Personalized Tumor Growth Prediction Using Multiscale Modeling

Year 2020, , 347 - 363, 01.09.2020

Serbulent Unsal Aybar Acar Mehmet Itik Ayse Kabatas Oznur Gedikli Feyyaz Ozdemir Kemal Turhan

https://doi.org/10.30621/jbachs.2020.1245

Cited By: 1

Abstract

Purpose: Cancer is one of the most complex phenomena in biology and medicine. Extensive attempts have been made to work around this complexity. In this study, we try to take a selective approach; not modeling each particular facet in detail but rather only the pertinent and essential parts of the tumor system are simulated and followed by optimization, revealing specific traits. This leads us to a pellucid personalized model which is noteworthy as it closely approximates existing experimental results. Methods: In the present study, a hybrid modeling approach which consists of cellular automata for discrete cell state representation and diffusion equations to calculate distribution of relevant substances in the tumor microenvironment is favored. Moreover, naive Bayesian decision making with weighted stochastic equations and a Bayesian network to model the temporal order of mutations is presented. The model is personalized according to the evidence using Markov Chain Monte Carlo. To validate the tumor model, a data set belonging to the A549 cell line is used. The data represents the growth of a tumor for 30 days. We optimize the coefficients of the stochastic decision-making equations using the first half of the timeline. Results: Simulation results of the developed model are promising with their low error margin all correlation coefficients are over 0.8 under different microenvironment conditions and simulated growth data is in line with laboratory results r=0.97, p

