Through observational and, to a lesser extent, empirical study, several theories have been developed on the role of certain mechanical stimuli in governing differentiation of pluripotent mesenchymal tissue into bone, cartilage, fibrocartilage, and fibrous tissue. For example, Carter et al.14
proposed that different combinations of hydrostatic pressure and tensile strain promote formation of different skeletal tissues, and Claes and Heigele15
postulated that these two stimuli regulate intramembranous versus endochondral ossification. Prendergast et al.16,17
instead proposed that the two key mechanical stimuli that govern mesenchymal tissue differentiation are shear strain and fluid flow. Direct comparison of the predictions of these theories to histological analyses of bone-healing suggests that the most accurate predictions are those based on shear strain and fluid flow18
. However, each of these theories is unable to predict certain features of the fracture-healing process16,18
, indicating that further research is needed in this area.
Testing the effects of specific mechanical variables on fracture-healing requires, above all, a method for quantifying the distribution of mechanical stimuli in the fracture callus. This is not a straightforward task, because these “tissue-level” mechanical stimuli are determined not only by the axial, transverse, and bending loads applied to the bone but also by the geometry of the bone and fracture gap and the mechanical properties of the callus tissues. A natural approach to tackling this complex problem is to estimate the mechanical stimuli via finite element analysis. In this computational approach, the investigator must supply the applied loads, the callus and bone geometry, and the tissue mechanical properties as inputs. The accuracy of these inputs must be carefully considered because errors in these inputs can substantially affect the quality of the analysis output.
Although many finite element analyses of local mechanical stimuli in bone-healing simply estimate or idealize the geometry, tissue mechanical properties, and applied loads, several techniques have been developed to measure or to obtain some of these quantities directly. Image data, such as those obtained via computed tomography, can be used to create a finite element model that captures the true geometry of the bone and callus (). The disadvantages of this “specimen-specific” modeling approach are the increased time required to generate the model and a potentially limited extent to which the results can be applied to other specimens. However, differences in distributions of stresses, strains, and fluid flow between models with idealized geometry and those with more realistic geometry can be substantial (), suggesting that the latter models may be necessary to rigorously test hypotheses on the role of certain mechanical stimuli in influencing bone repair and regeneration.
Fig. 1 Creation of a finite element model of a rat fracture callus from micro-computed tomography (μCT) image data. A: Semiautomated image segmentation is performed to define the boundaries of the cortex and callus in each image. B: The resulting finite (more ...)
Methods for measuring the mechanical properties of callus tissues must be able to account for the heterogeneous distribution of tissues in the callus. Particularly for fracture-healing studies that make use of small animal models, nanoindentation and microindentation are viable techniques to quantify the mechanical properties of tissue at many locations throughout the callus. For example, nanoindentation can provide highly repeatable measurements of tissue stiffness for granulation tissue as well as partially mineralized woven bone and fully mature cortical bone (). While stiffness is only one mechanical property, previous studies have demonstrated that indentation techniques can be used to quantify poroelastic and poroviscoelastic properties as well19,20
. It is important to note that, due to the invasive specimen preparation steps involved in indentation of callus tissues, this approach is limited to ex vivo mechanical characterization. In vivo estimates of callus tissue properties have been made based on x-ray attenuation values obtained from digitized radiographs21
; however, to our knowledge, no direct and noninvasive measurements of the mechanical properties of callus tissue have been reported as of the time of this writing.
Fig. 2 Elastic modulus of callus tissues obtained via nanoindentation. Indentations were performed on 200-μm-thick, longitudinal sections of a rat callus using a 50-μm conospherical tip. Sections were made with a sliding microtome, and no embedding, (more ...)
Measurement of applied loads or displacements also remains a major challenge. External fixators instrumented with strain gauges or displacement transducers can provide reasonably good estimates of displacements experienced by the fracture callus. However, because this approach does not measure movement of the callus relative to the fixator, these estimates likely underestimate the actual callus displacements to some degree. One class of techniques that holds promise for direct quantification of callus displacements is dynamic radiostereometric analysis, which has been used successfully to assess fracture stability and osseous union22,23
. Based on recent reports24,25
, the accuracy and precision of this technique may be sufficient for measuring callus displacements in humans and in large-animal models in all but the final stages of fracture-healing.