Dennis R. Carter

The compressive behavior of bone as a two-phase porous structure

Compression tests of human and bovine trabecular bone specimens with and without marrow in situ were conducted at strain rates of from 0.001 to 10.0 per second. A porous platen above the specimens allowed the escape of marrow during testing. The presence of marrow increased the strength, modulus, and energy absorption of specimens only at the highest strain rate of 10.0 per second. This enhancement of material properties at the highest strain rate was due primarily to the restricted viscous flow of marrow through the platen rather than the flow through the pores of the trabecular bone. In specimens without marrow, the strength was proportional to the square of the apparent density and the modulus was proportional to the cube of the apparent density. Both strength and modulus were approximately proportional to the strain rate raised to the 0.06 power. These power relationships, which were shown to hold for all bone in the skeleton, allow meaningful predictions of bone tissue strength and stiffness based on in vivo density measurements.

Mechanobiology of skeletal regeneration

Skeletal regeneration is accomplished by a cascade of biologic processes that may include differentiation of pluripotential tissue, endochondral ossification, and bone remodeling. It has been shown that all these processes are influenced strongly by the local tissue mechanical loading history. This article reviews some of the mechanobiologic principles that are thought to guide the differentiation of mesenchymal tissue into bone, cartilage, or fibrous tissue during the initial phase of regeneration. Cyclic motion and the associated shear stresses cause cell proliferation and the production of a large callus in the early phases of fracture healing. For intermittently imposed loading in the regenerating tissue: (1) direct intramembranous bone formation is permitted in areas of low stress and strain; (2) low to moderate magnitudes of tensile strain and hydrostatic tensile stress may stimulate intramembranous ossification; (3) poor vascularity can promote chondrogenesis in an otherwise osteogenic environment; (4) hydrostatic compressive stress is a stimulus for chondrogenesis; (5) high tensile strain is a stimulus for the net production of fibrous tissue; and (6) tensile strain with a superimposed hydrostatic compressive stress will stimulate the development of fibrocartilage. Finite element models are used to show that the patterns of tissue differentiation observed in fracture healing and distraction osteogenesis can be predicted from these fundamental mechanobiologic concepts. In areas of cartilage formation, subsequent endochondral ossification normally will proceed, but it can be inhibited by intermittent hydrostatic compressive stress and accelerated by octahedral shear stress (or strain). Later, bone remodeling at these sites can be expected to follow the same mechanobiologic adaptation rules as normal bone.

Mechanical loading history and skeletal biology

A comprehensive theory which relates tissue mechanical stresses to many features of skeletal morphogenesis, growth, regeneration, maintenance and degeneration is reviewed. The theory considers the repeated or intermittent mechanical forces which constitute the loading history on the chondro-osseous skeleton. The results of numerous mechanical stress analyses indicate that the local tissue stress history plays a major role in controlling connective tissue biology. The strong influence of mechanical energy in ontogenesis implies a comparably strong influence in phylogenesis. The fact that the mechanical stress histories in skeletal tissues are directly related to the force of gravity suggests that the life forms that have evolved on Earth are closely tied to our gravitational field.

Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy

The method of considering a single loading condition in the study of stress/morphology relationships in trabecular bone is expanded to include the multiple loading conditions experienced by bone in vivo. The bone daily loading histories are characterized in terms of stress magnitudes or cyclic strain energy density and the number of loading cycles. Relationships between local bone apparent density and loading history are developed which assume that bone mass is adjusted in response to strength or energy considerations. Three different bone maintenance criteria are described which are formulated based upon: (1) continuum model effective stress, (2) continuum model fatigue damage accumulation density, and (3) bone tissue strain energy density. These approaches can be applied to predict variations in apparent density within bone and among bones. We show that all three criteria have similar mathematical forms and may be related to the density (or concentration) of bone strain energy which is transferred (dissipated) in the mineralized tissue. The loading history and energy transfer concepts developed here can be applied to many different situations of growth, functional adaptation, injury, and aging of connective tissues.