Keywords

neoplasms, patient-specific modeling, adenocarcinoma of lung, precision medicine

References

• 1. Ward JP, King JR. Mathematical modelling of avascular-tumour growth. IMA J Math Appl Med Biol 1997;14:39–69. [CrossRef]
• 2. Sherratt JA, Chaplain MAJ. A new mathematical model for avascular tumour growth. J Math Biol 2001;43:291–312. [CrossRef]
• 3. Araujo RP, McElwain DLS. A history of the study of solid tumour growth: The contribution of mathematical modelling. Bull Math Biol 2004;66:1039–1091. [CrossRef]
• 4. Macklin P, McDougall S, Anderson ARA, Chaplain MAJ, Cristini V, Lowengrub J. Multiscale modelling and nonlinear simulation of vascular tumour growth. J Math Biol 2009;58:765–798. [CrossRef]
• 5. İtik M, Banks SP. Chaos in a three-dimensional cancer model. Int J Bifurc Chaos 2010;20:71–79. [CrossRef]
• 6. Golneshan AA, Nemati H. Continuum Based Tumor Growth Modeling. J Emerg Trends Eng Appl Sci 2011;2:546–550. https://journals.co.za/ content/sl_jeteas/2/3/EJC156688
• 7. Mansury Y, Kimura M, Lobo J, Deisboeck TS. Emerging patterns in tumor systems: Simulating the dynamics of multicellular clusters with an agent-based spatial agglomeration model. J Theor Biol 2002;219:343–370. [CrossRef]
• 8. Turner S, Sherratt JA. Intercellular adhesion and cancer invasion: A discrete simulation using the extended potts model. J Theor Biol 2002;216:85–100. [CrossRef]
• 9. Alarcón T, Byrne HM, Maini PK. A cellular automaton model for tumour growth in an inhomogeneous environment. J Theor Biol 2003;225:257–274. [CrossRef]
• 10. Zhang L, Athale CA, Deisboeck TS. Development of a threedimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J Theor Biol 2007;244:96–107. [CrossRef]
• 11. Sander LM, Deisboeck TS. Growth patterns of microscopic brain tumors. Phys Rev E Stat Nonlin Soft Matter Phys 2002;66:051901. [CrossRef]
• 12. Anderson ARA. A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion. Math Med Biol 2005;22:163–186. [CrossRef]
• 13. Giard DJ, Aaronson SA, Todaro GJ, et al. In vitro cultivation of human tumors: Establishment of cell lines derived from a series of solid tumors. J Natl Cancer Inst 1973;51:1417–1423. [CrossRef]
• 14. Anderson ARA. A hybrid mathematical model of solid tumour invasion: the importance off-cell adhesion. Math Med Biol 2005;22:163–186. [CrossRef]
• 15. Alarcón T, Byrne HM, Maini PK. A cellular automaton model for tumour growthin inhomogeneous environment. J Theor Biol 2003;225:257–274. [CrossRef]
• 16. Gerlee P, Anderson ARA. A hybrid cellular automaton model of clonal evolution in cancer: The emergence of the glycolytic phenotype. J Theor Biol 2008;250:705–722. [CrossRef]
• 17. Rossum G. Python reference manual, Release 2.1. Stichting Mathematisch Centrum Amsterdam, Amsterdam, The Netherlands; 1995. https://lab.demog.berkeley.edu/Docs/Refs/Python2.1/ref. pdf
• 18. Guyer JE, Wheeler D, Warren JA. FiPy: Partial Differential Equations with Python. Computing in Science and Engg 2009;11:6–15. [CrossRef]
• 19. Behnel S, Bradshaw R, Citro C, Dalcin L, Seljebotn DS, Smith K. Cython: The best of both worlds. Comput Sci Eng 2011;13:31–39. [CrossRef]
• 20. Shinners P. Python Pygame Introduction. https://www.pygame.org/ docs/tut/PygameIntro.html
• 21. Higareda-Mendoza AE, Pardo-Galván MA. Expression of human eukaryotic initiation factor 3f oscillates with cell cycle in A549 cells and is essential for cell viability. Cell Div 2010;5:1–10. [CrossRef]
• 22. Molter TW, McQuaide SC, Suchodolski MT, et al. A microwell array device capable of measuring single-cell oxygen consumption rates. Sensors Actuators: B Chem 2009;135:678–686. [CrossRef]
• 23. Wang Z, Zhang L, Sagotsky J, Deisboeck TS. Simulating non-small cell lung cancer with a multiscale agent-based model. Theor Biol Med Model 2007;4:50. [CrossRef]
• 24. Schroedl C, McClintock DS, Budinger GRS, Chandel NS. Hypoxic but not anoxic stabilization of HIF-1α requires mitochondrial reactive oxygen species. Am J Physiol - Lung Cell Mol Physiol 2002;283:L922– L931. [CrossRef]
• 25. Höckel M, Vaupel P. Tumor hypoxia: Definitions and current clinical, biologic, and molecular aspects. J Natl Cancer Inst 2001;93:266–276. [CrossRef]
• 26. Guo X, Wu G, Wei H, et al. Quantification of glucose diffusion in human lung tissues by using fourier domain optical coherence tomography. Photochem Photobiol 2012;88:311–316. [CrossRef]
• 27. Shankland EG, Livesey JC, Wiseman RW, Krohn KA. Multinuclear NMR studies of an actively dividing artificial tumor. Physiol Res 2002;51:49–58. http://www.biomed.cas.cz/physiolres/pdf/51/51_49. pdf
• 28. Freyer JP, Sutherland RM. Regulation of Growth Saturation and Development of Necrosis In EMT6/R0 Multicellular Spheroids by the Glucose and Oxygen Supply. Cancer Res 1986;46:3504–3512. https:// cancerres.aacrjournals.org/content/46/7/3504.full-text.pdf
