Rodent long bones are amenable to flexural testing, namely three‐point (3 pt) and four‐point (4 pt) bending. As discussed by Jepsen et al. [9], 3 pt is not as technically challenging as 4 pt, and, in general, mechanical properties from 3 pt bending tests are more widely reported. Thus, descriptions of this test and the mechanical property cal- culations follow.
The hydrated bone, most commonly the femur, is placed on the lower contact points (rounded) with a spec- ified span (eg, 8 mm for mouse femur and 16 mm for rat femur). The orientation of the bone (eg, medial forward and anterior down) must be consistent across animals. A preload of 0.5 N (mouse) and 1 N (rat) can be applied to prevent rotation of the bone during the initial loading
phase. In the center of the span, the upper contact point (rounded) engages the midpoint of the diaphysis), the region evaluated by μCT. For the radius, this is the point of curvature [35]. As with the compression test of the lumbar VB, the long bone is loaded at a specified rate in displacement control, and a force versus displacement curve is generated (Fig. 12.2). Usually, but not always, the bone snaps in two, thus giving an unequivocal failure point. Structural properties are stiffness (or rigidity), maximum force (or maximum moment) endured by the bone, and work to fracture (or span‐adjusted work to frac- ture) [36,37]. To determine post‐yield displacement, an indicator of brittleness, the yield point (proportional limit when elastic deformation transitions to permanent or plastic deformation) can be defined by the 0.2% offset or by 10% to 15% loss in secant stiffness (Fig. 12.2).
These measurements and the mechanical properties of bone are affected by state of hydration and loading rates.
Thus, these parameters should be kept constant among different test groups for comparison [9]. Span can be adjusted to match the bone size, but then rigidity, maxi- mum moment, and span‐adjusted work to fracture should be reported [38].
Mouse femur
(Left) Rat femur
(Right)
8.0 mm
16.0 mm
16 14 12 10
Force (N)
8 6 4 2
00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.10 0.20 0.30
Work to fracture
0.40 0.50
Displacement (mm) Displacement (mm)
PY PY
PM PM
PYD
0.2% ε offset
δ
180 160 140 120 100 80 60 40 20 0
0.9*δ δ
Fig. 12.2. Three‐point bending test of rodent femurs. The long bone should be consistently oriented within the three‐point fixture (eg, medial side forward and anterior side down), and the upper loading point should contact the midpoint that was evaluated by μCT.
The flexural test generates a force versus displacement curve from which the stiffness (δ), yield force (PY), maximum force (PM), post‐
yield displacement (PYD), and work to fracture (area under the force versus displacement curve) can be determined. There are two different ways to determine the yield point. Either one can be used for mouse or rat long bones. For clarity, PYD is arbitrarily depicted in the mouse curve and work to fracture in the rat curve.
Using the geometric characteristics from prior μCT evaluations of the midshaft, namely Imin/cmin or Ia‐p/ca‐p, material properties of the cortical bone can be estimated as follows [unit of measurement] at the apparent level:
Modulus stiffness span /I3 min/48[GPa] Strength maximum force span cmin/Imin/ MPa4 [ ] Toughness 3 work to fracture/span/Ct Ar MJ/m. [ 3] The calculation of toughness [39] is an alternative to the area under the stress versus strain curve. To derive the flex- ural formulas, the material is assumed to be homogenous and to behave in an elastic, not plastic, manner. Again, these calculations can only estimate material properties because rodent bones are not uniform in geometry and not long enough to minimize shear deformation.
Unlike work to fracture or toughness, fracture toughness (Kc) provides a measure of the resistance that the bone material provides against fracture. Fracture toughness relates to changes only at the material level such as changes in the composition, proportion, or inter- relationships between mineral, protein (cross‐linking, amount, distribution), and water content of bone, and
the porosity and organization of matrix (orientation, number, size of fiber bundles, lamellae) that are often altered with development, aging, exercise, and pharma- ceutical treatments.
Determining the fracture toughness of rodent bone involves introducing a notch in the mid‐diaphyseal region (Fig. 12.3) such that the maximum moment occurs at the notch during 3 pt bending tests [40]. The notch should be sharp, so typically after introducing the notch with a thin diamond‐embedded wafer blade, it is sharpened with a razor and diamond solution. Notched bones are loaded at a low displacement rate (0.06 mm/min) until fracture in displacement control (available on most mechanical test- ing machines), and the resulting load–displacement curve is used to calculate fracture toughness (see following equations) at initiation (ie, initiation toughness) and maximum load (ie, propagation toughness). Human and large animal bones (eg, cows, pigs, dogs) can readily be machined into standardized geometries to reduce varia- tions in measurements in material properties [41,42].
