Prediction of Phagocyte Transmigration for Foreign Body Responses to Subcutaneous Biomaterial Implantations Using Differential Transform Method

Abstract:

The complexity of the multiple interactive reactions of various cells/proteins and biochemical processes during phagocyte transmigration for foreign body responses to subcutaneous biomaterial implants have been studied through developed kinetics-based predictive models which have been numerically analyzed. However, the need for direct relationship between the kinetic-based predictive models parameters and the requirements for continuous insights into the significance of various process parameters affecting the phenomena have led to the quest for developing analytical solutions. Therefore, in this work, differential transform method is used to develop analytical solutions for the prediction of phagocyte transmigration for foreign body responses to subcutaneous biomaterial implants. The approximate analytical solutions are used to study the effect of various model parameters on phagocyte transmigration to foreign body responses in biomaterial implantation. The results of the analytical solutions are agreement with the results of the previous studies.

• Periodical: Journal of Biomimetics, Biomaterials and Biomedical Engineering (Volume 32)
• Pages: 98-114
• DOI: https://doi.org/10.4028/www.scientific.net/JBBBE.32.98
• Online since: May 2017
• Authors: Olurotimi A. Adeleye*, Olatutu Olawale, Gbeminiyi Sobamowo
• Keywords: Analytical Solutions, Differential Transform Method, Foreign Body Response, Phagocyte Transmigration, Subcutaneous Biomaterial Implants

References

[1] L. Zhang, Z. Cao, T. Bai, L. Carr, J. Ella-Menye, C. Irvin, B. D. Ratner, S. Jiang. Zwitterionic hydrogels implanted in mice resist the foreign-body reaction, Nature Biotechnology, 31, 553–556, (2013).

DOI: 10.1038/nbt.2580

[2] L. Tang, T.A. Jennings, J.W. Eaton. Mast cells mediate acute inflammatory responses to implanted biomaterials. Proc Nat Acad Sci. 95, (1998), 8841–8846.

DOI: 10.1073/pnas.95.15.8841

[3] W. K. Ward,. A review of the foreign-body response to subcutaneously-implanted devices: The role of macrophages and cytokines in biofouling and fibrosis. J Diabetes Sci Technol. 2, (2008), 768–777.

DOI: 10.1177/193229680800200504

[4] B. Rolfe, J. Mooney, B. Zhang, S. Jahnke, S.J. Le, Y.Q. Chau, Q. Huang, G. Wang, H. Campbell, J. Campbell. The fibrotic response to implanted biomaterials: Implications for tissue engineering. In: Eberli D., editor. Regenerative Medicine and Tissue Engineering: Cells and Biomaterials. Rijeka, Croatia: InTech Publishing; (2011).

DOI: 10.5772/21790

[5] J. Xue, J. Gao, L. Tang. A hybrid computational model for phagocyte transmigration. In: BioInformatics and BioEngineering, 8th IEEE International Conference On. Boston: IEEE; 2008. p.1–6.

DOI: 10.1109/bibe.2008.4696731

[6] J. Su, M. Todorov, H.P. Gonzales, L. Perkins, H. Kojouharov, H. Weng, L. Tang. A predictive tool for foreign body fibrotic reactions using 2-dimensional computational model. Open Access Bioinformatics. 3, (2011), 19–35.

DOI: 10.2147/oab.s14254

[7] J. Su, M. Todorov, H.P. Gonzales, L. Perkins, H. Kojouharov, H. Weng, L. Tang. A mathematical model for foreign body reactions in 2D. Int J Comput. Math. 88, (2011), 610–633.

DOI: 10.1080/00207161003640035

[8] J. Yang, J. Su, L. Owens, A. Ibraguimov, L. Tang. A computational model of fibroblast and macrophage spatial/temporal dynamics in foreign body reactions. J Immunol. Methods. 397 (1–2), 2013, 37–46.

DOI: 10.1016/j.jim.2013.08.013

[9] L. Tang, J.W. Eaton. Natural responses to unnatural materials: A molecular mechanism for foreign body reactions. Mol Med. 6 (5), 1999, 351–358.