• 29. al-Baldawi NF, Abercrombie RF. Cytoplasmic hydrogen ion diffusion coefficient. Biophys J 1992;61:1470–1479. [CrossRef]
• 30. Wood SC, Schaefer KE. Regulation of intracellular ph in lungs and other tissues during hypercapnia. J Appl Physiol 1978;45:115–118. [CrossRef]
• 31. Williams AC, Collard TJ, Paraskeva C. An acidic environment leads to p53 dependent induction of apoptosis in human adenoma and carcinoma cell lines: Implications for clonal selection during colorectal carcinogenesis. Oncogene 1999;18:3199–3204. [CrossRef]
• 32. Zhang X, Lin Y, Gillies RJ. Tumor pH and its measurement. Journal of Nuclear Medicine 2010;51:1167–1170. [CrossRef]
• 33. Bates MK. Culturing cells under hypoxic conditions for biologically relevant results. American Laboratory; 2012. https://www. americanlaboratory.com/913-Technical-Articles/123131-CulturingCells-
• 34. Danza G, Di Serio C, Rosati F, et al. Notch signaling modulates hypoxia-induced neuroendocrine differentiation of human prostate cancer cells. Mol Cancer Res 2012;10:230–238. [CrossRef]
• 35. Milane L, Duan Z, Amiji M. Role of hypoxia and glycolysis in the development of multidrug resistance in human tumor cells and the establishment of an orthotopic multi-drug resistant tumor model in nude mice using hypoxic preconditioning. Cancer Cell Int 2011;11:3. [CrossRef]
• 36. Terraneo L, Bianciardi P, Caretti A, Ronchi R, Samaja M. Chronic systemic hypoxia promotes LNCaP prostate cancer growth in vivo. Prostate 2010;70:1243–1254. [CrossRef]
• 37. McKeown SR. Defining normoxia, physoxia and hypoxia in tumours - Implications for treatment response. Br J Radiol 2014;87:20130676. [CrossRef]
• 38. Kagiya G, Ogawa R, Hyodo F, et al. Development of a real-time imaging system for hypoxic cell apoptosis. Mol Ther Methods Clin Dev 2016;5:16009. [CrossRef]
• 39. Brat DJ, Castellano-Sanchez AA, Hunter SB, et al. Pseudopalisades in Glioblastoma Are Hypoxic, Express Extracellular Matrix Proteases, and Are Formed by an Actively Migrating Cell Population. Cancer Res 2004;64:920–927. [CrossRef]
• 40. Parra-Bonilla G, Alvarez DF, Al-Mehdi AB, Alexeyev M, Stevens T. Critical role for lactate dehydrogenase A in aerobic glycolysis that sustains pulmonary microvascular endothelial cell proliferation. Am J Physiol Lung Cell Mol Physiol 2010;299:L513–L522. [CrossRef]
• 41. Birsoy K, Possemato R, Lorbeer FK, et al. Metabolic determinants of cancer cell sensitivity to glucose limitation and biguanides. Nature 2014;508:108–112. [CrossRef]
• 42. Li Y, Zhang Q, Tian R, et al. Lysosomal transmembrane protein LAPTM4B promotes autophagy and tolerance to metabolic stress in cancer cells. Cancer Res 2011;71:7481–7489. [CrossRef]
• 43. Otto AM, Hintermair J, Janzon C. NADH-linked metabolic plasticity of MCF-7 breast cancer cells surviving in a nutrient-deprived microenvironment. J Cell Biochem 2015;116:822–835. [CrossRef]
• 44. Ho VW, Leung K, Hsu A, et al. A low carbohydrate, high protein diet slows tumor growth and prevents cancer initiation. Cancer Res 2011;71:4484–4493. [CrossRef]
• 45. Hughes-Alford SK, Lauffenburger DA. Quantitative analysis of gradient sensing: Towards building predictive models of chemotaxis in cancer. Curr Opin Cell Biol 2012;24:284–291. [CrossRef]
• 46. Roussos ET, Condeelis JS, Patsialou A. Chemotaxis in cancer. Nat Rev Cancer 2011;11:573–587. [CrossRef]
• 47. Campbell M, Allen WE, Sawyer C, Vanhaesebroeck B, Trimble ER. Glucose-potentiated chemotaxis in human vascular smooth muscle is dependent on cross-talk between the PI3K and MAPK signaling pathways. Circ Res 2004;95:380–388. [CrossRef]
• 48. Mosadegh B, Lockett MR, Minn KT, et al. A paper-based invasion assay: Assessing chemotaxis of cancer cells in gradients of oxygen. Biomaterials 2015;52:262–271. [CrossRef]
• 49. Norton L. A Gompertzian Model of Human Breast Cancer Growth. Cancer Res 1988;48:7067–7071.
• 50. Bajzer Z, Carr T, Dingli D, Josic K. Optimization of tumor virotherapy with recombinant measles viruses. In: Lim GJ, Lee EK, editors. Optimization in Medicine and Biology. UK: Taylor and Francis; 2007.
• 51. Dingli D, Pacheco JM, Dispenzieri A, et al. In vivo and in silico studies on single versus multiple transplants for multiple myeloma. Cancer Sci 2007;98:734–739. [CrossRef]
• 52. Morvan D, Demidem A, Papon J, De Latour M, Madelmont JC. Melanoma tumors acquire a new phospholipid metabolism phenotype under cystemustine as revealed by high-resolution magic angle spinning proton nuclear magnetic resonance spectroscopy of intact tumor samples. Cancer Res 2002;62:1890–1897. https:// cancerres.aacrjournals.org/content/62/6/1890.full-text.pdf
