Biomechanics of Fracture Risk Prediction of the Hip

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Metabolic Bone Disease

Biomechanics of Fracture Risk Prediction of the Hip and Spine by Quantitative Computed Tomography

Stephen J. Piazza, BS, t

With aging, trabecular bone undergoes specific morphologic and biomechanical changes, including reductions in density, loss of trabecular thickness and contiguity, and dramatic losses of strength. 8. 9. 25. 29. 77. 'l8 These changes are associated with exponential increases among the elderly in fracture rates for the hip and vertebral regions where trabecular bone plays an important structural role. In the United States there are in excess of 500,000 vertebral fractures and 250,000 hip fractures annually. Hip fractures alone are fatal in 12% to 20% of patients,51 precipitate long-term nursing care for half of those that survive, and are associated with estimated costs of between $7 billion and $10 billion annually. 75. 79 If current demographic and incidence trends continue, the number of hip fractures may well double or triple by the middle of the next century. 13. 41 Comparable trends can be expected for fractures of the vertebrae. Thus, as measured by their frequency, influence on quality of life, and economic cost, age-related fractures of the hip and vertebrae are a public health problem of crisis proportions. Without successful national initiatives aimed at reducing the incidence of these

Wilson C. Hayes, PhD, * and Philippe K. Zysset, BSt

fractures, the implications for the allocation of health resources in this and the next century are staggering. The design and implementation of intervention efforts aimed at reduCing the number of age-related fractures are complicated by a fundamental uncertainty as to the relative importance of reduced bone strength and severity of trauma in fracture etiology. The steep rise with age in the incidence of hip and vertebral fractures, coupled with demonstrated age-dependent reductions in bone density and strength,33. 52. 64. 80 have led to the predominant view that age-related bone loss, or osteoporosis, is the most important determinant of this dramaticallv increased fracture incidence among the eiderly.4 A number of authors, however, have suggested instead that the increasing trends among the elderly for falls and for falls of increasing severity are the dominant factors in the etiology of age-related fractures of the hip!. 12. 19. 92 and may play a role in fractures of the spine. In fact, in support of the view that trauma severity is a potentially dominant confounding factor in age-related fractures, most densitometric indicators of osteoporosis of the proximal

~1 ueJler Professor of Biomechanics, Harvard Medical SchooL and Director, Orthopaedic Biomechanics Laboratory, Beth Israel Hospital, Boston, Massachusetts tResearch Assistant. Orthopaedic Biomechanics Laboratory. Beth Israel Hospital, Boston. Ivlassachusetts :l:Research Assistant, Orthopaedic Biomechanics Laboratory. Beth Israel Hospital. Boston, Massachusetts

* \laurice E.

This work was supported by grants CA41295 and CCRI0365 from the National Institutes of Health, CR102550 from the Centers for Disease Control, CA40211 from the National Cancer Institute, the /o,'laurice E. \1 ueller Professorship in Biomechanics at Harvard Medical School (WCH), and the Maurice E. MueJler Foundation in Bern. Switzerland (PKZ).

Radiologic Clinics of North America-Vol. 29. No.1. January 1991

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Wilsoll C. Hayes et ai.

femur and spine have failed to discriminate between fracture patients and age- and gender-matched controls.5. 17. ~O. 70. 76. 80 On the other hand, in support of the view that age-related fractures are associated primarily with osteoporosis, bone mineral densities of the hip and spine are known to decline with age, reaching lower levels in women than men. 2.1. 52.~. 79. 80 These reductions in density are also known from in vitro biomechanical studies of cadaveric material to be associated with reduced bone strength. * Clinical evidence now exists that the frequency of age-related fractures of the hip and spine increases as bone mineral density declines below densitometric thresh0Ids. 20: :lb. 60. 6~. 71. 78. 79 \10reover, some studies have shown statistically significant separations in densitometric measures at the hip and spine between fracture patients and age- and gendermatched controls. 5~. 5.'i. 59. 82 Faced with this sometimes conflicting evidence, ~Ielton and Riggs and co-workers 6J - M have suggested that both bone fragility and an increased tendency for high severity trauma among the elderly are important determinants of age-related fracture risk. However, the relative risk associated with bone loss and trauma severitv has not been determined. The most efficie~t strategy to reduce age-related fracture incidence clearly depends on the relative importance to fracture etiology of bone fragility and severitv of trauma. Thus, it mav be useful to take a broader perspective of f;acture risk prediction and examine those factors that influence fracture prediction in any engineering structure.

