Skip to main content

Advertisement

Log in

Flow dynamics analyses of pathophysiological liver lobules using porous media theory

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Blood flow inside the liver plays a key role in hepatic functions, and abnormal hemodynamics are highly correlated with liver diseases. To date, the flow field in an elementary building block of the organ, the liver lobule, is difficult to determine experimentally in humans due to its complicated structure, with radially branched microvasculature and the technical difficulties that derive from its geometric constraints. Here we established a set of 3D computational models for a liver lobule using porous media theory and analyzed its flow dynamics in normal, fibrotic, and cirrhotic lobules. Our simulations indicated that those approximations of ordinary flow in portal tracts (PTs) and the central vein, and of porous media flow in the sinusoidal network, were reasonable only for normal or fibrotic lobules. Models modified with high resistance in PTs and collateral vessels inside sinusoids were able to describe the flow features in cirrhotic lobules. Pressures, average velocities, and volume flow rates were profiled and the predictions compared well with experimental data. This study furthered our understanding of the flow dynamics features of liver lobules and the differences among normal, fibrotic, and cirrhotic lobules.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Wong, J., Johnston, B., Lee, S.S., et al.: A minimal role for selectins in the recruitment of leukocytes into the inflamed liver microvasculature. J. Clin. Invest. 99, 2782–2790 (1997)

    Article  Google Scholar 

  2. Li, N., Lu, S.Q., Zhang, Y., et al.: Mechanokinetics of receptor-ligand interactions in cell adhesion. Acta Mech. Sin. 31, 248–258 (2015)

  3. Sato, Y., Tsukada, K., Hatakeyama, K.: Role of shear stress and immune responses in liver regeneration after a partial hepatectomy. Surg. Today 29, 1–9 (1999)

    Article  Google Scholar 

  4. Monga, S.P.S.: Molecular Pathology of Liver Diseases. Springer Science & Business Media, Berlin (2011)

    Book  Google Scholar 

  5. Schuppan, D., Afdhal, N.H.: Liver cirrhosis. Lancet 371, 838–851 (2008)

    Article  Google Scholar 

  6. Tsochatzis, E.A., Bosch, J., Burroughs, A.K.: Liver cirrhosis. Lancet 383, 1749–1761 (2014)

    Article  Google Scholar 

  7. Rappaport, A., Borowy, Z., Lougheed, W., et al.: Subdivision of hexagonal liver lobules into a structural and functional unit. Role in hepatic physiology and pathology. Anat. Rec. 119, 11–33 (1954)

    Article  Google Scholar 

  8. Kiernan, F.: The anatomy and physiology of the liver. Philos. Trans. R. Soc. Lond. 123, 711–770 (1833)

    Article  Google Scholar 

  9. Debbaut, C., Vierendeels, J., Casteleyn, C., et al.: Perfusion characteristics of the human hepatic microcirculation based on 3D reconstructions and computational fluid dynamic analysis. J. Biomech. Eng. 134, 011003 (2012)

    Article  Google Scholar 

  10. Bataller, R., Brenner, D.A.: Liver fibrosis. J. Clin. Invest. 115, 209–218 (2005)

  11. Sharma, M., Rameshbabu, C.S.: Collateral pathways in portal hypertension. J. Clin. Exp. Hepatol. 2, 338–352 (2012)

    Article  Google Scholar 

  12. Groszmann, R.J., Glickman, M., Blei, A.T., et al.: Wedged and free hepatic venous pressure measured with a balloon catheter. Gastroenterology 76, 253–258 (1979)

    Google Scholar 

  13. Yzet, T., Bouzerar, R., Baledent, O., et al.: Dynamic measurements of total hepatic blood flow with Phase Contrast MRI. Eur. J. Radiol. 73, 119–124 (2010)

    Article  Google Scholar 

  14. Genzel-Boroviczény, O., Strötgen, J., Harris, A.G., et al.: Orthogonal polarization spectral imaging (OPS): a novel method to measure the microcirculation in term and preterm infants transcutaneously. Pediatr. Res. 51, 386–391 (2002)

    Article  Google Scholar 

  15. Puhl, G., Schaser, K.D., Vollmar, B., et al.: Noninvasive in vivo analysis of the human hepatic microcirculation using orthogonal polorization spectral imaging. Transplantation 75, 756–761 (2003)

    Article  Google Scholar 

  16. Nakata, M., Nakamura, K., Koda, Y., et al.: Alterations to hepatic microcirculation in thioacetamide-induced cirrhotic livers of rats. Osaka City Med. J. 48, 1–8 (2002)

    Google Scholar 

  17. Shibayama, Y., Nakata, K.: Localization of increased hepatic vascular resistance in liver cirrhosis. Hepatology 5, 643–648 (1985)

    Article  Google Scholar 

  18. Bonfiglio, A., Leungchavaphongse, K., Repetto, R., et al.: Mathematical modeling of the circulation in the liver lobule. J. Biomech. Eng. 132, 111011 (2010)

    Article  Google Scholar 

  19. Debbaut, C., Vierendeels, J., Siggers, J.H., et al.: A 3D porous media liver lobule model: the importance of vascular septa and anisotropic permeability for homogeneous perfusion. Comput. Method. Biomec. 17, 1295–1310 (2014)

