Mechanical regulation of bone regeneration: theories, models, and experiments

Abstract

How mechanical forces influence the regeneration of bone remains an open question. Their effect has been demonstrated experimentally, which has allowed mathematical theories of mechanically driven tissue differentiation to be developed. Many simulations driven by these theories have been presented, however, validation of these models has remained difficult due to the number of independent parameters considered. An overview of these theories and models is presented along with a review of experimental studies and the factors they consider. Finally limitations of current experimental data and how this influences modeling are discussed and potential solutions are proposed.

Keywords: bone regeneration; fracture healing; mechanobiology; simulation.

Figure 1

The healing of a tibial fracture. A hematoma (A) forms during the reactive phase, beneath the injured periosteum (B). During the reparative phase woven bone (C) forms through intramembranous ossification along with cartilage (C), which is eventually ossified (E), bony bridging occurs and finally the callus is remodeled into cortical bone.

Figure 2

The different loading modes for a fracture, shown on a femur (A). IFC causes in a narrowing of the fracture gap (B), IFS is a shear movement (C) across the gap plane, or a relative torsional movement around the axis of the bone (D), and IFB is a bending movement (E) centered around the fracture. Fixation methods for fractures are shown in (F,G), external fixator (F), the ring fixator (G), intramedullary nailing (H), and plating (I).

Figure 3

Structure of a typical fracture healing simulation. Initially a model is created consisting of the cortical bone fragments, soft callus, and the fixator. Material properties and boundary conditions are then applied to the model based on the tissue distribution and fixator properties, a finite element analysis is performed to determine the mechanicals stimuli, this then is used to drive cell proliferation and tissue differentiation, which updates the tissue distribution and thus new mechanical properties for the next iteration.

Figure 4

(A) The tissue differentiation rules based on fluid flow relative to solid phase and shear strain. Reprinted from Lacroix and Prendergast (37) with permission from Elsevier. (B) Tissue differentiation based on hydrostatic and octahedral shear strain. Reprinted from Shefelbine et al. (42) with permission from Elsevier. (C) The tissue differentiation rules with pressure line and tension line. Reprinted from Carter et al. (73) with permission from Lippincott Williams and Wilkins. (D) The tissue differentiation rules using hydrostatic pressure and strain. Reprinted from L. Claes and Heigele (4) with permission from Elsevier. (E) The tissue differentiation rule based on substrate stiffness and oxygen tension. Reprinted from Burke and Kelly (62) with permission from PLoS ONE.

Figure 5

The results of fracture healing simulations, (A) Burke and Kelly (62) reprinted with permission from PLoS ONE. (B) Lacroix and Prendergast (37) reprinted with permission from Elsevier. (C) Steiner et al. (65) reprinted with permission from PLoS ONE. (D) Histological section of healing ovine tibia, new woven bone is lightly stained, while cartilage is darkly stained. Reprinted with permission from Elsevier.