A Hybrid Plant-Soil Electrical Analogy and Control Engineering Framework for Dynamically Modeling Cancer Cell Growth in an Elastic Environment

Year 2024, Volume: 1 Issue: 2, 57 - 77, 27.11.2024

Bayram Arda Kuş , Mustafa Gürbüz

Abstract

This research introduces a novel approach to cancer cell growth modeling by integrating principles from the plant-soil analogy and control engineering. The proposed model offers a flexible alternative to traditional dynamic mathematical models, enabling simulations of tumor growth under therapeutic conditions. The simulator, operational on an annual basis, considers diverse patient characteristics and treatment approaches. Nonlinear simulation models provide a comprehensive comparison, showcasing trajectory and precision improvements relative to conventional time-dependent dynamic mathematical models. The study further proposes an elastic cancer modeling mechanism, exploring optimal drug dosage concentrations and patient resistance to cancer drugs. A dynamic model is introduced to identify optimal dosages and frequencies for cancer drugs, demonstrating enhanced operational flexibility through computer simulations. The proposed elastic modeling mechanism is validated through existing mathematical growth models, revealing its practical value within ethical constraints. This research offers a promising path for developing effective therapeutic strategies in cancer tumor growth.

Keywords

Cancer cell growth modeling, Plant-soil analogy, Control engineering, Dynamic mathematical models, Tumor growth simulations, Therapeutic conditions, Nonlinear simulation models