Because fracture toughness testing involves the introduc- tion of a defect (such as a microcrack) and measurements related to this defect, fracture toughness properties show less variation than those from traditional strength tests and often require a smaller sample size. To account 100μm
100μm
Crack propagation
132.6°
0.5 mm
Fig. 12.3. Fracture toughness testing of rodent bone. The starter crack is created by rubbing a razor blade coated with a dimond solution within the notch (3D μCT rendering). The notch angle is determined from the cross‐section of the notch (2Θ). When loaded in three‐point bending, a crack propogates from the micro‐notch (note the bone is kept hydrated during the test).
References 99 for inherent tissue heterogeneity and to reduce errors
associated with variations in bone geometry (eg, femur), μCT‐based measurements are recommended to estimate the geometric parameters required to calculate fracture toughness [39,43] by the following equations:
k F P S R
R R R
b c o
o i
* * *4 4 * * m*
F t
R A B C D E
b
m b b b b b
1 2
2 3 4
Ab 0 65133 0 5774. . 0 3427. 2 0 0681. 3 Bb 1 879 4 795. . 2 343. 2 0 6197. 3 Cb 9 779 38 14. . 6 611. 2 3 972. 3 Db 34 56 129 9. . 50 55. 2 3 374. 3
Eb 30 82 147 69. . 78 38. 2 15 54. 3 log t
Rm
where:
Fb = geometric factor for an edge‐cracked cylindrical pipe Pc = maximum load (propagation toughness via maxi- mum load method) or load at yield (initiation tough- ness; a secant line with a 5% lower slope than the elastic modulus was plotted on the load deformation curve, and its intersection with the curve was used to determine the load at initiation)
S = span length
Ro = periosteal radius of cortical shell Ri = endosteal radius of cortical shell Rm = mean radius of cortical shell Θ = half‐crack angle at crack initiation t = cortical thickness
Unlike the crack initiation point, Kc calculated at max- imum load provides a more comprehensive measurement of bone’s resistance to fracture [44] and has a smaller standard deviation (assuming consistent notching) com- pared with initiation or other methods of determining bone fragility including strength tests [39].
CONCLUSION
DXA, μCT, and mechanical testing (compression or three‐
point bending) are commonly used to determine how genetic manipulations or drug treatments affect bone in rodent studies. In vivo imaging with DXA and μCT can longitudinally assess changes in bone mineral density, trabecular architecture, and cortical structure. However,
ultimately, to know whether a manipulation or treatment affects the ability of bone to resist fracture, ex vivo destructive, mechanical testing is necessary. Using proper techniques and knowing the limitations of each technol- ogy can ensure proper interpretation of the observed dif- ferences in bone properties among experimental groups.
ACKNOWLEDGMENTS
We thank Sasidhar Uppuganti for his assistance in generating the figures.
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101
Primer on the Metabolic Bone Diseases and Disorders of Mineral Metabolism, Ninth Edition. Edited by John P. Bilezikian.
© 2019 American Society for Bone and Mineral Research. Published 2019 by John Wiley & Sons, Inc.
Companion website: www.wiley.com/go/asbmrprimer
13
INTRODUCTION
The process of skeletal repair is essential for resolution of: (i) orthopaedic trauma that has caused bony disjunction;
or (ii) surgical interventions that are intended to create bony injury with the aim of inducing a repair response.
Understanding the cellular and molecular basis of this healing process has been the focus of intense research both in humans and animal models over the past 25 years, with this work largely driven by the need to develop ther- apeutic strategies to enable or enhance healing of fibrous nonunions, critically‐sized defects, or other situations of impaired healing. Combined, failed, or delayed healing impacts up to 10% of all fracture patients seen clinically [1] and can result from multiple factors including com- minution, inadequate fixation, infection, tumor, hypoxia/
poor blood supply, metabolic dysfunction, and other chronic comorbid diseases [2]. Overall, research efforts have led to a general understanding of the molecular and genetic control over the inflammatory, cellular and tissue processes that are required for healing, which are generally conserved across species and are similar in structurally distinct skeletal elements. This chapter pro- vides a concise and up to date overview of our under- standing of the skeletal healing process at the cellular and molecular level, a discussion of a few key situations that complicate healing, and a summary of therapeutic modalities that are either in development or employed clinically to enhance repair or facilitate healing in nonunion situations.
It should be noted that since 2000, study of the biology and pathophysiology of bone healing has grown into a robust field, with >5200 primary citations and >550
clinical or scientific reviews in the published literature.
Since our need to accommodate space limitations has precluded inclusion of numerous seminal contributions, we sincerely apologize to authors whose work could not be directly quoted in this overview.