Mathematical Modeling of Tumor Organoids: Toward Personalized Medicine

  • Aleksandra Karolak
  • Katarzyna A. Rejniak
Part of the Cancer Drug Discovery and Development book series (CDD&D)


Three-dimensional organoid and organoidal cell cultures can recreate certain aspects of in vivo tumors and tumor microenvironments, and thus can be used to test intratumoral interactions and tumor response to treatments. In silico organoid models, when based on biological or clinical data, are an invaluable tool for hypothesis testing, and provide an opportunity to explore experimental conditions beyond what is feasible experimentally. In this chapter, three different approaches to building in silico organoids are described together with methods for integration with experimental or clinical data. The first model will be used to determine the mechanisms of development of breast tumor acini, based on their in vitro morphology. The second model will be used to predict conditions for the most effective cellular uptake of therapies targeting pancreatic cancers that incorporate intravital microscopy data. The third model will provide a procedure for assessing patients’ response to chemotherapeutic treatments, based on the biopsy data. For each of the models, a protocol will be proposed indicating how it can be used to generate testable hypotheses or predictions. These models can help biologists in determining what experiments should be performed in the laboratory. They can also assist clinicians in assessing cancer patients’ response to a given therapy and their risk of tumor recurrence.


In silico organoids Digitized tissue Organotypic cultures Mammary acini Drug penetration Single-cell delivery Targeted therapy Personalized medicine Mathematical modeling 



This work was supported in part by the U01-CA20229-01 grant from the National Institute of Health (NIH) via the National Cancer Institute—Physical Science Oncology Network (NCI-PSON). Data collection and analysis were supported by the Cancer Center Support Grant P30-CA-076292 from NIH to H. Lee Moffitt Cancer Center & Research Institute, an NCI-designated Comprehensive Cancer Center.


  1. 1.
    Chauhan VP, Stylianopoulos T, Boucher Y, Jain RK (2011) Delivery of molecular and nanoscale medicine to tumors: transport barriers and strategies. Annu Rev Chem Biomol Eng 2:281–298. doi: 10.1146/annurev-chembioeng-061010-114300 CrossRefPubMedGoogle Scholar
  2. 2.
    Chin LK, Xia Y, Discher DE, Janmey PA (2016) Mechanotransduction in cancer. Curr Opin Chem Eng 11:77–84CrossRefPubMedPubMedCentralGoogle Scholar
  3. 3.
    Debnath J, Brugge JS (2005) Modelling glandular epithelial cancers in three-dimensional cultures. Nat Rev Cancer 5(9):675–688. doi: 10.1038/nrc1695 CrossRefPubMedGoogle Scholar
  4. 4.
    Debnath J, Mills KR, Collins NL, Reginato MJ, Muthuswamy SK, Brugge JS (2002) The role of apoptosis in creating and maintaining luminal space within normal and oncogene-expressing mammary acini. Cell 111(1):29–40CrossRefPubMedGoogle Scholar
  5. 5.
    Debnath J, Muthuswamy SK, Brugge JS (2003) Morphogenesis and oncogenesis of MCF-10A mammary epithelial acini grown in three-dimensional basement membrane cultures. Methods 30(3):256–268CrossRefPubMedGoogle Scholar
  6. 6.
    Dow LE, Elsum IA, King CL, Kinross KM, Richardson HE, Humbert PO (2008) Loss of human Scribble cooperates with H-Ras to promote cell invasion through deregulation of MAPK signalling. Oncogene 27(46):5988–6001. doi: 10.1038/onc.2008.219 CrossRefPubMedGoogle Scholar
  7. 7.
    Fessart D, Begueret H, Delom F (2013) Three-dimensional culture model to distinguish normal from malignant human bronchial epithelial cells. Eur Respir J 42(5):1345–1356. doi: 10.1183/09031936.00118812 CrossRefPubMedGoogle Scholar
  8. 8.
    Foroutan P, Kreahling JM, Morse DL, Grove O, Lloyd MC, Reed D, Raghavan M, Altiok S, Martinez GV, Gillies RJ (2013) Diffusion MRI and novel texture analysis in osteosarcoma xenotransplants predicts response to anti-checkpoint therapy. PLoS One 8(12):e82875. doi: 10.1371/journal.pone.0082875 CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Fu F, Nowak MA, Bonhoeffer S (2015) Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy. PLoS Comput Biol 11(3):e1004142. doi: 10.1371/journal.pcbi.1004142 CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Gatenby RA, Grove O, Gillies RJ (2013) Quantitative imaging in cancer evolution and ecology. Radiology 269(1):8–15. doi: 10.1148/radiol.13122697 CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Gevertz JL, Aminzare Z, Norton KA, Perez-Velazquez J, Volkening A, Rejniak KA (2015) Emergence of anti-cancer drug resistance: exploring the importance of the microenvironmental niche via a spatial model. In: Radunskaya A, Jackson T (eds) Applications of dynamical systems in biology and medicine vol IMA volumes in mathematics and its applications. Springer, New York, NY pp 1–34Google Scholar
  12. 12.