Mechanical loading histories and cortical bone remodeling

SummaryA conceptual framework is presented for understanding and investigating structural adaptation of cortical bone. The magnitudes, orientations, and sense (tension or compression) of the physiologically incurred cyclic principal strains vary markedly throughout the skeleton. It is probable, therefore, that the strain/remodeling response of bone is site specific. Furthermore, there is some indication that immature bone is more responsive to alterations of cyclic strains than mature bone. Animal experimental studies and complementary stress and strain analyses suggest that the structural adaptation due to changes in cyclic strain fields may be a very nonlinear response. Bone loss in mature animals due to immobilization is sensitive to even small changes in the cyclic bone strains. Under normal conditions, however, there appears to be a broad range of physical activity in which bone is relatively unresponsive to changes in loading history. With severe repeated loading, bone hypertrophy can be pronounced. These observations open the possibility that bone atrophy and hypertrophy are controlled by different mechanisms. Therefore, two (or more) complementary control systems may be involved in the regulation of bone mass by bone cyclic strain histories. It is probable that bone mechanical microdamage is one control stimulus for affecting an increase in bone mass.

CYCLIC MECHANICAL PROPERTY DEGRADATION DURING FATIGUE LOADING OF CORTICAL BONE

Fatigue damage accumulation has been demonstrated in living bone and postulated as a stimulus to the bone modeling and remodeling response. Mechanical property degradation is one manifestation of fatigue damage accumulation. This study examines changes in secant modulus and cyclic energy dissipation behavior during axial load-controlled fatigue loading of cortical bone specimens. The findings suggest that secant modulus degradation and cyclic energy dissipation are greatly increased at loading levels above critical damage strain thresholds of 2500 and 4000 mu epsilon in tensile and compressive fatigue, respectively. Tensile and compressive fatigue loading also caused different forms of modulus degradation at loading levels above these thresholds. Bone behaves as a linear viscoelastic material below these thresholds, even after prior property degradation at higher loading levels. Cyclic energy dissipation was proportional to the 2.1 power of the applied effective strain range for all loadings below 2500 mu epsilon. Above 2500 mu epsilon, tensile fatigue loading caused cyclic energy dissipation proportional to the 5.8 power of the applied effective strain range. Compressive fatigue loading dissipated cyclic energy proportional to the 4.9 power of applied effective strain range over 4000 mu epsilon. Lifetime energy dissipation over all fatigue tests to fracture at a single loading level was well fitted by the same power law in the number of cycles to failure raised to the 0.6 power. Loading levels of 2500 mu epsilon in tension and 4000 mu epsilon in compression are within the ranges observed in living animals, and thus these phenomena may play a role in initiating the remodeling response in live bone tissue.

Articular cartilage functional histomorphology and mechanobiology: a research perspective

The histomorphogenesis of articular cartilage is regulated during skeletal development by the intermittent forces and motions imposed at diarthrodial joints. A key feature in this development is the formation of the superficial, transitional, radial, and calcified cartilage zones through the cartilage thickness. The histomorphological, biological, and mechanical characteristics of these zones can be correlated with the distributions of pressures, deformations, and pressure-induced fluid flow that are created in vivo. In a mature joint, cyclic loads produce cyclic hydrostatic fluid pressure through the entire cartilage thickness that is comparable in magnitude to the applied joint pressure. Prolonged physical activity can cause the total cartilage thickness to decrease about 5%, although the consolidation strains vary tremendously in the different zones. The superficial zone can experience significant fluid exudation and consolidation (compressive strains) in the range of 60% while the radial zone experiences relatively little fluid flow and consolidation. The topological variation in the histomorphologic appearance of articular cartilage is influenced by the local mechanical loading of chondrocytes in the different zones. Patterns of stress, strain, and fluid flow created in the joint result in spatial and temporal changes in the rates of synthesis and degradation of matrix proteins. When viewed over the course of a lifetime, even subtle difference in these cellular processes can affect the micro- and macro-morphology of articular cartilage. This hypothesis is supported by in vivo and ex vivo experiments where load-induced changes in matrix synthesis and catabolism, gene expression, and signal transduction pathways have been observed.

