Modeling function–perfusion behavior in liver lobules including tissue, blood, glucose, lactate and glycogen by use of a coupled two-scale PDE–ODE approach

Biomechanics and Modeling in Mechanobiology

Volumn 14, Issue 3, 2015, Pages 515-536

  Ricken, T ^a   Werner, D ^a   Holzhutter H G ^b   Konig M ^b   Dahmen, U ^c   Dirsch, O ^c  

^a TU DORTMUND UNIVERSITY   (Germany)

^b CHARITÉ UNIVERSITÄTSMEDIZIN BERLIN   (Germany)

^c JENA UNIVERSITY HOSPITAL   (Germany)

Author keywords

Cell metabolism; Coupled problem; Hydro diffusion advection reaction model; Liver perfusion; Liver tissue; Multi component; Multi phase; Porous media; Sinusoidal perfusion; Two scale

Indexed keywords

ADVECTION; BLOOD PRESSURE; CELLS; CYTOLOGY; DIFFUSION; GLUCOSE; METABOLISM; MIXTURES; ORDINARY DIFFERENTIAL EQUATIONS; TISSUE;

CELL METABOLISM; COUPLED PROBLEMS; DIFFUSION ADVECTIONS; HYDRO-DIFFUSION–ADVECTION-REACTION MODEL; LIVER PERFUSION; LIVER TISSUE; MULTI PHASE; MULTICOMPONENTS; POROUS MEDIUM; REACTION MODELLING; SINUSOIDAL PERFUSION; TWO SCALE;

POROUS MATERIALS;

GLUCOSE; GLYCOGEN; LACTIC ACID DERIVATIVE;

BIOLOGICAL MODEL; HUMAN; LIVER; METABOLISM;

GLUCOSE; GLYCOGEN; HUMANS; LACTATES; LIVER; MODELS, BIOLOGICAL;

EID: 84939950368     PISSN: 16177959     EISSN: 16177940     Source Type: Journal    
DOI: 10.1007/s10237-014-0619-z     Document Type: Article

References (69)

