The extremely complex biological and biochemical processes are mainly treated by laboratory and clinical investigations. In recent decades, the application of computational modeling has become more important in research and applications in the medical sciences. Despite enormous efforts and achievements in this modeling, there is still a need for new efficient and reliable methods, particularly within today's hot field – Artificial Intelligence (AI). In this report, we present a brief description of a methodology that we believe offers a basis for modeling gradient-driven physical fields in composite media, such as tissue. This methodology is based on the concept of multiscale smeared physical fields, termed the Kojic Transport Model (KTM), that is published in several journal papers and summarized in a recent book (Kojic et al. 2022). Our KTM includes modeling of partitioning, blood flow, molecular transport within the tissue, a multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. We present here two typical examples for the illustration of our KTM application.
Kojic M, Milosevic M, Ziemys A. *Computational Models in Biomedical Engineering – Finite Element Models Based on Smeared Physical Fields: Theory, Solutions, and Software*. 2022.
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Kojic M, Milosevic M, Simic V, Milicevic B, Terracciano R, Filgueira CS. On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic Transport Model. *Heliyon. 2024;10:263.
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Hyde ER, Michler C, Lee J, Cookson AN, Chabiniok R, Nordsletten DA, et al. Parameterisation of multi-scale continuum perfusion models from discrete vascular networks. *Med Biol Eng Comput. 2013;51:557–70.
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Gregorio S, Fedele M, Pontone G, Corno AF, Zunino P, Vergara C, et al. A multiscale computational model of myocardial perfusion in the human heart. 2019;
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Corrias A, Pathmanathan P, Gavaghan DJ, Buista ML. Modelling tissue electrophysiology with multiple cell types: applications of the extended bidomain framework. *Integr Biol. 2012;4:192–201.
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Kojic M. Smeared concept as a general methodology in finite element modeling of physical fields and mechanical problems in composite media. *J Serb Soc Comp Mech. 2018;12*(2:1–16.
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Kojic M, Milosevic M, Simic V, Koay EJ, Fleming JB, Nizzero S, et al. A composite smeared finite element for mass transport in capillary systems and biological tissue. *Comput Methods Appl Mech Eng. 2017;324:413–37.
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Kojic M, Milosevic M, Simic V, Koay EJ, Kojic N, Ziemys A, et al. 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. 2017;11*(2:108–20.
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Kojic M, Simic V, Milosevic M. Composite smeared finite element – some aspects of the formulation and accuracy. *IPSI Trans Adv Res. 2017;13*(2.
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Kojic M, Milosevic M, Simic V, Stojanovic D, Uskokovic P. A radial 1D finite element for drug release from drug loaded nanofibers. *J Serb Soc Comp Mech. 2017;11*(1:82–93.
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Kojic M, Milosevic M, Kojic N, Koay EJ, Fleming JB, Ferrari M, et al. Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue. Computers in Biology and Medicine. 2018;92:156–67.
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Kojic M, Milosevic M, Simic V, Koay EJ, Kojic N, Ziemys A, et al. Multiscale smeared finite element model for mass transport in biological tissue: from blood vessels to cells and cellular organelles. *Comput Biol Med. 2018;99:7–23.
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Kojic M, Milosevic M, Simic V, Ziemys A, Filipovic N, Ferrari M. Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue. *Comput Biol Med. 2019;108:288–304.
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Milosevic M, Simic V, Milicevic B, Koay EJ, Ferrari M, Ziemys A, et al. Correction function for accuracy improvement of the Composite Smeared Finite Element for diffusive transport in biological tissue systems. *Comput Methods Appl Mech. 2018;
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Milosevic M, Stojanovic D, Simic V, Milicevic B, Radisavljevic A, Uskokovic P, et al. A computational model for drug release from PLGA implant. *Materials. 2018;11*(12:2416.
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Milosevic M, Stojanovic DB, Simic V, Grkovic M, Bjelovic M, Uskokovic PS, et al. Preparation and modeling of three-layered PCL/PLGA/PCL fibrous scaffolds for prolonged drug release. *Sci Rep. 2020;10*(1:11126.
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Kojic M, Filipovic N, Milosevic M. PAK-KTM: Finite Element Program for Bioengineering Problems. 2006.
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Kojic M. Multiscale composite 3D finite element for lung mechanics. *J Serb Soc Comp Mech. 2020;14*(1:1–11.
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Kojic M, Milosevic M, Wu S, Blanco E, Ferrari M, Ziemys A. Mass partitioning effects in diffusion transport. *Phys Chem Chem Phys. 2015;17:20630–5.
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Kojic M. A multiscale multiphysics finite element for lung. *J Serb Soc Comp Mech. 2023;17*(2:1–15.
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Terracciano R, Milicevic B, Milosevic M, Simic V, Carcamo-Bahena Y, Royal ALR, et al. An insight into perfusion anisotropy within solid murine lung cancer tumors. 2023;
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Dimkic M, Rankovic V, Filipovic N, Stojanovic B, Isailovic V, Pusic M, et al. Modeling of radial well lateral screens using 1D finite elements. *J Hydroinformatics. 2013;15*(2:405–15.
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