Computational study of Wolff's law with trabecular architecture in the human proximal femur using topology optimization

2008 ◽  
Vol 41 (11) ◽  
pp. 2353-2361 ◽  
Author(s):  
In Gwun Jang ◽  
Il Yong Kim
Keyword(s):  
Topology Optimization ◽  
Proximal Femur ◽  
Computational Study ◽  
Trabecular Architecture ◽  
Wolff’S Law

Variation of trabecular architecture in proximal femur of postmenopausal women

2011 ◽  
Vol 44 (2) ◽  
pp. 248-256 ◽  
Author(s):  
Maria-Grazia Ascenzi ◽  
Nicole Hetzer ◽  
Alexandre Lomovtsev ◽  
Robert Rude ◽  
Aurelia Nattiv ◽  
...  
Keyword(s):  
Postmenopausal Women ◽  
Proximal Femur ◽  
Trabecular Architecture

Wolff’s Law of Trabecular Architecture at Remodeling Equilibrium

1986 ◽  
Vol 108 (1) ◽  
pp. 83-88 ◽  
Author(s):  
S. C. Cowin
Keyword(s):  
Stress Tensor ◽  
Bone Tissue ◽  
Constitutive Relation ◽  
Cancellous Bone ◽  
Strain Tensor ◽  
Constitutive Relationship ◽  
Trabecular Architecture ◽  
Fabric Tensor ◽  
Principal Axes ◽  
Wolff’S Law

An elastic constitutive relation for cancellous bone tissue is developed. This relationship involves the stress tensor T, the strain tensor E and the fabric tensor H for cancellous bone. The fabric tensor is a symmetric second rank tensor that is a quantitative stereological measure of the microstructural arrangement of trabeculae and pores in the cancellous bone tissue. The constitutive relation obtained is part of an algebraic formulation of Wolff’s law of trabecular architecture in remodeling equilibrium. In particular, with the general constitutive relationship between T, H and E, the statement of Wolff’s law at remodeling equilibrium is simply the requirement of the commutativity of the matrix multiplication of the stress tensor and the fabric tensor at remodeling equilibrium, T* H* = H* T*. The asterisk on the stress and fabric tensor indicates their values in remodeling equilibrium. It is shown that the constitutive relation also requires that E* H* = H* E*. Thus, the principal axes of the stress, strain and fabric tensors all coincide at remodeling equilibrium.

Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law

2009 ◽  
Vol 42 (8) ◽  
pp. 1088-1094 ◽  
Author(s):  
Ken-ichi Tsubota ◽  
Yusuke Suzuki ◽  
Tomonori Yamada ◽  
Masaki Hojo ◽  
Akitake Makinouchi ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Proximal Femur ◽  
Large Scale ◽  
Wolff’S Law
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