1. Ateshian GA (2007) On the theory of reactive mixtures for modeling biological growth. Biomech Model Mechanobiol 6:423–445
2. Ateshian GA, Costa KD, Azeloglu EU, Hung CT (2009) Continuum modeling of biological tissue growth by cell division, and alteratin of intracellular osmolytes and extracellular fixed charge density. J Biomech Eng 131(10):101001. doi:10.1115/1.3192138
3. Babcock M, Cardell J (1974) Hepatic glycogen patterns in fasted and fed rats. Am J Anat 140:299–337
4. Biot MA (1935) Le probl$$\acute{e}$$e´me de la consolidation des mati$$\grave{e}$$e`res argileuses sous une charge. Annales de la Societ$$\acute{e}$$e´ scientifique de Bruxelles 55:110–113
5. Biot MA (1941) General theory of three dimensional consolidation. J Appl Phys 12:155–164
6. Blouin A, Bolender RP, Weibel ER (1977) Distribution of organelles and membranes between hepatocytes and nonhepatocytes in the rat liver parenchyma. A stereological study. J Cell Biol 72(2):441–455
7. Bluhm J (2002) Modelling of saturated thermo-elastic porous solids with different phase temperatures. In: Ehlers W, Bluhm J (eds) Porous media: theory, experiments and numerical applications. Springer, Berlin
8. Bowen RM (1976a) Theory of mixtures. In: Eringen AC (ed) Continuum physics, vol III. Academic Press, New York, pp 1–127
9. Bowen RM (1976b) Theory of mixtures. In: Eringen AC (ed) Continuum physics. Academic Press, New York
10. Brown JD, Rosen J, Kim YS, Chang L, Sinanan M, Hannaford B (2003) In-vivo and in-situ compressive properties of porcine abdominal soft tissues. In: Westwood JD, Hoffman HM, Mogel GT, Phillips R, Robb RA, Stredney D (eds) Medicine meets virtual reality 11, vol 94. IOS Press, Amsterdam, pp 26–32
11. Burt A, Portmann B, Ferrell L (2007) MacSweens pathology of the liver. Elsevier, Churchill Livingstone
12. Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech Anal 13:167–178
13. Corrin B, Aterman K (1968) The pattern of glycogen distribution in the liver. Am J Anat 122:57–72
14. de Boer R (1996) Highlights in the historical development of the porous media theory: toward a transistent macroscopic theory. Appl Mech Rev 4:201–262
15. de Boer R (2000) Theory of porous media: highlights in the historical development and current state. Springer, Berlin
16. Debbaut C, Vierendeels J, Siggers JH, Repetto R, Monbaliu D, Segers P (2014) A 3d porous media liver lobule model: the importance of vascular septa and anisotropic permeability for homogeneous perfusion. Comput Methods Biomech Biomed Eng 17(12):1295–1310
17. Dirsch O, Madrahimov N, Chaudri N, Deng M, Madrahimova F, Schenk A, Dahmen U (2008) Recovery of liver perfusion after focal outflow obstruction and liver resection. Transplantation 85:748–756
18. Ehlers W (2002) Foundations of multiphasic and porous materials. In: Ehlers W, Bluhm J (eds) Porous media: theory, experiments and numerical applications. Springer, Berlin, pp 3–86
19. Eipper G (1998) Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten Porösen Medien. Dissertation, Bericht Nr. II-1 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart
20. Evans DW, Moran EC, Baptista PM, Soker S, Sparks J (2013) Scale-dependent mechanical properties of native and decellularized liver tissue. Biomech Model Mechanobiol 12(3):569–580
21. Garikipati K, Olberding JE, Narayanan H, Arruda EM, Grosh K, Calve S (2006) Biological remodelling: stationary energy, configurational change, internal variables and dissipation. J Mech Phys Solids 54(7):1493–1515
22. Gerich J (1993) Control of glycaemia. Baillieres Clin Endocrinol Metab 7(3):551–86
23. Greve R (2003) Kontinuumsmechanik: Ein Grundkurs. Springer, Berlin
24. Grytz R, Girkin CA, Libertiaux V, Downs JC (2012a) Perspectives on biomechanical growth and remodeling mechanisms in glaucoma. Mech Res Commun 42:92–106
25. Grytz R, Sigal IA, Ruberti JW, Meschke G, Downs C (2012b) Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach. Mech Mater 44:99–109
26. Hall C (2006) Regulation der hepatischen mikrozirkulation bei schrittweiser resektion im rattenlebermodell. PhD thesis, Medizinische Fakultät der Universität Duisburg-Essen, Zentrum für Chirurgie Klinikum für Allgemeinchirurgie, Viszeral-und Transplantationschirurgie
27. Hariton I, deBotton G, Gasser TC, Holzapfel GH (2007) Stress-driven collagen fiber remodeling in arterial walls. Biomech Model Mechanobiol 6(3):163–175
28. Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodelling of soft tissues. Math. Models Methods Appl Sci 12(3):407–430
29. Hutter K, Jöhnk K (2004) Continuum methods of physical modeling: continuum mechanics, dimensional analysis, turbulence. Springer, Berlin
30. Job G, Herrmann F (2006) Chemical potentiala quantity in search of recognition. Eur J Phys 27:353–371
31. Jungermann K (1986) Functional heterogeneity of periportal and perivenous hepatocytes. Enzyme 35:161–180
32. Kerdok AE (2006) Characterizing the nonlinear mechanical response of liver to surgical manipulation. PhD thesis, Harvard University, Engineering and Applied Sciences
33. König M, Bulik S, Holzhütter H (2012) Quantifying the contribution of the liver to glucose homeostasis: a detailed kinetic model of human hepatic glucose metabolism. PLoS Comput Biol 8(6):e1002,577
34. Kuhl E, Holzapfel GA (2007) A continuum model for remodeling in living structures. J Mater Sci 42:8811–8823
35. Kuntz E, Kuntz HD (2006) Hepatology: principles and practice. Springer, Berlin
36. Lai WM, Hou JS, Mow VC (1991) A triphasic theory for the swelling and deformation behaviours of articular cartilage. ASME J Biomech Eng 113:245–258
37. Lautt WW (2009) Hepatic circulation. University of Manitoba, San Rafael
