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Modeling Tumor Growth in Animals and Humans: An Evolutionary Approach

  • Dean C. BottinoEmail author
  • Arijit Chakravarty
Chapter

Abstract

Disease progression modeling allows more precise quantitation of therapeutic interventions, which in turn enables better decision-making in drug research and development. Cancer biology has a rich history of disease progression modeling both in the animal and patient setting, from exponential growth to carrying capacity models, not to mention enhancements that represent biochemical pathways, cell cycle state, and tumor microenvironment. Recent observations of tumor heterogeneity and treatment emergent resistance to every pharmacologic modality to date support an evolutionary approach to characterizing tumor kinetics. This approach represents an individual’s tumor burden as a collection of independently exponentially growing subpopulations with varying degrees of innate sensitivity or resistance to the therapeutic intervention being studied. A two-population simplified evolutionary model can recapitulate a wide variety of tumor kinetic trajectories observed in the clinic, including primary resistance, initial shrinkage followed by relapse, and durable response, depending on the estimated pre-existing fraction ϕR of initial tumor burden resistant to therapy. Under the assumption that tumor burden exceeding a critical threshold results in death of the patient, it can be shown that this initial resistant fraction ϕR and the growth rate gR of cells resistant to treatment are the key drivers of survival benefit, whereas the kill rate of the treatment on sensitive cells has a negligible effect on survival. By utilizing the totality of continuous tumor burden measurements over the entire course of treatment, evolutionary tumor kinetics modeling enables more accurate treatment benefit assessment and therefore better drug development decision-making than categorical, nontemporal criteria like RECIST.

Keywords

Oncology Mathematical modeling Mathematical oncology Xenograft Clinical trials Evolutionary dynamics 

References

  1. Abend M (2003) Reasons to reconsider the significance of apoptosis for cancer therapy. Int J Radiat Biol 79(12):927–941CrossRefPubMedGoogle Scholar
  2. Admiraal R, van Kesteren C, Boelens JJ, Bredius RG, Tibboel D, Knibbe CA (2014) Towards evidence-based dosing regimens in children on the basis of population pharmacokinetic pharmacodynamic modelling. Arch Dis Child 99(3):267–272CrossRefPubMedGoogle Scholar
  3. Aston PJ, Derks G, Raji A, Agoram BM, van der Graaf PH (2011) Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency. J Theor Biol 281(1):113–121CrossRefPubMedGoogle Scholar
  4. Bahlis NJ (2012) Darwinian evolution and tiding clones in multiple myeloma. Blood 120(5):927–928CrossRefPubMedGoogle Scholar
  5. Bernard A, Kimko H, Mital D, Poggesi I (2012) Mathematical modeling of tumor growth and tumor growth inhibition in oncology drug development. Expert Opin Drug Metab Toxicol 8(9):1057–1069CrossRefPubMedGoogle Scholar
  6. Bottino D (2009) Inference of imatinib effects on leukemic stem cell compartment via mathematical modeling of IRIS treatment response data. J Clin Oncol 27:15CrossRefGoogle Scholar
  7. Carroll KJ (2003) On the use and utility of the Weibull model in the analysis of survival data. Contemp Clin Trials 24(6):682–701. doi: 10.1016/S0197-2456(03)00072-2 CrossRefGoogle Scholar
  8. 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 CrossRefPubMedGoogle Scholar
  9. Claret L, Gupta M, Han K, Joshi A, Sarapa N, He J, Powell B, Bruno R (2013a) 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 CrossRefPubMedGoogle Scholar
