SELF-ASSEMBLED SCAFFOLDS USING REACTION–DIFFUSION SYSTEMS: A HYPOTHESIS FOR BONE REGENERATION

2011 ◽  
Vol 11 (01) ◽  
pp. 231-272 ◽  
Author(s):  
DIEGO A. GARZÓN-ALVARADO ◽  
MARCO A. VELASCO ◽  
CARLOS A. NARVÁEZ-TOVAR
Keyword(s):  
Bone Matrix ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Tissue Growth ◽  
New Bone Formation ◽  
Reaction Diffusion Systems ◽  
Bone Scaffolds ◽  
Full Control ◽  
Diffusion Systems ◽  
Biomaterial Scaffold

One area of tissue engineering concerns research into alternatives for new bone formation and replacing its function. Scaffolds have been developed to meet this requirement, allowing cell migration, bone tissue growth, transport of growth factors and nutrients, and the improvement of the mechanical properties of bone. Scaffolds are made from different biomaterials and manufactured using several techniques that, in some cases, do not allow full control over the size and orientation of the pores characterizing the scaffold. A novel hypothesis that a reaction–diffusion (RD) system can be used for designing the geometrical specifications of the bone matrix is thus presented here. The hypothesis was evaluated by making simulations in two- and three-dimensional RD systems in conjunction with the biomaterial scaffold. The results showed the methodology's effectiveness in controlling features such as the percentage of porosity, size, orientation, and interconnectivity of pores in an injectable bone matrix produced by the proposed hypothesis.

Effect of noise on chemical waves in three-dimensional reaction-diffusion systems with gradient

2008 ◽  
Vol 128 (11) ◽  
pp. 114505 ◽  
Author(s):  
Xiaochuan Lu ◽  
Chunyan Wang ◽  
Chun Qiao ◽  
Yabi Wu ◽  
Qi Ouyang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Chemical Waves

PATTERN FORMATION IN CHEMOTAXIC REACTION-DIFFUSION SYSTEMS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260013
Author(s):  
HIROTO SHOJI ◽  
KEITARO SAITOH
Keyword(s):  
Free Energy ◽  
Pattern Formation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Volume Filling ◽  
Reaction Diffusion Systems ◽  
Receptor Aggregation ◽  
Diffusion Systems

In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller–Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equilibrium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.

EXAMPLES OF FORCED SYMMETRY-BREAKING TO HETEROCLINIC CYCLES AND NETWORKS IN THREE-DIMENSIONAL EUCLIDEAN-INVARIANT SYSTEMS

2009 ◽  
Vol 19 (05) ◽  
pp. 1655-1678
Author(s):  
M. J. PARKER ◽  
M. G. M. GOMES ◽  
I. N. STEWART
Keyword(s):  
Symmetry Breaking ◽  
Nonlinear Optical ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Three Dimensions ◽  
Optical Systems ◽  
Heteroclinic Cycles ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Face Centered

In [Parker et al., 2008a] group theory was employed to prove the existence of homoclinic cycles in forced symmetry-breaking of simple (SC), face-centered (FCC), and body-centered (BCC) cubic planforms. In this paper we extend this classification demonstrating that more elaborate heteroclinic cycles and networks can arise through the same process. Our methods naturally generate graphs that represent possible heteroclinic cycles and networks. The results do not depend on the representation of the symmetry group and are thus quite general. This study is motivated by pattern formation in three dimensions which occur in reaction–diffusion systems, certain nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction. This work extends previous work by Parker et al. [2006, 2008a, 2008b] and Hou and Golubitsky [1997].

scholarly journals EXAMPLES OF FORCED SYMMETRY-BREAKING TO HOMOCLINIC CYCLES IN THREE-DIMENSIONAL EUCLIDEAN-INVARIANT SYSTEMS

2008 ◽  
Vol 18 (01) ◽  
pp. 83-107 ◽  
Author(s):  
M. J. PARKER ◽  
IAN STEWART ◽  
M. G. M. GOMES
Keyword(s):  
Symmetry Group ◽  
Three Dimensional ◽  
Direct Methods ◽  
Reaction Diffusion ◽  
Optical Systems ◽  
One Dimensional ◽  
Physical Systems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Group Orbit

We study perturbations of cubic planforms, proving there exists perturbations with homoclinic cycles between persistent steady states. Our results do not depend on the representation of the symmetry group of the lattice, and are thus quite general. The problem is studied using group theory rather than direct methods. We use the abstract action of the symmetry group of the perturbation on the group orbit to determine the existence of zero- and one-dimensional flow-invariant subspaces. The residual symmetry of the perturbation constrains the flows on these subspaces and, in certain cases, homoclinic cycles are guaranteed to exist. Cubic planforms are physically interesting due to their relevance to certain physical systems. Applications to reaction–diffusion systems, nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction are discussed.

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