Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Glioma growth modeling based on the effect of vital nutrients and metabolic products

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Glioma brain tumors exhibit considerably aggressive behavior leading to high mortality rates. Mathematical modeling of tumor growth aims to explore the interactions between glioma cells and tissue microenvironment, which affect tumor evolution. Leveraging this concept, we present a three-dimensional model of glioma spatio-temporal evolution based on existing continuum approaches, yet incorporating novel factors of the phenomenon. The proposed model involves the interactions between different tumor cell phenotypes and their microenvironment, investigating how tumor growth is affected by complex biological exchanges. It focuses on the separate and combined effect of vital nutrients and cellular wastes on tumor expansion, leading to the formation of cell populations with different metabolic, proliferative, and diffusive profiles. Several simulations were performed on a virtual and a real glioma, using combinations of proliferation and diffusion rates for different evolution times. The model results were validated on a glioma model available in the literature and a real case of tumor progression. The experimental observations indicate that our model estimates quite satisfactorily the expansion of each region and the overall tumor growth. Based on the individual results, the proposed model may provide an important research tool for patient-specific simulation of different tumor evolution scenarios and reliable estimation of glioma evolution.

Outline of the mathematical model functionality and application to glioma growth with indicative results

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. The cancer imaging archive–rider neuro mri. https://wiki.cancerimagingarchive.net/display/Public/ RIDER+ NEURO +MRI

  2. Sri24 atlas: Normal adult brain anatomy. https://www.nitrc.org/projects/sri24

  3. Anderson ARA (2005) A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Math Med Biol 22(2):163–186

    Article  PubMed  Google Scholar 

  4. Anderson ARA, Chaplain MAJ, Newman EL, Steele RJC, Thompson AM (2000) Mathematical modelling of tumour invasion and metastasis. J Theor Med 2:129–151

    Article  Google Scholar 

  5. Barry MA, Eastman A (1992) Endonuclease activation during apoptosis: the role of cytosolic Ca2+ and pH. Biochem Biophys Res Commun 1869(2):782–789

    Article  Google Scholar 

  6. Baumann BC, Kao GD, Mahmud A, Harada T, Swift J, Chapman C, Xu X, Discher DE, Dorse JF (2013) Enhancing the efficacy of drug-loaded nanocarriers against brain tumors by targeted radiation therapy. Oncotarget 4(1):64–79

    Article  PubMed  PubMed Central  Google Scholar 

  7. Casciari JJ, Sotirchos SV, Sutherland RM (1988) Glucose diffusivity in multicellular tumor spheroids. Cancer Res 48:3905–3909

    PubMed  CAS  Google Scholar 

  8. Casciari JJ, Sotirchos SV, Sutherland RM (1992) Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids. Cell Prolif 25:1–22

    Article  PubMed  CAS  Google Scholar 

  9. Fischer K, Hoffmann P, Voelkl S et al. (2007) Inhibitory effect of tumor cell-derived lactic acid on human T cells. Blood 109:3812–381

    Article  PubMed  CAS  Google Scholar 

  10. Folbergrová J, Zhao Q, Katsura K, Siesjö BK (1995) N-tert-butyl-alpha-phenylnitrone improves recovery of brain energy state in rats following transient focal ischemia. Proc Natl Acad Sci USA 92(11):5057–5061

    Article  PubMed  PubMed Central  Google Scholar 

  11. Freyer JP, Sutherland RM (1986) Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. Cancer Res 46:3504–3512

    PubMed  CAS  Google Scholar 

  12. Gao X, Tangney M, Tabirca S (2011) A multiscale model for hypoxia-induced avascular tumor growth. In: Proceedings of the international conference on bioscience, biochemistry and bioinformatics (IPCBEE): 26–28 February 2011; Singapore, pp 5:53–58

  13. Gatenby RA, Gawlinski ET (2003) The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models. Cancer Res 63:3847–3854

    PubMed  CAS  Google Scholar 

  14. Gatenby RA, Gawlinski ET, Gmitro AF, Kaylor B, Gillies RJ (2006) Acid-mediated tumor invasion: a multidisciplinary study. Cancer Res 66:5216–5223

