Abstract
Cancer is a complex disease that is characterized by an uncontrolled growth and spread of abnormal cells. Drug development in oncology is particularly challenging and is associated with one of the highest attrition rates of compounds despite substantial investments in resources. Pharmacokinetic and pharmacodynamic (PK/PD) modeling seeks to couple experimental data with mathematical models to provide key insights into factors controlling cytotoxic effects of chemotherapeutics and cancer progression. PK/PD modeling of anti-cancer compounds is equally challenging, partly based on the complexity of biological and pharmacological systems. However, reliable mechanistic and systems PK/PD models for anti-cancer agents have been developed and successfully applied to: (1) provide insights into fundamental mechanisms implicated in tumor growth, (2) assist in dose selection for first-in-human phase I studies (e.g., effective dose, escalating doses, and maximal tolerated doses), (3) design and optimize combination drug regimens, (4) design clinical trials, and (5) establish links between drug efficacy and safety and the concentrations of measured biomarkers. In this commentary, classes of relevant mechanism-based and systems PK/PD models of anti-cancer agents that have shown promise in translating preclinical data and enhancing stages of the drug development process are reviewed. Specific features of such models are discussed including their strengths and limitations along with a prospectus of using these models alone or in combination for cancer therapy.
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Gompertz B (1825) On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philos Trans R Soc Lond 115:513–585
Von Bertalanffy L (1957) The quarterly review of biology. http://www.ms.uky.edu/~ma138/Fall15/art1.pdf. Accessed 27 May 2016
Swierniak A, Kimmel M, Smieja J (2009) Mathematical modeling as a tool for planning anticancer therapy. Eur J Pharmacol 625(1–3):108–121
Arakawa A, Nishikawa H, Suzumori K, Kato N (2001) Pharmacokinetic and pharmacodynamic analysis of combined chemotherapy with carboplatin and paclitaxel for patients with ovarian cancer. Int J Clin Oncol/Jpn Soc Clin Oncol 6(5):248–252
Ratain MJ, Mick R, Schilsky RL, Vogelzang NJ, Berezin F (1991) Pharmacologically based dosing of etoposide: a means of safely increasing dose intensity. J Clin Oncol 9(8):1480–1486
Van Kesteren C, Mathot RA, Raymond E, Armand JP, Dittrich C, Dumez H, Roche H, Droz JP, Punt C, Ravic M, Wanders J, Beijnen JH, Fumoleau P, Schellens JH (2002) Population pharmacokinetics of the novel anticancer agent E7070 during four phase I studies: model building and validation. J Clin Oncol 20(19):4065–4073
Simonsen LE, Wahlby U, Sandstrom M, Freijs A, Karlsson MO (2000) Haematological toxicity following different dosing schedules of 5-fluorouracil and epirubicin in rats. Anticancer Res 20(3A):1519–1525
Levasseur LM, Slocum HK, Rustum YM, Greco WR (1998) Modeling of the time-dependency of in vitro drug cytotoxicity and resistance. Cancer Res 58(24):5749–5761
Karlsson MO, Port RE, Ratain MJ, Sheiner LB (1995) A population model for the leukopenic effect of etoposide. Clin Pharmacol Ther 57(3):325–334
Sheiner LB, Stanski DR, Vozeh S, Miller RD, Ham J (1979) Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharmacol Ther 25(3):358–371
Tham LS, Wang L, Soo RA, Lee SC, Lee HS, Yong WP, Goh BC, Holford NH (2008) A pharmacodynamic model for the time course of tumor shrinkage by gemcitabine + carboplatin in non-small cell lung cancer patients. Clin Cancer Res 14(13):4213–4218
Dayneka NL, Garg V, Jusko WJ (1993) Comparison of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 21(4):457–478
Minami H, Sasaki Y, Saijo N, Ohtsu T, Fujii H, Igarashi T, Itoh K (1998) Indirect-response model for the time course of leukopenia with anticancer drugs. Clin Pharmacol Ther 64(5):511–521
