Mass transport through interstitial structures

• Autorzy: Iwanowska-Chomiak B. , Walicka A.

Identyfikatory

DOI

10.2478/ijame-2019-0050

• Języki publikacji: EN

Abstrakty

EN

Interstitial space, also called interstitum, separating the vital organs of a human body, is the primary source of lymph and is a major fluid compartment in the body. Interstitial space (IS) is filled out by thick collagen (CL) bundles which form lattices represented by a network of capillaries. This network has the structure similar to a sponge porous matrix (SPM) with pores-capillaries of variable cross-section. To analyse the mass transport of interstitial fluids (IFs) through the porous matrix it is assumed that the SPM is composed of an irregular system of pores which may be modelled as a fractal porous matrix. The interstitial fluids can be either bio-suspensions or bio-solutions and therefore they have to be modelled as non-Newtonian fluids. Analysing the fluid flow through the porous matrix it is assumed that the SPM is modelled as capillary tubes of variable radii. Introducing a hindrance factor allowed us to consider the porous matrix as a system of fractal capillaries but of constant radii. Classical and fractal expressions for the flow rate, velocity and permeability are derived based on the physical properties of the capillary model of interstitial structures. Each parameter in the proposed expressions does not contain any empirical constant and has a clear physical meaning, and the proposed fractals models relate the flow properties of the fluids under consideration with the structural parameters of interstitium as a porous medium.

Słowa kluczowe

EN

interstitial space; interstitial fluid; fractal models

PL

modele fraktalne; płyn śródmiąższowy; śródmiąższe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2019
• Tom: Vol. 24, no. 4
• Strony: 66--91
• Opis fizyczny: Bibliogr. 29 poz., rys., tab.

Twórcy

autor

Iwanowska-Chomiak B.

• University Hospital of Zielona Góra, Oncology Department ul. Zyty 26, 65-046 Zielona Góra, POLAND

autor

Walicka A.

