Abstract
Conventional mammillary models are frequently used for pharmacokinetic (PK) analysis when only blood or plasma data are available. Such models depend on the quality of the drug disposition data and have vague biological features. An alternative minimal-physiologically-based PK (minimal-PBPK) modeling approach is proposed which inherits and lumps major physiologic attributes from whole-body PBPK models. The body and model are represented as actual blood and tissue (usually total body weight) volumes, fractions (f d ) of cardiac output with Fick’s Law of Perfusion, tissue/blood partitioning (K p ), and systemic or intrinsic clearance. Analyzing only blood or plasma concentrations versus time, the minimal-PBPK models parsimoniously generate physiologically-relevant PK parameters which are more easily interpreted than those from mammillary models. The minimal-PBPK models were applied to four types of therapeutic agents and conditions. The models well captured the human PK profiles of 22 selected beta-lactam antibiotics allowing comparison of fitted and calculated K p values. Adding a classical hepatic compartment with hepatic blood flow allowed joint fitting of oral and intravenous (IV) data for four hepatic elimination drugs (dihydrocodeine, verapamil, repaglinide, midazolam) providing separate estimates of hepatic intrinsic clearance, non-hepatic clearance, and pre-hepatic bioavailability. The basic model was integrated with allometric scaling principles to simultaneously describe moxifloxacin PK in five species with common K p and f d values. A basic model assigning clearance to the tissue compartment well characterized plasma concentrations of six monoclonal antibodies in human subjects, providing good concordance of predictions with expected tissue kinetics. The proposed minimal-PBPK modeling approach offers an alternative and more rational basis for assessing PK than compartmental models.
Similar content being viewed by others
References
Rowland M, Peck C, Tucker G (2011) Physiologically-based pharmacokinetics in drug development and regulatory science. Annu Rev Pharmacol Toxicol 51:45–73
Jusko WJ. (1980) Guidelines for collection and pharmacokinetic analysis of drug disposition data. In: Evans WE; Schentag JJ; Jusko WJ (eds) Applied pharmacokinetics: principles of therapeutic drug monitoring, 1st edn. Applied Therapeutics Inc., Vancouver, WA, pp 639–680
Chiou WL (1979) Potential pitfalls in the conventional pharmacokinetic studies: effects of the initial mixing of drug in blood and the pulmonary first-pass elimination. J Pharmacokinet Biopharm 7:527–536
Riegelman S, Loo JC, Rowland M (1968) Shortcomings in pharmacokinetic analysis by conceiving the body to exhibit properties of a single compartment. J Pharm Sci 57:117–123
Vaughan DP, Hope I (1979) Applications of a recirculatory stochastic pharmacokinetic model: limitations of compartmental models. J Pharmacokinet Biopharm 7:207–225
Krejcie TC, Henthorn TK, Shanks CA, Avram MJ (1994) A recirculatory pharmacokinetic model describing the circulatory mixing, tissue distribution and elimination of antipyrine in dogs. J Pharmacol Exp Ther 269:609–616
Veng-Pedersen P, Freise KJ, Schmidt RL, Widness JA (2008) Pharmacokinetic differentiation of drug candidates using system analysis and physiological-based modelling. Comparison of C.E.R.A. and erythropoietin. J Pharm Pharmacol 60:1321–1334
Nestorov IA, Aarons LJ, Arundel PA, Rowland M (1998) Lumping of whole-body physiologically based pharmacokinetic models. J Pharmacokinet Biopharm 26:21–46
Pilari S, Huisinga W (2010) Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models. J Pharmacokinet Pharmacodyn 37:365–405
Levy G, Mager DE, Cheung WK, Jusko WJ (2003) Comparative pharmacokinetics of coumarin anticoagulants L: physiologic modeling of S-warfarin in rats and pharmacologic target-mediated warfarin disposition in man. J Pharm Sci 92:985–994