  10. Claret L, Mancini P, Sebastien B, Veyrat-Follet C, Bruno R (2013b) Model-based estimates of tumor growth inhibition (TGI) metrics to predict for overall survival (OS) in first-line non-small cell lung cancer (NSCLC). J Clin Oncol e19049Google Scholar
  11. 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 CrossRefPubMedGoogle Scholar
  12. Driscoll DL, Chakravarty A, Bowman D, Shinde V, Lasky K, Shi J, Vos T, Stringer B, Amidon B, D’Amore N, Hyer ML (2014) Plk1 inhibition causes post-mitotic DNA damage and senescence in a range of human tumor cell lines. PLoS One 9(11), e111060CrossRefPubMedPubMedCentralGoogle Scholar
  13. Eisenhauer EA (2009) New response evaluation criteria in solid tumors: revised RECIST guideline (version 1.1). Eur J Cancer 5:228–247CrossRefGoogle Scholar
  14. Fakir H, Tan WY, Hlatky L, Hahnfeldt P, Sachs RK (2009) Stochastic population dynamic effects for lung cancer progression. Radiat Res 172(3):383–393CrossRefPubMedGoogle Scholar
  15. Foo J, Leder K, Mumenthaler SM (2013) Cancer as a moving target: understanding the composition and rebound growth kinetics of recurrent tumors. Evol Appl 6(1):54–69CrossRefPubMedGoogle Scholar
  16. Fuller LM, Banker FL, Butler JJ, Gamble JF, Sullivan MP (1975) The natural history of non-Hodgkin’s lymphomata stages I and II. Br J Cancer Suppl 2:270–285PubMedPubMedCentralGoogle Scholar
  17. Steel GG, Lamerton LF (1966) The growth rate of human tumours. Br J Cancer 20(1):74–86CrossRefPubMedPubMedCentralGoogle Scholar
  18. Gascoigne KE, Taylor SS (2008) Cancer cells display profound intra- and interline variation following prolonged exposure to antimitotic drugs. Cancer Cell 14(2):111–122CrossRefPubMedGoogle Scholar
  19. Gawad C, Koh W, Quake SR (2014) Dissecting the clonal origins of childhood acute lymphoblastic leukemia by single-cell genomics. Proc Natl Acad Sci U S A 111(50):17947–17952CrossRefPubMedPubMedCentralGoogle Scholar
  20. Gerlee P (2013) The model muddle: in search of tumor growth laws. Cancer Res 73(8):2407–2411CrossRefPubMedGoogle Scholar
  21. Gerlinger M, McGranahan N, Dewhurst SM, Burrell RA, Tomlinson I, Swanton C (2014) Cancer: evolution within a lifetime. Annu Rev Genet 48:215–236CrossRefPubMedGoogle Scholar
  22. Gerlinger M, Rowan AJ, Horswell S, Larkin J, Endesfelder D, Gronroos E, Martinez P, Matthews N, Stewart A, Tarpey P, Varela I, Phillimore B, Begum S, McDonald NQ, Butler A, Jones D, Raine K, Latimer C, Santos CR, Nohadani M, Eklund AC, Spencer-Dene B, Clark G, Pickering L, Stamp G, Gore M, Szallasi Z, Downward J, Futreal PA, Swanton C (2012) Intratumor heterogeneity and branched evolution revealed by multiregion sequencing. N Engl J Med 366(10):883–892CrossRefPubMedPubMedCentralGoogle Scholar
  23. Griggs RC, Donohoe KM, Utell MJ, Goldblatt D, Moxley RT 3rd (1981) Evaluation of pulmonary function in neuromuscular disease. Arch Neurol 38(1):9–12Google Scholar
  24. Hather G, Liu R, Bandi S, Mettetal J, Manfredi M, Shyu WC, Donelan J, Chakravarty A (2014) Growth rate analysis and efficient experimental design for tumor xenograft studies. Cancer Inform 13:65–72CrossRefPubMedPubMedCentralGoogle Scholar
  25. Heitjan DF (2011) Biology, models, and the analysis of tumor xenograft experiments. Clin Cancer Res 17(5):949–951CrossRefPubMedPubMedCentralGoogle Scholar
  26. Heng HH, Bremer SW, Stevens J, Ye KJ, Miller F, Liu G, Ye CJ (2006a) Cancer progression by non-clonal chromosome aberrations. J Cell Biochem 98(6):1424–1435CrossRefPubMedGoogle Scholar
  27. Heng HH, Stevens JB, Liu G, Bremer SW, Ye KJ, Reddy PV, Wu GS, Wang YA, Tainsky MA, Ye CJ (2006b) Stochastic cancer progression driven by non-clonal chromosome aberrations. J Cell Physiol 208(2):461–472CrossRefPubMedGoogle Scholar
  28. Holford N (2015) Clinical pharmacology = disease progression + drug action. Br J Clin Pharmacol 79(1):18–27CrossRefPubMedGoogle Scholar
  29. Holford NH, Peace KE (1992) Results and validation of a population pharmacodynamic model for cognitive effects in Alzheimer patients treated with tacrine. Proc Natl Acad Sci U S A 89(23):11471–11475CrossRefPubMedPubMedCentralGoogle Scholar
  30. Holford NH, Sheiner LB (1981) Understanding the dose-effect relationship: clinical application of pharmacokinetic-pharmacodynamic models. Clin Pharmacokinet 6(6):429–453CrossRefPubMedGoogle Scholar
  31. Huck JJ, Zhang M, McDonald A, Bowman D, Hoar KM, Stringer B, Ecsedy J, Manfredi MG, Hyer ML (2010) MLN8054, an inhibitor of Aurora A kinase, induces senescence in human tumor cells both in vitro and in vivo. Mol Cancer Res 8(3):373–384CrossRefPubMedGoogle Scholar
  32. Kong M, Yan J (2011) Modeling and testing treated tumor growth using cubic smoothing splines. Biom J 53(4):595–613CrossRefPubMedGoogle Scholar
  33. Laird AK (1964) Dynamics of tumor growth. Br J Cancer 18(3):490–502CrossRefPubMedCentralGoogle Scholar
  34. Landersdorfer CB, Jusko WJ (2008) Pharmacokinetic/pharmacodynamic modelling in diabetes mellitus. Clin Pharmacokinet 47(7):417–448CrossRefPubMedGoogle Scholar
  35. Le Pennec S, Konopka T, Gacquer D, Fimereli D, Tarabichi M, Tomás G, Savagner F, Decaussin-Petrucci M, Trésallet C, Andry G, Larsimont D, Detours V, Maenhaut C (2015) Intratumor heterogeneity and clonal evolution in an aggressive papillary thyroid cancer and matched metastases. Endocr Relat Cancer 22(2):205–216CrossRefPubMedGoogle Scholar
  36. Lobo ED, Soda DM, Balthasar JP (2003) Application of pharmacokinetic-pharmacodynamic modeling to predict the kinetic and dynamic effects of anti-methotrexate antibodies in mice. J Pharm Sci 92(8):1665–1676CrossRefPubMedGoogle Scholar
  37. Martinez P, Birkbak NJ, Gerlinger M, McGranahan N, Burrell RA, Rowan AJ, Joshi T, Fisher R, Larkin J, Szallasi Z, Swanton C (2013) Parallel evolution of tumour subclones mimics diversity between tumours. J Pathol 230(4):356–364CrossRefPubMedGoogle Scholar
  38. Mehine M, Heinonen HR, Sarvilinna N, Pitkänen E, Mäkinen N, Katainen R, Tuupanen S, Bützow R, Sjöberg J, Aaltonen LA (2015) Clonally related uterine leiomyomas are common and display branched tumor evolution. Hum Mol Genet 24(15):4407–4416, pii: ddv177 [Epub]CrossRefPubMedGoogle Scholar
  39. Merlo LM, Pepper JW, Reid BJ, Maley CC (2006) Cancer as an evolutionary and ecological process. Nat Rev Cancer 6(12):924–935CrossRefPubMedGoogle Scholar
  40. Michor F, Hughes TP, Iwasa Y, Brandford S, Shah NP, Sawyers CL, Nowak MA (2005) Dynamics of chronic myeloid leukemia. Nature 435(7046):1267–1270CrossRefPubMedGoogle Scholar
  41. Moertel CG, Hanlet JA (1976) The effect of measuring error on the results of therapeutic trials in advanced cancer. Cancer 38(1):388–394CrossRefPubMedGoogle Scholar
  42. Monsma DJ, Cherba DM, Eugster EE, Dylewski DL, Davidson PT, Peterson CA, Borgman AS, Winn ME, Dykema KJ, Webb CP, MacKeigan JP, Duesbery NS, Nickoloff BJ, Monks NR (2015) Melanoma patient derived xenografts acquire distinct Vemurafenib resistance mechanisms. Am J Cancer Res 5(4):1507–1518, eCollection 2015PubMedPubMedCentralGoogle Scholar
  43. Neal ML, Trister AD, Cloke T, Sodt R, Ahn S, Baldock A, Bridge CA, Lai A, Cloughesy TF, Mrugala MM, Rockhill JK, Rockne RC, Carrol KR (2013) Discriminating survival outcomes in patients with glioblastoma using a simulation-based, patient-specific response metric. PLoS One 8(1):e51951. doi: 10.1371/journal.pone.0051951
  44. Nielsen EI, Friberg LE (2013) Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs. Pharmacol Rev 65(3):1053–1090CrossRefPubMedGoogle Scholar