    Hagios C, Lochter A, Bissell MJ (1998) Tissue architecture: the ultimate regulator of epithelial function? Philosophical transactions of the Royal Society of London Series B. Biological sciences 353(1370):857–870. doi: 10.1098/rstb.1998.0250 CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Han J, Chang H, Giricz O, Lee GY, Baehner FL, Gray JW, Bissell MJ, Kenny PA, Parvin B (2010) Molecular predictors of 3D morphogenesis by breast cancer cell lines in 3D culture. PLoS Comput Biol 6(2):e1000684. doi: 10.1371/journal.pcbi.1000684 CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    Huang L, Holtzinger A, Jagan I, BeGora M, Lohse I, Ngai N, Nostro C, Wang R, Muthuswamy LB, Crawford HC, Arrowsmith C, Kalloger SE, Renouf DJ, Connor AA, Cleary S, Schaeffer DF, Roehrl M, Tsao MS, Gallinger S, Keller G, Muthuswamy SK (2015) Ductal pancreatic cancer modeling and drug screening using human pluripotent stem cell- and patient-derived tumor organoids. Nat Med 21(11):1364–1371. doi: 10.1038/nm.3973 CrossRefPubMedPubMedCentralGoogle Scholar
  15. 15.
    Imamura Y, Mukohara T, Shimono Y, Funakoshi Y, Chayahara N, Toyoda M, Kiyota N, Takao S, Kono S, Nakatsura T, Minami H (2015) Comparison of 2D- and 3D-culture models as drug-testing platforms in breast cancer. Oncol Rep 33(4):1837–1843. doi: 10.3892/or.2015.3767 CrossRefPubMedGoogle Scholar
  16. 16.
    Jaalouk DE, Lammerding J (2009) Mechanotransduction gone awry. Nat Rev Mol Cell Biol 10(1):63–73. doi: 10.1038/nrm2597 CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Jackson EL, Lu H (2016) Three-dimensional models for studying development and disease: moving on from organisms to organs-on-a-chip and organoids. Integr Biol (Quantitative Biosciences from Nano to Macro) 8(6):672–683. doi: 10.1039/c6ib00039h CrossRefGoogle Scholar
  18. 18.
    Karolak A, Estrella V, Chen T, Huynh A, Morse DL, Rejniak KA (2016) Using computational modeling to quantify targeted agent binding and internalization in pancreatic cancers. Cancer Res 76(Suppl 3):B21CrossRefGoogle Scholar
  19. 19.
    Karolak A, Estrella V, Chen T, Huynh A, Morse DL, Rejniak KA (2017) Imaged-based computational predictions of imaging agent efficacy in pancreatic tumors expressing TLR2. Cancer Res 77(Suppl 2):A28CrossRefGoogle Scholar
  20. 20.
    Kass L, Erler JT, Dembo M, Weaver VM (2007) Mammary epithelial cell: influence of extracellular matrix composition and organization during development and tumorigenesis. Int J Biochem Cell Biol 39(11):1987–1994. doi: 10.1016/j.biocel.2007.06.025 CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Kenny PA, Bissell MJ (2003) Tumor reversion: correction of malignant behavior by microenvironmental cues. Int J Cancer 107(5):688–695. doi: 10.1002/ijc.11491 CrossRefPubMedPubMedCentralGoogle Scholar
  22. 22.
    Kim M, Gillies RJ, Rejniak KA (2013) Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues. Front Oncol 3:278. doi: 10.3389/fonc.2013.00278 PubMedPubMedCentralGoogle Scholar
  23. 23.
    Kim M, Reed D, Rejniak KA (2014) The formation of tight tumor clusters affects the efficacy of cell cycle inhibitors: a hybrid model study. J Theor Biol 352:31–50. doi: 10.1016/j.jtbi.2014.02.027 CrossRefPubMedPubMedCentralGoogle Scholar
  24. 24.
    Kolahi KS, Mofrad MR (2010) Mechanotransduction: a major regulator of homeostasis and development. Wiley Interdiscip Rev Syst Biol Med 2(6):625–639. doi: 10.1002/wsbm.79 CrossRefPubMedGoogle Scholar
  25. 25.
