Composite Smeared Finite Element – Application to Electrical Field
- 29 Downloads
In this paper we present application of recently developed composite smeared finite element (CSFE) to electrophysiology problems and ionic transport, mainly in heart tissue. The main advantage of the CSFE is that discrete transport, approximated by 1D finite elements within nervous system, can be transformed into a continuum framework. The governing balance equation for electrical flow within neuron fibers is defined according to the cable theory. This governing equation is then transformed into continuum format represented by formulating a conductivity tensor. We include transport of ions which affects the electrical potential, therefore there exists a coupling between ion concentration and the electrical field. Besides general presentation of the smeared FE methodology, we give some additional details regarding the derivation of the coupling relations within the CSFE, and also accuracy analysis of the element. Accuracy is tested on several simple 2D and 3D examples of Purkinje fibers network with different electrical potential. Using the smeared field approach, we can analyze various complex problems in a simple form, with all important physical properties included in the model.
KeywordsComposite smeared finite element Electrophysiology Nerve network Ionic transport Conductivity tensor
The authors acknowledge support from the City of Kragujevac, Serbia.
This work is supported by the grant NCI U54 CA210181. Also, it is supported by the SILICOFCM project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 777204. This research was also funded by Ministry of Education and Science of Serbia, grants OI 174028 and III 41007.
- 1.Kojic, M., Milosevic, M., Simic, V., Koay, E.J., Fleming, J.B., Nizzero, S., Kojic, N., Ziemys, A., Ferrari, M.: A composite smeared finite element for mass transport in capillary systems and biological tissue. Comp. Meth. Appl. Mech. Engrg. 324, 413–437 (2017). https://doi.org/10.1016/j.cma.2017.06.019MathSciNetCrossRefGoogle Scholar
- 2.Kojic, M., Milosevic, M., Simic, V., Koay, E.J., Kojic, N., Ziemys, A., Ferrari, M.: Extension of the composite smeared finite element (CSFE) to include lymphatic system in modeling mass transport in capillary systems and biological tissue. J. Serb. Soc. Comp. Mech. 11(2), 108–120 (2017)CrossRefGoogle Scholar
- 3.Milosevic, M., Simic, V., Milicevic, B., Koay, E.J., Ferrari, M., Ziemys, A., Kojic, M.: Correction function for accuracy improvement of the composite smeared finite element for diffusive transport in biological tissue systems. Comput. Methods Appl. Mech. Eng. 338, 97–116 (2018). https://doi.org/10.1016/j.cma.2018.04.012. ISSN 0045-7825MathSciNetCrossRefGoogle Scholar
- 4.Kojic, M., Milosevic, M., Simic, V., Koay, E.J., Kojic, N., Ziemys, A., Ferrari, M.: Multiscale smeared finite element model for mass transport in biological tissue: from blood vessels to cells and cellular organelles. Comput. Biol. Med. 99, 7–23 (2018). https://doi.org/10.1016/j.compbiomed.2018.05.022CrossRefGoogle Scholar
- 11.Kojic, M., Simic, V., Milosevic, M.: Composite smeared finite element - some aspects of the formulation and accuracy. IPSI Trans. Internet Res. (2017)Google Scholar
- 12.Costabal, F.S., Hurtado, D.E., Kuhl, E.: Generating Purkinje networks in the human heart. J. Biomech. 49, 2455–2465 (2016)Google Scholar