نوع مقاله : مقاله کامل پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی پزشکی، دانشکده مهندسی، دانشگاه فردوسی مشهد

2 استادیار، گروه مهندسی برق، دانشکده مهندسی، دانشگاه فردوسی مشهد

10.22041/ijbme.2016.20249

چکیده

تومور در مرحلة رشد غیرعروقی نمی‌تواند بدون منبع خون­رسانی بیش از چند میلی‌متر رشد کند و برای رشد بیشتر باید فرآیند رگ‏زایی را آغاز کند. از سوی دیگر، تومور عروقی که عروق ‌خونی در آن نفوذ کرده است، با فراهم شدن اکسیژن به‌سرعت رشد می‌کند. در این مطالعه، مدل ریاضی گسسته‌ای از فرآیند رگ­زایی تومور همراه با اثرات جریان خون در شکل­گیری شبکة دوبعدی موردنظر ارائه‌شده‌ است. این ساختار با یک مدل وفقی مکان‌یابی جوانه‌های عروقی در طول رگ اصلی، در ابتدای فرآیند رگ­زایی ترکیب‌شده است و سپس پیشروی جوانه‌های عروقی در ماتریس خارج سلولی و نفوذ آن‌ها به داخل تومور و همچنین نفوذ جریان خون از­طریق ساختار مویرگی مدل ‌شده است. در این مدل سه مرحلة مکان‌یابی جوانه‌ها در طول رگ اصلی، پیشروی آن‌ها و جریان خون باهم ترکیب‌ شده‌اند. سپس بر­اساس شبکة عروقی به‌دست ‌آمده، انتقال اکسیژن و بقیة مواد لازم برای رشد بیشتر تومور شبیه‌سازی‌شده است. همچنین فرض­شده است رشد تومور درنتیجة تکثیر سلول‌های تومور اتفاق می‌افتد. مراحل رشد تومور و رگ­زایی به‌وسیلة تغییرات محیط میکرو شامل تراکم اکسیژن، فاکتور رگ­زایی تومور و ماتریس خارج سلولی باهم ترکیب ‌شده‌اند. همچنین سعی شده است تا تطبیق مکانی و زمانی مناسبی در پارامترهای مدل ایجاد شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Modeling and Simulation of Vascular Tumor Growth

نویسندگان [English]

  • Mahdie Roghani Yazdi 1
  • Nadia Naghavi 2
  • Faride Sadat Hosseini 1

1 M.Sc. student, Electrical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Assistant Professor, Electrical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

چکیده [English]

A tumor cannot grow more than a few millimeters without a blood supply (avascular tumor), and for further growth it must initiate angiogenesis process. A vascularized tumor, which is permeated with blood vessels, rapidly increases in mass because of the new source of oxygen. In this study, a discrete mathematical model of angiogenesis process with considering the penetration of blood flow through the vessels in the two-dimensional network is presented. This structure is coupled with an adaptive model of sprouts spacing along the parent blood vessel at the beginning of the angiogenesis process. Then, progression of these sprouts in the extracellular matrix and their penetration into the tumor as well as penetration of blood flow through the capillary structure is presented. This model incorporates three steps of adaptive sprout spacing along the parent blood vessel, sprout progression, and blood flow and network remodeling. Then, based on the simulated vasculature network, oxygentransmission and other vital chemicals needed for continuous tumor growth are simulated. In this model we assumed that the growth of the tumor is driven by cell division. The tumor growth and angiogenesis are coupled by the changes of micro environment including oxygen, tumor growth factor, and the extracellular matrix concentration. Also, we have tried to create space and time adaptations in parameters of the model.

