PERSPECTIVEUnderstanding Bone Strength: Size Isn’t EverythingM. C. H. VAN DER MEULEN,1,2K. J. JEPSEN,3and B. MIKIC´41Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA2Biomechanics and Biomaterials Section, Research Division, Hospital for Special Surgery, New York, NY, USA3Department of Orthopedics, Mount Sinai School of Medicine, New York, NY, USA4Picker Engineering Program, Smith College, Northampton, MA, USAIntroductionIn vivo models, particularly mouse mutations, are increasinglybeing used to investigate the impact of the absence or overex-pression of a gene product on musculoskeletal load-bearingcapacity.4,8,15,20,21Skeletal functional integrity can be assessedby structural strength tests that measure how well the whole bonecan bear loads. Although the importance of performing thesetests is well-recognized, care must be taken in designing theexperiments and interpreting the data. The aim of this report is toclarify the relationship of whole bone structural strength tomaterial and geometric properties and the interpretation of thesedata in the context of in vivo models, especially mice. Inparticular, we emphasize that there is no alternative to testingwhole bone strength and that conclusions regarding bone me-chanical function based solely on geometry or bone mineralcontent are inappropriate and likely misleading.What is a whole bone structural test and what does it measure?Different types of loads, such as bending or torsion, can be appliedto whole bones in vitro to determine the structure’s stiffness andfailure load (structural strength). The structural stiffness is a measureof the resistance to deformation under the applied load, and thestructural strength is the load required to fail the whole bone.18These two whole bone measurements are structural properties andare influenced by both the material from which the structure iscomposed (the tissue material properties) as well as how and wherethat material is distributed (the geometric form of the tissue) (Figure1).17,24Therefore, both material and geometric properties are re-quired to assess the structural integrity of a long bone, and neithermaterial nor geometry alone is sufficient to predict the structuralfailure load. Currently, there is no substitute for a mechanical test tomeasure whole bone structural behavior; no alternative parameterhas been identified that is fully indicative of strength and can serveas a surrogate measure.Bone material properties are the tissue level mechanicalproperties that describe the constituent material and are indepen-dent of the size and shape of the bone. Material propertiesinclude the tissue ultimate stress and modulus of elasticity. Thesetissue properties are determined by machining precise samplesfrom the bone of interest and testing them in a particular loadingmode.11The material properties are influenced by compositionalmeasures such as mineral density, collagen content, and ashfraction. In addition to composition, factors such as collagencross-linking, collagen fiber orientation, mineral crystal size, andthe microstructural organization (e.g., lamellae, osteons) alsoinfluence material behavior. From a mechanical perspective, thecomposition and organization of the material clearly influencethe tissue’s ability to bear loads, but most measures, except formineral density, have not yet been related directly to the tissueproperties derived from mechanical tests.6,21When designing a structural test, the relevant material andgeometric measures are determined by the loading mode applied tothe whole bone to measure strength (e.g., torsion, bending, orcompression) as well as the outcome parameter of interest (e.g.,stiffness or failure load) (Figure 1). For example, if we test a boneto failure in torsion, then we will measure the torsional load tofailure (a structural parameter). The appropriate geometric andmaterial properties are the torsional section modulus (a geometricparameter) and the ultimate shear stress of the bone (a materialparameter). The section modulus represents the geometric resistanceto torsion and increases as the material lies further from the axis ofrotation (Figure 2). The ultimate shear stress is the strength of thebone tissue when loaded in torsion. A biomechanics tutorial byTurner and Burr has provided a more complete presentation ofmechanical assessment of whole bone and bone tissue.18The contribution of structural, geometric and material analy-ses can be illustrated with a hypothetical example (Figure 3).Consider the case of a mutant and wild-type comparison in whichanimal age, gender, and weight are matched, but the bonematerial and geometry may be affected by the mutation. A wholebone torsion test to failure showed that both the control andmutant failed at the same torque of 8.7 N䡠mm. Based on thisanalysis alone, we would conclude that the mutation had noeffect. Additional analyses, either geometric or material, wouldbe necessary to reveal the true effect of the mutation. On theother hand, if we only measure the geometry, we find the mutantbone to have a 21% lower section modulus than wild-type.Therefore, based on geometry alone, we might conclude that themutant is structurally weaker than the control. However, com-bined with the structural information, we would know that thesmaller mutant bones must have increased material properties toachieve the same structural failure load. Conversely, a tissuelevel material test would determine that the ultimate shear stressis 26% higher in the mutant than the wild-type. Therefore, basedon material differences alone, we might conclude that the mutantis structurally stronger than the control. In each case, globalconclusions based on a single analysis (structural, geometric, ormaterial) are different, contradictory, and potentially incorrect.Ideally, all three tests would be required, but, at a minimum,combining two analyses is sufficient to understand the effect ofthe mutation on the structural properties of the whole bone.Address for correspondence and reprints: Marjolein C. H. van derMeulen, Ph.D., Sibley School of Mechanical and Aerospace Engineering,Cornell University, 219A Upson Hall, Ithaca, NY 14853. E-mail:[email protected] Vol. 29, No. 2August 2001:101–104101© 2001 by Elsevier Science Inc. 8756-3282/01/$20.00All rights reserved. PII S8756-3282(01)00491-4Several examples in the literature have illustrated the value ofintegrating the data from these
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