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Network Modeling Analysis in Health Informatics and Bioinformatics

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01.12.2023 | Original Article

Mathematical model of the tumor cells’ population growth

verfasst von: Nishant Namdev, Himanshu Jain, Arvind Kumar Sinha

Erschienen in: Network Modeling Analysis in Health Informatics and Bioinformatics | Ausgabe 1/2023

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Abstract

In medical science, the tumor is a critical situation and the grounds for failing life and places a significant hurdle on medical. Predicting the extension of tumors has been of matter since the initial periods of tumor examination, and investigators have been performing to illustrate a new medical approach for tumors. The tumor is a condition reached when uncommon cells erupt from the genetic rules and are experienced limitlessly. This state forms a cell group with uncontrolled growth inside. Metastasis is when some tumor cells shift and form other tumors. The model explains that the proliferation of the tumor cells is almost constant, and cell elongation would undoubtedly be limited and expand linearly when nutrients run down. In this paper, the mathematical understanding of the reaction of tumor cells to metastasis is presented. Therefore, we explore the dynamics of tumor cell growth in different organs. This paper connects numerical computation, applied mathematics, and applications of biological scenarios.

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American Tumors Society (2013) How is tumors diagnosed? https://www.cancer.org/research/cancer-facts-statistics/all-cancer-facts-figures/cancer-facts-figures-2013.html

American Tumors Society (2018) Heredity and tumors https://www.cancer.org/cancer/cancer-causes/genetics/family-cancer-syndromes.html. Accessed 14 Sept 2022

Anand P, Kunnumakkara AB, Kunnumakara AB, Sundaram C, Harikumar KB, Tharakan ST, Lai OS, Sung B, Aggarwal BB (2008) Tumors is a preventable disease that requires major lifestyle changes. Pharm Res 25:2097–2116. https://doi.org/10.1007/s11095-008-9661-9CrossRef

Batmani Y, Khaloozadeh H (2013) Optimal drug regimens in cancer chemotherapy: a multi-objective approach. Comput Biol Med 43:2089–2095. https://doi.org/10.1016/j.compbiomed.2013.09.026CrossRefMATH

Brodin NP, Vogelius IR, Eriksson TB, AfRosenschold PM, Maraldo MV, Aznar MC, Specht L, Bentzen SM (2014) Optimizing the radiation therapy dose prescription for pediatric medulloblastoma: Minimizing the life years lost attributable to failure to control the disease and late complication risk. Acta Oncol 53:462–470. https://doi.org/10.3109/0284186X.2013.858824CrossRef

Chou CS, Friedman A (2016) Introduction to the mathematical biology. Springer, New York. https://doi.org/10.1007/978-3-319-29638-8CrossRefMATH

Cooper GM (2000) The cell: a molecular approach. 2nd edition. Sunderland (MA): Sinauer Associates. Available from: https://www.ncbi.nlm.nih.gov/books/NBK9839/. Accessed 8 Apr 2017

Dániel AD, Levente K, Johanna S, Zoltán B (2011) Model-based analysis and synthesis of tumor growth under angiogenic inhibition: a case study. IFAC Proc Vol 44:3753–3758. https://doi.org/10.3182/20110828-6-IT-1002.02107CrossRef

De Pillis LG, Gu W, Radunskaya AE (2006) Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J Theor Biol 238:841–862. https://doi.org/10.1016/j.jtbi.2005.06.037MathSciNetCrossRefMATH

Deng Y, Liu M (2020) Analysis of a stochastic tumor-immune model with regime switching and impulsive perturbations. Appl Math Model 78:482–504. https://doi.org/10.1016/j.apm.2019.10.010MathSciNetCrossRefMATH

Dethlefsen LA, Prewitt JMS, Mendelsohn ML (1968) Analysis of tumors growth curves. J Natl Cancer Inst 40:389–405. https://doi.org/10.1093/jnci/40.2.389CrossRef

Dourado-Neto D, Teruel D, Reichardt K, Nielsen D, Frizzone J, Bacchi O (1998) Principles of crop modeling and simulation: I. uses of mathematical models in agricultural science. Sci Agricola 55:46–50. https://doi.org/10.1590/S0103-90161998000500008CrossRef

Elias J, Dimitrio L, Clairambault J, Natalini R (2014) The p53 protein and its molecular network: modelling a missing link between dna damage and cell fate. Biochim Biophys Acta 1844:232–247. https://doi.org/10.1016/j.bbapap.2013.09.019CrossRef

Enderling H, Chaplain AJM (2014) Mathematical modeling of tumors growth and treatment. Curr Pharm Des 20:4934–4940. https://doi.org/10.2174/1381612819666131125150434CrossRef

Evain S, Benzekry S. (2016) Mathematical modeling of tumor and metastatic growth when treated with sunitinib. [Research Report] Inria Bordeaux Sud-Ouest. ffhal-01377994ff. https://hal.archives-ouvertes.fr/hal-01377994. Accessed 9 Jan 2017

Gotzsche PC, Jorgensen KJ (2013) Screening for breast tumors with mammography. Cochrane Database Syst Rev. https://doi.org/10.1002/14651858CrossRef

