Composite Smeared Finite Element – Application to Electrical Field

  • Vladimir Geroski
  • Miljan MilosevicEmail author
  • Vladimir Simic
  • Bogdan Milicevic
  • Nenad Filipovic
  • Milos Kojic
Conference paper
Part of the Learning and Analytics in Intelligent Systems book series (LAIS, volume 11)


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.


Composite 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.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vladimir Geroski
    • 1
  • Miljan Milosevic
    • 2
    • 3
    Email author
  • Vladimir Simic
    • 1
    • 2
  • Bogdan Milicevic
    • 1
    • 2
  • Nenad Filipovic
    • 1
  • Milos Kojic
    • 2
    • 4
    • 5
  1. 1.Faculty for Engineering SciencesUniversity of KragujevacKragujevacSerbia
  2. 2.Bioengineering Research and Development Center BioIRC KragujevacKragujevacSerbia
  3. 3.Belgrade Metropolitan UniversityBelgradeSerbia
  4. 4.The Department of NanomedicineHouston Methodist Research InstituteHoustonUSA
  5. 5.Serbian Academy of Sciences and ArtsBelgradeSerbia

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