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2020 | OriginalPaper | Buchkapitel

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

verfasst von : Milos Kojic, Miljan Milosevic, Vladimir Simic, Vladimir Geroski, Bogdan Milicevic, Arturas Ziemys, Nenad Filipovic

Erschienen in: Computational Bioengineering and Bioinformatics

Verlag: Springer International Publishing

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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.

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Literatur
1.
Zurück zum Zitat Kojic, M., Filipovic, N., Stojanovic, B., Kojic, N.: Computer Modeling in Bioengineering - Theoretical Background, Examples and Software. Wiley, Chichester (2008)CrossRef Kojic, M., Filipovic, N., Stojanovic, B., Kojic, N.: Computer Modeling in Bioengineering - Theoretical Background, Examples and Software. Wiley, Chichester (2008)CrossRef
2.
Zurück zum Zitat Less, J.R., Skalak, T.C., Sevick, E.M., Jain, R.K.: Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions. Cancer Res. 51, 265–273 (1991) Less, J.R., Skalak, T.C., Sevick, E.M., Jain, R.K.: Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions. Cancer Res. 51, 265–273 (1991)
3.
Zurück zum Zitat Roberts, W.G., Palade, G.E.: Neovasculature induced by vascular endothelial growth factor is fenestrated. Cancer Res. 57, 765–772 (1997) Roberts, W.G., Palade, G.E.: Neovasculature induced by vascular endothelial growth factor is fenestrated. Cancer Res. 57, 765–772 (1997)
4.
Zurück zum Zitat Sevick, E.M., Jain, R.K.: Geometric resistance to blood flow in solid tumors perfused ex vivo: effects of tumor size and perfusion pressure. Cancer Res. 49, 3506–3512 (1989) Sevick, E.M., Jain, R.K.: Geometric resistance to blood flow in solid tumors perfused ex vivo: effects of tumor size and perfusion pressure. Cancer Res. 49, 3506–3512 (1989)
5.
Zurück zum Zitat Sevick, E.M., Jain, R.K.: Viscous resistance to blood flow in solid tumors: effect of hematocrit on intratumor blood viscosity. Cancer Res. 49, 3513–3519 (1989) Sevick, E.M., Jain, R.K.: Viscous resistance to blood flow in solid tumors: effect of hematocrit on intratumor blood viscosity. Cancer Res. 49, 3513–3519 (1989)
6.
Zurück zum Zitat Sevick, E.M., Jain, R.K.: Effect of red blood cell rigidity on tumor blood flow: increase in viscous resistance during hyperglycemia. Cancer Res. 51(51), 2727–2730 (1991) Sevick, E.M., Jain, R.K.: Effect of red blood cell rigidity on tumor blood flow: increase in viscous resistance during hyperglycemia. Cancer Res. 51(51), 2727–2730 (1991)
7.
Zurück zum Zitat Jain, R.: Determinants of tumor blood flow: a review. Cancer Res. 48, 2641–2658 (1988) Jain, R.: Determinants of tumor blood flow: a review. Cancer Res. 48, 2641–2658 (1988)
8.
Zurück zum Zitat Rangamani, P., Iyengar, R.: Modelling spatio-temporal interactions within the cell. J. Biosci. 32, 157–167 (2007)CrossRef Rangamani, P., Iyengar, R.: Modelling spatio-temporal interactions within the cell. J. Biosci. 32, 157–167 (2007)CrossRef
9.
Zurück zum Zitat Schaff, J., Fink, C.C., Slepohenko, B., Carson, J.H., Loew, L.M.: A general computational framework for modeling cellular structure and function. Biophys. J. 73, 1135–1146 (1997)CrossRef Schaff, J., Fink, C.C., Slepohenko, B., Carson, J.H., Loew, L.M.: A general computational framework for modeling cellular structure and function. Biophys. J. 73, 1135–1146 (1997)CrossRef
10.
