Abstract
This paper provides a unified mathematical framework so as to study the growth of biological tissues on an energetic basis. All the contributions to growth of solute chemicals and nutrients are here resumed in one scalar descriptor, the biochemical energy of the system. The free energy of the system accounts for both strain and biochemical storage. The exploitation of a dissipation inequality by standard means provides admissible couplings between growth, tension and energy. Specific admissible constitutive equations lead back, in some cases, to classical models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ambrosi D. and Guana F. (2007). Stress-modulated growth. Math. Mech. Solids 12(3): 319–342
Ateshian, G.A.: On the theory of reactive mixtures for modelling biological growth. Biomechan. Model. Mechanobiol. (2007, in press)
Cermelli P., Fried E. and Sellers S. (2001). Configurational stress, yield and flow in rate-independent plasticity. Proc. R. Soc. Lond. 457: 1447–1467
DiCarlo A. and Quiligotti S. (2002). Growth and balance. Mech. Res. Commun. 29: 449–456
Fusi L., Farina A. and Ambrosi D. (2006). Mathematical modelling of a solid–liquid mixture with mass exchange between constituents. Math. Mech. Solids 11(6): 575–595
Garikipati K., Arruda E.M., Grosh K., Narayanan H. and Calve S. (2004). A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics. J. Mech. Phys. Solids 52(7): 1595–1625
Guillou A. and Ogden R. (2006). Growth in soft biological tissue and residual stress development. In: Holzapfel, G.A. and Ogden, R.W. (eds) Mechanics of biological tissue., pp. Springer, Heidelberg
Han B., Bai X.H., Lodyga M., Xu J., Yang B.B., Keshavjee S., Post M. and Liu M. (2004). Conversion of mechanical forces into biochemical signalling. J. Biol. Chem. 279(52): 54793–54801
Hu Y., Bock G., Wick G. and Xu Q. (1998). Activation of PDGF receptor a in vascular smooth muscle cells by mechanical stress. FASEB J. 12: 1135–1142
Humphrey J.D. (2003). Continuum biomechanics of soft biological tissues. Proc. R. Soc. 459: 3–46
Liu S.Q. and Fung Y.C. (1989). Relationship between hypertension, hypertrophy and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 111: 325–335
Michaelis M. and Menten M. (1913). Die Kinetik der Invertinwirkung. Biochem. Z. 49: 333–369
Murray J.D. (2004). Mathematical biology, 3rd edn. Springer, Heidelberg
Rodriguez E.K., Hoger A. and McCulloch A. (1994). Stress dependent finite growth in soft elastic tissues. J. Biomech. 27: 455–467
Rachev A., Stergiopulos N. and Meister J.J. (1996). Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure. J. Biomech. 29(5): 635–642
Rachev A., Stergiopulos N. and Meister J.-J. (1998). A model for geometric and mechanical adaptation of arteries to sustained hypertension. J. Biomech. Eng. 120: 9–17
Taber L.A. (1995). Biomechanics of growth, remodeling and morphogenesis. Appl. Mech. Rev. 48(8): 487–545
Taber L.A. (1998). A model for aortic growth based on fluid shear and fiber stresses. J. Biomech. Eng. 120: 348–354
Zhu C., Bao G. and Wang N. (2000). Cell mechanics: mechanical response, cell adhesion, and molecular deformation. A. Rev. Biomed. Eng. 2: 189–226
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by P. Cermelli
Rights and permissions
About this article
Cite this article
Ambrosi, D., Guillou, A. Growth and dissipation in biological tissues. Continuum Mech. Thermodyn. 19, 245–251 (2007). https://doi.org/10.1007/s00161-007-0052-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00161-007-0052-y