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Finite Element Models with Smeared Fields Within Tissue – A Review of the Current Developments

  • Milos KojicEmail author
  • Miljan Milosevic
  • Vladimir Simic
  • Vladimir Geroski
  • Bogdan Milicevic
  • Arturas Ziemys
  • Nenad Filipovic
Conference paper
  • 29 Downloads
Part of the Learning and Analytics in Intelligent Systems book series (LAIS, volume 11)

Abstract

In this review we present the current stage and developments in the finite element modeling of mass transport by the smeared concept, introduced and conducted by the first author over several years. The basis of this methodology represents the formulation of a composite smeared finite element (CSFE). The CSFE consists of domains which can be at different length scale, where we have separate physical fields for each of the domains and with the corresponding governing laws. The continuum domains within the CSFE also include 1D transport represented in a continuum form by the appropriate transport tensors. The fields are coupled by the connectivity elements at each node, representing transport properties of the walls separating the domains. Formulation of this methodology and applications on various biomedical problems have been published in a number of recent publications. Here, we give an overview of these achievements and show some results of the current research.

Keywords

Smeared finite element methodology Composite smeared finite element Biological systems Multiscale models 

Notes

Acknowledgments

The authors acknowledge support from the City of Kragujevac, Serbia.

Funding

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

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

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