NIGERIAN JOURNAL OF SCIENCE AND ENVIRONMENT
Journal of the Faculties of Science and Agriculture, Delta State University, Abraka, Nigeria

ISSN: 1119-9008
DOI: 10.5987/UJ-NJSE
Email: njse@universityjournals.org


ON THE SOLUTIONS OF S-GTR AND D-GTR EQUATIONS OF BONE TISSUE REGENERATION MODELS

DOI: 10.5987/UJ-NJSE.17.119.1   |   Article Number: B32AE618   |   Vol.11 (1) - September 2012

Author:  Arunaye F. I.

In Arunaye and Ogunsalu (2010), we obtained mathematical models for osteobstruction in bone regeneration mechanism for skeletal tissue engineering procedures. In this paper we obtain the Lie point symmetries and hence the invariant solutions of these mathematical models for Bone tissue regeneration in 1-D systems.

Arunaye, F.I. and B.S. Bhatt. (2010). Group invariant solutions of evolution equations for composites. World Journal of Engineering. 7(3): 93-95.

Arunaye, F.I., Bhatt, B.S. and Nagarani, P. (2011). On the solution of the convective-diffusion equation. International Journal of Pure and Applied Mathematics 68(1): 37-53.

Arunaye, F.I. and Bhatt, B.S. (2011). Group invariant solutions for Fisher and Huxley’sequations for gene transportation. International Journal of Pure and Applied Sciences and Technology In Press with ISSN 2229–6107.

Arunaye, F.I. and Ogunsalu C. (2010). Bone regeneration model (a new phenomenon in bone grafting). World Journal of Engineering. 7 (Suppl. 2): 160-162.

Bhatt, B.S., and Krishnan, E.V. (1995). Group invariant solutions of unsteady flow equations. Advances in Modelling and Analysis. A. AMSE Press 29(2): 1-10.

Bluman, G.W., and Anco. S.O. (2002). Symmetry and Integration methods for Differential Equations. Springer-Verlag, New York.

Bluman, G.W. and Kumei, S. (1989). Symmetries and Differntial Equations. Spriger-Verlag, New York.

Butler, D.L., Goldstein, S.A. and Guilik, F. (2000). Functional Tissue Engineering: The Role of Biomechanics. Transactions of the ASME. 122: 570-575.

Ogunsalu, C., Arunaye, F., Ezeokoli, C., Gardner, M.T., Rohrer, M. and Prasad, H. (2010). Mathematical model for osteobstruction in Bone Regeneration mechanism; A headway in skeletal tissue engineering. Oral Surgery, Oral Medicine,Oral Pathology, Oral Radiology and Endodontology 110 (3): 315-16.

Olver, P.J. (1993). Applications of Lie Groups to Differential Equations 2nd ed. Springer-Verlag, New York.

Saglio, A.J., Coutinho, O.P. and Reis, R.L. (2004). Bone tissue engineering: State of the art and future trends. Macromolecular Bioscience. 4:743-765.

Stephani, H. (1989). Differential equations: Their solution using symmetries. Cambridge University Press, New York