A study of dense mineralized tissue by neutron diffraction

Lees, Sidney; Bonar, Laurence C.; Mook, H. A.

doi:10.1016/0141-8130(84)90017-5

Cited by 92 publications

(66 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such micromechanical models predict, on the basis of mechanical properties of bone elementary constituents (hydroxyapatite, collagen, water), the (poro-)elasticity tensors at the different hierarchical levels of the material, from tissue-specific composition data, such as porosities and mineral/collagen content. There-the explicit consideration of the extrafibrillar mineral crystals whose existence was evidenced earlier [Lees et al, 1984a, 1994, Prostak and Lees, 1996, Pidaparti et al, 1996, Benezra Rosen et al, 2002, and further confirmed by the kinetics of recent demineralization experiments [Balooch et al, 2008]. In this sense, the challenge of micromechanics-supported, consistently upscaled microstructure-property relationships for poroelasticity in bone has been met quite reasonably.…”

Section: Introductionmentioning

confidence: 99%

“…Again, we have to consider close packing of collagen as to get access to properties of molecular collagen. It is known from neutron diffraction studies [Lees et al, 1984a, Lees, 1987 that diffractional spacing (a measure for the lateral distance of collagen molecules) reduces from 1.5 nm (for wet collagen) to 1.1 nm (for maximally packed (dry) collagen). Accordingly, the cross sectional area of a tensile specimen would reduce by the ratio 1.5/1.1, so that the strength of molecular collagen follows to be 1.5/1.1 times higher than that of wet collagen, i.e.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Fritsch

Hellmich

Dormieux

2009

Journal of Theoretical Biology

175

128

View full text Add to dashboard Cite

To cite this version:Andreas Fritsch, Christian Hellmich, Luc Dormieux.Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength. Journal of Theoretical Biology, Elsevier, 2009, 260 (2) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A c c e p t e d m a n u s c r i p t AbstractThere is an ongoing discussion on how bone strength could be explained from its internal structure and composition. Reviewing recent experimental and molecular dynamics studies, we here propose a new vision on bone material failure: mutual ductile sliding of hydroxyapatite mineral crystals along layered water films is followed by rupture of collagen crosslinks. In order to cast this vision into a mathematical form, a multiscale continuum micromechanics theory for upscaling of elastoplastic properties is developed, based on the concept of concentration and influence tensors for eigenstressed microheterogeneous materials. The model reflects bone's hierarchical organization, in terms of representative volume elements for cortical bone, for extravascular and extracellular bone material, for mineralized fibrils and the extrafibrillar space, and for wet collagen. In order to get access to the stress states at the interfaces between crystals, the extrafibrillar mineral is resolved into an infinite amount of cylindrical material phases oriented in all directions in space. The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their intercrystalline, intermolecular, lacunar, and vascular porosities, and the elastic and strength properties of hydroxyapatite and (molecular) collagen. Preprint submitted to Journal of Theoretical Biology 6 May 2009A c c e p t e d m a n u s c r i p t

show abstract

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Fritsch

Hellmich

Dormieux

2009

Journal of Theoretical Biology

175

128

View full text Add to dashboard Cite

show abstract

“…In Eq. (35), v col = 335.6 nm 3 is the volume of a single collagen molecule [Lees, 1987]; v fib is the volume of one rhomboidal fibrillar unit with length 5D, width b, and height d s ; b = 1.47 nm is an average (rigid) collagen crosslink length valid for all mineralized tissues [Lees et al, 1984b], D ≈ 64 nm is the axial macroperiod of staggered assemblies of type I collagen [Hodge and Petruska, 1963], and d s is the tissue-specific neutron diffraction spacing between collagen molecules, which depends on the mineralization and the hydration state of the tissue [Lees et al, 1984a;Bonar et al, 1985;Lees et al, 1994b]. For wet tissues, d s can be given in a dimensionless form [Hellmich and Ulm, 2003], as a function of ρ ec only…”

Section: 'Universal' Relations Between Extracellular Mass Density Andmentioning

confidence: 99%

Bone fibrillogenesis and mineralization: Quantitative analysis and implications for tissue elasticity

Vuong

Hellmich

2011

Journal of Theoretical Biology

View full text Add to dashboard Cite

Data from bone drying, demineralization, and deorganification tests, collected over a time span of more than eighty years, evidence a myriad of different chemical compositions of different bone materials. However, careful analysis of the data, as to extract the chemical concentrations of hydroxyapatite, of water, and of organic material (mainly collagen) in the extracellular bone matrix, reveals an astonishing fact: it appears that there exists a unique bilinear relationship between organic concentration and mineral concentration, across different species, organs, and age groups, from early childhood to OLD AGE: During organ growth, the mineral concentration increases linearly with the organic concentration (which increases during fibrillogenesis), while from adulthood on, further increase of the mineral concentration is accompanied by a decrease in organic concentration. These relationships imply unique mass density-concentration laws for fibrillogenesis and mineralization, which -in combination with micromechanical models -deliver 'universal' mass density-elasticity relationships in extracellular bone matrix -valid across different species, organs, and ages. They turn out as quantitative reflections of the well-instrumented interplay of osteoblasts, osteoclasts, osteocytes, and their precursors, controlling, in a fine-tuned fashion, the chemical genesis and continuous transformation of the extracellular bone matrix. Considerations of the aformentioned rules may strongly affect the potential success of tissue engineering strategies, in particular when translating, via micromechanics, the aformentioned growth and mineralization characteristics into tissue-specific elastic properties.

show abstract

“…Skakle & Aspden did not cite the density of their material. Lees (2003) showed that the lateral spacing d for compact bone collagen is strongly linear with the inverse wet density,…”

Section: Sidney Leesmentioning

confidence: 99%

“…They found the lateral spacing of wet tissue human compact bone to be 1.230 nm, and 1.191 nm when dry. Lees et al (1984) reported ®nding the lateral spacing for cow bone, of density 2.04 Mg m À3 , to be 1.24 nm wet and 1.16 nm dry. Skakle & Aspden did not cite the density of their material.…”

Section: Sidney Leesmentioning

confidence: 99%

Comments onNeutron diffraction studies of collagen in human cancellous boneby Skakle & Aspden (2002)

Lees¹

2004

J Appl Cryst

Self Cite

View full text Add to dashboard Cite

show abstract

A study of dense mineralized tissue by neutron diffraction

Cited by 92 publications

References 12 publications

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Bone fibrillogenesis and mineralization: Quantitative analysis and implications for tissue elasticity

Comments onNeutron diffraction studies of collagen in human cancellous boneby Skakle & Aspden (2002)

Contact Info

Product

Resources

About