Application of Composite Smeared Finite Element Model in Drug Delivery Inside Organs
- 26 Downloads
We here implement the smeared field finite element methodology, formulated by the last listed author, which is presented in numerous of recent publications. This methodology enables modeling physical fields in biological systems in a simple way, which otherwise, by detailed representation of each biological constituents (capillaries, cell membranes, cell interior, etc.), would not be practical to use. Here we summarize the basic concept of the smeared modeling by describing briefly formulation of a composite smeared finite element (CSFE). Besides the standard FE representation of continuum fields of molecular transport, 1D transport is included in a continuum form using the appropriate transport tensors. Physical fields are coupled by the connectivity elements at each node, representing transport properties of the walls separating the domains. In this paper, methodology is applied to determine concentration field within liver of a mouse, generated from images, containing a tumor. Also, evolution of drug concentration within tumor is presented, which is important for improvement of cancer therapy.
The authors acknowledge support from the City of Kragujevac, Serbia.
This work 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.
- 2.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)Google Scholar
- 3.Roberts, W.G., Palade, G.E.: Neovasculature induced by vascular endothelial growth factor is fenestrated. Cancer Res. 57, 765–772 (1997)Google Scholar
- 4.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)Google Scholar
- 5.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)Google Scholar
- 6.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)Google Scholar
- 7.Jain, R.: Determinants of tumor blood flow: a review. Cancer Res. 48, 2641–2658 (1988)Google Scholar
- 12.Kojic, M., Milosevic, M., Kojic, N., Ferrari, M., Ziemys, A.: On diffusion in nanospace. J. Serbian. Soc. Comput. Mechanics 5, 84–109 (2011)Google Scholar
- 13.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)CrossRefGoogle Scholar
- 14.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)Google Scholar
- 16.Kojic, M., Milosevic, M., Simic, V., Koay, E.J., Fleming, J.B., Nizzero, S., Kojic, N., Ziemys, A., Ferrari, M.: A composite smeared finite element for mass transport in capillary systems and biological tissue. Comput. Meth. Appl. Mech. Eng. 324, 413–437 (2017). https://doi.org/10.1016/j.cma.2017.06.019MathSciNetCrossRefGoogle Scholar
- 17.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)CrossRefGoogle Scholar
- 18.Milosevic, M., Simic, V., Milicevic, B., Koay, E.J., Ferrari, M., Ziemys, A., Kojic, M.: Correction function for accuracy improvement of the composite smeared finite element for diffusive transport in biological tissue systems. Comput. Meth. Appl. Mech. Eng. 338, 97–116 (2018). https://doi.org/10.1016/j.cma.2018.04.012. ISSN: 0045-7825MathSciNetCrossRefGoogle Scholar
- 19.Kojic, M., Milosevic, M., Simic, V., Koay, E.J., Kojic, N., Ziemys, A., Ferrari, M.: Multiscale smeared finite element model for mass transport in biological tissue: from blood vessels to cells and cellular organelles. Comput. Biol. Med. 99, 7–23 (2018). https://doi.org/10.1016/j.compbiomed.2018.05.022CrossRefGoogle Scholar
- 23.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), 1–16 (2019). https://doi.org/10.3389/fbioe.2019.00381. ISSN 2296-4185CrossRefGoogle Scholar