Sun YN, Jusko WJ (1998) Transit compartments versus gamma distribution function to model signal transduction processes in pharmacodynamics. J Pharm Sci 87(6):732–737
Zamboni WC, D’Argenio DZ, Stewart CF, MacVittie T, Delauter BJ, Farese AM, Potter DM, Kubat NM, Tubergen D, Egorin MJ (2001) Pharmacodynamic model of topotecan-induced time course of neutropenia. Clin Cancer Res 7(8):2301–2308
Yorke ED, Fuks Z, Norton L, Whitmore W, Ling CC (1993) Modeling the development of metastases from primary and locally recurrent tumors: comparison with a clinical data base for prostatic cancer. Cancer Res 53(13):2987–2993
Guiot C, Degiorgis PG, Delsanto PP, Gabriele P, Deisboeck TS (2003) Does tumor growth follow a “universal law”? J Theor Biol 225(2):147–151
West GB, Brown JH, Enquist BJ (2001) A general model for ontogenetic growth. Nature 413(6856):628–631
Guiot C, Delsanto PP, Carpinteri A, Pugno N, Mansury Y, Deisboeck TS (2006) The dynamic evolution of the power exponent in a universal growth model of tumors. J Theor Biol 240(3):459–463
Jusko WJ (1971) Pharmacodynamics of chemotherapeutic effects: dose-time-response relationships for phase-nonspecific agents. J Pharm Sci 60(6):892–895
de Pillis LG, Radunskaya AE, Wiseman CL (2005) A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res 65(17):7950–7958
Garrett ER (1971) Drug action and assay by microbial kinetics. Prog Drud Res 15:271–352
Wang S, Zhou Q, Gallo JM (2009) Demonstration of the equivalent pharmacokinetic/pharmacodynamic dosing strategy in a multiple-dose study of gefitinib. Mol Cancer Ther 8(6):1438–1447
Jusko WJ (1973) A pharmacodynamic model for cell-cycle-specific chemotherapeutic agents. J Pharmacokinet Biopharm 1:175–200
Yano Y, Oguma T, Nagata H, Sasaki S (1998) Application of logistic growth model to pharmacodynamic analysis of in vitro bactericidal kinetics. J Pharm Sci 87(10):1177–1183
Gardner SN (2000) A mechanistic, predictive model of dose-response curves for cell cycle phase-specific and -nonspecific drugs. Cancer Res 60(5):1417–1425
Hamed SS, Straubinger RM, Jusko WJ (2013) Pharmacodynamic modeling of cell cycle and apoptotic effects of gemcitabine on pancreatic adenocarcinoma cells. Cancer Chemother Pharmacol 72(3):553–563. doi:10.1007/s00280-013-2226-6
Mager DE, Jusko WJ (2001) Pharmacodynamic modeling of time-dependent transduction systems. Clin Pharmacol Ther 70(3):210–216
Friberg LE, Brindley CJ, Karlsson MO, Devlin AJ (2000) Models of schedule dependent haematological toxicity of 2′-deoxy-2′-methylidenecytidine (DMDC). Eur J Clin Pharmacol 56(8):567–574
Friberg LE, Freijs A, Sandstrom M, Karlsson MO (2000) Semiphysiological model for the time course of leukocytes after varying schedules of 5-fluorouracil in rats. J Pharmacol Exp Ther 295(2):734–740
Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO (2002) Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20(24):4713–4721
Lobo ED, Balthasar JP (2002) Pharmacodynamic modeling of chemotherapeutic effects: application of a transit compartment model to characterize methotrexate effects in vitro. AAPS Pharm Sci 4(4):E42
Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, Germani M, Poggesi I, Rocchetti M (2004) Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res 64(3):1094–1101
Yang J, Mager DE, Straubinger RM (2010) Comparison of two pharmacodynamic transduction models for the analysis of tumor therapeutic responses in model systems. AAPS J 12(1):1–10. doi:10.1208/s12248-009-9155-7
Bissery MC, Vrignaud P, Lavelle F, Chabot GG (1996) Preclinical antitumor activity and pharmacokinetics of irinotecan (CPT-11) in tumor-bearing mice. Ann N Y Acad Sci 803:173–180
Magni P, Simeoni M, Poggesi I, Rocchetti M, De Nicolao G (2006) A mathematical model to study the effects of drugs administration on tumor growth dynamics. Math Biosci 200(2):127–151
