Trends in Applied Sciences Research1819-35792151-7908Science International10.3923/tasr.2012.132.141AhmadianAli Bin SuleimanMohamed IsmailFudziah 2201272This study is developed a mathematical model to describe interactions between tumor cells and a compliant blood vessel that supplies oxygen to the region. In addition to proliferating, it is assumed that the tumor cells die through apoptosis and necrosis. It is also assumed that pressure differences within the tumor mass, caused by spatial variations in proliferation and degradation, cause cell motion. The behavior of the blood vessel is coupled into the model for the oxygen tension. The model equations tracked the evolution of the densities of live and dead cells, the oxygen tension within the tumor, the live and dead cell speeds, the pressure and the width of the blood vessel. This study presented the exact solutions to the model for certain parameter regimes and then solve the model with artificial neural networks for more general parameter regimes. This study also showed the resulting steady-state and porous medium behavior varies as the time is changed.]]>Ahmadian, A. and R. Afsharinafar,20111138073810Ali, R., A.M. Alabsi, A.M. Ali, Ainideris, A.R. Omar and K. Yousoff,201172535Alberts, B., D. Bray, J. Lewis, M. Raff, K. Roberts and J.D. Watson,19943rd Edn.,Pages: 1408Pages: 1408Al-Daoud, E.,200925664Asadollahi-Baboli, M.,20114257268Bicknell, R., C.E. Lewis and N. Ferrara,1997Pages: 281Pages: 281Byrne, H.M. and M.A. Chaplain,199557461486Effati, S. and M. Pakdaman,201018014341457El-Naggar, S.A., A.A. El-Brabary, M.A. Mansour, F. Abdel-Shafy and S. Talat,20117278288Folkman, J.,195043175203 Yazdi, H.S., M. Pakdaman and H. Modaghegh,20117420622071Hahnfeldt, P., D. Panigrahy, J. Folkman and L. Hlatky,19995947704775Holmgren, L., M.S. O'Reilly and J. Folkman,19951149153Homaei-Shandiz, F., G. Maddah, A. Aledavood, M.M. Marjaneh and K. Ghaffarzadehgan et al.,200955357Khalaf, E.F., K. Daqrouq and M. Sherif,20111129402946Lagaris, I.E., A. Likas and D.I. Fotiadis,199899871000Looi, M.L., M.D.A.Z. Hatta, M.A.S. Aishah, M.H. Baizurah, W.N. Wan Zurinah and M.Y.Y. Anum,20062212218Myers, T.G.,1996Olanrewaju R.F., O.O. Khalifa, A. Abdullah, A.A. Aburas and A.M. Zeki,20111129072915Senol, D. and M. Ozturan,200817077Sodde, V., N. Dashora, K.S. Prabhu and R. Lobo,2011Macrosolen parasiticus (L.) danser on ehrlich's ascites carcinoma treated mice.]]>7135143Tortoe, C., J. Orchard, A. Beezer and J. Teetheh,20114233244Kumar, R.V., V. Ravikumar, K.S. Shivashangari, S. Kamaraj and T. Devaki,20062224233Yu, K.C., Y.H. Hung, S.H. Hsieh and S.J. Hung,20111130083014