Zurück zum Zitat Moraru, I.I., Schaff, J.C., Slepchenko, B.M., Blinov, M.L., Morgan, F., Lakshminarayana, A., Gao, F., Li, Y., Loew, L.M.: Virtual cell modelling and simulation software environment. IET Syst. Biol. 2, 352–362 (2008)CrossRef Moraru, I.I., Schaff, J.C., Slepchenko, B.M., Blinov, M.L., Morgan, F., Lakshminarayana, A., Gao, F., Li, Y., Loew, L.M.: Virtual cell modelling and simulation software environment. IET Syst. Biol. 2, 352–362 (2008)CrossRef
11.
Zurück zum Zitat Lipowsky, H.H., Zweifach, B.W.: Network analysis of microcirculation of cat mesentery. Microvasc. Res. 7, 73–83 (1974)CrossRef Lipowsky, H.H., Zweifach, B.W.: Network analysis of microcirculation of cat mesentery. Microvasc. Res. 7, 73–83 (1974)CrossRef
12.
Zurück zum Zitat Kojic, M., Milosevic, M., Simic, V., Ferrari, M.: A 1D pipe finite element with rigid and deformable walls. J. Serbian Soc. Comput. Mech. 8, 38–53 (2014)CrossRef Kojic, M., Milosevic, M., Simic, V., Ferrari, M.: A 1D pipe finite element with rigid and deformable walls. J. Serbian Soc. Comput. Mech. 8, 38–53 (2014)CrossRef
13.
Zurück zum Zitat Isailovic, V., Kojic, M., Milosevic, M., Filipovic, N., Kojic, N., Ziemys, A., Ferrari, M.: A computational study of trajectories of micro- and nano-particles with different shapes in flow through small channels. J. Serbian Soc. Comput. Mech. 8, 14–28 (2014)CrossRef Isailovic, V., Kojic, M., Milosevic, M., Filipovic, N., Kojic, N., Ziemys, A., Ferrari, M.: A computational study of trajectories of micro- and nano-particles with different shapes in flow through small channels. J. Serbian Soc. Comput. Mech. 8, 14–28 (2014)CrossRef
14.
Zurück zum Zitat Kiseliovas, V., Milosevic, M., Kojic, M., Mazutis, L., Kai, M., Liu, Y.T., Yokoi, K., Ferrari, M., Ziemys, A.: Tumor progression effects on drug vector access to tumor-associated capillary bed. J. Controlled Release 261, 216–222 (2017)CrossRef Kiseliovas, V., Milosevic, M., Kojic, M., Mazutis, L., Kai, M., Liu, Y.T., Yokoi, K., Ferrari, M., Ziemys, A.: Tumor progression effects on drug vector access to tumor-associated capillary bed. J. Controlled Release 261, 216–222 (2017)CrossRef
15.
Zurück zum Zitat Kojić, N., Milošević, M., Petrović, D., Isailović, V., Sarioglu, A.F., Haber, D.A., Kojić, M., Toner, M.: A computational study of circulating large tumor cells traversing microvessels. Comput. Biol. Med. 63, 187–195 (2015)CrossRef Kojić, N., Milošević, M., Petrović, D., Isailović, V., Sarioglu, A.F., Haber, D.A., Kojić, M., Toner, M.: A computational study of circulating large tumor cells traversing microvessels. Comput. Biol. Med. 63, 187–195 (2015)CrossRef
16.
Zurück zum Zitat Ziemys, A., Kojic, M., Milosevic, M., Kojic, N., Hussain, F., Ferrari, M., Grattoni, A.: Hierarchical modeling of diffusive transport through nanochannels by coupling molecular dynamics with finite element method. J. Comput. Phys. 230, 5722–5731 (2011)CrossRef Ziemys, A., Kojic, M., Milosevic, M., Kojic, N., Hussain, F., Ferrari, M., Grattoni, A.: Hierarchical modeling of diffusive transport through nanochannels by coupling molecular dynamics with finite element method. J. Comput. Phys. 230, 5722–5731 (2011)CrossRef
17.
Zurück zum Zitat Ziemys, A., Kojic, M., Milosevic, M., Ferrari, M.: Interfacial effects on nanoconfined diffusive mass transport regimes. Phys. Rev. Lett. 108, 236102 (2012)CrossRef Ziemys, A., Kojic, M., Milosevic, M., Ferrari, M.: Interfacial effects on nanoconfined diffusive mass transport regimes. Phys. Rev. Lett. 108, 236102 (2012)CrossRef
18.
Zurück zum Zitat Kojic, M., Milosevic, M., Kojic, N., Ferrari, M., Ziemys, A.: On diffusion in nanospace. J. Serbian Soc. Comput. Mech. 5, 84–109 (2011) Kojic, M., Milosevic, M., Kojic, N., Ferrari, M., Ziemys, A.: On diffusion in nanospace. J. Serbian Soc. Comput. Mech. 5, 84–109 (2011)