  45. Nik-Zainal S, Van Loo P, Wedge DC, Alexandrov LB, Greenman CD, Lau KW, Raine K, Jones D, Marshall J, Ramakrishna M, Shlien A, Cooke SL, Hinton J, Menzies A, Stebbings LA, Leroy C, Jia M, Rance R, Mudie LJ, Gamble SJ, Stephens PJ, McLaren S, Tarpey PS, Papaemmanuil E, Davies HR, Varela I, McBride DJ, Bignell GR, Leung K, Butler AP, Teague JW, Martin S, Jönsson G, Mariani O, Boyault S, Miron P, Fatima A, Langerød A, Aparicio SA, Tutt A, Sieuwerts AM, Borg Å, Thomas G, Salomon AV, Richardson AL, Børresen-Dale AL, Futreal PA, Stratton MR, Campbell PJ (2012) Breast cancer working group of the international cancer genome consortium: the life history of 21 breast cancers. Cell 149(5):994–1007CrossRefPubMedPubMedCentralGoogle Scholar
  46. Nowell PC (1976) The clonal evolution of tumor cell populations. Science 194(4260):23–28CrossRefPubMedGoogle Scholar
  47. Office of Laboratory Animal Welfare (2002) Institutional Animal Care and Use Committee GuidebookGoogle Scholar
  48. Orth JD, Tang Y, Shi J, Loy CT, Amendt C, Wilm C, Zenke FT, Mitchison TJ (2008) Quantitative live imaging of cancer and normal cells treated with Kinesin-5 inhibitors indicates significant differences in phenotypic responses and cell fate. Mol Cancer Ther 7(11):3480–3489CrossRefPubMedPubMedCentralGoogle Scholar
  49. Patel M, Zopf CJ, Mettetal J, Bottino D, Shyu WC, Chakravarty A (2015) A clonal evolution model of tumor growth kinetics predicts time to progression in prostate carcinoma, in preparationGoogle Scholar
  50. Port RE, Bernstein LJ, Barboriak DP, Xu L, Roberts TP, van Bruggen N (2010) Noncompartmental kinetic analysis of DCE-MRI data from malignant tumors: application to glioblastoma treated with bevacizumab. Magn Reson Med 64(2):408–417PubMedGoogle Scholar
  51. Ribba B, Holford NH, Magni P, Troconiz I, Gueorguieva I, Girard P, Sarr C, Elishmereni M, Kloft C, Friberg LE (2014) A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis. CPT Pharmacometrics Syst Pharmacol 3(5), e113CrossRefPubMedPubMedCentralGoogle Scholar
  52. Roninson IB, Broude EV, Chang BD (2001) If not apoptosis, then what? Treatment-induced senescence and mitotic catastrophe in tumor cells. Drug Resist Updat 4(5):303–313CrossRefPubMedGoogle Scholar
  53. Rösch J, Antonovic R, Trenouth RS, Rahimtoola SH, Sim DN, Dotter CT (1976) The natural history of coronary artery stenosis: a longitudinal angiographic assessment. Radiology 119(3):513–520CrossRefPubMedGoogle Scholar
  54. Sachs RK, Shuryak I, Brenner D, Fakir H, Hlatky L, Hahnfeldt P (2007) Second cancers after fractionated radiotherapy: stochastic population dynamics effects. J Theor Biol 249(3):518–531CrossRefPubMedPubMedCentralGoogle Scholar
  55. Shah NP, Skaggs BJ, Branford S, Hughes TP, Nicoll JM, Paquette RL, Sawyers CL (2007) Sequential ABL kinase inhibitor therapy selects for compound drug-resistant BCR-ABL mutations with altered oncogenic potency. J Clin Invest 117(9):2562–2569CrossRefPubMedPubMedCentralGoogle Scholar
  56. 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):1094–1101CrossRefPubMedGoogle Scholar
  57. Spencer SL, Gaudet S, Albeck JG, Burke JM, Sorger PK (2009) Non-genetic origins of cell-to-cell variability in TRAIL-induced apoptosis. Nature 459(7245):428–432CrossRefPubMedPubMedCentralGoogle Scholar
  58. Stein A, Kalebic T, Bottino D (2009) Bcr-Abl kinetics suggest self-renewing leukemic cells are reduced during imatinib treatment. American Society of Hematology Annual Meeting, Abstract #506Google Scholar
  59. Stein AM, Bottino D, Modur V, Branford S, Kaeda J, Goldman JM, Hughes TP, Radich JP, Hochhaus A (2011) BCR-ABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment. Clin Cancer Res 17(21):6812–6821. doi: 10.1158/1078-0432.CCR-11-0396 CrossRefPubMedGoogle Scholar