Kawahara M, Sakata A, Miyashita T, Tamai I, Tsuji A (1999) Physiologically based pharmacokinetics of digoxin in mdr1a knockout mice. J Pharm Sci 88:1281–1287
Rocci ML Jr, Szefler SJ, Acara M, Jusko WJ (1981) Prednisolone metabolism and excretion in the isolated perfused rat kidney. Drug Metab Dispos 9:177–182
Gallo JM, Vicini P, Orlansky A, Li S, Zhou F, Ma J, Pulfer S, Bookman MA, Guo P (2004) Pharmacokinetic model-predicted anticancer drug concentrations in human tumors. Clin Cancer Res 10:8048–8058
Henthorn TK, Avram MJ, Krejcie TC, Shanks CA, Asada A, Kaczynski DA (1992) Minimal compartmental model of circulatory mixing of indocyanine green. Am J Physiol 262:H903–H910
Rowland M, Benet LZ, Graham GG (1973) Clearance concepts in pharmacokinetics. J Pharmacokinet Biopharm 1:123–136
Lobo ED, Hansen RJ, Balthasar JP (2004) Antibody pharmacokinetics and pharmacodynamics. J Pharm Sci 93:2645–2668
Humbert G, Spyker DA, Fillastre JP, Leroy A (1979) Pharmacokinetics of amoxicillin: dosage nomogram for patients with impaired renal function. Antimicrob Agents Chemother 15:28–33
Champoux N, Du Souich P, Ravaoarinoro M, Phaneuf D, Latour J, Cusson JR (1996) Single-dose pharmacokinetics of ampicillin and tobramycin administered by hypodermoclysis in young and older healthy volunteers. Br J Clin Pharmacol 42:325–331
Pfeffer M, Gaver RC, Ximenez J (1983) Human intravenous pharmacokinetics and absolute oral bioavailability of cefatrizine. Antimicrob Agents Chemother 24:915–920
Lee FH, Pfeffer M, Van Harken DR, Smyth RD, Hottendorf GH (1980) Comparative pharmacokinetics of ceforanide (BL-S786R) and cefazolin in laboratory animals and humans. Antimicrob Agents Chemother 17:188–192
Lofgren S, Bucht G, Hermansson B, Holm SE, Winblad B, Norrby SR (1986) Single-dose pharmacokinetics of dicloxacillin in healthy subjects of young and old age. Scand J Infect Dis 18:365–369
Landersdorfer CB, Kirkpatrick CM, Kinzig-Schippers M, Bulitta JB, Holzgrabe U, Drusano GL, Sorgel F (2007) Population pharmacokinetics at two dose levels and pharmacodynamic profiling of flucloxacillin. Antimicrob Agents Chemother 51:3290–3297
Gambertoglio JG, Barriere SL, Lin ET, Conte JE Jr (1980) Pharmacokinetics of mecillinam in health subjects. Antimicrob Agents Chemother 18:952–956
Bulitta JB, Duffull SB, Kinzig-Schippers M, Holzgrabe U, Stephan U, Drusano GL, Sorgel F (2007) Systematic comparison of the population pharmacokinetics and pharmacodynamics of piperacillin in cystic fibrosis patients and healthy volunteers. Antimicrob Agents Chemother 51:2497–2507
Hampel B, Feike M, Koeppe P, Lode H (1985) Pharmacokinetics of temocillin in volunteers. Drugs 29(Suppl 5):99–102
Frimodt-Moller N, Maigaard S, Toothaker RD, Bundtzen RW, Brodey MV, Craig WA, Welling PG, Madsen PO (1980) Mezlocillin pharmacokinetics after single intravenous doses to patients with varying degrees of renal function. Antimicrob Agents Chemother 17:599–607
Vinge E, Nergelius G, Nilsson LG, Lidgren L (1997) Pharmacokinetics of cloxacillin in patients undergoing hip or knee replacement. Eur J Clin Pharmacol 52:407–411
Yaffe SJ, Gerbracht LM, Mosovich LL, Mattar ME, Danish M, Jusko WJ (1977) Pharmacokinetics of methicillin in patients with cystic fibrosis. J Infect Dis 135:828–831
Rumble RH, Roberts MS, Scott AR (1986) The effect of posture on the pharmacokinetics of intravenous benzylpenicillin. Eur J Clin Pharmacol 30:731–734
Meyers BR, Hirschman SZ, Strougo L, Srulevitch E (1980) Comparative study of piperacillin, ticarcillin, and carbenicillin pharmacokinetics. Antimicrob Agents Chemother 17:608–611
Kikuchi E, Kikuchi J, Nasuhara Y, Oizumi S, Ishizaka A, Nishimura M (2009) Comparison of the pharmacodynamics of biapenem in bronchial epithelial lining fluid in healthy volunteers given half-hour and three-hour intravenous infusions. Antimicrob Agents Chemother 53:2799–2803
Colaizzi PA, Polk RE, Poynor WJ, Raffalovich AC, Cefali EA, Beightol LA (1986) Comparative pharmacokinetics of azlocillin and piperacillin in normal adults. Antimicrob Agents Chemother 29:938–940