    Lloyd MC, Rejniak KA, Brown JS, Gatenby RA, Minor ES, Bui MM (2015) Pathology to enhance precision medicine in oncology: lessons from landscape ecology. Adv Anat Pathol 22(4):267–272. doi: 10.1097/PAP.0000000000000078 CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Lloyd MC, Rejniak KA, Johnson JO, Gillies R, Gatenby R, Bui MM (2012) Quantitative evaluation of the morphological heterogeneity in breast cancer progression. Mod Pathol 25:392AGoogle Scholar
  27. 27.
    Martin-Belmonte F, Yu W, Rodriguez-Fraticelli AE, Ewald AJ, Werb Z, Alonso MA, Mostov K (2008) Cell-polarity dynamics controls the mechanism of lumen formation in epithelial morphogenesis. Curr Biol (CB) 18(7):507–513. doi: 10.1016/j.cub.2008.02.076 CrossRefGoogle Scholar
  28. 28.
    Minchinton AI, Tannock IF (2006) Drug penetration in solid tumours. Nat Rev Cancer 6(8):583–592. doi: 10.1038/nrc1893 CrossRefPubMedGoogle Scholar
  29. 29.
    Mumenthaler SM, Foo J, Choi NC, Heise N, Leder K, Agus DB, Pao W, Michor F, Mallick P (2015) The impact of microenvironmental heterogeneity on the evolution of drug resistance in cancer cells. Cancer Informat 14(Suppl 4):19–31. doi: 10.4137/CIN.S19338 Google Scholar
  30. 30.
    Pampaloni F, Reynaud EG, Stelzer EH (2007) The third dimension bridges the gap between cell culture and live tissue. Nat Rev Mol Cell Biol 8(10):839–845. doi: 10.1038/nrm2236 CrossRefPubMedGoogle Scholar
  31. 31.
    Paszek MJ, Zahir N, Johnson KR, Lakins JN, Rozenberg GI, Gefen A, Reinhart-King CA, Margulies SS, Dembo M, Boettiger D, Hammer DA, Weaver VM (2005) Tensional homeostasis and the malignant phenotype. Cancer Cell 8(3):241–254. doi: 10.1016/j.ccr.2005.08.010 CrossRefPubMedGoogle Scholar
  32. 32.
    Perez-Velazquez J, Gevertz JL, Karolak A, Rejniak KA (2016) Microenvironmental niches and sanctuaries: a route to acquired resistance. In: Rejniak KA (ed) Systems biology of tumor microenvironment: quantitative models and simulations. Springer, SwitzerlandGoogle Scholar
  33. 33.
    Peskin CS (2002) The immersed boundary method. Acta Numerica:479–527Google Scholar
  34. 34.
    Picollet-D’hahan N, Dolega ME, Liguori L, Marquette C, Le Gac S, Gidrol X, Martin DK (2016) A 3D toolbox to enhance physiological relevance of human tissue models. Trends Biotechnol 34(9):757–769. doi: 10.1016/j.tibtech.2016.06.012 CrossRefPubMedGoogle Scholar
  35. 35.
    Plachot C, Chaboub LS, Adissu HA, Wang L, Urazaev A, Sturgis J, Asem EK, Lelievre SA (2009) Factors necessary to produce basoapical polarity in human glandular epithelium formed in conventional and high-throughput three-dimensional culture: example of the breast epithelium. BMC Biol 7:77. doi: 10.1186/1741-7007-7-77 CrossRefPubMedPubMedCentralGoogle Scholar
  36. 36.
    Radisky D, Hagios C, Bissell MJ (2001) Tumors are unique organs defined by abnormal signaling and context. Semin Cancer Biol 11(2):87–95. doi: 10.1006/scbi.2000.0360 CrossRefPubMedGoogle Scholar
  37. 37.
    Reginato MJ, Muthuswamy SK (2006) Illuminating the center: mechanisms regulating lumen formation and maintenance in mammary morphogenesis. J Mammary Gland Biol Neoplasia 11(3–4):205–211. doi: 10.1007/s10911-006-9030-4 CrossRefPubMedGoogle Scholar
  38. 38.
    Rejniak KA (2007) An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. J Theor Biol 247(1):186–204. doi: 10.1016/j.jtbi.2007.02.019 CrossRefPubMedGoogle Scholar
  39. 39.
    Rejniak KA (2014) IBCell Morphocharts: a computational model for linking cell molecular activity with emerging tissue morphology. In: Jonoska N, Saito M (eds) Discrete and toplogical models in molecular biology. Natural Computing Series. Springer, BerlinGoogle Scholar
  40. 40.
