Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc15792/doc.pdf Дата изменения: Mon Oct 29 13:21:34 2007 Дата индексирования: Mon Oct 1 20:43:35 2012 Кодировка:

.., .. () . , , , , , . Influence of cell motility on the stability of the tumour shape in the pre-angiogenic stage of growth Kolobov A.V., Polezhaev A.A. (Moscow) Influence of individual cellular motility on the tumour shape is investigated by means of a mathematical model. It is shown that the tumour shape is stable for any perturbation in the case of high cell motility while low cell motility results in breaking of stability of the tumour boundary that may lead to tumour growth in the predominant direction of nutrient source. , . : [1]. , . , 320


.. . -- -10, 2002, .320-321

, [2]. ; [1]. , . , , , , , [3]. , (necrotic zone) , , (viable rim), [4]. in vitro. , . , ( ) [5]. , . , . [5]. , , . , - [6,7]. , , ,
321


3. (II)

, , , - (in vitro) , , . , [8]. , . , . , (feelers). . . , , [9]: · , h. · `n', `m' . · B , P S () . . · , , DS
322


.. . -- -10, 2002, .320-323

Q(n,S). . · , Dn . (V ­ ), [10]. , , :
n = Bn - P ( S )n - .J , n t m = P( S )n - .J , m t S = -Q(n, S ) + D S , S t h = F - .J h h t (1)

.Ji ­ , , . , , , : n+m+h=1 (2) . (2) (1) [10]. :

323


3. (II)



n t m t S t

= Bn - n - P( S )n + .( Dn (1 - n )n ) - (n, ), = P( S )n - m - .( Dn mn ) - (m, ), = -Q ( n, S ) + DS S , = = Bn + Fh ,

- , (V=).

. 1. ( Dn=0,05) . (A ­ 1 ,B ­ 6 ,C ­ 11 ). z n, x,y ­ . (100;0) ( ) . n=0,4 . : B=0,05; qS=0,3; S*=0,03; DS=103.
324


.. . -- -10, 2002, .320-325

Fh. , Fh=0. - P(S) - Q(n,S) [9]. (3) x[0,500], y[0,100]. (x=0, y=0, y=100) . x=500 S=1 (), , , . , , - . x=0. . . , , , . , , , . , , , . 1 , , , . , , (, - ) , , . 2 , 325


3. (II)

, , . , , , , .

. 2. ( Dn=2,0) . (A ­ 2 ,B ­ 4 ,C ­ 7 ). ( ) 1.

, . 3 , , , .
326


.. . -- -10, 2002, .320-327

.

. 3. ( Dn=2,0) . (A ­ 2 ,B ­ 4 ,C ­ 6 ). z n, x,y ­ . 1 (100;0) , . 1.

, , , , , . . 327


3. (II)

. , , ( ) . ( ), , . , , . , , , in vitro , .
02-01-00064 .

. 1. J.Folkman. Tumour angiogenesis: Therapeutic implications. N.Engl.J.Med., 285 (1971),1182-86. 2. Freyer J.P. and Sutherland R.M. Regulation of growth saturation and development of necrosis in EMT6/Ro spheroids gluose and oxygen supply. Cancer Res., 46 (1986), 3504-12. 3. Liotta, L. A., Kleinerman, J., and Saidel, G. M. Quantitative relationships of intravascular tumor cells, tumor vessels, and pulmonary metastases following tumor implantation. Cancer Res., 34 (1974), 997­1004. 4. Adam J.A. A mathematical model of tumour growth: Effects of geometry and symmetry. Math.Biosci., 86 (1987), 183-211. 5. Holash J., Wiegand S.J. and Yancopoulos G.D. New model of tumour angiogenesis: dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF. Oncogene, 18 (1999), 5356-62. 6. Byrne H.M. and Matthews P. Asymmetric growth of models of avascular solid tumours: exploiting symmetries. IMA J.Math.Appl.Med.Biol., 19 (2002),1-29.
328


.. . -- -10, 2002, .320-329

7. Byrne H.M. and Chaplain M.A.J. Modelling of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Model., 24 (1996), 1-17. 8. Siegel, G., Malmsten, M. and Klussendorf, D. Tumor cell locomotion and metastatic spread. Microscopy Research and Technique, 43 (1998), 276-282. 9. Kolobov A.V., Polezhaev A.A. and Solyanik G.I. The Role of cell motility in metastatic cell dominance phenomenon: Analysis by a mathematical model. J. Theor.Med., 3 (2000), 63-77. 10. Gusev, A. and Polezhaev A. Modelling of a cell population evolution for the case existence of maximal possible total cell density. Kratkie soobscheniya po fizike FIAN, 11-12 (1997), 85-90. 11. Wyckoff J.B., Jones J.G., Condeelis J.S. and Segall J.E. A Critical Step in Metastasis: In vivo analysis of intravasation at the primary tumor. Cancer Res., 60 (2000), 2504­2511. 12. Bhujwalla Z.M., Artemov D., Natarajan K., Ackerstaff E. and Solaiyappan M. Vascular differences detected by MRI for metastatic versus nonmetastatic breast and prostate cancer xenografts. Neoplasia 2001 Mar-Apr, 3(2), 143-53.

329