• 53. Zhou J, Hualong Q, Zhou P, Guo F. Different maspin functions in the lung adenocarcinoma A549 and SPC-A1 cell lines. Int J Mol Med 2015;36:1440–1448. [CrossRef]
• 54. Esandi MC, Van Someren GD, Vincent AJPE, et al. Gene therapy of experimental malignant mesothelioma using adenovirus vectors encoding the HSVtk gene. Gene Ther 1997;4:280–287. [CrossRef]
• 55. Folkman J, Hochberg M. Self-regulation of growth in three dimensions. J Exp Med 1973;138:745–753. [CrossRef]
• 56. Rohatgi A, Webplotdigitizer, v. 4.1. Oakland, CA: Plotcon; 2017. https://automeris.io/WebPlotDigitizer
• 57. Eissing T, Kuepfer L, Becker C, et al. A computational systems biology software platform for multiscale modeling and simulation: Integrating whole-body physiology, disease biology, and molecular reaction networks. Front Physiol 2011;2:4. [CrossRef]
• 58. Jackson PR, Juliano J, Hawkins-Daarud A, Rockne RC, Swanson KR. Patient-Specific Mathematical Neuro-Oncology: Using a Simple Proliferation and Invasion Tumor Model to Inform Clinical Practice. Bull Math Biol 2015;77:846–856. [CrossRef]
• 59. Liu LL, Li F, Pao W, Michor F. Dose-dependent mutation rates determine optimum erlotinib dosing strategies for EGFR mutant nonsmall cell lung cancer patients. PLoS One 2015;10:1–17. [CrossRef]
• 60. Bearer EL, Lowengrub JS, Frieboes HB, et al. Multiparameter computational modeling of tumor invasion. Cancer Res 2009;69:4493–4501. [CrossRef]
• 61. Anderson ARA, Weaver AM, Cummings PT, Quaranta V. Tumor Morphology and Phenotypic Evolution Driven by Selective Pressure from the Microenvironment. Cell 2006;127:905–915. [CrossRef]
• 62. Sottoriva A, Sloot PMA, Medema JP, Vermeulen L. Exploring cancer stem cell niche directed tumor growth. Cell Cycle 2010;9:1472–1479. [CrossRef]
• 63. Misra N, Szczurek E, Vingron M. Learning gene networks underlying somatic mutations in cancer 22nd Annual Workshop on Mathematical and Statistical Aspects of Molecular Biology; 2012.
• 64. Prokopiou S, Moros EG, Poleszczuk J, et al. A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation. Radiat Oncol 2015;10:159. [CrossRef]
• 65. Saribudak A, Ganic E, Zou J, Gundry S, Uyar MÜ. Toward genomic based personalized mathematical models for breast cancer tumor growth. In: Proceedings - IEEE 14th International Conference on Bioinformatics and Bioengineering. BIBE 2014;2014:115–119. [CrossRef]
• 66. Kogan Y, Halevi-Tobias K, Elishmereni M, Vuk-Pavlović S, Agur Z. Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization. Cancer Res 2012;72:2218–2227. [CrossRef]
• 67. Magda D, Lecane P, Prescott J, et al. mtDNA depletion confers specific gene expression profiles in human cells grown in culture and in xenograft. BMC Genomics 2008;9:521. [CrossRef]
• 68. Ziegler A, Koch A, Krockenberger K, Großhennig A. Personalized medicine using DNA biomarkers: a review. Hum Genet 2012;131:1627–1638. [CrossRef]
• 69. Schleidgen S, Klingler C, Bertram T, Rogowski WH, Marckmann G. What is personalized medicine: sharpening a vague term based on a systematic literature review. BMC Med Ethics 2013;14:55. [CrossRef]
• 70. Papadakis GZ, Karantanas AH, Tsiknakis M, Tsatsakis A, Spandidos DA, Marias K. Deep learning opens new horizons in personalized medicine. Biomed Rep 2019;10:215–217. [CrossRef]
• 71. Kahraman M. Modelling functional dynamical systems by piecewise linear systems with delay, Master’s thesis, Scientific Computing, Institute of Applied Mathematics, Middle East Technical University; 2007.
• 72. Vogelstein B, Papadopoulos N, Velculescu VE, Zhou S, Diaz LA Jr, Kinzler KW. Cancer genome landscapes. Science 2013;339:1546– 1558. [CrossRef]
• 73. Thomas A, Rajan A, Lopez-Chavez A, Wang Y, Giaccone G. From targets to targeted therapies and molecular profiling in non-small cell lung carcinoma. Ann Oncol 2013;24:577–585. [CrossRef]
• 74. Do H, Krypuy M, Mitchell PL, Fox SB, Dobrovic A. High resolution melting analysis for rapid and sensitive EGFR and KRAS mutation detection in formalin fixed paraffin embedded biopsies. BMC Cancer 2008;8:142. [CrossRef]
• 75. Ding L, Getz G, Wheeler DA, et al. Somatic mutations affect key pathways in lung adenocarcinoma. Nature 2008;455:1069–1075. [CrossRef]
• 76. Tikhomirov VM. A Study of the Diffusion Equation with Increase in the Amount of Substance, and its Application to a Biological Problem. In: Tikhomirov VM, editor. Selected Works of Kolmogorov AN. Mathematics and Its Applications (Soviet Series). Springer; 1991.
• 77. Daileda RC. The two dimensional heat equation - lecture slides; 2012. http://ramanujan.math.trinity.edu/rdaileda/teach/s12/m3357/ lectures/lecture_3_6_short.pdf
• 78. Kirby BJ. Micro and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices. UK: Cambridge University Press; 2010.