Relationships between tissue dilatation and differentiation in distraction osteogenesis

Abstract

Mechanical factors modulate the morphogenesis and regeneration of mesenchymally derived tissues via processes mediated by the extracellular matrix (ECM). In distraction osteogenesis, large volumes of new bone are created through discrete applications of tensile displacement across an osteotomy gap. Although many studies have characterized the matrix, cellular and molecular biology of distraction osteogenesis, little is known about relationships between these biological phenomena and the local physical cues generated by distraction. Accordingly, the goal of this study was to characterize the local physical environment created within the osteotomy gap during long bone distraction osteogenesis. Using a computational approach, we quantified spatial and temporal profiles of three previously identified mechanical stimuli for tissue differentiation-pressure, tensile strain and fluid flow-as well as another candidate stimulus-tissue dilatation (volumetric strain). Whereas pressure and fluid velocity throughout the regenerate decayed to less than 31% of initial values within 20 min following distraction, tissue dilatation increased with time, reaching steady state values as high as 43% strain. This dilatation created large reductions and large gradients in cell and ECM densities. When combined with previous findings regarding the effects of strain and of cell and ECM densities on cell migration, proliferation and differentiation, these results indicate two mechanisms by which tissue dilatation may be a key stimulus for bone regeneration: (1) stretching of cells and (2) altering cell and ECM densities. These results are used to suggest experiments that can provide a more mechanistic understanding of the role of tissue dilatation in bone regeneration.

Fig. 1

Tissue dilatation (also known as volumetric strain) represents equal deformation of a region of tissue in all directions; this deformation results in a change in the volume that the tissue occupies. Positive dilatation corresponds to an increase in the occupied volume (A), while negative dilatation corresponds to a decrease in the occupied volume (B).

Fig. 2

(A) The diaphysis of a long bone undergoing distraction osteogenesis is idealized as a hollow cylinder with a transverse osteotomy gap. The regenerate is also represented as cylindrical in shape with an enlarged diameter across the osteotomy gap. (B) A longitudinal cross-section of osteotomized diaphysis shows the locations of cortical bone, osteotomy gap, and regenerate and medullary tissues. Idealizing the diaphysis and regenerate as cylindrical renders this cross-section symmetric about the diaphyseal axis and about the midline of the gap (shown with dotted lines). (C) As a result of this symmetry, a finite element model of only one-quarter of the cross-section is sufficient to capture the behavior of the entire section of the diaphysis shown at the bottom of (A). A 1-mm tensile displacement is applied to the diaphysis on each side of the gap, resulting in a 2-mm distraction. An enlarged view of the quarter of the cross-section that is explicitly modeled shows the finite element mesh as well as the boundary conditions that enforce the symmetry of the problem: no displacement or fluid flow in the transverse direction is allowed across the diaphyseal axis; and no displacement or fluid flow in the longitudinal direction is allowed across the midline of the gap. However, fluid may flow throughout other regions of the regenerate, the cortical bone and the surrounding medullary tissues. The cortex is outlined with a heavy line.

Fig. 3

Magnitudes of total pressure, tensile strain, tissue dilatation and fluid velocity vary substantially throughout the regenerate. For most of these mechanical stimuli (total pressure, tensile strain and fluid velocity), these gradients are large immediately after the 2-mm distraction (1 s), whereas the gradients in tissue dilatation are highest 12 h after distraction.

Fig. 4

Temporal profiles of (A) total pressure, (B) tensile strain, (C) tissue dilatation and (D) fluid velocity at six locations within and surrounding the osteotomy gap in the 12 h following the 2-mm distraction.

Fig. 5

The 2-mm distraction initially causes contraction of the regenerate in the transverse anatomical plane (perpendicular to the distraction vector). The magnitude of this contraction is depicted by the arrows. Over the subsequent 12-h period, the contraction completely dissipates, leaving pure elongation of the regenerate, as illustrated with the aid of the vertical lines.

Fig. 6

Temporal profiles of changes in tissue density at the locations depicted in Fig. 4.

Fig. 7

Tissue dilatation throughout the regenerate as a function of time for the different combinations of poroelastic material properties and different diameters of the regenerate listed in Table 2. (A)–(F) represent the six locations, A–F, shown in Fig. 4, respectively. Results corresponding to the combination of properties and regenerate size used for the main study (the “baseline” combination) are represented with the open triangles and a heavier line. Labels in the legend indicate how the combination of properties and regenerate size differ from the baseline combination.