Gunnarsson EB, Leder K, Foo J (2021) Exact site frequency spectra of neutrally evolving tumors: a transition between power laws reveals a signature of cell viability. Theor Popul Biol 142:67–90. https://doi.org/10.1016/j.tpb.2021.09.004CrossRefMATH

Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L (1999) Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res 59:4770–4775

Hartung N, Mollard S, Barbolosi D, Benabdallah A, Chapuisat G, Henry G, Giacometti S, Iliadis A, Ciccolini J, Faivre C, Hubert F (2014a) Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice. Can Res 74:1–11. https://doi.org/10.1158/0008-5472.CAN-14-0721CrossRef

Hartung N, Mollard S, Barbolosi D, Benabdallah A, Chapuisat G, Henry G, Giacometti S, Iliadis A, Ciccolini A, Faivre C, Hubert F (2014b) Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice. Can Res 74:6397–6407. https://doi.org/10.1158/0008-5472.CAN-14-0721CrossRef

Huang X, Ning J, Wahed AS (2014) Optimization of individualized dynamic treatment regimes for recurrent diseases. Stat Med 33:2363–2378. https://doi.org/10.1002/sim.6104MathSciNetCrossRef

Huang Y, Zhang Z, Hu B (2017) Bifurcation for a free-boundary tumor model with angiogenesis. Nonlinear Anal Real World Appl 35:483–502. https://doi.org/10.1016/j.nonrwa.2016.12.003MathSciNetCrossRefMATH

Hussanan A, Salleh MZ, Khan I (2018) Microstructure and inertial characteristics of a magnetite ferrofluid over a stretching/shrinking sheet using effective thermal conductivity model. J Mol Liq 255:64–75. https://doi.org/10.1016/j.molliq.2018.01.138CrossRef

National Tumors Institute (2017) Obesity and tumors risk. https://www.cancer.gov/about-cancer/causes-prevention/risk/obesity/obesity-fact-sheet. Accessed 5 Apr 2022

National Tumors Institute (2018) Defining tumors. https://www.cancer.gov/publications/dictionaries/cancer-terms. Accessed 5 May 2022

NHS Choices (2016) Tumors—signs and symptoms. https://www.nhs.uk/conditions/cancer/symptoms/. Accessed 13 Oct 2022

Jayasekara H, MacInnis RJ, Room R, English DR (2016) Long-term alcohol consumption and breast, upper aero-digestive tract and colorectal tumors risk: a systematic review and meta-analysis. Alcohol Alcohol 51:315–330. https://doi.org/10.1093/alcalc/agv110CrossRef

Jin Y, Yuanshun T, Robert AC (2019) Modelling effects of a chemotherapeutic dose response on a stochastic tumour-immune model. Chaos, Solitons Fractals 123:1–13. https://doi.org/10.1016/j.chaos.2019.03.029MathSciNetCrossRefMATH

Kushi LH, Doyle C, McCullough M, Rock CL, Wahnefried WD, Bandera EV, Gapstur S, Patel AV, Andrews K, Gansler T (2016) American tumors society guidelines on nutrition and physical activity for tumors prevention: reducing the risk of tumors with healthy food choices and physical activity. Catumors J Clin 62:30–67. https://doi.org/10.3322/caac.20140CrossRef

Kuznetsov VA, Makalkin IA, Taylor MA, Perelson AS (1994) Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull Math Biol 56:295–321. https://doi.org/10.1016/S0092-8240(05)80260-5CrossRefMATH

Laird AK (1965) Dynamics of tumors growth. Br J Cancer 19:278–291. https://doi.org/10.1038/bjc.1965.32CrossRef

Laird AK (1964) Dynamics of tumors growth. Br J Cancer 13:490–502. https://doi.org/10.1038/bjc.1964.55CrossRef

Moodie EEM, Richardson TS, Stephens DA (2014) Demystifying optimal dynamic treatment regimes. Biometrics 63:447–455. https://doi.org/10.1111/j.1541-0420.2006.00686.xMathSciNetCrossRefMATH

Namdev N, Sinha AK (2020) Mathematical analysis for the prediction of tumors. Int J Adv Res Eng Technol 11:644–652. https://doi.org/10.34218/IJARET.11.8.2020.063CrossRef

Namdev N, Sinha AK (2021) Prediction of the supportive vaccine type of the covid-19 for public health. J Math Comput Sci 11:5703–5719. https://doi.org/10.28919/jmcs/5738CrossRef

Namdev N, Sinha AK, Shende P (2022) Mathematical computation of the tumor growth. Netw Model Anal Health Inform Bioinform. https://doi.org/10.1007/s13721-022-00368-0CrossRef

Orme ME, Chaplain MA (1996) A mathematical model of vascular tumour growth and invasion. Math Comput Model 23:43–60. https://doi.org/10.1016/0895-7177(96)00053-2CrossRefMATH

Pack A, Murray-Smith D (1972) Mathematical models and their applications in medicine. Scott Med J. 17:401–409. http://eprints.gla.ac.uk/67359/. Accessed 23 Sept 2021

