Composite Smeared Finite Element – Application to Electrical Field

Vladimir Geroski, Miljan Milosevic, Vladimir Simic, Bogdan Milicevic, Nenad Filipovic, Milos Kojic

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationLearning and Analytics in Intelligent Systems
PublisherSpringer Nature
Number of pages9
StatePublished - 2020

Publication series

NameLearning and Analytics in Intelligent Systems
ISSN (Print)2662-3447
ISSN (Electronic)2662-3455


  • Composite smeared finite element
  • Conductivity tensor
  • Electrophysiology
  • Ionic transport
  • Nerve network

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Control and Systems Engineering


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