    Rejniak KA, Anderson AR (2008) A computational study of the development of epithelial acini: I. Sufficient conditions for the formation of a hollow structure. Bull Math Biol 70(3):677–712. doi: 10.1007/s11538-007-9274-1 CrossRefPubMedGoogle Scholar
  41. 41.
    Rejniak KA, Estrella V, Chen T, Cohen AS, Lloyd MC, Morse DL (2013) The role of tumor tissue architecture in treatment penetration and efficacy: an integrative study. Front Oncol 3:111. doi: 10.3389/fonc.2013.00111 CrossRefPubMedPubMedCentralGoogle Scholar
  42. 42.
    Rejniak KA, Lloyd MC, Reed DR, Bui MM (2015) Diagnostic assessment of osteosarcoma chemoresistance based on Virtual Clinical Trials. Med Hypotheses 85(3):348–354. doi: 10.1016/j.mehy.2015.06.015 CrossRefPubMedPubMedCentralGoogle Scholar
  43. 43.
    Rejniak KA, Quaranta V, Anderson AR (2012) Computational investigation of intrinsic and extrinsic mechanisms underlying the formation of carcinoma. Math Med Biol (A Journal of the IMA) 29(1):67–84. doi: 10.1093/imammb/dqq021 CrossRefGoogle Scholar
  44. 44.
    Rejniak KA, Wang SE, Bryce NS, Chang H, Parvin B, Jourquin J, Estrada L, Gray JW, Arteaga CL, Weaver AM, Quaranta V, Anderson AR (2010) Linking changes in epithelial morphogenesis to cancer mutations using computational modeling. PLoS Comput Biol 6(8). doi: 10.1371/journal.pcbi.1000900
  45. 45.
    Rizki A, Weaver VM, Lee SY, Rozenberg GI, Chin K, Myers CA, Bascom JL, Mott JD, Semeiks JR, Grate LR, Mian IS, Borowsky AD, Jensen RA, Idowu MO, Chen F, Chen DJ, Petersen OW, Gray JW, Bissell MJ (2008) A human breast cell model of preinvasive to invasive transition. Cancer Res 68(5):1378–1387. doi: 10.1158/0008-5472.CAN-07-2225 CrossRefPubMedPubMedCentralGoogle Scholar
  46. 46.
    Santner SJ, Dawson PJ, Tait L, Soule HD, Eliason J, Mohamed AN, Wolman SR, Heppner GH, Miller FR (2001) Malignant MCF10CA1 cell lines derived from premalignant human breast epithelial MCF10AT cells. Breast Cancer Res Treat 65(2):101–110CrossRefPubMedGoogle Scholar
  47. 47.
    Saunders NA, Simpson F, Thompson EW, Hill MM, Endo-Munoz L, Leggatt G, Minchin RF, Guminski A (2012) Role of intratumoural heterogeneity in cancer drug resistance: molecular and clinical perspectives. EMBO Mol Med 4(8):675–684. doi: 10.1002/emmm.201101131 CrossRefPubMedPubMedCentralGoogle Scholar
  48. 48.
    Shamir ER, Ewald AJ (2014) Three-dimensional organotypic culture: experimental models of mammalian biology and disease. Nat Rev Mol Cell Biol 15(10):647–664. doi: 10.1038/nrm3873 CrossRefPubMedPubMedCentralGoogle Scholar
  49. 49.
    Thoma CR, Zimmermann M, Agarkova I, Kelm JM, Krek W (2014) 3D cell culture systems modeling tumor growth determinants in cancer target discovery. Adv Drug Deliv Rev 69-70:29–41. doi: 10.1016/j.addr.2014.03.001 CrossRefPubMedGoogle Scholar
  50. 50.
    Tyson DR, Inokuchi J, Tsunoda T, Lau A, Ornstein DK (2007) Culture requirements of prostatic epithelial cell lines for acinar morphogenesis and lumen formation in vitro: role of extracellular calcium. Prostate 67(15):1601–1613. doi: 10.1002/pros.20628 CrossRefPubMedGoogle Scholar
  51. 51.
    Weigelt B, Bissell MJ (2008) Unraveling the microenvironmental influences on the normal mammary gland and breast cancer. Semin Cancer Biol 18(5):311–321. doi: 10.1016/j.semcancer.2008.03.013 CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Integrated Mathematical Oncology DepartmentH. Lee Moffitt Cancer Center & Research InstituteTampaUSA
  2. 2.Department of Oncologic Sciences, College of MedicineUniversity of South FloridaTampaUSA

Personalised recommendations