Table of Contents
Journal of Computational Medicine
Volume 2013, Article ID 534073, 8 pages
Research Article

Mathematical Modeling of Melanoma Cell Migration with an Elastic Continuum Model for the Evaluation of the Influence of Tumor Necrosis Factor-Alpha on Migration

1Instituto de Engenharia Biomédica, Departamento de Engenharia Elétrica, CTC, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC, Brazil
2Centro de Ciências da Saúde e do Esporte, Universidade do Estado de Santa Catarina, 88080-350 Florianópolis, SC, Brazil

Received 18 April 2013; Revised 23 August 2013; Accepted 23 August 2013

Academic Editor: Hiroshi Watabe

Copyright © 2013 Julia Vianna Gallinaro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An elastic continuum mathematical model was implemented to study collective C8161 melanoma cell migration during a “scratch wound” assay, in control and under the influence of the proinflammatory cytokine tumour necrosis factor-alpha (TNF-α). The model has four constants: force that results from lamellipod formation (F), adhesion constant between cells and extracellular matrix (ECM) (b), cell layer elasticity modulus (k), and growth rate (ρ). A nonlinear regression routine was used to obtain the parameters of the model with data from an experiment made with C8161 melanoma cells, with and without TNF-α. Coefficient of determination for both situations was and , respectively. The parameters values obtained were similar to the ones found in the literature. However, the adhesion constant value decreased with the introduction of TNF-α, which is not in accordance with expected since the presence of TNF-α is associated with an increased expression of integrins that would promote an enhanced adhesion among cells. The model was used in a study relating to the adhesion constant and cell migration, and the results suggested that cell migration decreases with higher adhesion, which is also not in accordance with expected. These differences would not occur if it was considered that TNF-α increases the elasticity modulus of the cell layer.