Abstract
Diseases due to infections might lead to death. Fever is often the first sign of an infection; other signs are skin hot to touch, shivering, aching muscles, pain, redness, swelling and so on, depending on the kind of infection. This study is a first attempt to model one of the infection symptoms, the edema. Briefly, edema may be caused by increased blood vessel wall permeability which lead to a swollen, red area. Neutrophil-bacteria iterations trigger a chain of cytokine reactions which in turn change the vessel wall permeability leading to an increase of interstitial fluid pressure. All the iterations are modeled using a n-phase partial differential equation system based on porous media assumptions. Model solutions are obtained using finite-volume method and the upwind scheme. Finally, the numerical results are qualitatively compared with experimental data available from the literature, presenting a good agreement.
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References
Abbas, A.K., Lichtman, A.H., Pillai, S.: Imunologia Celular e Molecular. Elsevier, Belo Horizonte (2012)
Peter, J.: Basser.: Interstitial pressure, volume, and flow during infusion into brain tissue. Microvasc. Res. 44(2), 143–165 (1992)
Bauernfeind, F., Ablasser, A., Bartok, E., Kim, S., Schmid-Burgk, J., Cavlar, T., Hornung, V.: Inflammasomes: current understanding and open questions. Cell. Mol. Life Sci. 68(5), 765–783 (2011)
Chen, Z., Ewing, R.E.: Comparison of various formulations of three-phase flow in porous media. J. Comput. Phys. 132(2), 362–373 (1997)
Guyton, A.C., Hall, J.E.: Textbook of Medical Physiology. Guyton Physiology Series. Elsevier Saunders, Philadelphia (2006)
Arthur, C.: Guyton.: Interstitial fluid pressure: Il. pressure-volume curves of interstitial space. Circ. Res. 16(5), 452–460 (1965)
Jain, R.K., Martin, J.D., Stylianopoulos, T.: The role of mechanical forces in tumor growth and therapy. Annu. Rev. Biomed. Eng. 16, 321 (2014)
Koneman, E., Win Jr., W., Allen, S., Janda, W., Procop, G., Scheckenberger, P., Woods, G.: Color Atlas and Textbook of Diagnostic Microbiology, 6th edn. LWW, Philadelphia (2005)
McDonald, B.E., Ambrosiano, J.: High-order upwind flux correction methods for hyperbolic conservation laws. J. Comput. Phys. 56(3), 448–460 (1984)
Phipps, C., Kohandel, M.: Mathematical model of the effect of interstitial fluid pressure on angiogenic behavior in solid tumors. Comput. Math. Methods Med. 2011, 9 (2011)
Pigozzo, A.B., Macedo, G.C., dos Santos, R.W., Lobosco, M.: On the computational modeling of the innate immune system. BMC Bioinform. 14(Suppl 6), S7 (2013)
Pigozzo, A.B., Macedo, G.C., dos Santos, R.W., Lobosco, M.: Computational modeling of microabscess formation. Comput. Math. Methods Med. 2012, 16 (2012)
Pinder, G.F., Gray, W.G.: Essentials of Multiphase Flow in Porous Media, 1st edn. Wiley, Hoboken (2008)
Pixley, F.J.: Macrophage migration and its regulation by csf-1. Inter. J. Cell Biol. 1–12, 2012 (2012)
Scallan, J., Huxley, V.H., Korthuis, R.J.: Capillary Fluid Exchange: Regulation, Functions, and Pathology, 2nd edn. Morgan & Claypool Publishers, San Rafael (2010)
Sompayrac, L.: How the Immune System Works. Wiley-Blackwell, Hoboken (2012)
Starling, E.H.: On the absorption of fluids from the connective tissue spaces. J. Physiol. 19(4), 312–326 (1896)
Tepole, A.B., Kuhl, E.: Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing. Comput. Method Biomech. Biomed. Eng. 19, 1–18 (2014)
Versteeg, H., Malalasekra, W.: An Introduction to Computational Fluid Dynamics: The Finite, vol. Method, 2nd edn. Prentice Hall, Upper Saddle River (2007)
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The financial support by CNPq, CAPES, UFJF and FAPEMIG is greatly acknowledged.
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Reis, R.F., dos Santos, R.W., Lobosco, M. (2016). A Plasma Flow Model in the Interstitial Tissue Due to Bacterial Infection. In: Ortuño, F., Rojas, I. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2016. Lecture Notes in Computer Science(), vol 9656. Springer, Cham. https://doi.org/10.1007/978-3-319-31744-1_30
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DOI: https://doi.org/10.1007/978-3-319-31744-1_30
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