Study of the combined effects of PTH treatment and mechanical loading in postmenopausal osteoporosis using a new mechanistic PK-PD model

Abstract

One of only a few approved and available anabolic treatments for severe osteoporosis is daily injections of PTH (1-34). This drug has a specific dual action which can act either anabolically or catabolically depending on the type of administration, i.e. intermittent or continuous, respectively. In this paper, we present a mechanistic pharmacokinetic–pharmacodynamic model of the action of PTH in postmenopausal osteoporosis. This model accounts for anabolic and catabolic activities in bone remodelling under intermittent and continuous administration of PTH. The model predicts evolution of common bone biomarkers and bone volume fraction (BV/TV) over time. We compared the relative changes in BV/TV resulting from a daily injection of 20 $\upmu$g of PTH with experimental data from the literature. Simulation results indicate a site-specific bone gain of 8.66$\%$ (9.4 ± 1.13$\%$) at the lumbar spine and 3.14$\%$ (2.82 ± 0.72$\%$) at the femoral neck. Bone gain depends nonlinearly on the administered dose, being, respectively, 0.68$\%$, 3.4$\%$ and 6.16$\%$ for a 10, 20 and 40 $\upmu$g PTH dose at the FN over 2 years. Simulations were performed also taking into account a bone mechanical disuse to reproduce elderly frail subjects. The results show that mechanical disuse ablates the effects of PTH and leads to a 1.08% reduction of bone gain at the FN over a 2-year treatment period for the 20 $\upmu$g of PTH. The developed model can simulate a range of pathological conditions and treatments in bones including different PTH doses, different mechanical loading environments and combinations. Consequently, the model can be used for testing and generating hypotheses related to synergistic action between PTH treatment and physical activity.

Appendices

Appendix 1: PK model calibrated on an Asian population

Asian populations are usually lighter than Caucasian populations. This will have an influence on the created PK model. Indeed, the volume of distribution $V_{ d}$ represents the one-compartment model described in Sect. 2.1. We consider an average weight of 50 kg for an Asian osteoporotic female population (Lin et al. 2004). We deduce the volume of distribution from the average weight as $V_{ d} = 1.7$ L/kg as the pharmacokinetics of PTH in humans is linear. Hence, we can simulate our PK model as we did previously in Sect. 2.1.

Appendix 2: $OB_a$ apoptosis rate H function

$$\begin{aligned} H^-_{ PTH} = \alpha _{A_{{ OB}_{ a}}} - \frac{(\alpha _{A_{{ OB}_{ a}}} - \rho _{A_{{ OB}_{ a}}}) \cdot Bcl\text{-}2^{\gamma _{A_{{ OB}_{ a}}}}}{\delta _{A_{{ OB}_{ a}}}^{\gamma _{A_{{ OB}_{ a}}}} + Bcl\text{-}2^{\gamma _{A_{{ OB}_{ a}}}}} \end{aligned}$$

(19)

The H function driving the OB$_{ a}$ apoptosis rate is important in our model as it will translate intracellular signal (Bcl-2 concentration) into a cell response and will be one of the major drivers of the dual response of PTH. We calibrated this function using the parameters shown in Table 2 such that $H_{ PTH}^- = 1$ at the PTH concentration baseline (cf. Fig. 8, green dot). In the case of intermittent daily injections, the $H_{ PTH}^-$ will decrease the value of osteoblast apoptosis rate (red dot in Fig. 8), whereas continuous administration (cf. Fig. 4) will lead to a catabolic answer and therefore will increase apoptosis rate of OB$_{ a}$ by setting the $H_{ PTH}^-$ above 1 (blue dot in Fig. 8).

Fig. 8

$H^-_{ PTH}$ plot in function of Bcl-2 concentration—green square represents the baseline value when PTH is only endogenously produced, i.e. no external PTH injection. Red square represents the catabolic value corresponding to the continuous PTH administration from Fig. 4. Blue square represents the anabolic value corresponding to the intermittent 20 $\upmu$g PTH injections from Fig. 4

Appendix 3: Model parameters

See Table 6.

Table 6 Parameters governing the present PK/PD model