Small Animal Bone Biomechanics

Abstract

Animal models, in particular mice, offer the possibility of naturally achieving or genetically engineering a skeletal phenotype associated with disease and conducting destructive fracture tests on bone to determine the resulting change in bone’s mechanical properties. Several recent developments, including nano- and micro- indentation testing, microtensile and microcompressive testing, and bending tests on notched whole bone specimens, offer the possibility to mechanically probe small animal bone and investigate the effects of aging, therapeutic treatments, disease, and genetic variation. In contrast to traditional strength tests on small animal bones, fracture mechanics tests display smaller variation and therefore offer the possibility of reducing sample sizes. This article provides an analysis of what such tests measure and proposes methods to reduce errors associated with testing smaller than ideal specimens.

Introduction

There has been considerable interest in the measurement of the mechanical properties of small animal bones. Animal models, in particular mice, offer the possibility of naturally achieving or genetically engineering a skeletal phenotype associated with disease and conducting destructive fracture tests on bone to determine the resulting change in bone’s mechanical properties. Unfortunately the repertoire of mechanical tests, available for small animal bones, is limited due to inherent limitations imposed by bone size.

In recent years, however, there has been an explosion in the type of mechanical tests proposed for mouse bones. And because mouse bone has well defined organizational hierarchy, these tests scale the natural length scale from mineral and protein levels to whole bone tests. For example nano- and micro- indentation testing have been done on inbred or genetic knockout mouse bones in monotonic or cyclic mode to determine the local elastic and viscoelastic properties associated with bone mineral and protein modifications^1–4. Next, at a scale comparable to lamellar level human bone specimens^5–7, Ramasamy and Akkus⁸ have recently demonstrated successful machining and testing of microtensile and microcompressive mouse bone specimens (0.5 × 0.7 mm gage section; 0.15 mm thickness). Finally, at the whole bone level, three- and four- point bending and torsional tests to failure have been popular due to the inherent simplicity of such tests in determining the mechanical properties associated with changes in the structure and material due to exercise, variations among different inbred mouse strains, growth factor deficiency, accelerated senescence and ovariectomy^9–13. Other less common testing methods for mouse bones include femoral neck tests to determine the effect of fluoride treatment on mineralization and whole bone fracture¹⁴.

The inherent hierarchy of bone’s extracellular matrix (ECM) has specific microstructural features and energy dissipation mechanisms at different length scales that allow the bone to effectively resist the different components of applied loading¹⁵. Tensile loading interacts with sublamellar structures including the mineralized collagen fibril matrix to produce time dependent diffuse damage containing submicron cracks < 1 µm¹⁵,¹⁷. Compressive loading interacts with lamellae and produces primarily cycle dependent short linear microcracks of the order of tens of microns in length a long bone cross-section^15–17. Torsional and other forms of mixed mode loading interact with osteons and produce primarily time dependent microcracks that either get deflected by the osteonal structure or penetrate the osteon and are consequently of the order tens to hundred microns in length in a long bone cross-section^18–19. Thus, in the selection of appropriate test/tests, a prior understanding of the length scales present in an animal bone and its expected modification by disease or treatment is often helpful.

In the study of engineering materials and structures, the theory of fracture mechanics and related experimentation has proven to be more effective than some of the strength-based testing methods described above. Reviewing the application of fracture mechanics to bone, three decades ago, Bonfield²⁰ was first to note that the presence of inherent flaws in bone, in the form unrepaired fatigue microcracks, caused significant variations in strength based measures and that the initiation and controlled propagation of a fracture crack from a sharp pre-machined notch (representing a flaw) in bone specimen reduced variations in the measured fracture properties. Working with Bonfield, the author found that, in contrast to initiation, properties measured during crack propagation more comprehensively captured the fracture behavior of bone²¹ and accurately distinguished tough from less tough bones²². Furthermore, Norman et. al. ²³ and Wang and Agrawal²⁴ extended the measurement of bone fracture from mode I (tensile) to mode II (in plane shear) and introduced smaller specimen designs. Zioupos and Currey²⁵ evaluated the effectiveness of various fracture mechanics based parameters and their comparison with traditional strength and work-to-fracture parameters.

Based on their recent work²⁶, in this issue of Bone, Ritchie et al have extended the application of the above concepts to small animal bones obtained from mice and rats. They present detailed techniques to characterize whole bone toughness by assuming femoral diaphysis to a pipe of uniform cylindrical shape and thickness. Through two- and six- point average of bone radius and thickness, they go on to reduce the error associated with the assumption. More importantly, compared to strength based measures, they find reduced scatter in some of the fracture mechanics parameters. This is an important new development and the further use of the proposed techniques is likely to improve the estimation of fracture in small animal bones. However, there are a number of issues and limitations that one must consider before applying these methods to interpret the effects of therapeutic treatments, disease, genetic variations and knock-outs. Also, the methods proposed in the tutorial have not been extensively investigated and additional considerations and testing will be needed in order to standardize the mechanical testing procedures. These are discussed below in turn.