    Article  Google Scholar 

  20. Eringen, A.C.: Continuum Physics. Vol III: Mixtures and Em Field Theories. Academic Press, London (1976)

    Google Scholar 

  21. Ricken, T., Dahmen, U., Dirsch, O.: A biphasic model for sinusoidal liver perfusion remodeling after outflow obstruction. Biomech. Model. Mechanobiol. 9, 435–450 (2010)

    Article  Google Scholar 

  22. Rani, H.P., Sheu, T.W., Chang, T.M., et al.: Numerical investigation of non-Newtonian microcirculatory blood flow in hepatic lobule. J. Biomech. 39, 551–563 (2006)

    Article  Google Scholar 

  23. Lettmann, K.A., Hardtke-Wolenski, M.: The importance of liver microcirculation in promoting autoimmune hepatitis via maintaining an inflammatory cytokine milieu-a mathematical model study. J. Theor. Biol. 348, 33–46 (2014)

  24. Rezania, V., Coombe, D., Tuszynski, J.A.: A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models. Theor. Biol. Med. Modell. 13, 1–22 (2016)

    Article  Google Scholar 

  25. Wambaugh, J., Shah, I.: Simulating microdosimetry in a virtual hepatic lobule. PLoS Comput. Biol. 6, e1000756 (2010)

    Article  Google Scholar 

  26. Nishii, K., Reese, G., Moran, E.C., et al.: Multiscale computational model of fluid flow and matrix deformation in decellularized liver. J. Mech. Behav. Biomed. Mater. 57, 201–214 (2016)

    Article  Google Scholar 

  27. Peeters, G., Debbaut, C., Cornillie, P., et al.: A multilevel modeling framework to study hepatic perfusion characteristics in case of liver cirrhosis. J. Biomech. Eng. 137, 051007 (2015)

    Article  Google Scholar 

  28. Maass-Moreno, R., Rothe, C.F.: Distribution of pressure gradients along hepatic vasculature. Am. J. Physiol Heart. C 272, H2826–H2832 (1997)

    Google Scholar 

  29. Noordergraaf, A., Li, J.K.-J., Campbell, K.B.: Mammalian hemodynamics: a new similarity principle. J. Theor. Biol. 79, 485–489 (1979)

    Article  Google Scholar 

  30. Yoneda, M., Yoneda, M., Mawatari, H., et al.: Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with nonalcoholic fatty liver disease (NAFLD). Dig. Liver Dis. 40, 371–378 (2008)

    Article  Google Scholar 

  31. Dixon, J.B., Bhathal, P.S., O’brien, P.E.: Nonalcoholic fatty liver disease: predictors of nonalcoholic steatohepatitis and liver fibrosis in the severely obese. Gastroenterology 121, 91–100 (2001)

    Article  Google Scholar 

  32. Schiff, E.R., Sorrell, M.F., Maddrey, W.C.: Schiff’s Diseases of the Liver. Lippincott Williams & Wilkins, Philadelphia (2007)

    Google Scholar 

  33. Hubscher, S.G., Burt, A.D., Portmann, B.C., et al.: MacSween’s Pathology of the Liver. Elsevier Health Sciences, Amsterdam (2011)

    Google Scholar 

  34. Sturesson, C., Milstein, D.M., Post, I.C., et al.: Laser speckle contrast imaging for assessment of liver microcirculation. Microvasc. Res. 87, 34–40 (2013)

    Article  Google Scholar 

  35. Siggers, J.H., Leungchavaphongse, K., Ho, C.H., et al.: Mathematical model of blood and interstitial flow and lymph production in the liver. Biomech. Model. Mechanobiol. 13, 363–378 (2014)

    Article  Google Scholar 

  36. West, G.B., Brown, J.H., Enquist, B.J.: A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997)

    Article  Google Scholar 

  37. Koo, A., Liang, I.Y., Cheng, K.-K.: Effect of the ligation of hepatic artery on the microcirculation in the cirrhotic liver in the rat. Aust. J. Exp. Biol. Med. Sci. 54, 287–295 (1976)

    Article  Google Scholar 

  38. Macphee, P., Schmidt, E., Groom, A.: Intermittence of blood flow in liver sinusoids, studied by high-resolution in vivo microscopy. Am. J. Physiol. Gastrl. 269, G692–G698 (1995)

    Google Scholar 

  39. Pan, Z., Wu, X.-J., Li, J.-S., et al.: Functional hepatic flow in patients with liver cirrhosis. World J. Gastroenterol. 10, 915–918 (2004)

    Google Scholar 

  40. Shaldon, S., Chiandussi, L., Guevara, L., et al.: The estimation of hepatic blood flow and intrahepatic shunted blood flow by colloidal heat-denatured human serum albumin labeled with I131. J. Clin. Invest. 40, 1346 (1961)

    Article  Google Scholar 

  41. Dancygier, H.: Clinical Hepatology: Principles and Practice of Hepatobiliary Diseases. Springer Science & Business Media, Berlin (2009)

    Google Scholar 

  42. Du, Y., Li, N., Yang, H., et al.: Mimicking liver sinusoidal structures and functions using a 3D-configured microfluidic chip. Lab. Chip. 17, 782–794 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 31230027, 91642203, and 31661143044) and the Frontier Science Key Project of Chinese Science Academy (Grant QYZDJ-SSW-JSC018).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mian Long.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, J., Lü, S., Feng, S. et al. Flow dynamics analyses of pathophysiological liver lobules using porous media theory. Acta Mech. Sin. 33, 823–832 (2017). https://doi.org/10.1007/s10409-017-0674-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-017-0674-7

Keywords

Navigation