النمذجة الرياضية لنمو الأورام: نموذج قائم على المنافسة وفق نموذج كَومبيرتز في البعدين
DOI:
https://doi.org/10.21123/bsj.2024.9220الكلمات المفتاحية:
المنافسة، التعايش، نقاط التوازن، الانقراض، نموذج كَومبيرتز.الملخص
بالنسبة لهذه المقالة، تمت دراسة المنافسة بين الخلايا السرطانية داخل جسم الإنسان اعتمادًا على نمو جومبيرتز. تعتمد هذه النماذج على نوعين من الخلايا السرطانية، وتنمو هذه الخلايا إلى حد ما يسمى بالقدرة الاستيعابية. يتم أخذ القدرة الاستيعابية في الاعتبار وتعريفها على أنها عدد الخلايا الذي يصل اليه الورم في النهاية. عندما يحدث هذا، يتقلب معدل النمو، إما أن يكون أعلى قليلاً أو أقل قليلاً من القدرة الاستيعابية. ستغطي هذه الدراسة جوانب النمذجة الرياضية لنمو جومبيرتز وطريقة لتحديد كيفية المنافسة لنموالورام وما إذا كانت تؤدي إلى الاستقرار أو عدم الاستقرار. يتضمن البحث معادلات نمو تظهر نوعين متنافسين يؤديان إلى الانقراض أو التعايش أو ظهور نوع متفوق على الآخر.
Received 09/06/2023
Revised 07/06/2023
Accepted 10/08/2023
Published Online First 20/01/2024
المراجع
De Wever O, Mareel M. Role of Tissue Stroma in Cancer Cell Invasion. J Pathol. 2003; 200(4): 429–447. https://doi.org/10.1002/path.1398.
Mattiuzzi C, Lippi G. Current Cancer Epidemiology. J Epidemiol Glob Health. 2019; 9(4): 217–222. https://doi.org/10.2991/jegh.k.191008.001.
Parkin DM. The Global Health Burden of Infection-Associated Cancers in the Year 2002. Int J Cancer. 2006; 118(12): 3030–3044. https://doi.org/10.1002/ijc.21731.
Mazzanti C, Zeiger MA, Costourous N, Umbricht C, Westra W H, Smith D,et al. Using Gene Expression Profiling to Differentiate Benign versus Malignant Thyroid Tumors. Cancer Res. 2004; 64(8): 2898–2903. https://doi.org/10.1158/0008-5472
Sa G, Das T. Anti Cancer Effects of Curcumin: Cycle of Life and Death. In: Recent Advances in Plant-Based, Traditional, and Natural Medicines. 2014; pp. 151–180. https://doi.org/arXiv:1807.03261v1.
Al-Saedi HM, Archer AJ, Ward J. Dynamical Density Functional Theory Based Modelling of Tissue Dynamics: Application to Tumour Growth. Phys Rev E. 2018; 98(2): 1–18. https://doi.org/arXiv:1807.03261v1.
Hameed HH, Al-Saedi HM. Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function. Baghdad Sci J. 2021; 18(2): 296-305. https://doi.org/10.21123/bsj.2021.18.2.0896
Menchón SA, Condat CA. Macroscopic Dynamics of Cancer Growth. Eur Phys J Spec Top. 2007; 143(1): 89–94. https://doi.org/10.1140/epjst/e2007-00075-1.
Khalaf AF, Al-Naqqash MA, Alwan NAS, et al. Biomarker Significance of Serum CXCL8, CXCL10 and CXCL16 in Breast Tumors of Iraqi Patients. Baghdad Sci J. 2020; 17(1): 199–206. https://doi.org/10.21123/bsj.2020.17.1(Suppl.).0199.
Siegel R, DeSantis C, Virgo K, Stein M, Mariotto A, Smith T,et al. Cancer Treatment and Survivorship Statistics, 2012. CA Cancer J Clin. 2012; 62(4): 220–241. https://doi.org/10.3322/caac.21149.
Tjørve KMC, Tjørve E. The Use of Gompertz Models in Growth Analyses, and New Gompertz-Model Approach: An Addition to the Unified-Richards Family. PLoS One. 2017; 12(6). https://doi.org/10.1371/journal.pone.017869.
