Fig 1.
Lateral distraction study by Claes et al. [32].
Left: In vivo setup of the study with (a) fixator, (b) hydroxyapatite-coated titanium plate and (c) face milled medial surface of the diaphysis; right: X-ray taken 4 weeks post-op, showing traces of initial bone formation above the medial surface.
Fig 2.
Tissue-level biological processes captured by our model.
Fig 3.
Overview of the simulation phases.
The numerical model consists of seven distinct phases (left) that are explained in detail in the corresponding Methods sections (right).
Fig 4.
The model’s 2D geometry corresponds to a slice through one row of the drill holes [37].
Fig 5.
Geometry and FE mesh, mechanical load and boundary conditions as well as initial tissue distribution [37].
Table 1.
Linear elastic material properties of tissue types.
Table 2.
Viscoplastic material properties relative to the composite Young’s modulus E.
Fig 6.
Illustration of the remeshing procedure on a simplified geometry.
After remeshing, the state (concentrations, elastic strains) is sampled (white crosses) and mapped to the new mesh [37].
Table 3.
Default parameter values.
Fig 7.
Predicted bone concentration, vascularity and effective mechanical stimuli for the in vivo experiment by Claes et al. [32].
The figure shows (from left to right) how the distribution of bone, vascularity and effective dilatational and distortional strain inside the healing area changes over time (from top to bottom). The legends beneath the columns explain the meaning of the color-coding for the corresponding column(s).
Fig 8.
Influence of time step size on predicted bone tissue distribution.
Each column displays the evolution of bone tissue over time (rows, top to bottom) from blue (0% bone) to red (100% mineralized bone) for five different temporal discretizations (columns, left to right).
Fig 9.
Influence of element size on predicted bone tissue distribution.
Each column displays the evolution of bone tissue over time (rows, top to bottom) from blue (0% bone) to red (100% mineralized bone) for four different FE mesh resolutions (columns, left to right).
Fig 10.
The figure shows how three choices for the parameter γ (columns) affects the predicted distribution of bone over time (rows, top to bottom).
Fig 11.
Influence of tangent modulus ET.
The figure illustrates the influence of the tangent modulus ET (columns) on the predicted distribution of bone over time (rows, top to bottom).
Fig 12.
Influence of yield stress σyield.
Each column represents one particular parameter value for the yield stress parameter σyield. The contour plots represent the corresponding predicted healing outcome in terms of the evolution of bone tissue inside the modeled healing region (from top to bottom).
Fig 13.
Evolution of the total reaction force (along the negative y-direction) acting on the top nodes on which the distraction displacement is applied.
Fig 14.
Paracrine signaling parameters control the propagation velocity of the bone front.
Fig 15.
The parameter tdelay shifts the prediction temporally.
Fig 16.
The stimuli decay rate needs to be low enough to allow the formation of bony cones.
Fig 17.
Comparison of seven different distraction protocols.