What is being measured?

Fracture toughness of bone, measured at initiation as critical stress intensity factor (K_c) or strain energy release rate (G_c) or at propagation as slope of crack growth resistance curve, is a material property only when certain conditions at the crack tip are met. For example, specimens below the recommended thickness yield plane stress conditions at the crack tip and result in higher K_c and G_c values that are geometry dependent and can only be compared among specimens with the similar dimensions. Norman et al. ²⁷ demonstrated that measured values of K_c and G_c for 3mm thick bovine compact tension specimens, giving plane stress conditions at the crack tip, were higher than 7mm thick specimens, giving plane strain conditions at the crack tip. Because cortical thickness frequently varies in inbred mouse strain and with aging, treatment and disease, the measured difference from fracture tests on whole bone may reflect both the changes in geometry and material properties.

Which bone to test?

Both mouse and rat skeletons offer a choice of at least five different long bones for whole bone fracture tests including femur, humerus, third metatarsal, radius and the tibia. The methods proposed by Ritchie et al. are valid for both thick and thin bones, however, the selection of an appropriate long bone for testing may be dictated by biological considerations including the turnover rate, site of interest (for example, site of fracture healing) and by mechanical considerations that reduce the errors related to deviations from theory and provide values close to the published material properties. Although neither material level fracture toughness values nor whole bone fracture toughness values of long bones from same mouse skeletons are currently available, a recommendation for an appropriate bone to test can be based on similar tests on unnotched specimens. In particular, similar to a three point bending test on unnotched whole bone, the fracture toughness test of a whole bone that is notched and subjected to crack initiation and propagation under tensile mode requires that bone has a straight morphology with a uniformly round and thick cross-section. Using the above criterion, and testing different long bones from skeletons of thirteen C57BL/6H (B6) and twelve C3H/HeJ (C3H) mice, Schriefer et al. ²⁸ found that mouse radius produced accurate and most consistent results. When tested in the largest possible aspect ratio (see below), the ratio of high cortical thickness to periosteal radius in the mouse forearm radius increases the ratio of bending to shear contributions and minimizes the ring-type deformation associated with thin bones that lose circular shape and become oval under load²⁸. Figure 1 provides representative cross-sectional images of each of these bones from B6 and C3H and photographs of the testing set-up.

Figure 1.

(a) µCT images of different mouse long bones at the midshaft region where notching and failure occur. (B) Testing setup showing largest possible span length for different mouse bones. (Reprinted from the Journal of Biomechanics Vol. 38. Schriefer J, Robling A, Warden S, Fournier A, Mason J and Turner C. A comparison of mechanical properties derived from multiple skeletal sites in mice. p.469 ©2005, with permission from Elsevier.)

Additional Testing Considerations Specific to Mouse Bones

Unlike machined human bone specimens where machining of a specialized notch and precracking are accomplished through automated machining of standard specimens held in fixtures^21,27, mouse bones are of the order of a few centimeters and do not lend themselves to similar procedures. Thus, ease of handing while notching and testing is an important factor to improve reproducibility of results in mouse bones. In general, the strength tests do not follow the practice of sawing off the ends of long bones and are able to achieve fracture through the use of narrow and long upper loading fixture (see figure 1). The use of the whole mouse bone (Length 12–15 mm), instead of a 4.5 mm diaphyseal section recommended by Ritchie et al., is likely to improve the ease of handling without affecting the results because the beam overhung outside the three loading points does not influence the test. More importantly, the use of whole mouse bone will allow an increase in span length to 10 mm²⁸ and increase the aspect ratio (Length/Diameter) of the femur to 6.0 mm from 2.74 reducing the error in toughness measurements due to relatively higher shear deformation.

Furthermore, the use of a microcomputed tomography (µCT) equipment is suggested as an alternative to digital calipers/SEM because standard algorithms for calculating cortical thickness, based on 360 measurements conducted in one degree increments, are available on most scanners (For example see Figure 2). Additionally the minimum and maximum radius at the notch as well as the notch size, representing initial crack length, can be evaluated non-invasively prior to testing to eliminate specimens with notch angle more or less than 2 standard deviations from the mean value. Maintaining similar initial crack length is important for materials including bone which show variation in toughness with crack extension²¹. The use of µCT also allows bone specific finite element analysis within the experimental design.