FRACTURE RISK PREDICTION

In engineering the design of failure-resistant structures requires three important pieces of information: (1) the geometry of the structure, (2) the mechanical properties of the materials from which the structure is made, and (3) the location and direction of the loads to which the . structure is subjected in service. Based on these data, engineering theories can be used to estimate the internal force intensities (or stresses) generated in the structure in response to the service loads. These stresses, in turn, can be compared against the known strengths of the materials used to build the structure. The ratio of the material strength to the imposed stresses • References 2. 6, 14, 18. 31, 43, 45, 49, 55, 66. 74, 86, 91.

at each point in the structure is referred to as the factor of safetv. An alternative and usually more reliable method for determining the fact;r of safety is to calculate the ratio of the force required to cause failure of the structure under a particular loading condition to the forces expected in service. The inverse of the safetv factor (sometimes referred to as the factor ~f risk in engineering design) thus provides a convenient measure of fracture risk under a particular set of loading conditions. When the factor of risk is low (i.e., much less than 1), the force required to cause failure is much greater than the in-service loads, and the structure can be expected to be at low risk of failure under those loads. Converselv, when the factor of risk is high (i. e., close to' or greater than 1), the structure is at high risk of failure. Note that in engineering design, to decrease the factor of risk, it is often possible to change geometry (i.e., make the structure larger), use stronger materials, or (in some cases) reduce the service loads. As a result, especially under circumstances in which size and weight are not paramount and there is considerable uncertaintv regarding service loads or strength, it is n~t unusual to have factors of risk in engineering structures of about 0.2 or 0.15. Fracture prediction in the human skeleton is complicated by the considerable uncertainty about the loads to which skeletal regions, such as the hip and spine, are subjected during the activities of daily living. Even less is known about the forces generated as a result of a traumatic event such as a fall. \loreover, skeletal regions at high risk of age-related fractures exhibit far more complex geometries than most engineering structures, and these geometries can change with aging and bone remodeling. As a consequence, it is far more complicated to estimate the internal stresses generated in the skeleton as a result of normal or traumatic in vivo loads. In addition, a number of factors such as density, microstructure, and morphologic characteristics influence the mechanical properties of cortical and trabecular bone.·n. 88. 89 These properties not only exhibit marked spatial heterogeneity but they also change dramatically as a consequence of aging and disease. In view of these complexities, it is not surprising that very little is known about the factors of risk that exist in skeletal regions, such as the hip and spine, under the loads associated with either normal daily activity or traumatic events. Nonetheless, realizing that engineering failure prediction requires information on loads, geometry, and mechanical properties, it should

Biomechanics of Fracture Risk Prediction of the Hip and Spine by QCT

also be clear that current densitometric estimates for fracture risk in the human skeleton at the very least neglect issues related to loading and in many instances fail to distinguish geometric factors from those related to mechanical properties and bone strength. In this regard, quantitative computed tomography (QCTl presents a number of Significant advantages over other densitometric techniques such as singleor dual-photon absorptiometry, dual energy xray absorptiometry, or conventional radiography. With the information available in QCT scans. it is possible to isolate densitometric and geometric changes in both cortical and trabecular compartments, whereas other densitometric methods provide integral measures that reflect the combined effects of both densitometric and geometric variations along the scan path in both cortical and trabecular compartments. With QCT, the cross-sectional geometric information is directly available and, with special calibration phantoms, densitometric data from both cortical and trabecular bone can be obtained in units that can be related directly to bone density and thereby to mechanical properties. With a view toward the development of more rigorous and objective QCT-based fracture risk predictors for the hip and spine, we review attempts to relate QCT densitometric measures to direct determinations of bone density and mechanical properties. We also summarize literature directed toward the development and in vitro validation of regional fracture-risk predictors for these two sites. We then discuss the findings in light of available evidence on in vivo loads associated with both the activities of daily living and with trauma. Through these analyses we draw conclusions regarding the potential discriminatory capabilities of such densitometric fracture risk predictors and suggest future research directions that might help improve their predictive power.

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mogenous specimens of regular geometry and subject them to well-defined loads. Figure lA illustrates a small cylindric specimen of trabecular bone subjected to compressive forces, F, applied at its ends by a materials-testing system. The geometry of the test specimen is defined by its length, L, and its cross-sectional area, A. The specimen's apparent density is found by dividing the marrow-free, hydrated specimen weight by its volume based on external dimensions, LA. When subjected to increasing levels of force, the specimen deflects (shortens) by an amount, .6.L, and the relation between force and deflection (Fig. IB) exhibits an approximately linear region followed by nonlinear behavior associated with trabecular bending, buckling, and fracture. This force-deflection curve can be characterized by two parameters, the slope of the linear region and the maximum force, F uit' prior to generalized failure. U nfortunately, different force-deflection curves result for each different combination of apparent density and specimen geometry, with the slope A

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Skeletal regions such as the hip and spine are geometrically complex constructs of both cortical and trabecular bone. :\1oreover, the densities (and presumably the physical properties) of both bone types can vary widely throughout each site. To focus on the intrinsic properties of either cortical or trabecular bone (as opposed to the combined behavior of the whole region), it is necessary to extract small, relatively ho-

Figure 1. :-'Iaterial versus structural behavior. A, Compressive loading of a cylinder of trabecular hone (with length L and cross-sectional area A) results in a deflection LlL. B. Plot of force versus deflection defines structural behavior because specimen geometry influences the stiffness AE/L and the ultimate load Full' C, Plot of stress versus strain defines material (or tissue-level) behavior, as the effects of geometry have been eliminated.