• University of Zielona Góra Szafrana Str. 4, POLAND

Bibliografia

• [1] Frantz C., Stewart K.M. and Weaver V.M. (2010): The extracellular matrix at a glance. – J. Cell. Sci., vol.123, pp.4195-4200.
• [2] Clause K.C. and Barker T.H. (2013): Extracellular matrix signaling in morphogenesis and repair. – Cur. Opin. Biotechnol., vol.24, pp.830-833.
• [3] Bonnas C., Chou J. and Werb Z. (2014): Remodeling the extracellular matrix in development and disease. – Nature Reviews. Molecular Cell Biology, vol.15, No.12, pp.786-801.
• [4] Theocharis A.D., Skandalis S.S., Gialeli C. and Karamanos N.K. (2016): Extracellular matrix structure. – Adv. Drug Delivery Rev., vol.97, No.1, pp.4-27.
• [5] Michel G., Tonon T., Scornet D., Cock J.M. and Kloareg B. (2010): The cell wall polysacchariel metabolism of the brown alga ectocarpus siliculosus. Insights into the evolution of extracellular matrix polysaccharides In eukaryotes. – New Phytologist, vol.188, No.1, pp.82-97.
• [6] Benias P.C., D'Souza L.S., Papafragkakis H., Kim J., Harshan M., Theise N.D. and Carr-Locke D.L. (2016): Needle-based confocal endomicroscopy for evaluation of malignant lymph nodes - a feasibility study. – Endoscopy, vol.48, No.4, pp.923-928.
• [7] Benias P.C., Wells R.G., Sackey-Aboagye B., Klavan H., Reidy J., Buonocore D., Miranda M., Kornacki S., Wayne M., Carr-Locke D.L. and Theise N.D. (2018): Structure and distribution of an unrecognized interstitium in human tissues. – Sci. Reports, 8:4947/Doi:10:1038/s41598-018-23062-6.
• [8] Wiig H. and Swartz M.A. (2012): Interstitial fluid and lymph formation and transport; physiological regulation and roles in inflamation and cancer. – Phys. Rev., vol.92, No.3, pp.1005-1060.
• [9] Eckhouse S.R. and Spinale F.G. (2012): Changes in the myocardial interstitium and contribution to the progression of the heart failure. – Heart Fail Clin., vol.8, No.1, pp.7-20.
• [10] Loeser C.S., Robert M.E., Mennene A., Nathanson M.H. and Jarnidar P. (2011): Confocal endermicroscopic examination of malignant biliary structures and histologic correlation with limphatics. – J. Clin Gastroenterol , vol.45, pp.246-252.
• [11] Berggreen E. and Wiig H. (2014): Lymphatic function and responses in periodontal disease. – Exp. Cell Res., vol.325, No.2, pp.130-137.
• [12] Louvean A., Smirnov I., Keves T.J., Eccles J.D., Rouhani S.J., Peske J.D. Derecki N.C., Castle D., Mandell J.W., Lee K.S., Harris T.H. and Kipnis J. (2015): Structural and functional features of central nervous system lymphatic vessels. – Nature, vol.523, pp.337-341.
• [13] Zeisberg M. and Kalluri R. (2015): Physiology of the renal interstitium. – Clin. J. Am. Soc. Nephrol., vol.10, No.10, pp.1831-1840.
• [14] de Wit S., van Dalum G. and Terstappe L.W. (2014): Detection of circulating tumor cells. – Scientifica, Doi: 10.1155/2014/819362.
• [15] Auang Q., Wang Y., Chen X., Wang Y.., Li Z., Du S., Wang L. and Chen S. (2018): Nanotechnology – based strategies for early cancer diagnosis using circulation tumor cells as a liquid biopsy. – Nanotheranostics, vol.2, No.1, pp.21-41.
• [16] Walicka A. (2017): Rheology of Fluids in Mechanical Engineering. – Zielona Góra University Press.
• [17] Walicka A. and Iwanowska-Chomiak B. (2018): Fractal model of the transdermal drug delivery. – Int. J. Appl. Mech. Eng., vol.23, No.4, pp.989-1004.
• [18] Walicka A., Falicki J. and Iwanowska-Chomiak B. (2019): Rheology of drugs for topical and transdermal delivery. – Int. J. Appl. Mech. Eng., vol.24, No.1, pp.179-198.
• [19] Walicka A. (2018a): Simulation of the flow through porous layer composed of converging - diverging capillary fissures and tubes. – Int. J. Appl. Mech. Eng., vol.23, No.1, pp.161-185.
• [20] Walicka A. (2018b): Flows of Newtonian and power-law fluids in symmetrically corrugated fissures and tubes. – Int. J. Appl. Mech. Eng., vol.23, No.1, pp.187-215.
• [21] Walicka A., Jurczak P. and Falicki J. (2018): Flows of Sisko fluid through symmetrically curved capillary fissures and tubes. – Machine Dynamics Research, vol.42, No.3, pp.27-54.
• [22] Walicka A., Walicki E., Jurczak P. and Falicki J. (2018): Effect of hindrance factors on a squeeze film of a porous bearing with a DeHaven fluid. – Machine Dynamics Research, vol.42, No.1, pp.15-33.
• [23] Mandelbrot B.B. (1967): How long is the coast of Britain? Statistical self-similarity and fractional dimension. – Science, vol.155, pp.636-638.
• [24] Mandelbrot B.B. (1982): The Fractal Geometry of Nature. – New York: W.H. Freeman.
• [25] Wheateraft S.W. and Tyler S.W. (1988): An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. – Water Resour. Res., vol.24, pp.566-578.
• [26] Yu B.M. and Li J.H. (2001): Some fractal characters of porous media. – Fractals, vol.9, No.3, pp.365-372.
• [27] Yu B.M. and Cheng P. (2002): A fractal model for permeability of bi-dispersed porous media. – Int. J. Heat Mass Transfer, vol.45, No.14, pp.2983-2993.
• [28] Yu B.M. (2005): Fractal character for tortuous stream tubes in porous media. – Chin. Phys. Lett., vol.22, No.1, pp.158-160.
• [29] Walicki E. (2005): Rheodynamics of Slide Bearings Lubrication (in Polish). – Zielona Góra: University Press.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)