scholarly journals Wolff's law

2020 ◽  
Author(s):  
Balint Botz
Keyword(s):  
Wolff’S Law

Boning up on Wolff's Law: Mechanical regulation of the cells that make and maintain bone

2010 ◽  
Vol 43 (1) ◽  
pp. 108-118 ◽  
Author(s):  
Jan-Hung Chen ◽  
Chao Liu ◽  
Lidan You ◽  
Craig A. Simmons
Keyword(s):  
Wolff’S Law ◽  
Mechanical Regulation

The Cellular Basis of Wolff’s Law

1988 ◽  
Vol 14 (3) ◽  
pp. 503-517
Author(s):  
Clinton T. Rubin ◽  
Michael R. Hausman
Keyword(s):  
Cellular Basis ◽  
Wolff’S Law

Bone Biology

2017 ◽  
Author(s):  
Elizabeth Weiss
Keyword(s):  
Trabecular Bone ◽  
Bone Remodeling ◽  
Calcium Homeostasis ◽  
Bone Biology ◽  
Diarthrodial Joint ◽  
Bone Damage ◽  
Bone Changes ◽  
Cartilage Cells ◽  
Wolff’S Law ◽  
Haversian System

This chapter introduces readers to the basics of understanding bone’s functions, which include calcium homeostasis and enabling movement, bone’s components, such as the collagen, and bone’s organization, such as the Haversian system found in cortical bone. The focus of this chapter is on explaining concepts of bone remodeling, which is thought to prevent fractures and other bone damage, and repair, which can take place at macro-levels and micro-levels. Wolff’s Law of bone remodeling, which was initially focused on trabecular bone changes, is discussed in terms of bone’s response to forces that result in strains and stresses. Finally, diarthrodial joint remodeling and repair are discussed; cartilage cells were once thought to be static, yet now they are known to also respond to stresses.

The shrew tamed by Wolff's law: Do functional constraints shape the skull through muscle and bone covariation?

2014 ◽  
Vol 276 (3) ◽  
pp. 301-309 ◽  
Author(s):  
Raphaël Cornette ◽  
Anne Tresset ◽  
Anthony Herrel
Keyword(s):  
Functional Constraints ◽  
Wolff’S Law

Structural Adaptation of Bones

1990 ◽  
Vol 43 (5S) ◽  
pp. S126-S133 ◽  
Author(s):  
S. C. Cowin
Keyword(s):  
Mechanical Properties ◽  
Bone Tissue ◽  
Structural Adaptation ◽  
Connective Tissues ◽  
Environmental Loading ◽  
Principal Axes ◽  
Living Bone ◽  
Wolff’S Law ◽  
Axes Of Symmetry ◽  
Algebraic Formulation

Living bone tissue, like many other connective tissues, is a structural material that adapts its form and microstructure to changing environmental loading conditions. Bone tissue adapts not only its shape, but also its density and the details of its microstructure including its anisotropy. The anisotropy of bone is adapted in both its degree or strength and in the orientation of its principal axes of symmetry. These adaptive features of bone tissue are often referred to as aspects of Wolff’s law, although, strictly speaking, the term “Wolff’s law” applies only to the structural adaptation of spongy or trabecular bone. In this paper the composition, microstructure, mechanical properties and structurally adaptive features of bone are briefly reviewed. An algebraic formulation of Wolff’s law at remodeling equilibrium is described, and the nature of an evolutionary Wolff’s law is sketched.

A Possible Mechanism of Wolff's Law: Trabecular Microfractures

1973 ◽  
Vol 81 (1) ◽  
pp. 27-40 ◽  
Author(s):  
J. W. Pugh ◽  
R. M. Rose ◽  
E. L. Radin
Keyword(s):  
Wolff’S Law

Internal Architecture of the Calcaneus: Implications for Calcaneus Fractures

2000 ◽  
Vol 21 (2) ◽  
pp. 114-118 ◽  
Author(s):  
Fady F. Sabry ◽  
Nabil A. Ebraheim ◽  
John N. Mehalik ◽  
Anthony T. Rezcallah
Keyword(s):  
Cortical Thickness ◽  
Anterior Part ◽  
Anterior Portion ◽  
Radiographic Images ◽  
Secondary Fracture ◽  
Wolff’S Law ◽  
Multiple Measurements ◽  
Resistance To Stress ◽  
Calcaneus Fractures ◽  
Internal Architecture

Study Design Fourteen cadaveri specimens were sectioned to analyze the internal architecture of the human calcaneus. We described the arrangement and orientation of trabecular patterns within the calcaneus and made multiple measurements of its cortical thickness. Objective To characterize the internal architecture of the calcaneus and correlate these findings with well-described patterns of calcaneus fracture in order to better understand the fracture mechanics of this common fracture. Methods Fourteen dry, frozen, human calcanei were sectioned using a saw. In each the coronal, sagittal and axial planes, we sectioned separate specimens into slices of 0.5mm thickness. High-resolution radiographic images were taken of the sectioned specimens. The internal trabecular arrays were described and measurements of cortical thickness were recorded. The correlation between these findings and the known pattern of calcaneal fractures was analyzed. RESULTS A dominant trabecular pattern running anteroposteriorly along the long axis of the calcaneus was observed. In the posterior tuberosity the trabeculae were arranged parallel to the posterior border. There was an area of sparse or absent mineralization in the anterior part of the calcaneus corresponding to the “neutral triangle” described by Wood and Harty 10, 23. The thickest sites of the calcaneal cortex were the lower pole of the posterior tuberosity, the upper surface at the angle of Gissane, and the lateral surface below the anterior portion of the posterior facet. Conclusion The trabecular architecture of the calcaneus is created by applied stress in concordance with Wolff's law. The weakest plane of resistance to stress is parallel to these organized trabeculae or through areas lacking trabeculae. This study demonstrates that the primary and secondary fracture lines commonly encountered in calcaneus fractures correlates with the internal architectural map of the calcaneal trabecular patterns.

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.

Performance Comparison of Frame Structures: Discrete Michell or Wolff?

2010 ◽  
Author(s):  
Maryam Gholamirad ◽  
Marcelo Epstein
Keyword(s):  
Principal Stress ◽  
Dynamic Environment ◽  
Performance Comparison ◽  
Frame Structures ◽  
Efficient Manner ◽  
Mechanical Loads ◽  
Bone Material ◽  
Wolff’S Law ◽  
Bone Trabeculae ◽  
Special Case

The presented work highlights parallels between natural and human designs for optimization purposes. Wolff’s law predicts that bone trabeculae orientation alterations within a dynamic environment occur in such a way as to use bone material in a structurally efficient manner; this occurs because trabeculae orientations align themselves along principal stress trajectories. Michell has also demonstrated how to optimize structures under a given a set of mechanical loads. Some researchers have recently defined a special case for optimal tensegrity structures that produces the discrete Michell truss. In this paper we have carried out a performance comparison between two different frame structures modeled based on the Wolff’s hypothesis and optimal tensegrity formulation.

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