  60. Stein A, Wang W, Carter AA, Chiparus O, Hollaender N, Kim H, Motzer RJ, Sarr C (2012) Dynamic tumor modeling of the dose-response relationship for everolimus in metastatic renal cell carcinoma using data from the phase 3 RECORD-1 trial. BMC Cancer 12:311. doi: 10.1186/1471-2407-12-311 CrossRefPubMedPubMedCentralGoogle Scholar
  61. Stein A, Bellmunt J, Escudier B, Kim D, Sterqiopoulos SG, Mietlowski W, Motzer RJ (2013) Survival prediction in everolimus-treated patients with metastatic renal cell carcinoma incorporating tumor burden response in the RECORD-1 trial. Eur Urol 64(6):994–1002. doi: 10.1016/j.eururo.2012.11.032 CrossRefPubMedGoogle Scholar
  62. Stein WD, Figg WD, Dahut W, Stein AD, Hoshen MB, Price D, Bates SE, Fojo T (2008) Tumor growth rates derived from data for patients in a clinical trial correlate strongly with patient survival: a novel strategy for evaluation of clinical trial data. Oncologist 13(10):1046–1054CrossRefPubMedPubMedCentralGoogle Scholar
  63. Stephens AD, Haggerty RA, Vasquez PA, Vicci L, Snider CE, Shi F, Quammen C, Mullins C, Haase J, Taylor RM 2nd, Verdaasdonk JS, Falvo MR, Jin Y, Forest MG, Bloom K (2013) Pericentric chromatin loops function as a nonlinear spring in mitotic force balance. J Cell Biol 200(6):757–772CrossRefPubMedPubMedCentralGoogle Scholar
  64. Stiehl T, Baran N, Ho AD, Marciniak-Czochra A (2014) Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. J R Soc Interface 11(94):20140079CrossRefPubMedPubMedCentralGoogle Scholar
  65. Swanson KR, Bridge C, Murray JD, Alvord EC (2003) Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol Sci 216(1):1–10. doi: 10.1016/j.jns.2003.06.001 CrossRefPubMedGoogle Scholar
  66. Tegze B, Szállási Z, Haltrich I, Pénzváltó Z, Tóth Z, Likó I, Gyorffy B (2012) Parallel evolution under chemotherapy pressure in 29 breast cancer cell lines results in dissimilar mechanisms of resistance. PLoS One 7(2), e30804CrossRefPubMedPubMedCentralGoogle Scholar
  67. Thurber GM, Yang KS, Reiner T, Kohler RH, Sorger P, Mitchison T, Weissleder R (2013) Single-cell and subcellular pharmacokinetic imaging allows insight into drug action in vivo. Nat Commun 4:1504CrossRefPubMedPubMedCentralGoogle Scholar
  68. Van Heesbeen RG, Tanenbaum ME, Medema RH (2014) Balanced activity of three mitotic motors is required for bipolar spindle assembly and chromosome segregation. Cell Rep 8(4):948–956CrossRefPubMedGoogle Scholar
  69. Vogelstein B, Kinzler KW (1993) The multistep nature of cancer. Trends Genet 9(4):138–141CrossRefPubMedGoogle Scholar
  70. 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 Therapeut 86(2):167–174CrossRefGoogle Scholar
  71. Wu J (2011) Assessment of antitumor activity for tumor xenograft studies using exponential growth models. J Biopharm Stat 21(3):472–483CrossRefPubMedPubMedCentralGoogle Scholar
  72. Wu J, Houghton PJ (2009) Assessing cytotoxic treatment effects in preclinical tumor xenograft models. J Biopharm Stat 19(5):755–762CrossRefPubMedPubMedCentralGoogle Scholar
  73. 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):1177–1183CrossRefPubMedGoogle Scholar
  74. Zhang J, Fujimoto J, Zhang J, Wedge DC, Song X, Zhang J, Seth S, Chow CW, Cao Y, Gumbs C, Gold KA, Kalhor N, Little L, Mahadeshwar H, Moran C, Protopopov A, Sun H, Tang J, Wu X, Ye Y, William WN, Lee JJ, Heymach JV, Hong WK, Swisher S, Wistuba I, Futreal PA (2014) Intratumor heterogeneity in localized lung adenocarcinomas delineated by multiregion sequencing. Science 346(6206):256–259CrossRefPubMedPubMedCentralGoogle Scholar
  75. Zhao L, Morgan MA, Parsels LA, Maybaum J, Lawrence TS, Normolle D (2011) Bayesian hierarchical changepoint methods in modeling the tumor growth profiles in xenograft experiments. Clin Cancer Res 17(5):1057–1064CrossRefPubMedGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Takeda Pharmaceuticals International Co.CambridgeUSA

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