Phukoetphim N, Salakkam A, Laopaiboon P, Laopaiboon L. Kinetic Models for Batch Ethanol Production from Sweet Sorghum Juice under Normal and High Gravity Fermentations: Logistic and Modified Gompertz Models. J Biotechnol. 2017; 243: 69-75. http://dx.doi.org/10.1016/j.biotec.2016.12.012
Lo CF. Stochastic Gompertz Model of Tumour Cell Growth. J Theor Biol. 2007; 248(2): 317–321. http://doi.org/10.1016/j.jtbi.2017.04.024
Ose NJ, Ohmann PR. The Selfish Herd: Noise Effects in Local Crowded Horizon and Voronoi models. J Theor Biol. 2017; 424(3) :84–90. https://doi.org/10.1016/j.jtbi.2017.04.024
Vaidya VG, Alexandro FJ. Evaluation of Some Mathematical Models for Tumor Growth. Int J Biomed Comput. 1982; 13(1): 19–35. http://doi.org/10.1016/0020-7101(82)90048-4.
Dagogo J, Cynthia OU, Oyinebifun BE. Comparative Analysis of Additive and Multiplicative Error Terms of Weibull, Logistic Gompertz, Hills and Richards Models with Four Parameters. J Adv Math Comput Sci. 2023; 38(5): 1–34. http://doi.org/10.9734/jamcs/2023/v38i51758.
Badawi H, Shawagfeh N, Abu Arqub O. Fractional Conformable Stochastic Integrodifferential Equations: Existence, Uniqueness, and Numerical Simulations Utilizing the Shifted Legendre Spectral Collocation Algorithm. Math Probl Eng. 2022; 2022. http://doi.org/10.1155/2022/5104350.
Vaghi C, Rodallec A, Fanciullino R, Ciccolini J, Mochel J, Mastri M, et al.Population Modeling of Tumor Growth Curves and the Reduced Gompertz Model Improve Prediction of the Age of Experimental Tumors. PLoS Comput Biol.2020; 16(2): 1–24. http://doi.org/10.1371/journal.pcbi.1007178.
Ma Y, Yu X. Chaos, Solitons and Fractals Impact of Correlated Gaussian Colored Noises on Stability and Stationary Probability Density for the Randomly Forced Two-Species Competitive Gompertz Model. Chaos, Solitons Fractals Interdiscip J Nonlinear Sci Nonequilibrium Complex Phenom. 2023; 169(October 2022): 113288. http://doi.org/10.1016/j.chaos.2023.113288 .
Yu Y, Wang W, Lu Z. Global Stability of Gompertz Model of Three Competing Populations. J Math Anal Appl. 2007; 334(1): 333–348. http://doi.org/10.1016/j.jmaa.2006.12.060.
Hossain AKMS, Steihaug T. Computing a Sparse Jacobian Matrix by Rows and Columns. Optim Methods Softw. 1998; 10(1): 33–48. http://doi.org/10.1080/10556789808805700.
Crișan A, Negrean I. The Jacobian Matrix Based on the Transfer Matrices. 2019; 127-134 p.
Liao J, Zhou N, Wang Q. DC grid protection method based on phase planes of single-end common-and differential-mode components. IEEE Trans Power Deliv. 2021; 36(1): 299–310. http://doi.org/10.1109/TPWRD.2020.2976721.
Safeera K, Anil Kumar V. Stability of Complement Degree Polynomial of Graphs. Baghdad Sci J. 2023; 20(1(SI): 300–304. http://doi.org/10.21123/bsj.2023.8417.
Al-Momen S, Naji RK. The dynamics of sokol-howell prey-predator model involving strong Allee effect. Iraqi J Sci. 2021; 62(9): 3114–3127. http://doi.org/10.24996/ijs.2021.62.9.27.
Al-Momen S, Naji RK. The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect. Iraqi J Sci. 2022; 63(1): 259–282.http://doi.org/10.24996/ijs.2022.63.1.27.
Abdulhussein H, Abdulhadi AM. The Effect of Rotation on the Heat Transfer of a Couple Stress Fluid in A Nonuniform Inclined Asymmetrical Channel with Inclined MHD. Ibn AL-Haitham J Pure Appl Sci. 2023; 36(2): 314–330. https://doi.org/10.30526/36.2.2987.
Ouda EH. Direct Method for Variational Problems Using Boubaker Wavelets. Ibn Al-Haitham J Pure Appl Sci. 2023; 6: 427–436 . https://doi.org/10.30526/36.3.3048.
Jasim WI, AL-Husseiny HF. A Study of Shigellosis Bacteria disease Model with Awareness Effects. Ibn AL- Haitham J Pure Appl Sci. 2021; 34(2): 129–143. https://doi.org/10.30526/34.2.2619.
Rahma AMS, Abd NB. Modeling Dynamic Background based on Linear Equation. Ibn AL-Haitham J Pure. Appl Sci. 2019; 32(2): 156–165. https://doi.org/10.30526/32.2.2122
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