کلیدواژه‌ها [English]

  • Tumor angiogenesis
  • Adaptive sprouting
  • Blood flow
  • Vascular tumor growth
  • Finite difference method
[1]           S. R. McDougall et al., "Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies,"Bull. Math. Biol.,vol. 64, no. 4, pp. 673-702, July, 2002.
[2]           H. A. Levine and B. D. Sleeman, "Modelling Tumour-Induced Angiogenesis"in Cancer Modelling and Simulation. 1sted, CRC Press, 2003, ch. 6, pp.147-183.
[3]           F. Billy et al.,"A pharmacologically-based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy," J. Theor. Biol., vol. 260, no. 4, pp. 545-562, Oct, 2009.
[4]           N.V. Mantzaris, S. Webb, H.G. Othmer, "Mathematical modeling of tumor-induced angiogenesis," J. Math. Biol., vol. 49, no. 2, pp. 111-187, Aug, 2004.
[5]           R.K. Jain, "Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy," Science, vol. 307, no. 5706, pp. 58-62, Jan, 2005.
[6]           J. Folkman, M. Klagsbrun, "Angiogenic factors,"Science, vol. 235, no. 4787, pp. 442-447, Jan, 1987.
[7]           B. Addison-Smith, D.L.S. McElwain, P.K. Maini, "A simple mechanistic model of sprout spacing in tumour-associated angiogenesis,"J. Theor. Biol., vol. 250, no. 1, pp. 1-15, Jan, 2008.
[8]           A.R.A. Anderson et al.,"A gradient-driven mathematical model of antiangiogenesis,"Math Comput Model., vol. 32, no. 10, pp. 1141-1152, Nov, 2000.
[9]           G.J. Beattie, J.F. Smyth, "Phase I study of intraperitoneal metalloproteinase inhibitor BB94 in patients with malignant ascites,"Clin. Cancer Res.,vol. 4, no. 8, pp. 1899-1902, Aug, 1998.
[10]         V.P. Terranova et al.,"Human endothelial cells are chemotactic to endothelial cell growth factor and heparin,"J Cell Biol., vol. 101, no. 6, pp. 2330-2334, Dec, 1985.
[11]         C.L. Stokes et al.,"Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor,"Lab Invest., vol. 63, no. 5, pp. 657-668, Nov, 1990.
[12]         A.R.A. Anderson, M.A.J. Chaplain, "Continuous and discrete mathematical models of tumor-induced angiogenesis,"Bull. Math. Biol., vol. 60, no. 5, pp. 857-899, Sep., 1998.
[13]         J. Panovska, H.M. Byrne, P.K. Maini, "Mathematical modelling of vascular tumour growth and implications for therapy," in Mathematical Modeling of Biological Systems, Volume I, Birkhäuser Boston, 2007, ch. 18, p. 205-216.
[14]         Y. Cai, S.X. Xu, J. Wu, Q. Long, "Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion,"J. Theor. Biol., vol. 279, no. 1, pp. 90-101, Jun, 2011.
[15]         J. Folkman,"Tumor angiogenesis: therapeutic implications," N Engl J Med, vol. 285, no. 2,pp. 1182-1186, Nov., 1971.
[16]         A.R.A. Anderson et al., "Mathematical modelling of tumour invasion and metastasis,"Comput Math Methods Med,vol. 2, no. 2, pp. 129-154, 2000.
[17]         I. Ramis-Conde, M.A.J. Chaplain, A.R.A. Alexander, "Mathematical modelling of cancer cell invasion of tissue,"Math Comput Model, vol. 47, no. 5,pp. 533-545, March, 2008.
[18]         H.B. Frieboes et al., "Three-dimensional multispecies nonlinear tumor growth-II: Tumor invasion and angiogenesis,"J. Theor. Biol., vol. 264, no. 4, pp. 1254-1278, Jun, 2010.
[19]         H. Levine, B.D. Sleeman, M. Nilsen-hamilton, "Mathematical modeling of the onset of capillary formation initiating angiogenesis,"J Math Biol, vol. 4, no. 3,pp. 195-238, March, 2001.
[20]         M.E. Orme, M.A.J. Chaplain, "A mathematical model of vascular tumour growth and invasion,"Math Comput Model,vol. 23, no. 10, pp. 43-60, May, 1996.
[21]         S. Sun et al., "A deterministic model of growth factor-inducedangiogenesis,"Bull. Math. Biol., vol. 67, no. 2, pp. 313-337, March, 2005.
[22]         V. Capasso, D. Morale, "Stochastic modelling of tumour-induced angiogenesis,"J Math Biol, vol. 58, no. 1-2 , pp. 219-233, Jan, 2009.
