Figure 1.
Prediction of bone tissue regeneration in a virtual model of a critical sized femoral defect tested in an ovine experimental model.
(A) Schematic depiction of experimental model in longitudinal plane. Proximal (upper) and distal (lower) bone are represented in light gray, with the intramedullary nail in dark gray and the periosteum (lines) in black). The middle of the defect is indicated by the cut (dashed) line, giving the transverse orthogonal plane for the radial perspective (in B). (B) Spatial system diagram for the current model. System diagram depicting nascent tissue genesis (‘callus’) in the defect, defined as the region between the intramedullary (IM) nail and the surrounding periosteum. (C) Tissue genesis in the defect proceeds predominantly from the outside in, radially from the periosteum, rather than from the proximal and proximal and distal edges (longitudinally) toward the center of the defect, as evidenced by high resolution micro-CT of actual healing in the experimental ovine defect described by the predictive model [1], [4].
Figure 2.
Set-up of mechanical finite element model.
Simulation of the one-stage bone transport technique at the mid-diaphysis of a human femur, stabilized by an intramedullary (IM) nail and four locking screws.
Table 1.
Material properties applied to the mechanical finite element model.
Figure 3.
Relationship between nascent tissue material properties and axial strain.
(A) Map of axial strains at the outer surface, representing periosteal mechanical environment. (B) Extracted average axial strain on the lateral aspect as a function of tissue modulus, fit with logarithmic relationship.
Figure 4.
System diagram of cellular processes.
Periosteally mediated bone regeneration following mechanical strain stimulus of progenitor cells located in the periosteum, mediated by expression of, e.g. BMP-2. For the purposes of the current model as a foundation for next generation models, BMP is an isolated representative factor implicated in regulating all of the described processes and as such represents a class of signaling molecules whose mechanistic roles can be probed explicitly in follow on studies.
Figure 5.
Parameter analysis for total defect infilling.
Parameters optimized to achieve defect healing as a mineralization of the cartilage precursor template over the dimensionless time scale.
Figure 6.
Spatial depiction of total tissue genesis for one representative set of parameter values, showing concentrations of BMP, chondrocytes, and osteoblasts, as well as area fractions of cartilage and bone as functions of radius at several time increments.
Figure 7.
Increasing the rate of differentiation of progenitor cells to chondrocytes increases the density of chondrocytes and contributes to a more rapid consumption of BMP. Increased area fraction of cartilage is produced slightly sooner, indicative of more rapid tissue genesis.
Figure 8.
Increasing the rate of progenitor differentiation into osteoblasts results in a greater density of osteoblasts, more rapid consumption of BMP, and a more rapid mineralization of cartilage to bone.
Figure 9.
Increasing the rate of chondrocyte proliferation results in a greatly increased density of chondrocytes, and faster rate of consumption of BMP.
Figure 10.
Increasing the rate of osteoblast proliferation results in a greatly increased density of osteoblasts, and more rapid mineralization with a more homogenous distribution of bone tissue at the final time.
Figure 11.
Increasing the rate of consumption of BMP by chondrocytes and osteoblasts results in negative values for BMP, which is not physiologically plausible. A decrease in leaves considerably more BMP in the defect space, but does not notably alter ECM production as the processes are likely saturated.
Figure 12.
Increasing the maximum rate of cartilage production by chondrocytes, results in a much greater fraction of cartilage at early time points, and a slightly more gradual mineralization process.
Figure 13.
Spatiotemporal assessment of endochondral ossification.
Although from different experimental cohorts, the time course of endochondral ossification observed as a gradient of green to red in the right hand case study in (B) can be tied to the spatial gradient of mineralization observed as a gradient from pink to blue in (A). (A) Endochondral ossification of cartilage template (c) to bone (b) by osteoblasts seen as the densely blue-staining rounded cells lining the interface of mineralized tissue and cartilage. Staining of histological specimens enables quantitative assessment of ECM outcome and cell density at a given time in the healing process. Chondrocytes are present in the cartilage matrix, and appear more irregularly shaped. Scale bar = 100 µm. (B) Spatial and temporal aspects of defect filling via cellular tissue genesis. Insets in upper right and lower left quadrants (note length scale compared to length scale of defect and IM nail) depict temporal bone formation through visualization of fluorochromes, which chelate to mineral as the ECM is mineralized. The upper right quadrant shows the case study in which patent periosteum is sutured in situ around the defect; direct intramembranous bone formation (rapid mineralization of callus) is observed within two weeks (green), and subsequent osteoblastic bone formation (red, blue) occurs via lamellar apposition. The lower left quadrant demonstrates a case in which bone graft is packed in the defect before suturing of patent periosteum around the defect; bone remodeling is observed in the graft-filled defect zone (blue, green) and endochondral bone formation is observed between the underside of the periosteum and the outer edge of the packed bone graft (not shown). Cf. [18] for original micrographs showing full field of view.
Figure 14.
Parametric elucidation of callus healing at 16 weeks in ovine models.
Simulation of observed outcomes in two experimental cases where a critical sized femoral defect is enveloped by periosteum or a periosteum substitute.
Figure 15.
Comparison of model-predicted spatial profiles with experimental measurements.
(A) Experimental result: radial distribution of mineralization from the periosteum (0) to the intramedullary nail (10) at 2 weeks indicates more bone formation adjacent to the periosteum, with mineralization/chelation significant correlated to radius, and little to no bone present at the intramedullary nail. [18] (B) Model predictions at early times (for a 16-week experiment, t = 0.25 corresponds to 4 weeks) indicate a similar distribution of bone, with no mineralized tissue at the surface of the nail.