Plasticity and toughness in bone Robert O. Ritchie, Markus J. Buehler, and Paul Hansma Our bones are full of microscopic cracks, but the hierarchical character of the bones’ structure—from molecular to macroscopic scales—makes them remarkably resistant to fracture. Rob Ritchie is a professor of materials science at the University of California, Berkeley, and a senior scientist at Lawrence Berkeley National Laboratory. Markus Buehler is a professor in the department of civil and environmental engineering at the Massachusetts Institute of Technology in Cambridge. Paul Hansma is a professor of physics at the University of California, Santa Barbara. Built primarily from collagen molecules, mineral in those various structural elements. crystals, water, and ions, bone forms the lightweight but The physics of fracture is characterized by dissipation of tough and protective load-bearing framework of the body. elastically stored energy from an applied load. Materials Bone’s elastic modulus—its stiffness during elastic deforma- begin to fracture when the elastic energy dissipated by the tion—spans 15–25 GPa, roughly a third of metallic alu- advance of a crack is equal to or larger than the energy re- minum; its strength, the applied stress at the onset of plastic quired to create a new surface. Thus, the more energy- deformation, is a few hundred MPa, comparable with alu- dissipation (or toughening) mechanisms that exist, the more mina ceramics; and its fracture toughness, a measure of the difficult it is to break a material. One hypothesis is that in material’s resistance to fracture, is typically 3−10 MPa/m, bone, toughening mechanisms exist at all characteristic some 3 to 10 times as high as silicon. length scales. But as bone changes with age, so can structural Although other materials may be mechanically superior, features and phenomena—from the cross-linking of collagen bone is unique for its capacity for self-repair and adaptation.1 proteins to the actual macroscopic path taken by a crack. Un- Unfortunately, aging-related changes to the musculoskeletal fortunately, it’s difficult to discern the roles that structural system increase bone’s susceptibility to fracture,2 which can constituents play during the initiation of a crack and the be especially serious in the case of the elderly. Several vari- crack’s subsequent propagation. ables are involved, among them the frequency of traumatic If the links between biological factors, bone structure falls, prior fractures, and loading history, but bone tissue it- (from molecular to macroscopic levels), fracture mechanism, self appears to deteriorate with age.3 A primary factor in that and toughness can be established, then the concept of bone deterioration is bone quality, a loosely defined term used to quality will hopefully become a quantifiable entity. More- describe some, but not yet all, microscopic and macroscopic over, once the structural mechanisms underlying any change structural characteristics that influence bone’s mechanical in bone quality are identified, it is entirely feasible that new properties. and perhaps more effective therapeutic treatments can be de- Traditional thinking on bone’s deterioration has focused veloped to treat bone disorders. on bone quantity—described by the bone mass or bone- In this article, we outline what is known about how bone mineral density (BMD)—as a predictor of fracture risk. For derives its resistance to permanent deformation and fracture example, the elevation in bone repair activity, known as re- by examining the multidimensional nature of its structure. modeling, among aging postmenopausal women in particu- lar can lead to osteoporosis. Disease statistics from the Na- Hierarchical structure tional Osteoporosis Foundation bear out the magnitude of Along with materials such as hair, skin, and spider silk, bone the problem: One in two women and one in four men over belongs to a family of biological proteins that constitute crit- the age of 50 will suffer an osteoporosis- related fracture over ical building blocks of life. Not surprisingly, bone provides a their remaining lifetimes. variety of mechanical, synthetic, and metabolic functions for Mounting evidence indicates that low BMD, however, is the body.5 Beyond its support for our skeletal frames, bone not the sole factor responsible for the fracture risk. A land- enables sound transduction in the ear, facilitates blood pro- mark study 20 years ago by Sui Hui and colleagues showed duction in its marrow—the interstitial spaces of what is a roughly 10-fold increase in fracture risk with aging, inde- known as spongy, cancellous, or trabecular bone—and pro- pendent of BMD.2 That result and the fact that BMD alone vides a reservoir of calcium and phosphorous. An under- cannot