Abstract
Since the main purpose of generation of organ-on-chips is to reduce and, at some point, replace experiments on the animals, several different organs were point of interest in developing on-chip technology. The paper will therefore focus on creating mathematical model of liver cell aggregation, generating a basis for creation of artificial organs in that way. Some studies have shown that in the case of hepatocytes (liver cells), improved cell viability and functionality is connected to the formation of spheroidal multicellular aggregates in comparison to the traditional monolayer culture techniques. We present one-dimensional mathematical model of liver cell aggregation, meaning how the liver cell clusters are formed on an extracellular matrix (ECM) layer. Model is based on partial differential equations in the function of space and time, which are solved numerically using finite difference method. Results show that velocity of the cells at the beginning is slow, only to increase later on during the formation of the aggregates. Material properties and initial cell seeding have great effects on the formation of the aggregates. With this model, we aim to achieve a prediction of number of cell clusters, velocity during and before/after clustering etc., which is important in experiments to examine how different parameters, such as initial cell seeding or material characteristics affect cell aggregation and viability of liver cells.
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References
O’Dea, R.D., Byrne, H.M., Waters, S.L.: Continuum modelling of in vitro tissue engineering: a review. In: Computational Modeling in Tissue Engineering, pp. 229–266. Springer, Berlin, Heidelberg (2012)
Green, J.E.E.: Mathematical modelling of cell aggregation in liver tissue engineering. Doctoral dissertation, University of Nottingham (2006)
Jauregui H.O.: Liver. In: Principles of Tissue Engineering, 2nd edn, pp. 541–551. Academic Press (2000)
Mitaka, T.: The current status of primary hepatocyte culture. Int. J. Exp. Pathol. 79(6), 393–409 (1998)
Selden, C., Khalil, M., Hodgson, H.J.F.: What keeps hepatocytes on the straight and narrow? Maintaining differentiated function in the liver. Gut 44(4), 443–446 (1999)
Riccalton-Banks, L., Liew, C., Bhandari, R., Fry, J., Shakesheff, K.: Long-term culture of functional liver tissue: three-dimensional coculture of primary hepatocytes and stellate cells. Tissue Eng. 9(3), 401–410 (2003)
Bhandari, R.N., Riccalton, L.A., Lewis, A.L., Fry, J.R., Hammond, A.H., Tendler, S.J., Shakesheff, K.M.: Liver tissue engineering: a role for co-culture systems in modifying hepatocyte function and viability. Tissue Eng. 7(3), 345–357 (2001)
Abu-Absi, S.F., Friend, J.R., Hansen, L.K., Hu, W.S.: Structural polarity and functional bile canaliculi in rat hepatocyte spheroids. Exp. Cell Res. 274(1), 56–67 (2002)
Green, J.E.F., Waters, S.L., Shakesheff, K.M., Byrne, H.M.: A mathematical model of liver cell aggregation in vitro. Bull. Math. Biol. 71(4), 906–930 (2009)
Riccalton-Banks, L.A.: Maintenance of primary rat hepatocytes in vitro using co culture techniques. Doctoral dissertation, University of Nottingham (2002)
Glicklis, R., Shapiro, L., Agbaria, R., Merchuk, J.C., Cohen, S.: Hepatocyte behavior within three-dimensional porous alginate scaffolds. Biotechnol. Bioeng. 67(3), 344–353 (2000)
Thomas, R.J., Bhandari, R., Barrett, A.J., et al.: The effect of three-dimensional co-culture of hepatocytes and hepatic stellate cells on key hepatocyte functions in vitro. Cells Tissues Organs 181(2), 67–79 (2005)
Higuchi, A., Tsukamoto, Y.: Cell separation of hepatocytes and fibroblasts through surface-modified polyurethane membranes. J. Biomed. Mater. Res. Part A Official J. Soc. Biomater. Jpn. Soc. Biomater. Aust. Soc. Biomater. Korean Soc. Biomater. 71(3), 470–479 (2004)
Breward, C.J.W., Byrne, H.M., Lewis, C.E.: The role of cell-cell interactions in a two-phase model for avascular tumour growth. J. Math. Biol. 45(2), 125–152 (2002)
Byrne, H.M., King, J.R., McElwain, D.S., Preziosi, L.: A two-phase model of solid tumour growth. Appl. Math. Lett. 16(4), 567–574 (2003)
Lubkin, S.R., Jackson, T.: Multiphase mechanics of capsule formation in tumors. J. Biomech. Eng. 124(2), 237243 (2002)
Owen, M.R., Byrne, H.M., Lewis, C.E.: Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites. J. Theor. Biol. 226(4), 377–391 (2004)
Glicklis, R., Merchuk, J.C., Cohen, S.: Modeling mass transfer in hepatocyte spheroids via cell viability, spheroid size, and hepatocellular functions. Biotechnol. Bioeng. 86(6), 672–680 (2004)
Compressed Mortality File, CDC WONDER On-line Database, [Online]. Available http://wonder.cdc.gov). Accessed 25 Nov 2018
Thomas, T.W., DiMilla, P.A.: Spreading and motility of human gliobastoma cells on sheets of silicone rubber depend on substratum compliance. Comput. Med. Biol. Eng. 38, 360–370 (2000)
Riccalton-Banks, L., Liew, C., Bhandari, R., Fry, J., Shakesheff, K.: Longterm culture of functional liver tissue: three-dimensional coculture of primary hepatocytes and stellate cells. Tissue Eng. 9(3), 401–409 (2003)
Acknowledgements
This study was funded by the European Project H2020 PANBioRA [grant number 760921] and grants from the Serbian Ministry of Education, Science, and Technological Development [grant number III41007 and grant number OI174028]. This article reflects only the author’s view. The Commission is not responsible for any use that may be made of the information it contains.
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Sustersic, T., Nikolic, M., Vrana, N.E., Filipovic, N. (2020). Discrete Modelling of Liver Cell Aggregation Using Partial Differential Equations. In: Badnjevic, A., Škrbić, R., Gurbeta Pokvić, L. (eds) CMBEBIH 2019. CMBEBIH 2019. IFMBE Proceedings, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-17971-7_57
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