Panetta JC (1998) A mathematical model of drug resistance: Heterogeneous tumors. Math Biosci 147:41–61. https://doi.org/10.1016/S0025-5564(97)00080-1CrossRefMATH

Pokhariyal G, Rodrigues A (1993) An accurate epidemiological model. Appl Math Comput 53:1–12. https://doi.org/10.1016/0096-3003(93)90112-RCrossRefMATH

Ramli N, Ahmad S, Pop I (2017) Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate. AIP Conf Proc 1870:040015. https://doi.org/10.1063/1.4995847CrossRef

Rashad A (2017) Impact of anisotropic slip on transient three-dimensional MHD flow of ferrofluid over an inclined radiate stretching surface. J Egypt Math Soc. 25:230–237. https://doi.org/10.1016/j.joems.2016.12.001MathSciNetCrossRefMATH

Rihan FA, Lakshmanan S, Maurer H (2019) Optimal control of tumour-immune model with time-delay and immuno-chemotherapy. Appl Math Comput 353:147–165. https://doi.org/10.1016/j.amc.2019.02.002MathSciNetCrossRefMATH

Sakode CM, Padhi R, Kapoor S, Rallabandi VPS, Roy PK (2014) Multimodal therapy for complete regression of malignant melanoma using constrained nonlinear optimal dynamic inversion. Biomed Signal Process Control 13:198–211. https://doi.org/10.1016/j.bspc.2014.04.010CrossRef

Sinha AK, Namdev N (2021) A mathematical model of tumor growth in human body with the rough set. Sci Technol Asia 26:30–38. https://doi.org/10.14456/scitechasia.2021.4CrossRef

Sinha AK, Namdev N (2020a) Feature selection and pattern recognition for different types of skin disease in human body using the rough set method. Netw Model Anal Health Inform Bioinform. https://doi.org/10.1007/s13721-020-00232-zCrossRef

Sinha AK, Namdev N (2020b) Mathematical modeling of lung cancer using rough sets. Int J Adv Res Eng Technol 11:1–10. https://ssrn.com/abstract=3565100. Accessed 30 Mar 2020

Sinha AK, Namdev N, Kumar A (2018) Rough set method accurately predicts unknown protein class/family of leishmania donovani membrane proteome. Math Biosci 301:37–49. https://doi.org/10.1016/j.mbs.2018.03.027MathSciNetCrossRefMATH

Sinha AK, Namdev N, Kumar A (2020) A mathematical model of adiponectin resistance. J Theor Biol. https://doi.org/10.1016/j.jtbi.2020.110246MathSciNetCrossRefMATH

Sinha AK, Namdev N, Shende P (2022) Mathematical Modeling of the Outbreak of COVID-19. Netw Model Anal Health Inform Bioinform. https://doi.org/10.1007/s13721-021-00350-2CrossRef

Stepanova NV (1979) Immune response dynamics during malignant tumor development. Biofizika 24:897–902

Summers WC (1966) Dynamics of tumors growth—a mathematical model. Growth 30:333

Tabatabaie SMH, Bolte JP, Murthy GS (2018) A regional scale modeling framework combining biogeochemical model with life cycle and economic analysis for integrated assessment of cropping systems. Sci Total Environ 625:428–439. https://doi.org/10.1016/j.scitotenv.2017.12.208CrossRef

Wang Z, Deisboeck TS (2014) Mathematical modeling in cancer drug discovery. Drug Discovery Today 19:45–50. https://doi.org/10.1016/j.drudis.2013.06.015CrossRef

World Health Organization (2014a) World Tumors Report. http://www.who.int/cancer/publications/WRC_2014a/en/. Accessed 3 Feb 2022

World Health Organization (2014b) World Tumors Report. ISBN 9283204298. http://www.who.int/cancer/publications/WRC_2014b/en/. Accessed 3 Feb 2022

World Health Organization (2018) Tumors fact sheet N°297. http://www.who.int/news-room/fact-sheets/detail/cancer. Accessed 3 Feb 2022

Zeeshan A, Majeed A, Ellahi R (2016) Effect of magnetic dipole on viscous ferrofluid past a stretching surface with thermal radiation. J Mol Liq 215:549–554. https://doi.org/10.1016/j.molliq.2015.12.110CrossRef

Zheng J, Cui S (2019) Analysis of a tumor-model free boundary problem with a nonlinear boundary condition. J Math Anal Appl. https://doi.org/10.1016/j.jmaa.2019.05.056MathSciNetCrossRefMATH

Titel: Mathematical model of the tumor cells’ population growth
verfasst von: Nishant Namdev
Himanshu Jain
Arvind Kumar Sinha
Publikationsdatum: 01.12.2023
Verlag: Springer Vienna
Erschienen in: Network Modeling Analysis in Health Informatics and Bioinformatics / Ausgabe 1/2023
Print ISSN: 2192-6662
Elektronische ISSN: 2192-6670
DOI: https://doi.org/10.1007/s13721-022-00399-7

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