38. Lu JF, Hanyga A (2005) Linear dynamic model for porous media saturated by two immiscible fluids. Int J Solids Struct 42:2689–2709
39. Maass-Moreno R, Rothe CF (1997) Distribution of pressure gradients along hepatic vasculature. Am J Physiol Heart Circ Physiol 272(6):H2826–H2832. http://ajpheart.physiology.org/content/272/6/H2826.full.pdf
40. MacPhee PJ, Schmidt EE, Groom AC (1995) Intermittence of blood flow in liver sinusoids, studied by high-resolution in vivo microscopy. Am J Physiol Gastrointest Liver Physiol 269(5):G692–G698. http://ajpgi.physiology.org/content/269/5/G692.full.pdf
41. Millonig G, Friedrich S, Adolf S, Fonouni H, Golriz M, Mehrabi A, Stiefel P, Pschl G, Bchler MW, Seitz HK, Mueller S (2010) Liver stiffness is directly influenced by central venous pressure. J Hepatol 52(2):206–210
42. Mow VC, Gibbs MC, Lai WM, Zhu WB, Athanasiou KA (1989) Biphasic indentation of articular cartilage-ii. A numerical algorithm and an experimental study. J Biomech 22:853–861
43. Nava A, Mazza E, Furrer M, Villiger P, Reinhart WH (2008) In vivo mechanical characterization of human liver. Med Image Anal 12(2):203–216
44. Nuttal FQ, Ngo A, Gannon MC (2008) Regulation of hepatic glucose production and the role of gluconeogenesis in humans: is the rate of gluconeogenesis constant? Diabetes Metab Res Rev 24:438–458
45. Pierce DM, Ricken T, Holzapfel GA (2013a) A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications. Comput Methods Biomech Biomed Eng 16(12):1344–1361
46. Pierce DM, Ricken T, Holzapfel GA (2013b) Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI. Int J Numer Methods Biomed Eng 29(8):807–821
47. Radziuk J, Pye S (2001) Hepatic glucose uptake, gluconeogenesis and the regulation of glycogen synthesis. Diabetes Metab Res Rev 17:250–272
48. Ricken T (2002) Kapillarität in porösen medien—theoretische untersuchung und numerische simulation. PhD thesis, Dissertation, Shaker Verlag, Aachen
49. Ricken T, Bluhm J (2009) Evolutional growth and remodeling in multiphase living tissue. Comput Mater Sci 45(3):806–811
50. Ricken T, Bluhm J (2010) Remodeling and growth of living tissue: a multiphase theory. Arch Appl Mech 80(5):453–465
51. Ricken T, de Boer R (2003) Multiphase flow in a capillary porous medium. Comput Mater Sci 28:704–713
52. Ricken T, Dahmen U, Dirsch O (2010) A biphasic model for sinusoidal liver perfusion remodeling after outflow obstruction. Biomech Model Mechanobiol 9:435–450
53. Saitoh Y, Terada N, Saitoh S, Ohno N, Fujii Y, Ohno S (2010) Histochemical approach of cryobiopsy for glycogen distribution in living mouse livers under fasting and local circulation loss conditions. Histochem Cell Biol 133(2):229–239
54. Samur E, Sedef M, Basdogan C, Avtan L, Duzgun O (2005) A robotic indenter for minimally invasive characterization of soft tissues. In: International congress series, CARS 2005: computer assisted radiology and surgery proceedings of the 19th international congress and exhibition, vol 1281, no 0, pp 713–718
55. Sasse D (1975) Dynamics of liver glycogen: the topochemistry of glycogen synthesis, glycogen content and glycogenolysis under the experimental conditions of glycogen accumulation and depletion. Histochemistry 45:237–254
56. Schwartz JM, Denninger M, Rancourt D, Moisan C, Laurendeau D (2005) Modelling liver tissue properties using a non-linear visco-elastic model for surgery simulation. Med Image Anal 9(2):103–112
57. Siggers JH, Leungchavaphongse K, Ho CH, Repetto R (2014) Mathematical model of blood and interstitial flow and lymph production in the liver. Biomec Model Mechanobiol 13(2):363–378
58. Stanhope KL, Griffen SC, Bair BR, Swarbrick MM, Keim NL, Havel PJ (2008) Twenty-four-hour endocrine and metabolic profiles following consumption of high-fructose corn syrup-, sucrose-, fructose-, and glucose-sweetened beverages with meals. Am J Clin Nutr 87:1194–1203
59. Teutsch HF (2005) The modular microarchitecture of human liver. Hepatology 42(2):317–325
60. Teutsch HF, Schuerfeld D, Groezinger E (1999) Three-dimensional reconstruction of parenchymal units in the liver of the rat. Hepatology 29(2):494–505
61. Truesdell C (1984) Thermodynamics of diffusion. In: Truesdell C (ed) Rational thermodynamics. Springer, New York, pp 219–236
62. Truesdell C, Toupin R (1960) The classical field theory. In: Flügge S (ed) Handbuch der Physik, vol 3/1. Springer, Berlin
63. Valentin A, Humphrey JD, Holzapfel GA (2013) A finite element-based constrained mixture implementation for arterial growth, remodeling, and adaptation: theory and numerical verification. Int J Numer Methods Biomed Eng 29(8):822–849
64. Villeneuve JP, Dagenais PM, Huet P, Roy A, Lapointe R, Marleau D (1996) The hepatic microcirculation in the isolated perfused human liver. Hepatology 23(1):24–31
65. Wahren J, Ekberg K (2007) Splanchnic regulation of glucose production. Annu Rev Nutr 27:329–345
66. Walpole J, Papin J, Peirce S (2013) Multiscale computational models of complex biological systems. Ann Rev Biomed Eng 15:137–154
67. Warren A, Chaberek S, Ostrowski K, Cogger VC, Hilmer SN, McCuskey RS, Fraser R, Le Couteur DG (2008) Effects of old age on vascular complexity and dispersion of the hepatic sinusoidal network. Microcirculation 15(3):191–202
68. Werner D, Ricken T, Dahmen U, Dirsch O (2012) A biphasic fem model for the microperfusion in liver lobules. PAMM 12:89–90
69. Yuen K, McDaniel P, Riddle M (2012) Twenty-four-hour profiles of plasma glucose, insulin, c-peptide and free fatty acid in subjects with varying degrees of glucose tolerance following short-term, medium-dose prednisone (20 mg/day) treatment: evidence for differing effects on insulin secretion and action. Clin Endocrinol 77:224–232