Mathematical Model for Stiffness and Energy of Extracellular Matrix in the Growth of Cancer
Main Article Content
Abstract
Stiffness of Extracellular matrix (briefly, ECM) plays an important role in providing a tumor microenvironment and the increased stiffness has been associated with the development of tumor. The notions of potential energy and kinetic energy are developed and used to explain the growth of cancer from incubation stage to the asymptotic stage by maintaining the law of conservation of energy. The product of model parameters , and is shown to be constant, which reflects their complimentary nature for the growth of cancer in patients and can be used to formulate control strategies for treatment.
Downloads
Article Details
Section

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
References
IT Swinehart and SF Badylak; Extracellular matrix bioscaffolds in tissue remodeling and morphogenesis, Dev Dyn 2016 March. 245(3), 351-60.
A Acuna, MA.Drakopoulos, CJ. Georgen and S Calve; Three-dimensional visualization of ECM network during murine development, Developmental Biology, 435-2 (March 2018), 122-129.
EL Baker, RT Bonnecage and MH Zaman; Extracellular matrix stiffness and Architecture govern Intracellular Rheology in cancer, Biophys J. 97(4) (2009) 1013-1021. Doi:10.1016J. bpj2009.05.054.
C Walker, E Mojares, A Del Rio Hernandez; Role of Extracellular matrix in development and cancer progression, Int. J.Mol. Sci. 19(10) (2018) 3028. doi: 10.3390/ijms 19103028. PMUD 30287763.
MR Ng and JS Brugge; A stiff blow from the stroma: collagen cross-linking drives tumor progression, Cancer Cell, 16 (2009), 455-7.
I Levental, P. C. Georges, P.A Janmey; Soft Biological materials and their impact on cell matter, Soft Matter, 1 (2007) 299-306.
JT Erler and V.M Weaver; Three-dimensional context regulation of metastasis, Clin. Exp Metastasis, 26 (2009), 35-49.
CD Cone; Transmembrane Potentials and Characteristics of Immune and Tumor Cells, Boca Raton, Florida: CRC Press, 1985.
F.W. Cope; A medical application of the Ling Association-Induction Hypothesis: The high potassium, low sodium diet of the Gerson cancer therapy, Physiol. chem. Phys, 10(5) (1978), 465-468.
HA Nieper, AD Alexander, GS Eagle-Ogden; The curious Man: the life and work of Dr. Hans Nieper, Garden City Park, NY AT Avery Publishing Group, 1999.
DC Nieman, DA Henson, MC Austin and W Sha; Upper respiratory tract infection is reduced in physcilly fit and active adults, Br. J Sports Med, 45(12) (2011), 987-92.
CV Dang, Le Anne and Gao Ping; MYC-induced cancer cell energy metabolism and therapeutic opportunities, Clinical cancer Research, 15(21) (2009), 6479-6483.
T. Kulkarni et al; Machine learning-based approach for automated classification of cell and extracellular matrix using nanomechanical properties, Materials Today Bio, 25 (2024), 100970.
G.P. Pokhariyal; A model for the growth of infection, Jour. of Theo. Bio., 119 (1986), 181-188.
J.E. Van der Plank; Plant Diseases, Epidemics and Control, Academic Press, NewYork, 1963.
J. Kranz; The Role and Scope of Mathematical Analysis and Modeling in Epidemiology, S - V, Berlin, 1974.
G.P. Pokhariyal, and A.J. Rodrigues; An accurate epidemiological model, Applied Maths and Computation, 53 (1993), 1-12.
European Union cancer prevention: https:www.cancer.eu; Google search, 3/3/2023.
Mayo clinic; Cancer prevention: 7 tips to reduce your risk; Google search, 14-3-2023.
C Pucci, C Martinelli and G. Ciofani; Innovative approaches for cancer treatment: Current perspectives and challenges; ecancer, 2019,13.961; www. cancer.org; https://doi.org/10.3332/ecancer.2019.961.
G.B. West, J.H. Brown, and Enquist; A general model for ontogenetic growth, Nature, 413 (2001), 628-631.
S. Benzekry, Clare Lamont, Afshin Beheshti et al.; Classical Mathematical Models for description and prevention of experimental tumor growth; Computational Biology, 10(8) (2014).
L.W Kivuti-Bitok, Ganesh P Pokhariyal, McDonnell and A. Roudsari; A Mathematical model for cervical cancer in Kenya, IJSR, 4(2) (2015), 458-465.