Figure 2.

Cross-sectional images of mice bone showing cortical thickness, endosteal and periosteal diameters measured at three diphyseal location using microCT (Scanco Viva CT).

The quadrant of the mouse bone selected for notching and failure under mode I (tensile) loading can also have a significant effect on the measured toughness value. Using equine radius Reilly and Currey²⁹ demonstrated that bone optimizes its resistance to failure in the mode under which its loaded in vivo. Consequently testing consideration for mouse bone should include loading it in an anatomically correct configuration. Based on strain gage measurements in rats³⁰, strength testing on mouse bones is generally done with the anterior quadrant in tension and posterior quadrant in compression^{8, 10}. Translating these requirements to fracture mechanics testing of mouse bone would imply reversing Ritchie at al.’s recommendations and notching the bone on the anterior side and imposing compressive loading on the posterior side.

Measures of Toughness to Represent Small Bone Fracture

Based on the previous studies on a variety of animal and human bones, Ritchie et al. have applied and compared test on unnotched and notched specimens to measure fracture toughness of mouse and rat bones. Unlike unnotched whole bone specimens, in which the application of force results in the initiation and propagation of fracture from a random distribution of natural flaws, the notched specimens contain a sharp precrack as the dominant flaw from which a crack initiates and can be measured to yield four different fracture toughness parameters, each based on different sets of assumption and material behavior. Thus, the notched specimens show a smaller variation in fracture toughness indices than the unnotched design. This feature is particularly beneficial in comparative studies of genetic knock-outs with their littermate controls due to the limited supply and associated cost. Furthermore, similar to previous work on human and animal bones^{21, 25, 31–32}, notched specimens can be used to investigate the effects of the alterations in the fracture mechanisms due to therapeutic treatments, disease, genetic variation and knock-outs.

The evaluation of toughness measures from unnotched specimens is relatively straightforward and is based on the calculation of work-to-fracture or modulus of toughness from the area under the load-deformation and stress-strain curves, respectively. Fracture mechanics tests, however, produce three parameters [Stress Intensity Factor (K_c), Strain Energy Release Rate (G_c) and J-Integral (J_c)] related to initiation and propagation of fracture. The use of propagation based measures over initiation has already been advocated for some time²². Bone fractures by formation of microcracks that initiate close to the yield point and continue to form and coalesce until fracture³³. This process generates a host of toughening mechanisms that allow bone to resist crack propagation^{21, 31–36}. Unlike initiation, propagation covers all energy dissipation mechanisms from initiation to complete fracture and these mechanisms are subjected to alterations due to changes in the inherent hierarchy of bone at various levels of organization with aging, therapeutic treatments, disease, and genetic variation.

The use of J-integral to measure bone toughness of small and large mammalian bones and to identify changes associated with aging, therapeutic treatments, disease, and genetic variation is, however, controversial. To date only two studies have been conducted to characterize this parameter. The first study, by Zioupos and Currey²⁵, found that J-integral performed poorly compared to all other fracture mechanics parameters as well as work-to-fracture in identifying age-related changes in human bone. The second study³⁷ conducted on specimens from two bovine bones, did not measure the sensitivity of J-integral to detect any changes in bone. Even Ritchie et al. find that J-integral methods produce a coefficient of variation (29 to 53%) higher than work-to-fracture (22%) and K_c measurements (9 to 13%). Further work to demonstrate the utility of J-integral method in detecting any meaningful change in human or in animal bone is required to support its use.

Summary

Animal models, in particular mice, offer the possibility of naturally achieving or genetically engineering a skeletal phenotype and determining the resulting change in bone’s mechanical properties. In contrast to traditional strength tests on small animal bones, fracture mechanics tests display smaller variation and therefore offer the possibility of reducing sample sizes. However a careful selection of bones and test variables is needed to achieve reliable and accurate results. From all the possible long bones, radius, due to its uniformly round and thick cross-section, provides most consistent results when tested in anatomically correct configuration and at the largest possible aspect ratio (length/diameter). Small values of cortical thickness in mouse long bones and related dimensions should be measured over the entire diaphyseal cross-section containing the notch, preferably by microCT or other imaging modalities, in order to reduce the operator error and measurement bias. Small cortical thickness of mouse bones also imposes plane stress conditions on the crack tip making it difficult to obtain fracture toughness values independent of geometry. Among different measures of fracture toughness, K_c or stress intensity parameter related to maximum load or fracture instability is the most reliable parameter explaining small animal bone’s resistance to fracture.