References

• Al-Tuwairqi, S. M., Al-Johani, N. O., and Simbawa, E. A. (2020). Modeling dynamics of cancer radiovirotherapy. Journal of Theoretical Biology, 506, 110405. https://doi.org/10.1016/j.jtbi.2020.110405
• Altrock, P. M., Liu, L. L., and Michor, F. (2015). The mathematics of cancer: Integrating quantitative models. Nature Reviews Cancer, 15(12), 730–745. https://doi.org/10.1038/nrc4029
• Anayochukwu, A. V. (2013). Analogous electrical model of water processing plant as a tool to study “The Real Problem” of process control. International Journal of Control Theory and Computer Modeling, 3(1), 1-18. https://doi.org/10.5121/ijctcm.2013.3101
• Bähr, A., and Wolf, E. (2012). Domestic animal models for biomedical research. Reproduction in Domestic Animals, 47(SUPPL.4), 59–71. https://doi.org/10.1111/j.1439-0531.2012.02056.x
• Bernard, A., Kimko, H., Mital, D., and Poggesi, I. (2012). Mathematical modeling of tumor growth and tumor growth inhibition in oncology drug development. Expert Opinion on Drug Metabolism and Toxicology, 8(9), 1057–1069. https://doi.org/10.1517/17425255.2012.693480
• Brodaczewska, K. K., Szczylik, C., Fiedorowicz, M., Porta, C., and Czarnecka, A. M. (2016). Choosing the right cell line for renal cell cancer research. Molecular Cancer, 15:83. BioMed Central Ltd. https://doi.org/10.1186/s12943-016-0565-8
• Buosi, S., Timilsina, M., Janik, A., Costabello, L., Torrente, M., Provencio, M., Fey, D., and Nováček, V. (2024). Machine learning estimated probability of relapse in early-stage non-small-cell lung cancer patients with aneuploidy imputation scores and knowledge graph embeddings. Expert Systems with Applications, 235, 121127. https://doi.org/10.1016/j.eswa.2023.121127
• Chapman, N., Miller, A. J., Lindsey, K., and Whalley, W. R. (2012). Roots, water, and nutrient acquisition: Let’s get physical. In Trends in Plant Science 17(12), 701–710. https://doi.org/10.1016/j.tplants.2012.08.001
• Collins, V. P., Loeffler, R. K., and Tivey, H. (1956). Observations on growth rates of human tumors. The American Journal of Roentgenology, Radium Therapy, and Nuclear Medicine, 76(5), 988–1000.
• Cunningham, J. J., Brown, J. S., Gatenby, R. A., and Staňková, K. (2018). Optimal control to develop therapeutic strategies for metastatic castrate resistant prostate cancer. Journal of Theoretical Biology, 459, 67–78. https://doi.org/10.1016/j.jtbi.2018.09.022
• Das, A. K., Biswas, S. K., Mandal, A., Bhattacharya, A., and Sanyal, S. (2024). Machine learning based ıntelligent system for breast cancer prediction (MLISBCP). Expert Systems with Applications, 242, 122673. https://doi.org/10.1016/j.eswa.2023.122673
• De Pauw, D. J. W., Steppe, K., and De Baets, B. (2008). Identifiability analysis and improvement of a tree water flow and storage model. Mathematical Biosciences, 211(2), 314–332. https://doi.org/10.1016/j.mbs.2007.08.007
• Dethlefsen, L. A., Prewitt, J. M. S., and Mendelsohn, M. L. (1968). Analysis of tumor growth curves. JNCI: Journal of the National Cancer Institute, 40(2), 389–405. https://doi.org/10.1093/JNCI/40.2.389
• Dhoruri, A., Ratna Sari, E., and Lestari, D. (2020). Mathematical model of tumor cell growth based on age structure. International Journal of Modeling and Optimization, 10(2), 57–60. https://doi.org/10.7763/ijmo.2020.v10.747
• Ducheyne, S. (2005). Mathematical models in Newton’s Principia: A new view of the “Newtonian style.” International Studies in the Philosophy of Science, 19(1), 1–19. https://doi.org/10.1080/02698590500051035
• Edwards, W. R. N., Jarvis, P. G., Landsberg, J. J., and Talbot, H. (1986). A dynamic model for studying flow of water in single trees. Tree Physiology, 1(3), 309–324. https://doi.org/10.1093/treephys/1.3.309
• Fischer, H. P. (2008). Mathematical modeling of complex biological systems: From parts lists to understanding systems behavior. Alcohol Research and Health, 31(1), 49–59. http://teaching.anhb.uwa.edu.au/mb140/
• Forys, U., and Marciniak-Czochra, A., (2003). Logistic equations in tumour growth modelling. International Journal of Applied Mathematics and Computer Science, 13(3), 317–325.
• Freyei, J. P., and Sutherland, R. M. (1986). Regulation of growth saturation and development of necrosisin emt6/r0 multicellular spheroids by the glucose and oxygen supply. Cancer Research, 46(7), 3504–3512.
• Friberg, S., and Mattson, S. (1997). On the growth rates of human malignant tumors: Implications for medical decision making. Journal of Surgical Oncology, 65(4), 284–297. https://doi.org/10.1002/(SICI)1096-9098(199708)65:4<284::AID-JSO11>3.3.CO;2-2
• Gerlee, P. (2013). The model muddle: In search of tumor growth laws. Cancer Research, 73(8), 2407–2411. https://doi.org/10.1158/0008-5472.CAN-12-4355