[23]         R.D.M Travasso et al., "Tumor angiogenesis and vascular patterning: amathematical model," PLoS One, vol. 6, no. 5, p. e19989, May, 2011.
[24]         P. Macklin et al., "Multiscale modelling and nonlinear simulation of vascular tumour growth," J Math Biol, vol. 58, no. 4-5, pp. 765-798, Apr., 2009.
[25]         A. Stéphanou et al., "Mathematical modelling of the influence of blood rheological properties upon adaptativetumour-induced angiogenesis,"Math Comput Model, vol. 44, no. 1, pp. 96-123, Jul., 2006.
[26]         J. Wu et al., "Coupled modeling of blood perfusion in intravascular, interstitial spaces in tumor microvasculature,"J Biomech, vol. 41, no. 5, pp. 996-1004, Dec., 2008.
[27]         J.A. Sherratt, M.A.J Chaplain, "A new mathematical model for avascular tumour growth,"J Math Biol, vol. 43, no. 4, pp. 291-312, Oct., 2001.
[28]         J.P. Ward, J.R. King, "Mathematical modelling of avascular-tumour growth II:Modelling growth saturation,"Math Med Biol, vol. 16, no. 2, pp. 171-211, Jun, 1999.
[29]         H.M. Byrne, M.A.J. Chaplain, "Mathematical models for tumour angiogenesis:numerical simulations and nonlinear wave solutions,"Bull. Math. Biol., vol. 57, no. 3, pp. 461-486, May, 1995.
[30]         M.E. Orme, M.A.J. Chaplain, "Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies,"Math Med Biol, vol. 14, no. 3, pp. 189-205, Sep., 1997.
[31]         C.J.W. Breward, H.M.Byme, C. E. Lewis "A multiphase model describing vascular tumour growth,"Bull. Math. Biol., vol. 65, no. 4, pp. 609-640, Jul., 2003.
[32]         C.J.W. Breward, H.M. Byrne, C.E. Lewis, "Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour,"Eur J Appl Math, vol. 12, no. 5, pp. 529-556, Oct., 2001.
[33]         P. Hahnfeldt et al.,"Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy,"Cancer Res,vol. 59, no. 19, pp. 4770–4775, Oct., 1999.
[34]         E. Bavafaye-Haghighi et al., "Multiscale cancer modeling: In the line of fast simulation and chemotherapy," Math Comput Model, vol. 49, no. 7, pp.1449-1464, Apr, 2009.
[35]         A. Stéphanou et al., "Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies,"Math Comput Model, vol. 41, no.10, pp. 1137-1156, May, 2005.
[36]         S. R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, "Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies,"J Therm Biol, vol. 241, no. 3,pp. 564-589, Aug, 2006.
[37]         S. R. McDougall et al, "Modelling the impact of pericyte migration and coverage of vessels on the efficacy of vascular disrupting agents,"MathModel Nat Phenom, vol. 5, no. 1, pp. 163-202, 2010.
[38]         A. R. A. Anderson et al., "Tumor morphology andphenotypic evolution driven by selective pressure from the microenvironment," Cell, vol. 127, no. 5, pp. 905-915, Dec, 2006.
[39]         R.P. Araujo, D.L.S. McElwain, "A mixture theory for the genesis of residual stresses in growing tissues II: solutions to the biphasic equations fora multicell spheroid,"SIAM J APPL MATH, vol. 66, no. 2, pp. 447-467, 2005.
[40]         P. Gerlee,A.R.A. Anderson, "Evolution of cell motility in an individual-based model of tumour growth,"J Therm Biol, vol. 259, no.1,pp. 67-83, Jul, 2009.
[41]         F. Hosseini, N. Naghavi, "Two dimensional  mathematical model of tumor angiogenesis: coupling of avascular growth and vascularization," Iranian Journal of Medical Physics, vol. 12, no. 3, pp.145-166, Sep, 2015.
[42]         F. Hosseini, N. Naghavi, "Modeling of tumor induced angiogenesis: combination of stochastic sprout spacing and sprout progression," Journal of Biomedical Physics and Engineering, Accepted.
[43]         N. Naghavi et al., "Simulation of tumor induced angiogenesis using an analytical adaptive modeling including dynamic sprouting and blood flow modeling," Microvasc. Res., 107, pp. 51-64, Sep, 2016.