×

Mathematical modeling of blood flow alteration in microcirculatory network due to angiogenesis. (English) Zbl 1388.76459


MSC:

76Z05 Physiological flows
92C35 Physiological flow
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] J. Folkman, “Tumor angiogenesis: therapeutic implications,” N. Engl. J.Med. 285, 1182-1186 (1971). · doi:10.1056/NEJM197108122850711
[2] F. Bost, A.-G. Decoux-Poullot, J. F. Tanti, and S. Clave, “Energy disruptors: rising stars in anticancer therapy?” Oncogenesis 5, e188 (2016).
[3] S. K. Stamatelos et al., “A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions,” Microvascular Research 91, 8-21 (2014). · doi:10.1016/j.mvr.2013.12.003
[4] J. E. Fletcher, “Mathematical modeling of the microcirculation,” Mathematical Biosciences 38 (3), 159-202 (1978). · Zbl 0381.92003 · doi:10.1016/0025-5564(78)90044-5
[5] V. P. Srivastava, “A theoretical model for blood flow in small vessels,” Applications and AppliedMathematics 2 (1), 51-65 (2007). · Zbl 1331.92038
[6] J. B. Geddes et al., “Blood flow in microvascular networks: a study in nonlinear biology,” Chaos: An Interdisciplinary Journal of Nonlinear Science 20 (4), 045123 (2010). · Zbl 1311.92057 · doi:10.1063/1.3530122
[7] Kholodov, A. S.; Evdokimov, A. V.; Simakov, S. S.; Chandra, P. (ed.); Kumar, R. (ed.), Numerical simulation of peripheral circulation and substance transfer with 2D models, 22-29 (2006)
[8] Kholodov, A. S.; Simakov, S. S.; Evdokimov, A. V.; Kholodov, Y. A.; Rodrigues, H. (ed.); etal., Matter transport simulations using 2D model of peripheral circulation coupled with the model of large vessels, 479-490 (2005)
[9] S. K. Stamatelos, E. Kim, A. P. Pathak, and A. S. Popel, “A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions,” Microvascular Research 91, 8-21 (2014). · doi:10.1016/j.mvr.2013.12.003
[10] Su Shen-Wei, M. Catherall, and S. Payne, “The influence of network structure on the transport of blood in the human cerebral microvasculature,” Microcirculation 19 (2), 175-187 (2012). · doi:10.1111/j.1549-8719.2011.00148.x
[11] E. M. Renkin and F. E. Curry, “Transport of water and solutes across capillary endothelium,” Membrane Transport in Biology 4, 1-45 (1979).
[12] L. J. Rodney, An Introduction to Cardiovascular Physiology (Butterworth-Heinemann, 2013).
[13] Konerding, M.; Van Ackern, C.; Fait, E.; Steinberg, F.; Streffer, C., Morphological aspects of tumor angiogenesis and microcirculation, 5-17 (1998), Berlin
[14] E. M. Renkin, “Filtration, diffusion, and molecular sieving through porous cellulose membranes,” The Journal of General Physiology 38 (2), 225-243 (1954).
[15] E. M. Renkin, “Multiple pathways of capillary permeability,” Circulation Research 41 (6), 735-743 (1977). · doi:10.1161/01.RES.41.6.735
[16] Simakov, S.; Ispolatov, I.; Maslov, S.; Nikitin, A., Algorithmic basis for pathway visualization (2008)
[17] A. V. Kolobov and M. B. Kuznetsov, “Investigation of angiogenesis influence on tumor growth rate. Analysis by mathematical modeling,” Biophysics 60 (3), 555-563 (2015). · doi:10.1134/S0006350915030082
[18] O. Warburg, “On the origin of cancer cells,” Science 123, 309-314 (1956). · doi:10.1126/science.123.3191.309
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.