• Gompertz B. (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. & C. Philosophical Transactions of the Royal Society of London, 115, 513–583. https://doi.org/10.1098/rstl.1825.0026
• Ghimire, B., Riley, W. J., Koven, C. D., Mu, M., and Randerson, J. T. (2016). Representing leaf and root physiological traits in CLM improves global carbon and nitrogen cycling predictions. Journal of Advances in Modeling Earth Systems, 8(2), 598–613. https://doi.org/10.1002/2015MS000538
• Guocheng, Z., Huaili, Z., Peng, Z., Shaojie, J., Jiangya, M., and Wenyuan, C. (2011). Decision model for optimization of coagulation/flocculation process for wastewater treatment. 2011 Third International Conference on Measuring Technology and Mechatronics Automation, 821–826. https://doi.org/10.1109/ICMTMA.2011.207
• Gurumurthy, C. B., and Kent Lloyd, K. C. (2019). Generating mouse models for biomedical research: Technological advances. DMM Disease Models and Mechanisms, 12(1). https://doi.org/10.1242/dmm.029462
• Hanahan, D., and Weinberg, R. A. (2011). Hallmarks of cancer: The next generation. Cell, 144(5), 646–674. https://doi.org/10.1016/j.cell.2011.02.013
• Hartung, N., Mollard, S., Barbolosi, D., Benabdallah, A., Chapuisat, G., Henry, G., Giacometti, S., Iliadis, A., Ciccolini, J., Faivre, C., and Hubert, F. (2014). Mathematical modeling of tumor growth and metastatic spreading: Validation in tumor-bearing mice. Cancer Research, 74(22), 6397–6407. https://doi.org/10.1158/0008-5472.CAN-14-0721
• He, W., Demas, D. M., Conde, I. P., Shajahan-Haq, A. N., and Baumann, W. T. (2020). Mathematical modelling of breast cancer cells in response to endocrine therapy and Cdk4/6 inhibition. Journal of the Royal Society Interface, 17(169). https://doi.org/10.1098/rsif.2020.0339rsif20200339
• Hrynevich, A., Li, Y., Cedillo-Servin, G., Malda, J., and Castilho M.,(2023). (Bio) fabrication of microfluidic devices and organs-on-a-chip. In Kalaskar, D.M., (Ed.) 3D Printing in Medicine (2nd Ed. pp 273-336) Woodhead Publising.
• Hunt, E. R., Running, S. W., and Federer, C. A. (1991). Extrapolating plant water flow resistances and capacitances to regional scales. Agricultural and Forest Meteorology, 54(2–4), 169–195. https://doi.org/10.1016/0168-1923(91)90005-B
• Hussein, M., Elnahas, M., and Keshk, A. (2024). A framework for predicting breast cancer recurrence. Expert Systems with Applications, 240. https://doi.org/10.1016/j.eswa.2023.122641
• Jackson, R. B., Sperry, J. S., and Dawson, T. E. (2000). Root water uptake and transport: using physiological processes in global predictions. Trends in Plant Science, 5(11), 482–488. https://doi.org/10.1016/S1360-1385(00)01766-0
• Jakubaszek, A., and Stadnik, A. (2019). Efficiency of sewage treatment plants in the sequential batch reactor. Civil and Environmental Engineering Reports, 28(3), 121–131. https://doi.org/10.2478/ceer-2018-0040
• Jarrett, A. M., Lima, E. A. B. F., Hormuth, D. A., McKenna, M. T., Feng, X., Ekrut, D. A., Resende, A. C. M., Brock, A., and Yankeelov, T. E. (2018). Mathematical models of tumor cell proliferation: A review of the literature. Expert Review of Anticancer Therapy, 18(12), 1271–1286. https://doi.org/10.1080/14737140.2018.1527689
• LaBarbera, D. V., Reid, B. G., and Yoo, B. H. (2012). The multicellular tumor spheroid model for high-throughput cancer drug discovery. Expert Opinion on Drug Discovery, 7(9), 819–830. https://doi.org/10.1517/17460441.2012.708334
• Lee, N. P., Chan, C. M., Tung, L. N., Wang, H. K., and Law, S. (2018). Tumor xenograft animal models for esophageal squamous cell carcinoma. In Journal of Biomedical Science (Vol. 25, Issue 1). BioMed Central Ltd. https://doi.org/10.1186/s12929-018-0468-7
• Lo, W. C., Martin, E. W., Hitchcock, C. L., and Friedman, A. (2013). Mathematical model of colitis-associated colon cancer. Journal of Theoretical Biology, 317, 20–29. https://doi.org/10.1016/j.jtbi.2012.09.025
• Ma, J., Wang, Y., and Liu, J., (2018). Bioprinting of 3D tissues/organs combined with microfluidics. RSC Advances. 8, 21712-21727.
• Marušić, M. (1996). Mathematical models of tumor growth. Mathematical Communications, 1(2), 175–188.
• Mi, S., Du, Z., Xu, Y., and Sun, W. (2018). The crossing and integration between microfluidic technology and 3D printing for organ-on-chips. Journal of Materials Chemistry B. 6(39):6191-6206. doi: 10.1039/c8tb01661e.
• Michaelson, J. S., Halpern, E., and Kopans, D. B. (1999). Breast cancer: Computer simulation method for estimating optimal intervals for screening. Radiology, 212(2), 551–560. https://doi.org/10.1148/radiology.212.2.r99au49551
• Molz, F. J., and Remson, I. (1970). Extraction term models of soil moisture use by transpiring plants. Water Resources Research, 6(5), 1346-1356. https://doi.org/10.1029/WR006i005p01346