    Article  PubMed  CAS  Google Scholar 

  15. Gerlee P, Anderson ARA (2008) A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype. J Theor Biol 250:705–722

    Article  PubMed  CAS  Google Scholar 

  16. Harpold HLP, Alvord EC, Swanson KR (2007) The evolution of mathematical modeling of glioma proliferation and invasion. J Neuropathol Exp Neurol 66(1):1–9

    Article  PubMed  Google Scholar 

  17. Hatzikirou H, Deutsch A (2008) Cellular automata as microscopic models of cell migration in heterogeneous environments. Curr Top Dev Biol 81:401–434

    Article  PubMed  Google Scholar 

  18. Jeon J, Quaranta V, Cummings PT (2010) An off-lattice hybrid discrete-continuum model of tumor growth and invasion. Biophys J 98(1):37–47

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  19. Jiang Y, Pjesivac-Grbovic J, Cantrell C, Freyer JP (2005) A multiscale model for avascular tumor growth. Biophys J 89:3884–3894. world Scientific Publishing Company

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  20. Jones RG, Thompson CB (2009) Tumor suppressors and cell metabolism: a recipe for cancer growth. Genes Dev 23:537– 548

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  21. Jossin Y, Cooper JA (2011) Reelin, Rap1 and N-cadherin orient the migration of multipolar neurons in the developing neocortex. Nat Neurosc 14(6):697–703

    Article  CAS  Google Scholar 

  22. Kim Y, Lawler S, Nowicki MO, Chiocca EA, Friedman A (2009) A mathematical model for pattern formation of glioma cells outside the tumor spheroid core. J Theor Biol 260:359–371

    Article  PubMed  Google Scholar 

  23. Kiran KL, Jayachandran D, Lakshminarayanan S (2009) Mathematical modelling of avascular tumour growth based on diffusion of nutrients and its validation. Can J Chem Eng 87:732–740

    Article  CAS  Google Scholar 

  24. Martinez-Gonzalez A, Calvo GF, Romasanta LAP, Perez-Garcia VM (2012) Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications. Bull Math Biol 74:2875–2896. world Scientific Publishing Company

    Article  PubMed  PubMed Central  Google Scholar 

  25. Mendoza-Juez B, Martinez-Gonzalez A, Calvo GF, Perez-Garcia VM (2012) A mathematical model for the glucose-lactate metabolism of in vitro cancer cells. Bull Math Biol 74:1125–1142

    Article  PubMed  CAS  Google Scholar 

  26. Moriguchi T, Gotoh Y, Nishida E (1996) Roles of the map kinase cascade in vertebrates. Adv Pharmacol 36(C):121–137

    Article  PubMed  CAS  Google Scholar 

  27. Orlowski P, Chappell M, Park CS, Grau V, Payne S (2011) Modelling of ph dynamics in brain cells after stroke. Interf Foc 1(3):408–416

    Article  Google Scholar 

  28. Papadogiorgaki M, Koliou P, Kotsiakis X, Zervakis ME (2013) Mathematical modelling of spatio-temporal glioma evolution. Theor Biol Med Model 10(1):47–83

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  29. Papadogiorgaki M, Kounelakis MG, Koliou P, Zervakis ME (2015) A glycolysis based in-silico model for the solid tumor growth. IEEE J Biomed Health Inf 19(3):1106–1117

    Google Scholar 

  30. Piotrowska MJ, Angus SD (2009) A quantitative cellular automaton model of in vitro multicellular spheroid tumour growth. J Theor Biol 258:165–178

    Article  PubMed  Google Scholar 

  31. Rejniak KA, Anderson AR (2010) Hybrid models of tumor growth. Wiley Inter Rev 3(1):115–125

    Google Scholar 

  32. Roniotis A, Manikis G, Sakkalis V, Zervakis M, Karatzanis I, Marias K (2012) High grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases. IEEE Trans Inf Tech Biomed 16(2):255–263

    Article  Google Scholar 

  33. Roniotis A, Sakkalis V, Marias K, Karatzanis I, Zervakis M (2012) In-depth analysis and evaluation of diffusive glioma models. IEEE Trans Inf Tech Biomed 16(3):299–307

    Article  Google Scholar 

  34. Roose T, Chapman SJ, Maini PK (2007) Mathematical models of avascular tumor growth. SIAM 49 (2):179–208

    Article  Google Scholar 

  35. Serganova I, Rizwan A, Ni X, Thakur SB, Vider J, Russell J, Blasberg R, Koutcher JA (2011) Metabolic imaging: a link between lactate dehydrogenase a, lactate, and tumor phenotype. Clin Cancer Res 17:6250–6261