19.
Zurück zum Zitat Kojic, M., Milosevic, M., Kojic, N., lsailovic, V., Petrovic, D., Filipovic, N., Ferrari, M., Ziemys, A.: Transport phenomena: computational models for convective and diffusive transport in capillaries and tissue. In: De, S., Hwang, W., Kuhl, E. (eds.) Multiscale Modeling in Biomechanics and Mechanobiology, pp. 131–156. Springer, London (2015)CrossRef Kojic, M., Milosevic, M., Kojic, N., lsailovic, V., Petrovic, D., Filipovic, N., Ferrari, M., Ziemys, A.: Transport phenomena: computational models for convective and diffusive transport in capillaries and tissue. In: De, S., Hwang, W., Kuhl, E. (eds.) Multiscale Modeling in Biomechanics and Mechanobiology, pp. 131–156. Springer, London (2015)CrossRef
20.
Zurück zum Zitat Kojic, M., Ziemys, A., Milosevic, M., Isailovic, V., Kojic, N., Rosic, M., Filipovic, N., Ferrari, M.: Transport in biological systems. J. Serbian Soc. Comput. Mech. 5, 101–128 (2011) Kojic, M., Ziemys, A., Milosevic, M., Isailovic, V., Kojic, N., Rosic, M., Filipovic, N., Ferrari, M.: Transport in biological systems. J. Serbian Soc. Comput. Mech. 5, 101–128 (2011)
21.
Zurück zum Zitat Kojic, M., Milosevic, M., Kojic, N., Kim, K., Ferrari, M., Ziemys, A.: A multiscale MD–FE model of diffusion in composite media with internal surface interaction based on numerical homogenization procedure. Comput. Methods Appl. Mech. Eng. 269, 123–138 (2014)MathSciNetCrossRef Kojic, M., Milosevic, M., Kojic, N., Kim, K., Ferrari, M., Ziemys, A.: A multiscale MD–FE model of diffusion in composite media with internal surface interaction based on numerical homogenization procedure. Comput. Methods Appl. Mech. Eng. 269, 123–138 (2014)MathSciNetCrossRef
22.
Zurück zum Zitat Yokoi, K., Kojic, M., Milosevic, M., Tanei, T., Ferrari, M., Ziemys, A.: Capillary-wall collagen as a biophysical marker of nanotherapeutic permeability into the tumor microenvironment. Cancer Res. 74, 4239–4246 (2014)CrossRef Yokoi, K., Kojic, M., Milosevic, M., Tanei, T., Ferrari, M., Ziemys, A.: Capillary-wall collagen as a biophysical marker of nanotherapeutic permeability into the tumor microenvironment. Cancer Res. 74, 4239–4246 (2014)CrossRef
23.
Zurück zum Zitat Ruiz-Esparza, G.U., Wu, S., Segura-Ibarra, V., Cara, F.E., Evans, K.W., Milosevic, M., Ziemys, A., Kojic, M., Meric-Bernstam, F., Ferrari, M., Blanco, E.: Polymer nanoparticles encased in a cyclodextrin complex shell for potential site- and sequence-specific drug release. Adv. Funct. Mater. (2014). https://doi.org/10.1002/adfm.201400011 Ruiz-Esparza, G.U., Wu, S., Segura-Ibarra, V., Cara, F.E., Evans, K.W., Milosevic, M., Ziemys, A., Kojic, M., Meric-Bernstam, F., Ferrari, M., Blanco, E.: Polymer nanoparticles encased in a cyclodextrin complex shell for potential site- and sequence-specific drug release. Adv. Funct. Mater. (2014). https://​doi.​org/​10.​1002/​adfm.​201400011
24.
Zurück zum Zitat Kojic, M., Milosevic, M., Kojic, N., Starosolski, Z., Ghaghada, K., Serda, R., Annapragada, A., Ferrari, M., Ziemys, A.: A multi-scale FE model for convective-diffusive drug transport within tumor and large vascular networks. Comput. Methods Appl. Mech. Eng. 294, 100–122 (2015)MathSciNetCrossRef Kojic, M., Milosevic, M., Kojic, N., Starosolski, Z., Ghaghada, K., Serda, R., Annapragada, A., Ferrari, M., Ziemys, A.: A multi-scale FE model for convective-diffusive drug transport within tumor and large vascular networks. Comput. Methods Appl. Mech. Eng. 294, 100–122 (2015)MathSciNetCrossRef
26.
