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

Abstract

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-). 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 ( ). 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-. Coefficient of determination for both situations was 2 = 0.89 and 2 = 0.92, 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-, which is not in accordance with expected since the presence of TNF-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-increases the elasticity modulus of the cell layer.

Oral Mucosa Model for Electrochemotherapy Treatment of Dog Mouth Cancer: Ex Vivo, In Silico, and In Vivo Experiments

“…The relative permeabilized tissue conductivity (r MAX /r 0 ) was 3.5. This value is compatible with muscle (2.5-5 (11)(12)(13)(14)), connective tissues (3 (30)), and dermis (4 (16)) electroporation experiments. The threshold electric field values (E rev 5 20 kV/m and E irrev 5 80 kV/m) are similar to muscle electroporation models (12,13).…”

“…The intensity of applied electric field will be higher than necessary, and this EQT may produce tissue damage. The electroporation models present tissue electric conductivity dependent on local electric field (11)(12)(13)(14)18).…”

Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer

“…Regarding alternative computational models for skin cancer, we note the studies by Poleszczuk and Enderling (2013), Morais et al (2017), Gallinaro et al (2013) and Ciarletta et al (2001). In Poleszczuk and Enderling (2013), a cellular-automata framework for tumor growth in general has been developed.…”

“…The model by Morais et al (2017) is interesting in the sense that it incorporates more biological processes, like contact inhibition, it still is a somewhat more complicated model than our formalism with a larger number of parameters that are difficult to get from literature or measurements. Gallinaro et al (2013) model melanoma cell (melanocyte) migration by the use of an elastic continuum. Their approach is based on a system of ordinary differential equation to describe the displacement of the spatial coordinate in the tissue in a one-dimensional configuration.…”

“…We list three mathematical studies devoted to melanoma. The first study is due to Gallinaro et al (2013) and treats a model for melanoma cell migration with an elastic continuum. The second study by Morais et al (2017) treats a 2D probabilistic Widom-Rowlinson model that shares some features with the current model and with the model by Poleszczuk and Enderling (2013).…”