Analytical description of growth

Skalak, Richard; Dasgupta, Gautam; Moss, Melvin L.; Otten, Egbert; Dullemeijer, P.; Vilmann, H.

doi:10.1016/0022-5193(82)90301-0

Cited by 235 publications

(139 citation statements)

References 14 publications

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“…Others refer explicitly to evolving natural configurations, which the current approach precludes. In the study of Skalak et al (1982), specific attention is given to surface growth, though their approach differs from the one followed here. In particular, these authors define a vector growth rate on an interface between two solids, rather than the scalar area density of mass supply appearing in the current analysis.…”

Section: Discussionmentioning

confidence: 99%

“…In the more general treatment of growth and remodeling, more subtle descriptions of the reference configuration have been proposed. Since the early work of Hsu (1968), Cowin and Hegedus (1976) and Skalak et al (1982), considerable advances have been made in the field of growth and remodeling of biological tissues. Some of the recent developments address various challenges in the identification of natural reference configurations for the tissue, whether modeled as a single solid constituent (Rodriguez et al, 1994;Chen and Hoger, 2000;Guillou and Ogden, 2006), a mixture of solid constituents Rajagopal, 2002, 2003), or a mixture of solid and fluid constituents (Klisch et al, 2003).…”

Section: Reference Configurationmentioning

confidence: 99%

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On the theory of reactive mixtures for modeling biological growth

Ateshian

2007

Biomech Model Mechanobiol

185

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Mixture theory, which can combine continuum theories for the motion and deformation of solids and fluids with general principles of chemistry, is well suited for modeling the complex responses of biological tissues, including tissue growth and remodeling, tissue engineering, mechanobiology of cells and a variety of other active processes. A comprehensive presentation of the equations of reactive mixtures of charged solid and fluid constituents is lacking in the biomechanics literature. This study provides the conservation laws and entropy inequality, as well as interface jump conditions, for reactive mixtures consisting of a constrained solid mixture and multiple fluid constituents. The constituents are intrinsically incompressible and may carry an electrical charge. The interface jump condition on the mass flux of individual constituents is shown to define a surface growth equation, which predicts deposition or removal of material points from the solid matrix, complementing the description of volume growth described by the conservation of mass. A formu-lation is proposed for the reference configuration of a body whose material point set varies with time. State variables are defined which can account for solid matrix volume growth and remodeling. Constitutive constraints are provided on the stresses and momentum supplies of the various constituents, as well as the interface jump conditions for the electrochem cal potential of the fluids. Simplifications appropriate for biological tissues are also proposed, which help reduce the governing equations into a more practical format. It is shown that explicit mechanisms of growth-induced residual stresses can be predicted in this framework.

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Section: Discussionmentioning

confidence: 99%

Section: Reference Configurationmentioning

confidence: 99%

On the theory of reactive mixtures for modeling biological growth

Ateshian

2007

Biomech Model Mechanobiol

185

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“…Skalak et al (1982) later formulated a continuum model of growth. Carter et al (1987) proposed bone remodelling was targeted to produce a homeostatic level of an 'effective stimulus ' and Huiskes et al (1987) proposed that the process of bone remodelling was an adaptation that returned the strain energy density in the tissue to a homeostatic value.…”

Section: Introductionmentioning

confidence: 99%

Evolution of mechanoregulation of bone growth will lead to non-optimal bone phenotypes

Nowlan

Prendergast

2005

Journal of Theoretical Biology

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Mechanical forces acting on the bones during growth affect their final shape and strength.Mechanoregulation of bone growth may be recognised in embryogenesis, and also in the adaptation of the adult skeleton to changes in mechanical loading. Mechanoregulatory responses for tissues have arisen during evolution, but does evolution give rise to responses that produce optimal skeletal phenotypes? In this paper, we investigate the emergence of an optimal mechanoregulation response in a population.By combining equations describing long bone growth with a genetic algorithm to describe evolutionary change, we created a computational model to simulate the evolution of mechanoregulation in bone growth. A population of individuals is created where each individual is assigned a diploid gene set which controls the growth and remodelling of the bone. At maturity, each bone is assessed and its 'fitness' calculated; fitness is quantified as bone strength relative to bone mass. The simulation continues for many generations, and includes mutations and a varying environment. The genes present in the population are tracked and the evolution of parameters governing mechanoregulation is calculated.The results indicate that a population may converge to one bone growth algorithm but, more usually, a range of mechanoregulation algorithms for different individuals will persist after many generations. Even if the population converges to one mechanoregulation law, convergence to the 'optimum' bone was never found. Although many researchers propose that natural selection has pushed skeletal structure towards an optimum, our computational model suggests that this is unlikely to be the case.

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“…It is well known that synthesized polymers and natural rubbers are both in very high demand from both industry and society, especially after World War II. Notable figures like Eugene Bingham (1878-1945), Markus Reiner (1886-1976), Paul Flory (1910-1985, Leslie Treolar (1906-1985, Ronald Rivlin (1915Rivlin ( -2005, Albert Green (1912Green ( -1999, Clifford Truesdell (1919-2000, James Oldroyd (1921-1982), Anthony Spencer (1929-2008), Jerald Ericksen (1924-), Walter Noll (1925-), Richard Toupin (1926-), Bernard Coleman (1930-), and Morton Gurtin (1934 are all involved in the development of shaping continuum mechanics into a general theoretical framework for the mechanics of continua. A significant contributor in this area is Ronald Rivlin, who spent nine years in the British Rubber Producers Research Association (BRPRA), which played an important and critical role in the theoretical and experimental developments of rubber elasticity.…”

Section: Present Continuum Mechanicsmentioning

confidence: 99%

The renaissance of continuum mechanics

Chen

2014

J. Zheijang Univ.-Sci.

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Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical (or mechanical) properties are assumed to vary continuously in the spaces they occupy. Continuum mechanics may be seen as the symbol of modern mechanics, which differs greatly from current physics, the two often being mixed up by people and even scientists. In this short paper, I will first try to give an illustration on the differences between (modern) mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modern science, and is much closer to physics, chemistry, biology, etc. than ever before.

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Analytical description of growth

Cited by 235 publications

References 14 publications

On the theory of reactive mixtures for modeling biological growth

On the theory of reactive mixtures for modeling biological growth

Evolution of mechanoregulation of bone growth will lead to non-optimal bone phenotypes

The renaissance of continuum mechanics

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