Abstract
The paper is concerned with modeling cancer growth, metastasis and response to anticancer treatment in a heterogeneous population of patients. Following a discussion of existing models, multicompartmental models are compared using Kaplan-Meier survival curves. Subsequently, different death conditions are analyzed, leading to the final conclusion that a simple, two-compartmental model describes primary and metastatic tumors well enough but death condition must fine-tuned to available clinical survival curves.
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References
Dela Cruz, C.S., Tanoue, L.T., Matthay, R.A.: Lung cancer: epidemiology, etiology, and prevention. Clin. Chest Med. 32(4), 605–644 (2011). https://doi.org/10.1016/j.ccm.2011.09.001
Inamura, K.: Lung cancer: understanding its molecular pathology and the 2015 WHO classification. Front. Oncol. 7, 193 (2017). https://doi.org/10.3389/fonc.2017.00193
Popper, H.H.: Progression and metastasis of lung cancer. Cancer Metastasis Rev. 35(1), 75–91 (2016). https://doi.org/10.1007/s10555-016-9618-0
Ten Haaf, K., van der Aalst, C.M., de Koning, H.J., Kaaks, R., Tammemägi, M.C.: Personalising lung cancer screening: an overview of risk-stratification opportunities and challenges. Int. J. Cancer, 149(2): 250–263 (2021), doi:https://doi.org/10.1002/ijc.33578
Ten Haaf, K., et al.: Risk prediction models for selection of lung cancer screening candidates: a retrospective validation study. PLoS Med. 14(4), e1002277 (2017). https://doi.org/10.1371/journal.pmed.1002277
Yeo, Y., et al.: Individual 5-Year lung cancer risk prediction model in Korea using a nationwide representative database. Cancers (Basel). 13(14), 3496 (2021), doi:https://doi.org/10.3390/cancers13143496
Tufail, A.B., et al.: Deep learning in cancer diagnosis and prognosis prediction: a minireview on challenges, recent trends, and future directions. Comput Math Meth. Med. 2021, 9025470 (2021). https://doi.org/10.1155/2021/9025470
Swierniak, A., Kimmel, M., Smieja, J., Puszynski, K., Psiuk-Maksymowicz, K.: System Engineering Approach to Planing Anticancer Therapies. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28095-0
Schaettler, H., Ledzewicz, U.: Optimal Control for Mathematical Models of Cancer Therapies. An Application of Geometric Methods, Springer, Cham (2015). https://doi.org/10.1007/978-1-4939-2972-6
Dudley, W.N., Wickham, R., Coombs, N.: An introduction to survival statistics: kaplan-meier analysis. J. Adv. Pract. Oncol. 7(1), 91–100 (2016). https://doi.org/10.6004/jadpro.2016.7.1.8
Bilous, M., et al.: Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer. Sci. Rep. 9(1), 13018 (2019). https://doi.org/10.1038/s41598-019-49407-3
Iwata, K., Kawasaki, K., Shigesada, N.: A dynamical model for the growth and size distribution of multiple metastatic tumors. J. Theor. Biol. 203(2), 177–186 (2000). https://doi.org/10.1006/jtbi.2000.1075
Swierniak, A., Polanski, A., Smieja, J., Kimmel, M.: Modelling growth of drug resistant cancer populations as the system with positive feedback. Math. Comput. Model. 37(11), 1245–1252 (2003). https://doi.org/10.1016/S0895-7177(03)00134-1
Hanin, L., Seidel, K., Stoevesandt, D.: A universal model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases. J. Math. Biol. 72(6), 1633–1662 (2015). https://doi.org/10.1007/s00285-015-0928-6
Serre, R., et al.: Mathematical Modeling of cancer immunotherapy and its synergy with radiotherapy. Cancer Res. 76(17), 4931–4940 (2016). https://doi.org/10.1158/0008-5472.CAN-15-3567
Rhodes, A., Hillen, T.: A mathematical model for the immune-mediated theory of metastasis. J Theor Biol. 482, 109999 (2019). https://doi.org/10.1016/j.jtbi.2019.109999
Smieja, J., Psiuk-Maksymowicz, K., Swierniak, A.: A framework for modeling and efficacy evaluation of treatment of cancer with metastasis. In: Pijanowska, D.G., Zieliński, K., Liebert, A., Kacprzyk, J. (eds.) Biocybernetics and Biomedical Engineering – Current Trends and Challenges. LNNS, vol. 293, pp. 88–97. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-83704-4_9
Bar, J., et al.: Long-term survival of patients with metastatic non-small-cell lung cancer over five decades. J Oncol. 12, 7836264 (2021). https://doi.org/10.1155/2021/7836264
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This work has been supported by the NCN grant DEC-2020/37/B/ST6/01959.
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Smieja, J., Swierniak, A., Kimmel, M. (2022). A Minimal Model of Cancer Growth, Metastasis and Treatment. In: Szczerbicki, E., Wojtkiewicz, K., Nguyen, S.V., Pietranik, M., Krótkiewicz, M. (eds) Recent Challenges in Intelligent Information and Database Systems. ACIIDS 2022. Communications in Computer and Information Science, vol 1716. Springer, Singapore. https://doi.org/10.1007/978-981-19-8234-7_44
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