A General Framework for Multiscale Modeling of Tumor–Immune System Interactions

作者: Marina Dolfin , Mirosław Lachowicz , Zuzanna Szymańska

DOI: 10.1007/978-1-4939-0458-7_5

关键词:

摘要: In this paper we review methods that allow the construction of a consistent set models may describe interactions between tumor and immune system on microscopic, mesoscopic, macroscopic scales. The presented structures be basis for description sub–cellular, cellular, levels. Important open problems are indicated.

参考文章(66)
Mirosław Lachowicz, Lins Between Microscopic and Macroscopic Descriptions Lecture Notes in Mathematics. pp. 201- 267 ,(2008) , 10.1007/978-3-540-78362-6_4
Reinhard Illner, Mario Pulvirenti, Carlo Cercignani, The mathematical theory of dilute gases ,(1994)
Zuzanna Szymańska, ANALYSIS OF IMMUNOTHERAPY MODELS IN THE CONTEXT OF CANCER DYNAMICS International Journal of Applied Mathematics and Computer Science. ,vol. 13, pp. 407- 418 ,(2003)
Leland H. Hartwell, John J. Hopfield, Stanislas Leibler, Andrew W. Murray, From molecular to modular cell biology. Nature. ,vol. 402, ,(1999) , 10.1038/35011540
Markus R. Owen, Jonathan A. Sherratt, Pattern Formation and Spatiotemporal Irregularity in a Model for Macrophage–Tumour Interactions Journal of Theoretical Biology. ,vol. 189, pp. 63- 80 ,(1997) , 10.1006/JTBI.1997.0494
Nicola Bellomo, Abdelghani Bellouquid, Juan Nieto, Juan Soler, None, MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS Mathematical Models and Methods in Applied Sciences. ,vol. 20, pp. 1179- 1207 ,(2010) , 10.1142/S0218202510004568
L. Arlotti, N. Bellomo, M. Lachowicz, Kinetic equations modelling population dynamics Transport Theory and Statistical Physics. ,vol. 29, pp. 125- 139 ,(2000) , 10.1080/00411450008205864
M. Cobbold, H. De La Pena, A. Norris, J. M. Polefrone, J. Qian, A. M. English, K. L. Cummings, S. Penny, J. E. Turner, J. Cottine, J. G. Abelin, S. A. Malaker, A. L. Zarling, H.-W. Huang, O. Goodyear, S. D. Freeman, J. Shabanowitz, G. Pratt, C. Craddock, M. E. Williams, D. F. Hunt, V. H. Engelhard, MHC Class I–Associated Phosphopeptides Are the Targets of Memory-like Immunity in Leukemia Science Translational Medicine. ,vol. 5, ,(2013) , 10.1126/SCITRANSLMED.3006061
O. Lejeune, M.A.J. Chaplain, I. El Akili, Oscillations and bistability in the dynamics of cytotoxic reactions mediated by the response of immune cells to solid tumours Mathematical and Computer Modelling. ,vol. 47, pp. 649- 662 ,(2008) , 10.1016/J.MCM.2007.02.026