Modeling and Simulation Keloid Scar Formation from Biphasic Contact Blunt-Prosthesis

Article Preview

Abstract:

The definition of the "prosthetic man" system represents the recording, gathering data, identifying problems, formulating hypotheses and decision making for therapeutic interventions processes. The analyzing of this problem has led to the need to study in detail the changes that occur at the interface of the blunt-liner-socket. The mathematic methods of the kinetic theory can be used to develop models described by equations which characterizes the behavior of the particle group based on a description of the microscopically interactions. Interactions that are taken into account are as: conservative interactions that alter the microscopic activity; Proliferation or destruction interactions, the birth or death of a particle; stochastic interactions that modify speed according to a speed leap process. The causes of release and key changes responsible for the formation of a keloid scar remain elusive and there is no satisfactory treatment for this disorder. A current approach in tissue engineering is to use a three-dimensional precursor similar to a tissue of cells called matrix (scaffold) for growth (cell density localized spatially and temporally). We thus propose a mathematical model and its numerical implementation in Matlab, using finite differences, to describe the development and distribution of cells in such arrays. In addition, we propose an algorithm to optimize the model parameters in order to minimize the error occurred between the experimental data and the numerical generated data.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

489-494

Citation:

Online since:

October 2014

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] J.A. Sherratt, J.C. Dallon, Theoretical models of wound healing: past successes and future challenges, Comptes Rendus Biologies. 325(5) (2002) 557–564.

DOI: 10.1016/s1631-0691(02)01464-6

Google Scholar

[2] D. Ambrosia, et. all, Perspectives on biological growth and remodeling, Journal of the Mechanics and Physics of Solids. 59 (4), (2011) 863–883.

Google Scholar

[3] J. A. Adams, General aspects of modeling tumor growth and immune response in A Survey of Models for Tumor-Immune System Dynamics, Birkhauser, (1997).

DOI: 10.1007/978-0-8176-8119-7_2

Google Scholar

[4] C. Bianca, Mathematical modelling for keloid formation triggered by virus: malignant effects and immune system competition, Mathematical Models and Methods in Applied Sciences. 21(2) (2011) 389-419.

DOI: 10.1142/s021820251100509x

Google Scholar

[5] N. Bellomo, A. Bellouquid, On the mathematical kinetic theory of active particles with discrete states: The derivation of macroscopic equations, Mathematical and Computer Modelling. 44(3-4) (2006) 397-404.

DOI: 10.1016/j.mcm.2006.01.025

Google Scholar

[6] C. Bianca, N. Bellomo, Towards a mathematical theory of complex biological system, Mathematical Biology and Medicine, vol. 11, World Scientific, London, Singapore, (2010).

Google Scholar

[7] M. Turnea, M. Rotariu, D. Arotaritei, Mathematical Modeling and Simulation for Keloid Scars Formation for Prosthetic Blunt Socket, The 8th International Symposium on Advanced Topics in Electrical Engineering (ATEE). (2013) 1-4.

DOI: 10.1109/atee.2013.6563527

Google Scholar

[8] J. Lund, K.L. Bowers, Sinc Methods for Quadrature and Differential Equations, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (1992).

Google Scholar

[9] N. Bellomo, Modeling Complex Living Systems, A Kinetic Theory and Stochastic Game Approach, Birkhaüser Boston, (2008).

Google Scholar

[10] C. Bianca, L. Fermo, Bifurcation diagrams for the moments of a kinetic type model of keloid–immune system competition, Computers and Mathematics with Applications. 61 (2011) 277–288.

DOI: 10.1016/j.camwa.2010.11.003

Google Scholar

[11] J.C.Y. Dunn, et. all., Analysis of Cell Growth in Three-Dimensional Scaffolds, Tissue Eng. 12(4) (2006) 705-716.

Google Scholar