Terranova N, Germani M, Del Bene F, Magni P (2013) A predictive pharmacokinetic-pharmacodynamic model of tumor growth kinetics in xenograft mice after administration of anticancer agents given in combination. Cancer Chemother Pharmacol 72(2):471–482. doi:10.1007/s00280-013-2208-8
Magni P, Germani M, De Nicolao G, Bianchini G, Simeoni M, Poggesi I, Rocchetti M (2008) A minimal model of tumor growth inhibition. IEEE Trans Biomed Eng 52(11):2683–2690
Rocchetti M, Simeoni M, Pesenti E, De Nicolao G, Poggesi I (2007) Predicting the active doses in humans from animal studies: a novel approach in oncology. Eur J Cancer 43(12):1862–1868
Aarons L (2005) Physiologically based pharmacokinetic modelling: a sound mechanistic basis is needed. Br J Clin Pharmacol 60(6):581–583
Steimer JL, Dahl SG, De Alwis DP, Gundert-Remy U, Karlsson MO, Martinkova J, Aarons L, Ahr HJ, Clairambault J, Freyer G, Friberg LE, Kern SE, Kopp-Schneider A, Ludwig WD, De Nicolao G, Rocchetti M, Troconiz IF (2010) Modelling the genesis and treatment of cancer: the potential role of physiologically based pharmacodynamics. Eur J Cancer 46(1):21–32
Xu L, Eiseman JL, Egorin MJ, D’Argenio DZ (2003) Physiologically-based pharmacokinetics and molecular pharmacodynamics of 17-(allylamino)-17-demethoxygeldanamycin and its active metabolite in tumor-bearing mice. J Pharmacokinet Pharmacodyn 30(3):185–219
Sharma J, Lv H, Gallo JM (2013) Intratumoral modeling of gefitinib pharmacokinetics and pharmacodynamics in an orthotopic mouse model of glioblastoma. Cancer Res 73(16):5242–5252. doi:10.1158/0008-5472.CAN-13-0690
Pawaskar DK, Straubinger RM, Fetterly GJ, Hylander BH, Repasky EA, Ma WW, Jusko WJ (2013) Physiologically based pharmacokinetic models for everolimus and sorafenib in mice. Cancer Chemother Pharmacol 71(5):1219–1229. doi:10.1007/s00280-013-2116-y
Hidalgo M, Amant F, Biankin AV, Budinska E, Byrne AT, Caldas C, Clarke RB, de Jong S, Jonkers J, Maelandsmo GM, Roman-Roman S, Seoane J, Trusolino L, Villanueva A (2014) Patient-derived xenograft models: an emerging platform for translational cancer research. Cancer Discov 4(9):998–1013. doi:10.1158/2159-8290.CD-14-0001
Loewe S, Muischnek H (1926) Effect of combinations: mathematical basis of problem. Arch Exp Pathol Pharmakol 114:313–326
Koch G, Walz A, Lahu G, Schropp J (2009) Modeling of tumor growth and anticancer effects of combination therapy. J Pharmacokinet Pharmacodyn 36(2):179–197
Chakraborty A, Jusko WJ (2002) Pharmacodynamic interaction of recombinant human interleukin-10 and prednisolone using in vitro whole blood lymphocyte proliferation. J Pharm Sci 91(5):1334–1342
Zhu X, Straubinger RM, Jusko WJ (2015) Mechanism-based mathematical modeling of combined gemcitabine and birinapant in pancreatic cancer cells. J Pharmacokinet Pharmacodyn 42(5):477–496. doi:10.1007/s10928-015-9429-x
Rocchetti M, Del Bene F, Germani M, Fiorentini F, Poggesi I, Pesenti E, Magni P, De Nicolao G (2009) Testing additivity of anticancer agents in pre-clinical studies: a PK/PD modelling approach. Eur J Cancer 45(18):3336–3346
Benson N, van der Graaf PH (2014) The rise of systems pharmacology in drug discovery and development. Future Med Chem 6(16):1731–1734. doi:10.4155/fmc.14.66
Sorger PK, Allerheiligen SRB, Abernethy DR, Altman RB, Brouwer KLR, Califano A, D’Argenio DZ, Iyengar R, Jusko WJ, Lalonde R, Lauffenburger DA, Shoichet B, Stevens JS, Subramaniam S, Van der Graaf PPV (2011) Quantitative and systems pharmacology in the post-genomic era: new approaches to discovering drugs and understanding therapeutic mechanisms 1–47 [online]. Availabe: http://www.nigms.nih.gov/training/documents/systemspharmawpsorger2011.pdf
Iyengar R, Zhao S, Chung SW, Mager DE, Gallo JM (2012) Merging systems biology with pharmacodynamics. Sci Transl Med. doi:10.1126/scitranslmed.3003563
Ait-Oudhia S, Straubinger RM, Mager DE (2012) Systems pharmacological analysis of paclitaxel-mediated tumor priming that enhances nano-carrier deposition and efficacy. J Pharmacol Exp Ther. doi:10.1124/jpet.112.199109