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  36. Smallbone K, Gatenby RA, Maini PK (2008) Mathematical modelling of tumour acidity. J Theor Biol 255:106–112

    Article  PubMed  CAS  Google Scholar 

  37. Sonveaux P, Vegran F, Schroeder T et al. (2008) Targeting lactate-fueled respiration selectively kills hypoxic tumor cells in mice. J Clin Invest 118(12):3930–3942

    PubMed  PubMed Central  CAS  Google Scholar 

  38. Swanson KR, Bridgea C, Murray JD, Alvord EC (2003) Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol Sc 216:1–10

    Article  Google Scholar 

  39. Swanson KR, Rockne RC, Claridge J, Chaplain MA, Alvord EC Jr, Anderson ARA (2011) Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Int Sys Tech: Math Onc Cancer Res 71(24):7366–7375

    CAS  Google Scholar 

  40. Szeto MD, Chakraborty G, Hadley J (2009) Quantitative metrics of net proliferation and invasion link biological aggressiveness assessed by MRI with hypoxia assessed by FMISO-PET in newly diagnosed glioblastomas. Cancer Res 69(10):4502–4509

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  41. Stein AM, Demuth T, Mobley D, Berens LM, Sander K (2007) A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. Biophys J 92:356–365

    Article  PubMed  CAS  Google Scholar 

  42. Tanaka ML, Debinski W, Puri IK (2009) Hybrid mathematical model of glioma progression. Cell Prolif 42:637–646

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  43. Tzamali E, Favicchio R, Roniotis A, Tzedakis G, Grekas G, Ripoll J, Marias K, Zacharakis G, Sakkalis V (2013) Employing in-vivo molecular imaging in simulating and validating tumor growth. In: Proceedings of 35th IEEE-EMBS, engineering in medicine and biology society (EMBC 2013): 3-7 July; Osaka, pp 5533–5536

  44. Venkatasubramanian R, Henson MA, Forbes NS (2006) Incorporating energy metabolism into a growth model of multicellular tumor spheroids. J Theor Biol 242:440–453

    Article  PubMed  CAS  Google Scholar 

  45. Warburg O (1956) On the origin of cancer cells. Science 123:309–314

    Article  PubMed  CAS  Google Scholar 

  46. Webb SD, Sherratt JA, Fish RG (1999) Mathematical modelling of tumour acidity: regulation of intracellular ph. J Theor Biol 196:237–250

    Article  PubMed  CAS  Google Scholar 

  47. Xu L, Fukumura D, Jain RK (2002) Acidic extracellular ph induces vascular endothelial growth factor (VEGF) in human glioblastoma cells via ERK1/2 MAPK signaling pathway. mechanism of low ph-induced VEGF. J Biol Chem 277(13):11368–11374

    Article  PubMed  CAS  Google Scholar 

Download references

Funding

This work is supported by the ECOSCALE project (grant agreement 671632) funded by the European Commission under the H2020 Programme.

Author information

Authors and Affiliations

  1. Digital Image and Signal Processing Laboratory, School of Electrical and Computer Engineering, Technical University of Crete, University Campus, Akrotiri, Chania, 73100, Crete, Greece

    Maria Papadogiorgaki

  2. Department of Oncology, General Hospital of Chania “Agios Georgios”, Mournies, Chania, 73300, Crete, Greece

    Panagiotis Koliou

  3. Digital Image and Signal Processing Laboratory, School of Electrical and Computer Engineering, Technical University of Crete, Polytechnioupolis, Kounopidiana Campus, Chania, 73100, Crete, Greece

    Michalis E. Zervakis

Authors
  1. Maria Papadogiorgaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Panagiotis Koliou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michalis E. Zervakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria Papadogiorgaki.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(PDF 279 KB)

(PDF 346 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Papadogiorgaki, M., Koliou, P. & Zervakis, M.E. Glioma growth modeling based on the effect of vital nutrients and metabolic products. Med Biol Eng Comput 56, 1683–1697 (2018). https://doi.org/10.1007/s11517-018-1809-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-018-1809-0

Keywords

Search

Navigation