DOI: 10.1007/bf03402124

[10] J. Zdolsek, J. Eaton, L. Tang. Histamine release and fibrinogen adsorption mediate acute inflammatory responses to biomaterial implants in humans. J Transl. Med. 5(1), 2007 31.

DOI: 10.1186/1479-5876-5-31

[11] L. Tang, W. Jiang, S.E. Welty. The participation of p- and e-selectins onbiomaterial-mediated tissue responses. J Biomed Mater Res. 62 (4), 2002, 471–477.

DOI: 10.1002/jbm.10271

[12] M. Kang, J.X. Gao, L. Tang. Computational modeling of phagocyte transmigration during biomaterial-mediated foreign body responses. In: Bioinformatics and Biomedicine (BIBM), 2010 IEEE International Conference On. Hong Kong: IEEE; 2010. p.609–612.

DOI: 10.1109/bibm.2010.5706638

[13] L. Tang, Y. Wu, R.B. Timmons. Fibrinogen adsorption and host tissue responses to plasma functionalized surfaces. J Biomed Mater Res. 42 (1) 1998, 156–163.

DOI: 10.1002/(sici)1097-4636(199810)42:1<156::aid-jbm19>3.0.co;2-j

[14] P.T. Thevenot, D.W. Baker, H. Weng, M.W. Sun, L. Tang. The pivotal role of fibrocytes and mast cells in mediating fibrotic reactions to biomaterials. Biomaterials. 32 (33), 2011, 8394–8403.

DOI: 10.1016/j.biomaterials.2011.07.084

[15] S. Yamasaki, ST. Regulation of mast cell activation through fcepsilonri. ChemImmunol Allergy. 87, 2005, 22–31.

[16] J.K. Zhou, Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China. (1986).

[17] A. Arikoglu, and I. Ozkol, Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method, Compos Struct. 92, (2010), 3031-3039.

DOI: 10.1016/j.compstruct.2010.05.022

[18] Z. Odibat, C. Bertelle, M. A. Aziz-Alaoui, and G.H.E. Duchampd, A multi-step differential transform method and application to non-chaotic or chaotic systems. Comput. Math. Appl. 59, (2010), 1462-1472.

DOI: 10.1016/j.camwa.2009.11.005

[19] P. Salehi, H. Yaghoobi, and M. Torabi, Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load, Journal of Mechanical Science and Technology, 26, (2012).

DOI: 10.1007/s12206-012-0730-y

[20] M. Madani, M. Fathizadeh, Y. Khan and A. Yildirim, On the coupling of the homotopy perturbation method and Laplace transformation, J. Mathematical and Computer Modelling, 53 (9-10), (2011), 1937-(1945).

DOI: 10.1016/j.mcm.2011.01.023

[21] D. Carlos, A. Sa-Nunes, L. de Paula, C. Matias-Peres, M.C. Jamur, C. Oliver, M.F. Serra, M.A. Martins, L.H. Faccioli. Histamine modulates mast cell granulation through an indirect mechanism in a model ige-mediated reaction. Eur J Immunol. 36 (6), 2006, 1494–1503.

DOI: 10.1002/eji.200535464

[22] C. K Chen, and S.H. Ho, Solving partial differential equations by two dimensional differential transform. Appl. Math. Comput. 106, 1999, 171-179.

DOI: 10.1016/s0096-3003(98)10115-7

[23] M. Thongmoon, and S. Pusjuso, The numerical solution of differential transform method and Laplace transform method for a system of differential equations. Nonlinear Anal. Hybrid Syst. 4, 2010, 425-431.

DOI: 10.1016/j.nahs.2009.10.006

[24] M. Kang, L. Tang, J. Gao, Computational modeling of phagocyte transmigration for foreign body responses to subcutaneous biomaterial implants in mice, BMC Bioinformatics 111 (17), 2016, 1-13.

DOI: 10.1186/s12859-016-0947-3