Barza M, Melethil S, Berger S, Ernst EC (1976) Comparative pharmacokinetics of cefamandole, cephapirin, and cephalothin in healthy subjects and effect of repeated dosing. Antimicrob Agents Chemother 10:421–425
Kampf D, Schurig R, Korsukewitz I, Bruckner O (1981) Cefoxitin pharmacokinetics: relation to three different renal clearance studies in patients with various degrees of renal insufficiency. Antimicrob Agents Chemother 20:741–746
Waller ES, Sharanevych MA, Yakatan GJ (1982) The effect of probenecid on nafcillin disposition. J Clin Pharmacol 22:482–489
Dudley MN, Shyu WC, Nightingale CH, Quintiliani R (1986) Effect of saturable serum protein binding on the pharmacokinetics of unbound cefonicid in humans. Antimicrob Agents Chemother 30:565–569
Rowell FJ, Seymour RA, Rawlins MD (1983) Pharmacokinetics of intravenous and oral dihydrocodeine and its acid metabolites. Eur J Clin Pharmacol 25(3):419–424
Krecic-Shepard ME, Barnas CR, Slimko J, Jones MP, Schwartz JB (2000) Gender-specific effects on verapamil pharmacokinetics and pharmacodynamics in humans. J Clin Pharmacol 40:219–230
Li C, Choi DH, Choi JS (2012) Effects of efonidipine on the pharmacokinetics and pharmacodynamics of repaglinide: possible role of CYP3A4 and P-glycoprotein inhibition by efonidipine. J Pharmacokinet Pharmacodyn 39:99–108
Heizmann P, Eckert M, Ziegler WH (1983) Pharmacokinetics and bioavailability of midazolam in man. Br J Clin Pharmacol 16(Suppl 1):43S–49S
Siefert HM, Domdey-Bette A, Henninger K, Hucke F, Kohlsdorfer C, Stass HH (1999) Pharmacokinetics of the 8-methoxyquinolone, moxifloxacin: a comparison in humans and other mammalian species. J Antimicrob Chemother 43(Suppl B):69–76
Li J, Zhou B, Shentu J, Du L, Tan M, Hou S, Qian W, Li B, Zhang D, Dai J, Wang H, Zhang X, Chen J, Guo Y (2010) Phase I trial of a humanized, Fc receptor nonbinding anti-CD3 antibody, hu12F6mu in patients receiving renal allografts. MAbs 2:449–456
Wakelee HA, Patnaik A, Sikic BI, Mita M, Fox NL, Miceli R, Ullrich SJ, Fisher GA, Tolcher AW (2010) Phase I and pharmacokinetic study of lexatumumab (HGS-ETR2) given every 2 weeks in patients with advanced solid tumors. Ann Oncol 21:376–381
White B, Leon F, White W, Robbie G (2009) Two first-in-human, open-label, phase I dose-escalation safety trials of MEDI-528, a monoclonal antibody against interleukin-9, in healthy adult volunteers. Clin Ther 31:728–740
Busse WW, Katial R, Gossage D, Sari S, Wang B, Kolbeck R, Coyle AJ, Koike M, Spitalny GL, Kiener PA, Geba GP, Molfino NA (2010) Safety profile, pharmacokinetics, and biologic activity of MEDI-563, an anti-IL-5 receptor alpha antibody, in a phase I study of subjects with mild asthma. J Allergy Clin Immunol 125(1237–1244):e1232
Hawthorne T, Giot L, Blake L, Kuang B, Gerwien R, Smithson G, Hahne W, Mansfield T, Starling GC, Pochart P, Hoelscher D, Halvorsen YD (2008) A phase I study of CR002, a fully-human monoclonal antibody against platelet-derived growth factor-D. Int J Clin Pharmacol Ther 46:236–244
Emu B, Luca D, Offutt C, Grogan JL, Rojkovich B, Williams MB, Tang MT, Xiao J, Lee JH, Davis JC (2012) Safety, pharmacokinetics, and biologic activity of pateclizumab, a novel monoclonal antibody targeting lymphotoxin alpha: results of a phase I randomized, placebo-controlled trial. Arthritis Res Ther 14:R6
Rodionov N (2000) Graph digitizer version 1.9. http://www.geocities.com/graphdigitizer
Brown RP, Delp MD, Lindstedt SL, Rhomberg LR, Beliles RP (1997) Physiological parameter values for physiologically based pharmacokinetic models. Toxicol Ind Health 13:407–484
Boxenbaum H (1982) Interspecies scaling, allometry, physiological time, and the ground plan of pharmacokinetics. J Pharmacokinet Biopharm 10:201–227
D’Argenio DZ, Schumitzky A, Wang XN. (2009). ADAPT V user’s guide: pharmacokinetic/pharmacodynamic system analysis software, biomedical simulations resource, Los Angeles