Mechanical properties of the human achilles tendon

OBJECTIVE To determine whether the human Achilles tendon has higher material properties than other tendons and to test for strain rate sensitivity of the tendon. DESIGN Mechanical testing of excised tendons. BACKGROUND While the human Achilles tendon appears to experience higher in vivo stresses than other tendons, it is not known how the Achilles tendons material properties compare with the properties of other tendons. METHODS Modulus, failure stress, and failure strain were measured for excised human Achilles tendons loaded at strain rates of 1% s(-1) and 10% s(-1). Paired t-tests were used to examine strain rate effects, and average properties from grouped data were used to compare the Achilles tendons properties with properties reported in the literature for other tendons. RESULTS Failure stress and failure strain were higher at the faster strain rate, but no significant difference in modulus was observed. At the 1% s(-1)rate, the mean modulus and failure stress were 816 MPa (SD, 218) and 71 MPa (SD, 17), respectively. The failure strain was 12.8% (SD, 1.7) for the bone-tendon complex and 7.5% (SD, 1.1) for the tendon substance. At the 10% s(-1) rate, the mean modulus and failure stress were 822 MPa (SD, 211) and 86 MPa (SD, 24), respectively. The mean failure strain was 16.1% (SD, 3.6) for the bone-tendon complex and 9.9% (SD, 1.9) for the tendon substance. These properties fall within the range of properties reported in the literature for other tendons. CONCLUSIONS The material properties of the human Achilles tendon measured in this study are similar to the properties of other tendons reported in the literature despite higher stresses imposed on the Achilles tendon in vivo.

Compact bone fatigue damage: a microscopic examination.

Flexural fatigue tests of bovine bone specimens produced fracture surfaces that were transverse on the tension side and oblique on the compression side. Similar fracture patterns were produced by bending tests with a single applied loading. Microscopic examination of flexural fatigue specimens prior to complete established that fatigue fracture is caused by the progressive accumulation of diffuse structural damage. The microdamage observed on the tension side consisted primarily of separation (or debonding) at cement lines and interlamellar cement bands. Tensile cracks in interstitial bone were also observed. The major damage modes on the compression side were oblique cracking and longitudinal splitting. The fatigue fracture patterns observed for the bone specimens correspond to the types of fatigue fractures observed clinically. Compact bone fatigue fractures in areas of longitudinal tensile stresses are generally seen as transverse lesions, whereas fatigue fractures in areas of longitudinal compressive stresses are normally oblique fractures. The diffuse nature of the observed fatigue damage is consistent with the hypothesis that microdamage caused by mechanical loading may serve as a stimulus for in vivo bone remodeling.

Influence of physical activity on the regulation of bone density

Using a mathematical model which relates bone density to daily stress histories, the influence of physical activities on the apparent density of the calcaneal cancellous bone was investigated. Assuming that the mechanical bone maintenance stimulus is constant for all bone tissue, bone apparent density was calculated by a linear superposition of the mechanical stimulus provided by different daily physical activities. An empirical weighting factor, m, accounted for possible differences in the relative importance of load magnitude and number of cycles in each activity. By considering hypothetical variations in body weight and occupational activity levels, the range of probable m values was established. The model was then applied to the results of two previous running studies in which calcaneal density was measured to obtain an estimate of the stress exponent parameter, m. The results indicate that stress magnitudes (or joint forces) have a greater influence on bone mass than the number of loading cycles. We demonstrate that by carefully considering the magnitudes of imposed skeletal forces and the number of loading cycles, it may be possible to design exercise programs to achieve predictable changes in bone mass.