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2 Acta of Bioengineering and Biomechanics

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Principles of bone remodelling - the limit cycles of bone remodelling

Petrtyl M., Danešová J.

Acta of Bioengineering and Biomechanics

2001

Vol. 3, nr 1

75-91

The bone tissue remodelling is a relatively slow process. In physiologically "normal" conditions, it tends towards the state of remodelling equilibrium. In the state of final remodelling equilibrium, the strain energy reaches its minimum. In the life of each human being, the bone tissue passes through the repeating limit cycles of its development, functioning and destruction. The paper presented is aimed at the biomechanochemical processes within one limit cycle of bone remodelling using the stoichiometric equations and kinetic equations. Each limit cycle of the bone tissue remodelling (in its assumed volume element) consists of several stages, in which the biochemical reactions are proceeding in a highly intensive way, and of several periods in which the tissue is in weakly steady states (i.e.. the biochemical reactions are very slow or they almost do not take place). Generally, throughout the life of a human, a bone tissue is several times in the principal weakly steady state, i.e., in such a state in which the long-term remodelling equilibrium is reached. This period lasts for several years (roughly for 6-8 years) in the life of an adult human in his/her productive age, while in the life of a child this period is shorter. Figuratively speaking, the stages of the bone tissue remodelling (during one limit cycle) can be compared to the tissue "childhood and maruraiion" (i.e., n stage of remodelling - apposition of the tissue), and "aging-demise" (I stage of remodelling - resorption). One limit cycle of the bone tissue life (out of the series of the subsequent periodic limit cycles) that is characterized by the bone tissue development, functioning and destruction (in the unit volume element) can be synoptically, and in the real time, described by four stages. The limit cycle is a close trajectory of solution of kinetic equations of bone remodelling. The bone tissue (in its unit volume element) passes through the repeating harmonic limit cycles (i.e., the stable periodic processes) of its development and destruction.

Bone remodeling and bone adaptation

Petrtyl M., Danesova J.

Acta of Bioengineering and Biomechanics

1999

Vol. 1, nr 1

107-116

Bone remodelling is a very complicated process that can be characterised as close relationship of biomechnical effects and biomechanical reactions. It is not possible to give an exact definition of the bone remodeling if we take into consideration the aspects related merely to biomechanics or to biochemistry. Biomechanical processes in a remodelled bone tissue depend on the dominant force and moment effects or on the stress and strain state of the tissue. The stress (strain) tensors initiate and govern the rate of biochemical remodelling processes. The paper presented deals with fundamental stoichiometric equations of bone remodelling, kinetic equations of remodelling and rate constants of remodelling. The rates of bone remodelling depend on mechanical effects or on stress (strain) tensors. The spherical stress tensor controls the rate of biomechanical remodelling reactions, while the deviator of a stress (strain) tensor initiates biomechanical reactions. The micro-strains cause the flow of a liquid in the extra-celluar space of osteocytes and initiate the receptor activity of integrins A,B, The micro-strains of a mineralised matrix and the flow of an extra-cellular liquid result, for example in the production of prostaglandin E2 and in the subsquent resorption of a bone tissue.