A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling

Biomechanics and Modeling in Mechanobiology

Volumn 9, Issue 4, 2010, Pages 403-419

  Wan, William ^a   Hansen, Laura ^b   Gleason, Rudolph L ^a,b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Arterial mechanics; Constitutive model; Growth kinetics; Mechanical properties

Indexed keywords

GROWTH KINETICS; MIXTURES; PHYSIOLOGICAL MODELS; PHYSIOLOGY; RESTORATION; SHEAR FLOW; SHEAR STRESS;

3-DIMENSIONAL; ARTERIAL MECHANICS; COMPUTATIONAL FRAMEWORK; GROWTH AND REMODELING; MIXTURE MODELING; SOFT TISSUE; TISSUE REMODELING; VASCULAR GROWTHS; VASCULAR REMODELING; VOLUMETRIC GROWTH;

CONSTITUTIVE EQUATIONS;

COLLAGEN;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; BLOOD FLOW VELOCITY; BLOOD PRESSURE; BLOOD VESSEL; COMPUTER SIMULATION; GROWTH, DEVELOPMENT AND AGING; METABOLISM; MOUSE; PHYSIOLOGY;

ANIMALS; BIOMECHANICS; BLOOD FLOW VELOCITY; BLOOD PRESSURE; BLOOD VESSELS; COLLAGEN; COMPUTER SIMULATION; MICE; MODELS, CARDIOVASCULAR;

EID: 77956392459     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-009-0184-z     Document Type: Article

References (40)

