample, pediatric data. In: Nuclear science symposium conference record, 2006 IEEE, 1986-1994
65. GB West JH Brown BJ Enquist 1997 A general model for the origin of allometric scaling laws in biology Science 276 122 126 10.1126/science.276.5309. 122 9082983 1:CAS:528:DyaK2sXitl2jtro%3D (Pubitemid 27161259)
66. GB West JH Brown BJ Enquist 1999 The fourth dimension of life: fractal geometry and allometric scaling of organisms Science 284 1677 1679 10.1126/science.284.5420.1677 10356399 1:CAS:528:DyaK1MXjs1Kitbo%3D (Pubitemid 29291379)
67. West GB, Woodruff WH, Brown JH (2002) Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. Proc Natl Acad Sci USA 99(Suppl 1):2473-2478
68. L Khinkis W Krzyzanski WJ Jusko WR Greco 2009 D-optimal designs for parameter estimation for indirect pharmacodynamic response models J Pharmacokinet Pharmacodyn 36 523 539 10.1007/s10928-009-9135-7 19904585
69. C Chantler TM Barratt 1972 Estimation of glomerular filtration rate from plasma clearance of 51-chromium edetic acid Arch Dis Child 47 613 617 10.1136/adc.47.254.613 4625784 1:CAS:528:DyaE3sXhslan
70. H Schwilden J Honerkamp C Elster 1993 Pharmacokinetic model identification and parameter estimation as an ill-posed problem Eur J Clin Pharmacol 45 545 550 10.1007/BF00315312 8157040 1:STN:280:DyaK2c3gvVGktQ%3D%3D
71. MN Maisey CS Ogg JS Cameron 1969 Measuring glomerular filtration-rate Lancet 1 733 10.1016/S0140-6736(69)92685-3 4182684 1:STN:280: DyaF1M3hslOhsg%3D%3D
72. CD Russell 1993 Optimum sample times for single-injection, multisample renal clearance methods J Nucl Med 34 1761 8410295 1:STN:280: DyaK2c%2FhsFCgsQ%3D%3D
73. R Fux T Biedermann T Sander-Wiecker K Morike C Gleiter 2004 Anaphylaxis to intravenous sinistrin Ann Pharmacother 38 2175 10.1345/aph.1E267 15536136 (Pubitemid 40169400)
74. R Chandra JL Barron 2002 Anaphylactic reaction to intravenous sinistrin (Inutest) Ann Clin Biochem 39 76 10.1258/0004563021901621 11853197 (Pubitemid 34098504)
75. Weisstein EW (2010) Error propagation. From MathWorld-a Wolfram Web Resource. http://mathworld.wolfram.com/ErrorPropagation.html