ICRP Publication 89 (2002) Basic anatomical and physiological data for use in radiological protection: reference values. A report of age- and gender-related differences in the anatomical and physiological characteristics of reference individuals. Ann ICRP 32(3–4):5–265
Jusko WJ, Chiang ST (1982) Distribution volume related to body weight and protein binding. J Pharm Sci 71:469–470
Cars O (1990) Pharmacokinetics of antibiotics in tissues and tissue fluids: a review. Scand J Infect Dis Suppl 74:23–33
Shiran MR, Proctor NJ, Howgate EM, Rowland-Yeo K, Tucker GT, Rostami-Hodjegan A (2006) Prediction of metabolic drug clearance in humans: in vitro-in vivo extrapolation vs allometric scaling. Xenobiotica 36:567–580
McNamara PJ, Gibaldi M, Stoeckel K (1983) Fraction unbound in interstitial fluid. J Pharm Sci 72:834–836
Wise R, Gillett AP, Cadge B, Durham SR, Baker S (1980) The influence of protein binding upon tissue fluid levels of six beta-lactam antibiotics. J Infect Dis 142:77–82
Barza M, Weinstein L (1974) Some determinants of the distribution of penicillins and cephalosporins in the body. Practical and theoretical considerations. Ann N Y Acad Sci 235:613–620
Fujiwara K, Shin M (2011) Immunocytochemistry for amoxicillin and its use for studying uptake of the drug in the intestine, liver, and kidney of rats. Antimicrob Agents Chemother 55(1):62–71
Griaznova NS, Subbotina NA (1986) Penicillin-binding proteins. Their enzymatic activity and properties. Antibiot Med Biotekhnol 31(7):487–498
Hamann SR, Blouin RA, McAllister RG Jr (1984) Clinical pharmacokinetics of verapamil. Clin Pharmacokinet 9:26–41
Eichelbaum M, Mikus G, Vogelgesang B (1984) Pharmacokinetics of (+)-, (−)- and (±)-verapamil after intravenous administration. Br J Clin Pharmacol 17:453–458
Sjogren E, Bredberg U, Lennernas H (2012) The pharmacokinetics and hepatic disposition of repaglinide in pigs: mechanistic modeling of metabolism and transport. Mol Pharm 9:823–841
Lin YS, Dowling AL, Quigley SD, Farin FM, Zhang J, Lamba J, Schuetz EG, Thummel KE (2002) Co-regulation of CYP3A4 and CYP3A5 and contribution to hepatic and intestinal midazolam metabolism. Mol Pharmacol 62:162–172
Tsunoda SM, Velez RL, von Moltke LL, Greenblatt DJ (1999) Differentiation of intestinal and hepatic cytochrome P450 3A activity with use of midazolam as an in vivo probe: effect of ketoconazole. Clin Pharmacol Ther 66:461–471
Thummel KE, O’Shea D, Paine MF, Shen DD, Kunze KL, Perkins JD, Wilkinson GR (1996) Oral first-pass elimination of midazolam involves both gastrointestinal and hepatic CYP3A-mediated metabolism. Clin Pharmacol Ther 59:491–502
Bjorkman S, Wada DR, Berling BM, Benoni G (2001) Prediction of the disposition of midazolam in surgical patients by a physiologically based pharmacokinetic model. J Pharm Sci 90:1226–1241
Cox SK (2007) Allometric scaling of marbofloxacin, moxifloxacin, danofloxacin and difloxacin pharmacokinetics: a retrospective analysis. J Vet Pharmacol Ther 30:381–386
Beckmann J, Kees F, Schaumburger J, Kalteis T, Lehn N, Grifka J, Lerch K (2007) Tissue concentrations of vancomycin and moxifloxacin in periprosthetic infection in rats. Acta Orthop 78:766–773
Garg A, Balthasar JP (2007) Physiologically-based pharmacokinetic (PBPK) model to predict IgG tissue kinetics in wild-type and FcRn-knockout mice. J Pharmacokinet Pharmacodyn 34:687–709
Baxter LT, Zhu H, Mackensen DG, Butler WF, Jain RK (1995) Biodistribution of monoclonal antibodies: scale-up from mouse to human using a physiologically based pharmacokinetic model. Cancer Res 55:4611–4622
Rippe B, Haraldsson B (1994) Transport of macromolecules across microvascular walls: the two-pore theory. Physiol Rev 74:163–219
Junghans RP (1997) Finally! The Brambell receptor (FcRB). Mediator of transmission of immunity and protection from catabolism for IgG. Immunol Res 16:29–57