1. Baer E, Cassidy JJ, Hiltner A (1992) Hierarchial structure of collagen composite systems-lessons from biology. ACS Symp Ser 489: 2-23
2. Barocas VH, Tranquillo RT (1997a) A finite element solution for the anisotropic biphasic theory of tissue-equivalent mechanics: The effect of contact guidance on isometric cell traction measurement. J Biomech Eng 119(3):261-268
3. Barocas VH, Tranquillo RT (1997b) An anisotropic biphasic theory of tissue-equivalent mechanics: The interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. J Biomech Eng 119(2):137-145
4. Brankov G, Rachev AI, Stoychev S (1975) A composite model of large blood vessels. In: Brankov G (ed) Mechanics of biological solid: Proceedings of the Euromech colloquium. Publishing House of the Bulgarian Academy of Sciences, Varna, pp 71-78
5. Chuong CJ, Fung YC (1986) On residual stresses in arteries. J Biomech Eng 108(2):189-192
6. Driessen NJB, Boerboom RA, Huyghe JM, Bouten CVC, Baaijens FPT (2003a) Computational analyses of mechanically induced collagen fiber remodeling in the aortic heart valve. J Biomech Eng 125:549-557
7. Driessen NJB, Peters GWM, Huyghe JM, Bouten CVC, Baaijens FPT (2003b) Remodelling of continuously distributed collagen fibres in soft connective tissues. J Biomech 36:1151-1158
8. Driessen NJB, Wilson W, Bouten CVC, Baaijens FPT (2004) A computationalmodel for collagen fibre remodelling in the arterialwall. J Theor Biol 226(1):53-64
9. Driessen NJB, Bouten CVC, Baaijens FPT (2005) A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution. J Biomech Eng 127(3):494-503
10. Fridez P, Rachev A, Meister J-J, Hayashi K, Stergiopulos N (2001) Model of geometrical and smooth muscle tone adaptation of carotid artery subject to step change in pressure. Am J Physiol Heart Circ Physiol 280:H2752-H2760
11. Gleason RL, Humphrey JD (2004) A mixture model of arterial growth and remodeling in hypertension: Altered muscle tone and tissue turnover. J Vasc Res 41(4):352-363
12. Gleason RL, Humphrey JD (2005a) Effects of a sustained extension on arterial growth and remodeling: A theoretical study. J Biomech 38(6):1255-1261
13. Gleason RL, Humphrey JD (2005b) A 2-D constrained mixture model for arterial adaptations to large changes in flow, pressure, and axial stretch. Math Med Biol 22(4):347-369
14. Gleason RL,WanW (2008) Theory and experiments for mechanicallyinduced remodeling of tissue engineered blood vessels. Adv Sci Technol 57:226-234
15. Gleason RL, Taber LA, Humphrey JD (2004a) A 2-D model of flowinduced alterations in the geometry, structure, and properties of carotid arteries. J Biomech Eng 126:371-381
16. Gleason RL, Hu J-J, Humphrey JD (2004b) Building a functional artery: issue from the perspective of mechanics. Front Biosci 9:2045-2055
17. Gleason RL, Wilson E, Humphrey JD (2007) Biaxial biomechanical adaptations of mouse carotid arteries cultured at altered axial extension. J Biomech 40(4):766-776
18. Hansen L, Wan W, Gleason RL (2009) Microstructurally-motivated constitutive modeling of mouse arteries cultured under altered axial stretch. J Biomech Eng 131(10):101015 (11 p)
19. Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues, organs. Springer, New York
20. Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Models Meth Appl Sci 12(3):407-430
21. Humphrey JD, Rajagopal KR (2003) A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomech Model Mechanobiol 2:109-126
22. Kamiya A, Togawa T (1980) Adaptive regulation of wall shear stress to flow change in the canine carotid artery. Am J Physiol 239(1): H14-H21
23. Kuhl E, Garikipati K, Arruda EM, Grosh K (2005) Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. J Mech Phys Solids 53(7):1552-1573
24. Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16:1-12
25. Martinez-Lemus LA, Hill MA, Bolz SS, Pohl U, Meininger GA (2004) Acute mechanoadaptation of vascular smooth muscle cells in response to continuous arteriolar vasoconstriction: implications for functional remodeling. FASEB J 18(6):708-710
26. Matsumoto T, Hayashi K (1996) Stress and strain distribution in hypertensive and normotensive rat aorta considering residual stress. J Biomech Eng 118:62-73
27. MowVC,Kuei SC, LaiWM, Armstrong CG (1980) Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J Biomech Eng 102(1):73-84
28. Rachev A (1997) Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions. J Biomech 30(8):819-827
29. Rachev A (2000) A model of arterial adaptation to alterations in blood flow. J Elast 61:83-111
30. Rachev A, Hayashi K (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann Biomed Eng 27:459-468
31. Raykin J, Rachev AI, Gleason RL (2009) A phenomenological model formechanically mediated growth, remodeling, damage, and plasticity of gel-derived tissue engineered blood vessels. J Biomech Eng 131(10):101016 (12 p)
32. RodriguezEK, HogerA,McCullochAD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455-467
33. RodriguezEK, HogerA,McCullochAD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455-467 Skalak R (1981) Growth as a finite displacement field. Martinus Nijhoff, The Hague
34. Skalak R, Zargaryan S, Jain RK, Netti PA, Hoger A (1996) Compatibility and the genesis of residual stress by volumetric growth. J Math Biol 34(8):889-914
35. Taber LA (1998) A model of aortic growth based on fluid shear and fiber stresses. J Biomech Eng 120:348-354
36. Taber LA, Eggers DW (1996) Theoretical study of stress-modulated growth in the aorta. J Theor Biol 180(4):343-357
37. Taber LA, Eggers DW (1996) Theoretical study of stress-modulated growth in the aorta. J Theor Biol 180(4):343-357 Taber LA, Lin IE, Clark EB (1995) Mechanics of cardiac looping. Dev Dyn 203(1):42-50
38. Wicker B, Hutchens H,Wu Q, Yeh A, Humphrey J (2008) Normal basilar artery structure and biaxial mechanical behavior.Comput Methods Biomech Biomed Eng 11(5):539-551
39. Yang M, Mun C, Choi Y, Baik J, Park A, Lee W, Lee J (2007) Agmatine inhibits matrix metalloproteinase-9 via endothelial nitric oxide synthase in cerebral endothelial cells. Neurol Res 29:749-754
40. Zarins CK, Zatina MA, Giddens DP, Ku DN, Glagov S (1987) Shear stress regulation of artery lumen diameter in experimental atherogenesis. J Vasc Surg 5(3):413-420