Engineering Transactions, 49, 2-3, pp. 155–164, 2001

On a Class of Bone Cell-Based Remodeling Laws with Spatial Fading Influence of Stimuli

T. Lekszycki
Polish Academy of Sciences
Poland

In the present paper the class of cell-based bone remodeling laws is considered. The fundamental assumption is that of fading in space influence on actor cells osteocytes functioning as sensors. The actor cells — osteoclasts and osteoclasts are responsible for the changes of bone micro-structure. The model proposed in the previous publications of other authors, is based on the assumption of exponential influence function and density of strain energy as the stimulus to which the osteocytes are sensitive, see [11, 12, 14]. As the result of the adaptation according to such remodeling law the porous material is created. The topology of the micro-structure of this material is dependent on the mechanical loading conditions and the characteristics of the interactions of cells. The aim of the present work was to examine if this phenomenon is characteristic only for this specific law or represents a rather general property associated with the hypothesis of fading influence of the cells. Different influence functions were examined for different functionals selected to represent the stimulus. It follows from the these considerations that the fading influence of the cells plays fundamental role for the remodeling process and the creation of trabecular structure. Such structures were obtained for several adaptation laws based on different influence functions and functionals representing the stimulus. They were compared with the results obtained for the adaptation law proposed and discussed in [11, 12, 14]. The numerical calculations suggest that the idea of spatial fading influence of the cells can be possibly combined in future with the results of the research on the biological mechanisms of the bone remodeling to propose more sophisticated models.
Keywords: adaptation; bone remodeling; fading influence; osteocyte; osteoblast; osteoclast; porous material; stimulus; trabecular structure
Full Text: PDF

References

D.B. BURR, R.B. MARTIN, Mechanisms of bone adaptation to the mechanical environment, Triangle, 31, 2/3, 59–76, 1992.

D.H. HEGEDUS, S.C. COWIN, Bone remodeling II: small strain adaptive elasticity, J. Elasticity, 6, 337–355, 1976.

D.R. CARTER, T.E. ORR, Skeletal development and bone functional adaptation (review, 36 refs.), Journal of Bone & Mineral Research, 7, S389–95, Dec. 1992.

G. LUO, S.C. COWIN, A.M. SADEGH, Y.P. ARRAMON, Implementation of strain rate as a bone remodeling stimulus, J. of Biomechanical Engineering, 117, 3, 329–338, 1995.

G. MAROTTI, V. CANE, S. PALAZZINI, C. PALUMBO, Structure-function relationship in the osteocyte, Ital. J. Miner. Electrolyte Metab., 4, 93–106, 1990.

J.D. CURREY, The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone, J. of Biomech., 21, 131–139, 1988.

L.A. TABER, Biomechanics of growth, remodeling and morphogenesis, Appl. Mech. Rev., 48, 8, 487–545, 1995.

L.E. LANYON, Osteocytes, strain detection, bone modeling and remodeling, Calcif Tissue Int., 53, S1, 102–106, 1993.

M.E. LEVENSTON, D.R. CARTER, An energy dissipation-based model for damage stimulated bone adaptation, J. of Biomechanics, 31, 7, 579–586, 1998.

M.G. MULLENDER, D. D. van der MEER, R. HUISKES, P. LIPS, Osteocyte density changes in aging and osteoporosis, Bone, 18, 2, 109–113, 1996.

M.G. MULLENDER, R. HUISKES, Proposal for the regulatory mechanism of Wolf's law, J. of Orthopaedic Research, 13, 4, 503–512, 1995.

M.G. MULLENDER, R. HUISKES, The regulation of functional adaptation in trabecular bone, [In:] Bone Structure and Remodeling, A. ODGAARD and H. WEINANS [Eds.], Recent Advances in Human Biology — Volume 2, World Scientific, 181–187, 1996.

M.G. MULLENDER, R. HUISKES, Osteocytes and bone lining cells: which are the best candidates for mechano-sensors in cancellous bone?, Bone, 20, 6, 527–532, 1997.

M.G. MULLENDER, R. HUISKES, H. WEINANS, A physiological approach to the simulation of bone remodeling as a self-organizational control process, J. of Biomechanics, 27, 11, 1389–1394, 1994.

P.J. PRENDERGAST, D. TAYLOR, Prediction of bone adaptation using damage accumulation, J. Biomech., 27, 1067–1076, 1994.

P.J. PRENDERGAST, R. HUISKES, Microdamage and osteocyte-lacuna strain in bone: a microstructural finite element analysis, J. of Biomechanical Engineering, 118, 2, 240–246, 1996.

P.J. PRENDERGAST, R. HUISKES, K. SOBALLE, ESB Research Award 1996. Biophysical stimuli on cells during tissue differentiation at implant interfaces, J. of Biomechanics, 30, 6, 539–548, 1997.

R.T. HART, D.T. DAVY, Theories of bone modeling and remodeling, Bone Mechanics, S. C. CowIN [Ed.], CRC Press, Boca Raton, FL, 253–277, 1989.

R.T. HART, D.T. DAVY, K.G. HEIPLE, A computational method for stress analysis of adaptive elastic materials with a view toward application in strain-induced bone remodeling, J. Biomech. Engng., 106, 342–350, 1984.

S.C. COWIN, On the minimization and maximization of the strain energy density in cortical bone tissue, J. of Biomechanics, 28, 4, 445–447, 1995.

S.C. COWIN, The search for mechanism in bone adaptation studies, Mechanics in Biology, ASME 2000, AMD-Vol. 242/BED-Vol. 46, 173–184, 2000.

S.C. COWIN, D. H. HEGEDUS, Bone remodeling I: theory of adaptative elasticity, J. Elasticity, 6, 3, 313–326, 1976.

S.C. COWIN, L. MOSS-SALENTIJN, M. L. Moss, Candidates for the mechanosensory system in bone, J. Biomech. Engng., 113, 191–197, 1991.

S.C. COWIN, S. WEINBAUM, Strain amplification in the bone mechanosensory system (review, 30 refs.), American Journal of the Medical Sciences, 316, 3, 184–188, 1998.

S.C. COWIN, R.R. NACHLINGER, Bone remodeling III: uniqueness and stability in adaptive elasticity theory, J. Elasticity, 8, 3, 285–295, 1978.

S. WEINBAUM, S.C. COWIN, Y. ZENG, A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses, J. of Biomechanics, 27, 3, 339–360, 1994.

T.P. HARRINGAN, J.J. HAMILTON, Bone strain sensation via transmenbrane potential changes in surface osteoblasts: loading rate and microstructural implications, J. of Biomechanics, 26, 183–200, 1993.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland