Mechanoregulation of Bone Remodeling and Healing as Inspiration for Self-Repair in Materials

Abstract

The material bone has attracted the attention of material scientists due to its fracture resistance and ability to self-repair. A mechanoregulated exchange of damaged bone using newly synthesized material avoids the accumulation of fatigue damage. This remodeling process is also the basis for structural adaptation to common loading conditions, thereby reducing the probability of material failure. In the case of fracture, an initial step of tissue formation is followed by a mechanobiological controlled restoration of the pre-fracture state. The present perspective focuses on these mechanobiological aspects of bone remodeling and healing. Specifically, the role of the control function is considered, which describes mechanoregulation as a link between mechanical stimulation and the local response of the material through changes in structure or material properties. Mechanical forces propagate over large distances leading to a complex non-local feedback between mechanical stimulation and material response. To better understand such phenomena, computer models are often employed. As expected from control theory, negative and positive feedback loops lead to entirely different time evolutions, corresponding to stable and unstable states of the material system. After some background information about bone remodeling and healing, we describe a few representative models, the corresponding control functions, and their consequences. The results are then discussed with respect to the potential design of synthetic materials with specific self-repair properties.

Keywords: adaptive material; bone healing; bone remodeling; control function; feedback loop; mechanical stimulus; mechanobiology; mechanoregulation; programmable material.

Figure 1

Comparison between different material behaviors: in the simplest case a material property like resistance or modulus is characterized by a fixed value (left); in responsive materials (middle) the property can be influenced by an external stimulation; in adaptive materials the stimulation is created internally by feeding back a signal related to the material’s output (right).

Figure 2

Comparison between a control function, which has been suggested for the mechanoregulation of total bone mass by Harold Frost in his mechanostat theory (a), and a control function obtained in experiments on adult mice using a combination of in vivo microcomputed tomography, in vivo loading and Finite Element modeling (b) (from [36]).

Figure 3

(a) The negative feedback loop used as a control function resulted in a homeostatic configuration of the trabecular bone orientation. (b) Changing the loading direction to be 20 degrees away from the vertical direction leads to a reorientation of the trabecular architecture (from [45] with permission).

Figure 4

Six snapshots of a computer model showing the time evolution of different tissues during bone healing. The succession of images should be read from left to right starting with the top row. A top/bottom and left/right symmetry is assumed in the model. The starting configuration shows the disconnected cortical bone (black) surrounded by a callus of soft tissue (red) and bone marrow (orange). During the course of healing cartilage is formed (green) within the callus. Darker shades of the same color denote more mature tissue. In the case of bone, darker grey refers to a bone of higher mass density.

Figure 5

(a) 2D geometry of the model, where the black rectangles correspond to the disconnected stiff material surrounded by a soft, mechanoresponsive material (white). Loading of the broken material by a force F results in a vertical deformation ΔH. Due to symmetry, only a quarter of the system shown had to be modeled (marked by the dashed line). (b,c) Snapshots of two different simulations, which demonstrate that healing can progress either directly via a bridging of the fracture gap or indirectly, by reconnecting the broken ends circumferentially. (d) Parameter study varying the upper and lower bound of the range of mechanoresponsiveness, s₂, and s₁, respectively [63]. The colors denote whether the course of healing was more direct or indirect. Grey pixels indicate an unsuccessful healing defined by a failed reduction of ΔH below 1%.

Figure 6

(a) Basic polymeric building block of a programmable metamaterial obtained by 3D printing in its initial state. (b) The intricate structure of this building block implies that under uniaxially loading (red arrows) above a specific threshold the bistable element in the center of the building block changes to a different configuration by snapping through. This structural change is accompanied by a change of the mechanical properties (from [70] with permission). (c) Two examples of molecules including mechanophores. Both belong to the class of gem-dihalocyclopropanes (top: gem-dibromocyclopropane, bottom: gem-dichlorocyclopropane). When applying a force as indicated by the red arrows, both molecules undergo a disrotatory ring opening reaction resulting also in a change of their mechanical properties. Using single molecule force spectroscopy experiments, the necessary force to trigger the ring opening reaction were determined to be 1210 pN and 1330 pN, respectively (from [71] licensed under CC BY 3.0). In contrast to the control functions described for processes in bone, both the mechanical metamaterial and the polymer including a mechanophore are characterized by a control function with an abrupt change in the mechanical properties at the setpoint of the mechanical stimulus.