Computational Analysis of the Influence of Menopause and Ageing on Bone Mineral Density, Exploring the Impact of Bone Turnover and Focal Bone Balance-A Study on Overload and Underload Scenarios

Abstract

This study aims to investigate the impact of hormonal imbalances during menopause, compounded by the natural ageing process, on bone health. Specifically, it examines the effects of increased bone turnover and focal bone balance on bone mass. A three-dimensional computational bone remodeling model was employed to simulate the response of the femur to habitual loads over a 19-year period, spanning premenopause, menopause, and postmenopause. The model was calibrated using experimental bone mineral density data from the literature to ensure accurate simulations. The study reveals that individual alterations in bone turnover or focal bone balance do not fully account for the observed experimental outcomes. Instead, simultaneous changes in both factors provide a more comprehensive explanation, leading to increased porosity while maintaining the material-to-apparent density ratio. Additionally, different load scenarios were tested, demonstrating that reaching the clinical osteoporosis threshold is independent of the timing of load changes. However, underload scenarios resulted in the threshold being reached approximately 6 years earlier than overload scenarios. These findings hold significant implications for strategies aimed at delaying the onset of osteoporosis and minimizing fracture risks through targeted mechanical stimulation during the early stages of menopause.

Keywords: bone health; bone remodeling; computational simulation; mathematical model; menopause; osteoporosis.

Figure 1

Free surface area $S_{\mathrm{v}}$ as a function of porosity from the analysis produced by Martin [31] (solid curve) and precise measurements by Adams et al. [32] (circles with a dashed line, which is a fifth degree polynomial fit). Different shaded areas show the regions of cortical bone (CB), trabecular bone (TB) and transition zone (TZ) [8]. Figure adapted from Berli et al. [8].

Figure 2

(a) $\kappa \left(t\right)$ functions for parameter variation. These functions affects the parameters $f_{\mathrm{bio}}$ and $f_{\mathrm{bb}}$, gradually increasing the former while decreasing the latter over time. The beginning of the perimenopausal stage is depicted by $t_1$, and the beginning of the postmenopausal stage by $t_2$. The value 0 indicates the instant of the last menses. (b) $\kappa$ effect on $f_{\mathrm{bb}}$ curve. As time progresses, as $\kappa \left(t\right)$ decreases, the $f_{\mathrm{bb}}$ curve shifts downward, indicating a diminishing capacity for bone formation. The width of the dead zone is depicted by w, and the width depicts the linear variation zone by v.

Figure 3

Diagram of loadings showing the application points and direction of the forces. The corresponding values are listed in Table 2.

Figure 4

(a) Experimental measures of average bone mineral density relative change from the work by Recker et al. [40] (femoral neck and spine) and the work by Ahlborg et al. [41] (Ulna 1 cm and Ulna 6 cm). The measurements are expressed as relative values to the beginning of the perimenopausal stage. (b) Normalized space-averaged BMD ($\overline{\mathrm{BMD}}$) as a function of time for different fitting settings. The data can be fitted by different combinations of parameters. The resorption caused by increased bone turnover (model fitted solely on $f_{\mathrm{bio}}$) leads to subsequent bone formation, which can be seen in the undulations of the green curve.

Figure 5

Space-averaged $v_{\mathrm{b}}$ as a function of time for different fitting settings. The increase in bone turnover does not lead to a net imbalance, and therefore, the volume fraction does not significantly change. Instead, this results in a decrease in mineral content and a net formation of bone at the end of the simulated period due to the mechanical stimulation caused by its weakening (green curve). The focal balance drift towards resorption implies a significant decrease in bone volume fraction (red curve).

Figure 6

${\rho }_{\mathrm{app}}$ vs. ${\rho }_{\mathrm{mat}}$ at 15 years after last menses. Experimental data from the work by Zioupos et al. [30]. Different shaded areas show the regions of cortical bone (CB), trabecular bone (TB) and transition zone (TZ) [8]. Every point on the graph represents the value of ${\rho }_{\mathrm{mat}}$ and ${\rho }_{\mathrm{app}}$ at a specific location within the modeled femur. The points are distributed to cover all internal regions of the femur model.

Figure 7

Relative change in BMD (simulated) at 15 years from last menses due to simultaneous increases in bone turnover ($f_{\mathrm{bio}}$) and decreases in focal bone balance ($f_{\mathrm{bb}}$) leading to resorption.

Figure 8

Normalized space-averaged BMD ($\overline{\mathrm{BMD}}$) as a function of time for overload and underload settings. ToLC: time of load change. Overload: 30% load increase. Underload: 30% load decrease. Osteoporosis threshold ($\overline{\mathrm{BMD}}$ = 0.7) represented by dash-dotted horizontal line.