Principles of bone remodelling – the limit cycles of bone remodelling

Czasopismo : Acta of Bioengineering and Biomechanics
Tytuł artykułu : Principles of bone remodelling – the limit cycles of bone remodelling

Autorzy :
Gentle, R.
Nottingham Trent University, Department of Mechanical and Manufacturing Engineering, Burtton Street, Nottingham NG1 4BU, United Kingdom,,
Filipiak, J.
Wrocław University of Technology [Politechnika Wrocławska], Wybrzeże Wyspiańskiego 27, 50-370 Wrocław,
Chladek, W.
Silesian Technical University, Chair of Mechanics and Plastic Working Technology [Politechnika Śląska], Krasińskiego 8, 40-019 Katowice,
Prevorovská, S.
Institute of Thermomechanics CAS, Prague 8, 182-100 Dolejškova 5, Czech Republic,,
Minari, Ch.
Instituti Ortopedici Rizzoli, V. Barbiano 1/10, 40136 Bologna, Italy,,
Jiroušek, O.
Academy of Science of Czech Republic, Institute of Theoretical and Applied Mechanics, Prague 1, Národni tr. 3,
Petrtyl, M.
Czech Technical University in Prague, Faculty of Civil Engineering, Prague 6, Zikova 4,
Abstrakty : 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.

Słowa kluczowe : biochemia, biomechanika, kości, osteologia, bone remodelling, steady states, bifurcation points, kinetic equations, osteoid, osteoblasts, osteoclasts, limit cycle/cycles,
Wydawnictwo : Oficyna Wydawnicza Politechniki Wrocławskiej
Rocznik : 2001
Numer : Vol. 3, nr 1
Strony : 75 – 91
Bibliografia :
Cytuj : Gentle, R. ,Filipiak, J. ,Chladek, W. ,Prevorovská, S. ,Minari, Ch. ,Jiroušek, O. ,Petrtyl, M. , Principles of bone remodelling – the limit cycles of bone remodelling. Acta of Bioengineering and Biomechanics Vol. 3, nr 1/2001