New suggestions for the mechanical control of bone remodeling

Abstract

Bone is constantly renewed over our lifetime through the process of bone (re)modeling. This process is important for bone to allow it to adapt to its mechanical environment and to repair damage from everyday life. Adaptation is thought to occur through the mechanosensitive response controlling the bone-forming and -resorbing cells. This report shows a way to extract quantitative information about the way remodeling is controlled using computer simulations. Bone resorption and deposition are described as two separate stochastic processes, during which a discrete bone packet is removed or deposited from the bone surface. The responses of the bone-forming and -resorbing cells to local mechanical stimuli are described by phenomenological remodeling rules. Our strategy was to test different remodeling rules and to evaluate the time evolution of the trabecular architecture in comparison to what is known from micro-CT measurements of real bone. In particular, we tested the reaction of virtual bone to standard therapeutic strategies for the prevention of bone deterioration, i.e., physical activity and medications to reduce bone resorption. Insensitivity of the bone volume fraction to reductions in bone resorption was observed in the simulations only for a remodeling rule including an activation barrier for the mechanical stimulus above which bone deposition is switched on. This is in disagreement with the commonly used rules having a so-called lazy zone.

Fig. 1

Sketch of a bone-resorption event in a trabecula of trabecular bone (left) followed either by new bone formation (path a) or by further resorption (path b) leading to perforation and loss of the trabecula

Fig. 2

a–d Bone deposition (black) and resorption (gray) probabilities for the different remodeling rules investigated (for numerical values, see also Table 1). Upper images illustrate the remodeling rules used: a step, b Frost, c linear 1, and d linear 2. Remodeling rules a–c all use constant bone resorption probabilities. Remodeling rule d has a linear response for both deposition and resorption resulting in a net response which is equivalent to c. Lower images show the simulation output after 40 years for the different remodeling rules (a–d) applied on a cubic lattice of dimensions 256 × 256 × 256 and a voxel size of 17 μm. Arrow marks the main loading direction along the spine

Fig. 3

Time evolution of morphological parameters for the simulations considered in Fig. 2a–c (step, Frost, and linear 1) on the left and Fig. 2d–f (linear 1 and linear 2) on the right. BV/TV trabecular bone volume fraction, Tb.N average number of trabeculae per millimeter in the principal loading direction, Tb.Th average trabecular thickness. Error bars give the standard deviation from three independent simulations

Fig. 4

a Evolution of trabecular area (Tb.A) distributions for the step remodeling rule. b Comparison of trabecular area distributions for the different remodeling rules after 30 simulated years of bone remodeling. Gray bars denote the mean of seven trabecular area distributions of healthy lumbar vertebrae measured by μ-CT with 14 μm resolution (courtesy of Müller et al.)

Fig. 5

a–d Sensitivity of morphological parameters (steady-state BV/TV and Tb.N after 40 years) to changing external load with constant resorption probability (=0.01) (a, b) and changing resorption probability for constant load (=2,000 N) (c, d), for the three different remodeling rules (step, Frost, and linear 1). The decrease in trabecular number at low resorption probabilities in (d) is due to a very high value for BV/TV (c)

Fig. 6

a–d Comparison of the simulation (solid lines) with experimental values (black dots) for the most important morphological parameters as a function of age. Dashed gray lines give a LOWESS fit of the experimental data. a Normalized BV/TV, b normalized BS/TV, c normalized Tb.N, and d normalized Tb.Th. Data taken from [41]