• Nicholson, D. J. (2019). Is the cell really a machine? Journal of Theoretical Biology, 477, 108–126. https://doi.org/10.1016/j.jtbi.2019.06.002
• Piantadosi, S., Hazelrig, J. B., and Turner, M. E. (1983). A model of tumor growth based on cell cycle kinetics. Mathematical Biosciences, 66(2), 283–306. https://doi.org/10.1016/0025-5564(83)90094-9
• Rivaz, A., Azizian, M., and Soltani, M. (2019). Various mathematical models of tumor growth with reference to cancer stem cells: A Review. Iranian Journal of Science and Technology, Transaction A: Science, 43(2), 687–700. https://doi.org/10.1007/s40995-019-00681-w
• Ruggiero, C., De Pascale, S., and Fagnano, M. (1999). Plant and soil resistance to water flow in faba bean (Vicia faba L. major Harz.). Plant and Soil. https://doi.org/10.1023/A:1004690101953
• Sachs, R. K., Hlatky, L. R., and Hahnfeldt, P. (2001). Simple ODE models of tumor growth and anti-angiogenic or radiation treatment. Mathematical and Computer Modelling, 33(12-13), 1297-1305. https://doi.org/10.1016/S0895-7177(00)00316-2
• Sethanan, K., Pitakaso, R., Srichok, T., Khonjun, S., Thannipat, P., Wanram, S., Boonmee, C., Gonwirat, S., Enkvetchakul, P., Kaewta, C., and Nanthasamroeng, N. (2023). Double AMIS-ensemble deep learning for skin cancer classification. Expert Systems with Applications, 234. https://doi.org/10.1016/j.eswa.2023.121047
• Stare, A., Hvala, N., and Vrecko, D. (2006). Modeling, identification, and validation of models for predictive ammonia control in a wastewater treatment plant--a case study. ISA Transactions, 45(2), 159–174. https://doi.org/10.1016/S0019-0578(07)60187-6
• Stirzaker, R. J., and Passioura, J. B. (1996). The water relations of the root-soil interface. Plant, Cell and Environment, 19(2), 201-208. https://doi.org/10.1111/j.1365-3040.1996.tb00241.x
• Sutherland, R. M. (1988). Cell and enrivonment ineractions in tumor microregions: The spheroid model. Science, 240(4849), 177–184.
• Talkington, A., and Durrett, R. (2015). Estimating tumor growth rates in vivo. Bulletin of Mathematical Biology, 77, 1934-1954. https://doi.org/10.1007/s11538-015-0110-8
• Tuzet, A., Perrier, A., and Leuning, R. (2003). A coupled model of stomatal conductance, photosynthesis and transpiration. Plant, Cell and Environment, 26(7), 1097–1116. https://doi.org/10.1046/j.1365-3040.2003.01035.x
• Vallverdú, J., Castro, O., Mayne, R., Talanov, M., Levin, M., Baluška, F., Gunji, Y., Dussutour, A., Zenil, H., and Adamatzky, A. (2018). Slime mould: The fundamental mechanisms of biological cognition. BioSystems, 165, 57–70. https://doi.org/10.1016/j.biosystems.2017.12.011
• van Bavel, C. H. M. (1996). Water relations of plants and soils. Soil Science, 161(4), 257-260. https://doi.org/10.1097/00010694-199604000-00007
• Varalta, N., Gomes, A. V, and Camargo, R. F. (2014). A prelude to the fractional calculus applied to tumor dynamic. Tendências Em Matemática Aplicada e Computacional, 15(2), 211–221. https://doi.org/10.5540/tema.2014.015.02.0211
• Verfaillie, C. M. (2002). Adult stem cells: Assessing the case for pluripotency. Trends in Cell Biology, 12(11), 502–508. https://doi.org/10.1016/S0962-8924(02)02386-3
• West, J., and Newton, P. K. (2019). Cellular interactions constrain tumor growth. Proceedings of the National Academy of Sciences of the United States of America, 116(6), 1918–1923. https://doi.org/10.1073/pnas.1804150116
• Yang, J., Virostko, J., Hormuth, D. A., Liu, J., Brock, A., Kowalski, J., and Yankeelov, T. (2021). An experimental-mathematical approach to predict tumor cell growth as a function of glucose availability in breast cancer cell lines. PloS one, 16(7), e0240765. https://doi.org/10.1371/journal.pone.0240765
• Young, H. E., and Black, A. C. (2004). Adult stem cells. Anatomical Record - Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology, 276(1), 75-102 Wiley-Liss Inc. https://doi.org/10.1002/ar.a.10134
• Zhang, C., Jia, D., Li, Z., Wu, N., He, Z., Jiang, H., and Yan, Q. (2024). Esophageal cancer detection framework based on time series information from smear images. Expert Systems with Applications, 238. https://doi.org/10.1016/j.eswa.2023.122362
• Zhuang, J., Yu, G. R., and Nakayama, K. (2014). A series RCL circuit theory for analyzing non-steady-state water uptake of maize plants. Scientific Reports, 4(1), 1–7, 6720. https://doi.org/10.1038/srep06720
• Zweifel, R., Steppe, K., and Sterck, F. J. (2007). Stomatal regulation by microclimate and tree water relations: interpreting ecophysiological field data with a hydraulic plant model. Journal of Experimental Botany, 58(8), 2113–2131. https://doi.org/10.1093/jxb/erm050