Mortar Finite Element Method for solving cells response to applied electric field
Cesar Conopoima1; Bernardo Martins Rocha1; Iury Igreja1; Rodrigo Weber Dos Santos1
1 Universidade Federal de Juiz de Fora
doi:10.20906/CPS/CILAMCE2017-0097
Resumo
In this work we investigate the response of passive and active biological cell to an applied electrical field. This phenomenon is a two-stage process where cell polarization occurs at a time scale of microseconds, and change of physiological state of the cells occurs at the time scale of milliseconds. This problem is solved using a Mortar Finite Element Method (MFEM) that is characterized by the introduction of an additional variable, known as Lagrange multiplier. This additional variable allow to decouple the boundary value problem that describes the conservation of electrical flux from the non-linear initial value system related to the response of active cells. This two problems are solved sequentially, within the time integration scheme. The proposed method allows to solve arbitrary cells distribution in tissues and complex ion-channel dynamics at the membrane. In order to validate the presented methodology, numerical results are compared with exact solutions of isolated circular cells in an applied electrical field. Finally, to demonstrate the robustness of the method, applied electrical field in clusters of cells and arbitrary cell geometry problems are solved.
Palavras-chave: Mortar finite element method; Lagrange multiplier; Cell polarization; Active cell response