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Wilson C. Hayes et ai.

increasing with either increased cross-sectional area or decreased specimen length and the maximum force increasing with increased crosssectional area. Both slope and maximum force increase with increased apparent density. To account for the geometric influences and thereby describe the intrinsic properties of trabecular bone at a particular apparent density, both the force, F, and the deformation, ~L, are normalized by their respective geometric parameters. By dividing F by A, we arrive at a measure of internal force intensity, or stress, CT, where IT

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Because the force is acting to compress the specimen, CT is referred to as a compressive stress and has units of N/m 2 (1 Pa in the SI system!. Typically, stresses in bone are described in megaPascals (MPa), which is I X 106 N/m 2 . Similarly, if we divide the deformation, ~L, by the original length, L, we arrive at a measure of deformation called the engineering strain. E, where E

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~ote that the units of strain are nondimensional. The resulting stress-strain curve (Fig. Ie) exhibits a shape similar to the force-deflection curve except that in this instance it relates normalized force (stress) to normalized deflection (strain). The slope of the stress-strain curve is called the Young's modulus, E, and has units of stress (MPa), as strain is nondimensional. The normalized maximum force, FjA, is referred to as the compressive strength CTc and also has units of stress (MPa). By contrast to a force-deflection curve (which changes with each specimen geometry), a stress-strain curve describes the intrinsic behavior of the trabecular bone for any combination of specimen length and cross-sectional area. vVe can, therefore, contrast this intrinsic tissue-level or material behavior (which is independent of specimen geometry) from behavior in which both material and geometry playa role. The latter is usually referred to as structural behavior.

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Properties of Trabecular Bone

The major physical difference between trabecular and cortical bone is the increased porosity of trabecular bone. This porosity is reflected by measuring the apparent density (i. e.,

the mass of bone tissue present divided by the bulk volume of the test specimen). In the human skeleton, the apparent density of trabecular bone ranges from approximately 100 to 1000 mglcc. The apparent density of cortical bone is about 1800 mglcc. A trabecular bone specimen with an apparent density of 200 mgl cc has a porosity of about 90%. Apparent density has a profound influence on the compressive mechanical properties of trabecular bone. 8 . 9. 25. 77 Figure 2A shows compressive strength data for trabecular bone from a wide variety of studies plotted against apparent density.26 The dependence of compressive strength on apparent density can be described by a power-law function of the form (3)

The data of Figure 2A indicate that the compressive strength of trabecular bone is related to the square of the apparent density. Data for compressive modulus (Fig. 2B) indicate that the modulus also is related to apparent density by a power-law function with an exponent ranging from 2 to 3. These relationships between mechanical properties and the apparent density of trabecular bone are of great physiologic and biomechanical importance. First, they indicate that the strength and modulus of trabecular bone change dramatically with small changes in apparent density. Conversely, subtle changes in apparent density result in large variations in strength and modulus, a finding that indicates that order of magnitude reductions in trabecular strength and modulus can occur by the time density reductions of 30% to 50% are apparent radiographically. To summarize, the intrinsic material-level behavior of trabecular bone is characterized by removing small, homogenous specimens of regular geometry and uniform density, subjecting them to well-characterized forces, and plotting a stress-strain curve. From stress-strain curves obtained for specimens exhibiting a range of apparent densities, mechanical properties such as compressive strength and modulus can be obtained as functions of densitv. For trabecular bone, both the compressive st~ength and modulus are strong, power-law functions of apparent density, with exponents of about 2. In contrast to material or tissue-level behavior, in loading situations in which both material behavior and specimen geometry come into play (as with whole bone specimens or specimens involving both cortical and trabecular bone), the mechan-

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Biomechanics of Fracture Risk Prediction of the Hip and Spine by QCT

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ical response to load is described by a loaddeflection curve and is referred to as structural behavior.

MATERIAL PROPERTY ESTIMATES BY QCT IN VITRO To determine precision and accuracy of densitometric measurements, QCT data must be compared against direct measurements of the apparent density or ash density (defined as the ash weight divided by the bulk specimen volume) and material properties of cortical and trabecular bone. As noted, QCT is well suited to this purpose because the technique allows separate visualization and direct densitometric estimations from both bony compartments. QCT presents the additional advantage that cross-sectional geometry is determined directly from the image and can thus be used along with Table 1. Trabecular Density \lTHORS

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density-based estimates of material properties in theoretic predictions of fracture risk. Given these advantages, it is not surprising that a number of investigators have used in vitro experiments to evaluate the use of QCT for determinations of density and material properties of trabecular and cortical bone.

Trabecular Bone QCT Versus Density. To determine correlations between direct measures of apparent or ash density and QCT data, scans are taken at defined locations within the vertebral bodv or proximal femur and then small (usually c;'lindrical) specimens of trabecular bone are harvested from regions corresponding to the locations of the QCT scans. Table 1 summarizes literature values for the linear correlations between QCT measures (reported either in

QCT in Femoral and Vertebral Trabecular BOlle