explain therapeutic benefits of antiresorptive agents standing of how microscopic structural features combine into in treating osteoporosis emphasize the need to understand macroscopic ones is thus vital to discern the links between the factors that control bone quality. structural organization and function. Although bone is a simple composite of a mineral phase, The smallest-scale features of bone include a protein calcium phosphate–based hydroxyapatite, embedded in an phase composed of tropocollagen molecules, each built from organic matrix of collagen protein, its structure is highly com- three polypeptides arranged in a triple helical geometry and plex and hierarchical: Features at smaller length scales form stabilized by hydrogen bonding between different amino- the basis for features at higher ones,4 as shown in figure 1. A acid building blocks (see figure 2). The soft collagen gives vital question is the origin of the material’s fracture resistance bone its elasticity and the ability to dissipate energy under © 2009 American Institute of Physics, S-0031-9228-0906-030-X June 2009 Physics Today 41 Figure 1. Multiscale structure of bone. Collagen protein molecules known as Amino acids tropocollagen form from three chains of amino acids and provide the structural ~1 nm basis for mineralized collagen fibrils, the basic building blocks of bone. Several Tropocollagen collagen fibrils, each linked by an organic phase, form fibril arrays. Each array (TC) makes up a single collagen fiber, and several fibers form geometric patterns that ~300 nm provide structure—more precisely, lamellar structure—to the cellular compo- Mineralized nents of bone. The boundaries between packets of fibers create what are known collagen Mineral crystal as lamellar interfaces. That microstructure forms distinct mesoscale arrange- fibrils TC molecule ~1μ m ments: compact, or cortical, bone (the dense material found at the surface of all bones) and spongy, or cancellous, bone (foamlike material whose struts are Fibril arrays μ μ some 100 m thick and separated by 1-mm-wide holes). Macroscopic cortical ~10 m bone is complex. Osteons surround and protect blood vessels. Osteocytes, which pervade the whole tissue, are mature bone cells connected to each other through thin channels called canaliculi. (Adapted from ref. 4, Weiner and Wagner, Fiber and from G. J. Tortora, Principles of Human Anatomy, Wiley, New York, 2002.) patterns ~50μ m Interstitial Concentric lamellae Haversian lamellae canal Blood vessels Osteon and Lacuna Osteocyte Haversian canal Canaliculi ~100μ m 10 μm Osteon Bone tissue ~50 cm 0.5 cm Macroscopic Spongy bone bone ~1 m Compact bone Lymphatic vessel mechanical deformation. The most abundant protein on channels that are surrounded by lamellar rings with so-called Earth, collagen is arguably also the most important structural cement lines at their outer boundaries. They also contain cells protein in biology. It is vital in tissues such as cartilage, skin, that dissolve old bone and renew tissue. Thanks to that re- and the eye’s cornea, and can stretch up to 50% tensile strain modeling, the structure of bone is highly dynamic. For a with stresses near 10–20 GPa before breaking.6 deeper treatment of the crucial effect of remodeling on many Staggered arrays of tropocollagen molecules form colla- of bone’s remarkable properties, such as its adaptability to gen fibrils, which themselves arrange into arrays. Collagen changing mechanical load patterns, see references 4 and 7. fibrils are particularly significant because they act as the At the macroscopic scale, differences in the density of structural template for bone formation: Tiny crystals of hy- bone tissue become apparent. Compact, or cortical, bone, the droxyapatite assemble in the gap between collagen fibrils, il- principal focus of this article, is essentially solid, just porous lustrated in figure 3, and the fibrils become mineralized as enough to accommodate cells and a vascular network. It the bone tissue grows and matures. The mineral crystals makes up the dense material found at the surface of all bones. grow to a few tens of nanometers in length but remain quite Spongy bone is extremely porous and fills the insides of thin, roughly 1−2 nm, in the out-of-plane direction. Each many bones. array of fibrils, connected by a protein phase that provides In addition to the hierarchical complexity, the composi- additional dissipative properties by acting as glue, twists into tion and the structure of both compact and spongy bone vary an individual fiber. with factors such as skeletal site, age, sex, physiological func- Those fibers, in turn, arrange into randomly oriented, tion, and mechanical loading. Those factors, when combined parallel, tilted, or woven bundles in bone. The