Hayashi N, Tsukamoto Y, Sallas WM, Lowe PJ (2007) A mechanism-based binding model for the population pharmacokinetics and pharmacodynamics of omalizumab. Br J Clin Pharmacol 63:548–561
Lammerts van Bueren JJ, Bleeker WK, Bogh HO, Houtkamp M, Schuurman J, van de Winkel JG, Parren PW (2006) Effect of target dynamics on pharmacokinetics of a novel therapeutic antibody against the epidermal growth factor receptor: implications for the mechanisms of action. Cancer Res 66:7630–7638
Huisinga W, Solms A, Fronton L, Pilari S (2012) Modeling interindividual variability in physiologically based pharmacokinetics and its link to mechanistic covariate modeling. Pharmacometrics Syst Pharmacol 1:e4
Weiss M (1983) Modelling of initial distribution of drugs following intravenous bolus injection. Eur J Clin Pharmacol 24:121–126
Levitt DG (2003) The pharmacokinetics of the interstitial space in humans. BMC Clin Pharmacol 3:3–14
Stec GP, Atkinson AJ Jr (1981) Analysis of the contributions of permeability and flow of intercompartmental clearance. J Pharmacokinet Biopharm 9:167–180
Kety SS (1951) The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol Rev 3:1–41
Renkin EM (1955) Effects of blood flow on diffusion kinetics in isolated, perfused hindlegs of cats; a double circulation hypothesis. Am J Physiol 183:125–136
Renkin EM (1959) Transport of potassium-42 from blood to tissue in isolated mammalian skeletal muscles. Am J Physiol 197:1205–1210
Crone C (1963) The permeability of capillaries in various organs as determined by use of the ‘Indicator diffusion’ method. Acta Physiol Scand 58:292–305
Watanabe T, Kusuhara H, Sugiyama Y (2010) Application of physiologically based pharmacokinetic modeling and clearance concept to drugs showing transporter-mediated distribution and clearance in humans. J Pharmacokinet Pharmacodyn 37:575–590
Thompson MD, Beard DA (2011) Development of appropriate equations for physiologically based pharmacokinetic modeling of permeability-limited and flow-limited transport. J Pharmacokinet Pharmacodyn 38:405–421
Goldstein A, Aronow L, Kalman SM (1974) Principles of drug action: the basis of pharmacology. Harper & Row, New York, p 147
Renkin EM (1977) Multiple pathways of capillary permeability. Circ Res 41:735–743
Bischoff KB, Dedrick RL, Zaharko DS, Longstreth JA (1971) Methotrexate pharmacokinetics. J Pharm Sci 60:1128–1133
Poulin P, Kenny JR, Hop CE, Haddad S (2012) In vitro–in vivo extrapolation of clearance: modeling hepatic metabolic clearance of highly bound drugs and comparative assessment with existing calculation methods. J Pharm Sci 101:838–851
Chiba M, Ishii Y, Sugiyama Y (2009) Prediction of hepatic clearance in human from in vitro data for successful drug development. AAPS J 11:262–276
Grimsrud KN, Ait-Oudhia S, Durbin-Johnson BP, Rocke DM, Mama KR, Rezende ML, Stanley SD, Jusko WJ. (2012) Population pharmacokinetic and pharmacodynamic analysis comparing diverse effects of detomidine, medetomidine and dexmedetomidine in the horse (Presented at the Annual Symposium of the Veterinary Science Training Program, University of California, Davis, March 2012)
Acknowledgments
This research was supported by the National Institutes of Health Grant GM57980, the University at Buffalo—Pfizer Strategic Alliance, and the UB Center for Protein Therapeutics. Review of this manuscript by Drs. Sihem Ait-Oudhia, Peter Bonate, Wilhelm Huisinga, Wojciech Krzyzanski, Donald E. Mager, and Marilyn E. Morris is appreciated.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
10928_2012_9280_MOESM1_ESM.docx
Supplementary material provides the ADAPT-5 code for operation of the models in Figure 2 and 3. Supplementary material 1 (DOCX 29 kb)
Rights and permissions
About this article
Cite this article
Cao, Y., Jusko, W.J. Applications of minimal physiologically-based pharmacokinetic models. J Pharmacokinet Pharmacodyn 39, 711–723 (2012). https://doi.org/10.1007/s10928-012-9280-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10928-012-9280-2