iBone: A Reaction Diffusion Based Shape Optimization Method

Bone is a highly specialized form of connective tissue consisting of org anic and inorganic materials. Bone is continuously remodeled by bone forming osteoblasts and resorbing ost eoclast . In terrestrial vertebrates, these two activities are strictl y ba anced and adapt the shape of bone to the local stress with limited calcium intake from foods. However, the cell based-adaptation mechanism underlying this system have not been well considered. Recently, we have found that human mesenchymal stem cells strongly stimulated towards osteoblasti c lineage form a condensation pattern similar to Turing patterns observed in reaction-diffusion models. We c onstructed a hypothetical model of bone remodeling (iBone), by coupling the bone forming and resorbing ac t vities based on the reaction-diffusion model weighed by local stress. When an externa l mechanical stress was applied to a sample model, stimulated bone formation and subsequent activation of bone resorption efficiently adapted the shape of it to the given stress, and created flat stress distribution. iB one could also repair fractures which caused uneven stress distribution. The efficacy of i Bone proposes a principal model how bone cells can form a cooperative system that adapt the microst ru ture of bone to the voluntary mechanical loads; and, suggests that element based-parallel computi ng system, such as reaction-diffusion system, can be applied for designing efficient stress adapta tion models.

[1]  S. Kondo,et al.  A reaction–diffusion wave on the skin of the marine angelfish Pomacanthus , 1995, Nature.

[2]  S. Y. Han Shape optimization for general two-dimensional structures , 2000 .

[3]  K. Tezuka,et al.  Stimulation of Osteoblastic Cell Differentiation by Notch , 2002, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[4]  C. Jacobs,et al.  Functional Gap Junctions Between Osteocytic and Osteoblastic Cells , 2000, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[5]  L. Bonewald,et al.  PGE2 Is Essential for Gap Junction-Mediated Intercellular Communication between Osteocyte-Like MLO-Y4 Cells in Response to Mechanical Strain. , 2001, Endocrinology.

[6]  S J Hollister,et al.  Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. , 2001, Journal of biomechanical engineering.

[7]  H. Weinans,et al.  A Three‐Dimensional Simulation of Age‐Related Remodeling in Trabecular Bone , 2001, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[8]  Rik Huiskes,et al.  Effects of mechanical forces on maintenance and adaptation of form in trabecular bone , 2000, Nature.

[9]  I. Epstein,et al.  Modeling of Turing Structures in the Chlorite—Iodide—Malonic Acid—Starch Reaction System , 1991, Science.

[10]  H. Swinney,et al.  Transition from a uniform state to hexagonal and striped Turing patterns , 1991, Nature.

[11]  T. Skerry Identification of novel signaling pathways during functional adaptation of the skeleton to mechanical loading: the role of glutamate as a paracrine signaling agent in the skeleton , 1999, Journal of Bone and Mineral Metabolism.

[12]  Hideyuki Azegami A Proposal of a Shape-0ptimization Method Using a Constitutive Equation of Growth : In the Case of a Static Elastic Body , 1990 .

[13]  M. Bendsøe,et al.  Optimal design of material properties and material distribution for multiple loading conditions , 1995 .