Harrold JM, Straubinger RM, Mager DE (2012) Combinatorial chemotherapeutic efficacy in non-hodgkin lymphoma can be predicted by a signaling model of CD20 pharmacodynamics. Cancer Res 72(7):1632–1641. doi:10.1158/0008-5472.CAN-11-2432
Kirouac DC, Du JY, Lahdenranta J, Overland R, Yarar D, Paragas V, Pace E, McDonagh CF, Nielsen UB, Onsum MD (2013) Computational modeling of ERBB2-amplified breast cancer identifies combined ErbB2/3 blockade as superior to the combination of MEK and AKT inhibitors. Sci Signal. doi:10.1126/scisignal.2004008
Lindner AU, Concannon CG, Boukes GJ, Cannon MD, Llambi F, Ryan D, Boland K, Kehoe J, McNamara DA, Murray F, Kay EW, Hector S, Green DR, Huber HJ, Prehn JH (2013) Systems analysis of BCL2 protein family interactions establishes a model to predict responses to chemotherapy. Cancer Res 73(2):519–528. doi:10.1158/0008-5472.CAN-12-2269
Wang Y, Sung C, Dartois C, Ramchandani R, Booth BP, Rock E, Gobburu J (2009) Elucidation of relationship between tumor size and survival in non-small-cell lung cancer patients can aid early decision making in clinical drug development. Clin Pharmacol Ther 86(2):167–174
Claret L, Girard P, Hoff PM, Van Cutsem E, Zuideveld KP, Jorga K, Fagerberg J, Bruno R (2009) Model-based prediction of phase III overall survival in colorectal cancer on the basis of phase II tumor dynamics. J Clin Oncol 27(25):4103–4108. doi:10.1200/JCO.2008.21.0807
Claret L, Gupta M, Han K, Joshi A, Sarapa N, He J, Powell B, Bruno R (2013) Evaluation of tumor-size response metrics to predict overall survival in Western and Chinese patients with first-line metastatic colorectal cancer. J Clin Oncol 31(17):2110–2114. doi:10.1200/JCO.2012.45.0973
Ribba B, Holford N, Mentre F (2014) The use of model-based tumor-size metrics to predict survival. Clin Pharmacol Ther 96(2):133–135. doi:10.1038/clpt.2014.111
Claret L, Bruno R (2014) Assessment of tumor growth inhibition metrics to predict overall survival. Clin Pharmacol Ther 96(2):135–137. doi:10.1038/clpt.2014.112
Claret L, Gupta M, Han K, Joshi A, Sarapa N, He J, Powell B, Bruno R (2014) Prediction of overall survival or progression free survival by disease control rate at week 8 is independent of ethnicity: western versus Chinese patients with first-line non-small cell lung cancer treated with chemotherapy with or without bevacizumab. J Clin Pharmacol 54(3):253–257. doi:10.1002/jcph.191
Claret L, Mercier F, Houk BE, Milligan PA, Bruno R (2015) Modeling and simulations relating overall survival to tumor growth inhibition in renal cell carcinoma patients. Cancer Chemother Pharmacol 76(3):567–573. doi:10.1007/s00280-015-2820-x
Claret L, Zheng J, Mercier F, Chanu P, Chen Y, Rosbrook B, Yazdi P, Milligan PA, Bruno R (2016) Model-based prediction of progression-free survival in patients with first-line renal cell carcinoma using week 8 tumor size change from baseline. Cancer Chemother Pharmacol. doi:10.1007/s00280-016-3116-5
Han K, Claret L, Sandler A, Das A, Jin J, Bruno R (2016) Modeling and simulation of maintenance treatment in first-line non-small cell lung cancer with external validation. BMC Cancer 16:473. doi:10.1186/s12885-016-2455-2
Dawson TH (2010) Scaling laws for plasma concentrations and tolerable doses of anticancer drugs. Cancer Res 70(12):4801–4808. doi:10.1158/0008-5472.CAN-09-3261
Huntjens DR (2010) Pharmacokinetic-pharmacodynamic (PK-PD) modeling and simulation of serdemetan-induced QTc effects in a first-in-human study. J Clin Oncol 28(Suppl):e13011
Bennouna J, Fumoleau P, Armand JP, Raymond E, Campone M, Delgado FM, Puozzo C, Marty M (2003) Phase I and pharmacokinetic study of the new vinca alkaloid vinflunine administered as a 10-min infusion every 3 weeks in patients with advanced solid tumours. Ann Oncol 14(4):630–637
Simon R, Freidlin B, Rubinstein L, Arbuck SG, Collins J, Christian MC (1997) Accelerated titration designs for phase I clinical trials in oncology. J Natl Cancer Inst 89(15):1138–1147
Paoletti X, Kramar A (2009) A comparison of model choices for the continual reassessment method in phase I cancer trials. Stat Med 28(24):3012–3028
Greco WR, Bravo G, Parsons JC (1995) The search for synergy: a critical review from a response surface perspective. Pharmacol Rev 47(2):331–385
Drewinko B, Loo TL, Brown B, Gottlieb JA, Freireich EJ (1976) Combination chemotherapy in vitro with adriamycin. Observations of additive, antagonistic, and synergistic effects when used in two-drug combinations on cultured human lymphoma cells. Cancer Biochem Biophys 1(4):187–195
Chou TC, Talalay P (1984) Quantitative analysis of dose-effect relationships: the combined effects of multiple drugs or enzyme inhibitors. Adv Enzyme Regul 22:27–55
Greco WR, Park HS, Rustum YM (1990) Application of a new approach for the quantitation of drug synergism to the combination of cis-diamminedichloroplatinum and 1-beta-D-arabinofuranosylcytosine. Cancer Res 50(17):5318–5327
Gallo JM, Brennan J, Hamilton TC, Halbherr T, Laub PB, Ozols RF, O’Dwyer PJ (1995) Time-dependent pharmacodynamic models in cancer chemotherapy: population pharmacodynamic model for glutathione depletion following modulation by buthionine sulfoximine (BSO) in a Phase I trial of melphalan and BSO. Cancer Res 55(20):4507–4511
Swanson KR, Rostomily RC, Alvord EC Jr (2008) A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle. Br J Cancer 98(1):113–119
Zandvliet AS, Huitema AD, Copalu W, Yamada Y, Tamura T, Beijnen JH, Schellens JH (2007) CYP2C9 and CYP2C19 polymorphic forms are related to increased indisulam exposure and higher risk of severe hematologic toxicity. Clin Cancer Res 13(10):2970–2976
Joerger M (2012) Covariate pharmacokinetic model building in oncology and its potential clinical relevance. AAPS J 14(1):119–132. doi:10.1208/s12248-012-9320-2
Mellor HR, Callaghan R (2008) Resistance to chemotherapy in cancer: a complex and integrated cellular response. Pharmacology 81(4):275–300
Vega MI, Jazirehi AR, Huerta-Yepez S, Bonavida B (2005) Rituximab-induced inhibition of YY1 and Bcl-xL expression in Ramos non-Hodgkin’s lymphoma cell line via inhibition of NF-kappa B activity: role of YY1 and Bcl-xL in Fas resistance and chemoresistance, respectively. J Immunol 175(4):2174–2183
Idikio HA (2011) Human cancer classification: a systems biology- based model integrating morphology, cancer stem cells, proteomics, and genomics. J Cancer 2:107–115
Hua F, Cornejo MG, Cardone MH, Stokes CL, Lauffenburger DA (2005) Effects of Bcl-2 levels on Fas signaling-induced caspase-3 activation: molecular genetic tests of computational model predictions. J Immunol 175(2):985–995
Smieja J, Jamaluddin M, Brasier AR, Kimmel M (2008) Model-based analysis of interferon-beta induced signaling pathway. Bioinformatics 24(20):2363–2369
Paiva LR, Binny C, Ferreira SC Jr, Martins ML (2009) A multiscale mathematical model for oncolytic virotherapy. Cancer Res 69(3):1205–1211
Ribeiro D, Pinto JM (2009) An integrated network-based mechanistic model for tumor growth dynamics under drug administration. Comput Biol Med 39(4):368–384
Zhou Q, Gallo JM (2011) The pharmacokinetic/pharmacodynamic pipeline: translating anticancer drug pharmacology to the clinic. AAPS J 13(1):111–120. doi:10.1208/s12248-011-9253-1
Acknowledgments
SAO would like to acknowledge the Department of Pharmaceutical Sciences faculty at the University at Buffalo, SUNY for outstanding training in PK/PD and systems pharmacology and for the wonderful years spent there as a graduate student, postdoctoral associate, and research assistant professor.
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Ait-Oudhia, S., Mager, D.E. Array of translational systems pharmacodynamic models of anti-cancer drugs. J Pharmacokinet Pharmacodyn 43, 549–565 (2016). https://doi.org/10.1007/s10928-016-9497-6
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DOI: https://doi.org/10.1007/s10928-016-9497-6