Zurück zum Zitat 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. Serbian Soc. Comput. Mech. 11(2), 108–120 (2017)CrossRef 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. Serbian Soc. Comput. Mech. 11(2), 108–120 (2017)CrossRef
27.
29.
Zurück zum Zitat Kojic, M.: Smeared concept as a general methodology in finite element modeling of physical fields and mechanical problems in composite media. J. Serbian Soc. Comput. Mech. 12(2), 1–16 (2018)CrossRef Kojic, M.: Smeared concept as a general methodology in finite element modeling of physical fields and mechanical problems in composite media. J. Serbian Soc. Comput. Mech. 12(2), 1–16 (2018)CrossRef
30.
Zurück zum Zitat 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. 108, 288–304 (2019)CrossRef 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. 108, 288–304 (2019)CrossRef
32.
Zurück zum Zitat Zhang, X., Shedden, K., Rosania, G.R.: A cell-based molecular transport simulator for pharmacokinetic prediction and cheminformatic exploration. Molec. Pharm. 3, 704–716 (2006)CrossRef Zhang, X., Shedden, K., Rosania, G.R.: A cell-based molecular transport simulator for pharmacokinetic prediction and cheminformatic exploration. Molec. Pharm. 3, 704–716 (2006)CrossRef
33.
Zurück zum Zitat Noble, D.: A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 160, 317–352 (1962)CrossRef Noble, D.: A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 160, 317–352 (1962)CrossRef
34.
Zurück zum Zitat O’Hara, T., Virág, L., Varró, A., Rudy, Y.: Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation. PLoS Comput. Biol. 7, e1002061–e1002090 (2011)CrossRef O’Hara, T., Virág, L., Varró, A., Rudy, Y.: Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation. PLoS Comput. Biol. 7, e1002061–e1002090 (2011)CrossRef
35.
Zurück zum Zitat Hunter, P.J., McCulloch, A.D., ter Keurs, H.E.D.J.: Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69, 289–331 (1998)CrossRef Hunter, P.J., McCulloch, A.D., ter Keurs, H.E.D.J.: Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69, 289–331 (1998)CrossRef
36.
Zurück zum Zitat Kojic, M., Milosevic, M., Simic, V., Milicevic, B., Geroski, V., Nizzero, S., Ziemys, A., Filipovic, N., Ferrari, M.: Smeared multiscale finite element models for mass transport and electrophysiology coupled to muscle mechanics. Front. Bioeng. Biotechnol. 7, 381 (2019)CrossRef Kojic, M., Milosevic, M., Simic, V., Milicevic, B., Geroski, V., Nizzero, S., Ziemys, A., Filipovic, N., Ferrari, M.: Smeared multiscale finite element models for mass transport and electrophysiology coupled to muscle mechanics. Front. Bioeng. Biotechnol. 7, 381 (2019)CrossRef
37.
Zurück zum Zitat Ziemys, A., Yokoi, K., Kai, M., Liu, Y.T., Kojic, M., Simic, V., Milosevic, M., Holder, A., Ferrari, M.: Progression-dependent transport heterogeneity of breast cancer liver metastases as a factor in therapeutic resistance. J. Controlled Release 291, 99–105 (2018). ISSN 0168–3659CrossRef Ziemys, A., Yokoi, K., Kai, M., Liu, Y.T., Kojic, M., Simic, V., Milosevic, M., Holder, A., Ferrari, M.: Progression-dependent transport heterogeneity of breast cancer liver metastases as a factor in therapeutic resistance. J. Controlled Release 291, 99–105 (2018). ISSN 0168–3659CrossRef
Metadaten
Titel
Finite Element Models with Smeared Fields Within Tissue – A Review of the Current Developments
verfasst von
Milos Kojic
Miljan Milosevic
Vladimir Simic
Vladimir Geroski
Bogdan Milicevic
Arturas Ziemys
Nenad Filipovic
Copyright-Jahr
2020
DOI
https://doi.org/10.1007/978-3-030-43658-2_3

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