Cortical thickness adaptation to combined mechanical loading and parathyroid hormone treatments is site specific and synergistic in the mouse tibia model.

In this study, we aimed to quantify the localised effects of mechanical loading (ML), low (20 µg/kg/day), moderate (40 µg/kg/day) or high (80 µg/kg/day) dosages of parathyroid hormone (PTH), and combined (PTHML) treatments on cortical bone adaptation in healthy 19-week old female C57BL/6 mice. To this end, we utilise a previously reported image analysis algorithm on µCT data of the mouse tibia published by Sugiyama et al. (2008) to measure changes in cortical area, marrow cavity area and local cortical thickness measures (ΔCt.Ar, ΔMa.Ar, ΔCt.Th respectively), evaluated at two cross-sections within the mouse tibia (proximal-middle (37 %) and middle (50 %)), and are compared to a superposed summation (P + M) of individual treatments to determine the effectiveness of combining treatments in vivo. ΔCt.Ar analysis revealed a non-linear, synergistic interactions between PTH and ML in the 37 % cross-section that saturates at higher PTH dosages, whereas the 50 % cross-section experiences an approximately linear, additive adaptation response. This coincided with an increase in ΔMa.Ar (indicating resorption of the endosteal surface), which was only counteracted by combined high dose PTH with ML in the middle cross-section. Regional analysis of ΔCt.Th changes reveal localised cortical thinning in response to low dose PTH treatment in the posteromedial region of the middle cross-section, signifying that PTH does not provide a homogeneous adaptation response around the cortical perimeter. We observe a synergistic response in the proximal-middle cross-section, with regions of compressive strain experiencing the greatest adaptation response to PTHML treatments, (peak ΔCt.Th of 189.32, 213.78 and 239.30 µm for low, moderate and high PTHML groups respectively). In contrast, PTHML treatments in the middle cross-section show a similar response to the superposed P + M group, with the exception of the combined high dose PTHML treatment which shows a synergistic interaction. These analyses suggest that, in mice, adding mechanical loading to PTH treatments leads to region specific bone responses; synergism of PTHML is only achieved in some regions experiencing high loading, while other regions respond additively to this combined treatment.

Beam theory for rapid strain estimation in the mouse tibia compression model.

The mouse tibia compression model is a leading model for studying bone's mechanoadaptive response to load. In studying this mechanoadaptive response, (FE) modelling is often used to determine the stress/strain within the tibia. The development of such models can be challenging and computationally expensive. An alternate approach is to use continuum mechanics based analytical theories, such as beam theory (BT). However, applying BT to the mouse tibia requires the fibula be neglected, introducing error in the stress/strain distribution. While several studies have applied BT to the mouse tibia, no study has explored the accuracy of this approach. To address these questions, this work investigates the use of BT in determining stress/strain within the mouse tibia. By comparing BT against FE modelling, it was found that BT can accurately predict tibial stress/strain if correction factors are applied to account for the effect of the fibula. The 25, 37, 50 and 75% cross sections are studied. Focusing on the 37% cross section, without correction, BT can have errors of approximately 21.6%. With correction, this is reduced to 6.6%. Such correction factors are presented. The developed BT model is applicable in the diaphysis and distal metaphysis, where the assumptions of BT are valid. This work verifies BT for determining localised strains in a mouse tibia compression model. This is anticipated to provide efficiency dividends, allowing for high throughput modelling of the mouse tibia, advancing study of bone's mechanoadaptive response.

Cortical Thickness Adaptive Response to Mechanical Loading Depends on Periosteal Position and Varies Linearly With Loading Magnitude.

The aim of the current study was to quantify the local effect of mechanical loading on cortical bone formation response at the periosteal surface using previously obtained µCT data from a mouse tibia mechanical loading study. A novel image analysis algorithm was developed to quantify local cortical thickness changes (ΔCt.Th) along the periosteal surface due to different peak loads (0N ≤ F ≤ 12N) applied to right-neurectomised mature female C57BL/6 mice. Furthermore, beam analysis was performed to analyse the local strain distribution including regions of tensile, compressive, and low strain magnitudes. Student's paired t-test showed that ΔCt.Th in the proximal (25%), proximal/middle (37%), and middle (50%) cross-sections (along the z-axis of tibia) is strongly associated with the peak applied loads. These changes are significant in a majority of periosteal positions, in particular those experiencing high compressive or tensile strains. No association between F and ΔCt.Th was found in regions around the neutral axis. For the most distal cross-section (75%), the association of loading magnitude and ΔCt.Th was not as pronounced as the more proximal cross-sections. Also, bone formation responses along the periosteum did not occur in regions of highest compressive and tensile strains predicted by beam theory. This could be due to complex experimental loading conditions which were not explicitly accounted for in the mechanical analysis. Our results show that the bone formation response depends on the load magnitude and the periosteal position. Bone resorption due to the neurectomy of the loaded tibia occurs throughout the entire cross-sectional region for all investigated cortical sections 25, 37, 50, and 75%. For peak applied loads higher than 4 N, compressive and tensile regions show bone formation; however, regions around the neutral axis show constant resorption. The 50% cross-section showed the most regular ΔCt.Th response with increased loading when compared to 25 and 37% cross-sections. Relative thickness gains of approximately 70, 60, and 55% were observed for F = 12 N in the 25, 37, and 50% cross-sections. ΔCt.Th at selected points of the periosteum follow a linear response with increased peak load; no lazy zone was observed at these positions.

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

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 [Formula: see text]g of PTH with experimental data from the literature. Simulation results indicate a site-specific bone gain of 8.66[Formula: see text] (9.4 ± 1.13[Formula: see text]) at the lumbar spine and 3.14[Formula: see text] (2.82 ± 0.72[Formula: see text]) at the femoral neck. Bone gain depends nonlinearly on the administered dose, being, respectively, 0.68[Formula: see text], 3.4[Formula: see text] and 6.16[Formula: see text] for a 10, 20 and 40 [Formula: see text]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 [Formula: see text]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.

Computational model of the dual action of PTH - Application to a rat model of osteoporosis.

This paper presents a pharmacokinetic/pharmacodynamic (PK/PD) model of the action of PTH(1-34) on bone modelling and remodelling, developed for quantitatively investigating the dose- and administration pattern-dependency of the bone tissue response to this drug. Firstly, a PK model of PTH(1-34) was developed, accounting for administration via subcutaneous injections. Subsequently, the PK model was coupled to a (mechanistic) bone cell population model of bone modelling and remodelling, taking into account the effects of PTH(1-34) on the differentiation of lining cells into active osteoblasts, on the apoptosis of active osteoblasts, and on proliferation of osteoblast precursors, as well as on the key regulatory pathways of bone cell activities. Numerical simulations show that the coupled PK/PD model is able to distinguish between continuous and intermittent administration patterns of PTH(1-34), in terms of yielding both catabolic bone responses (if drug administration is carried out continuously) and anabolic bone responses (if drug administration is carried out intermittently). The model also features a non-linear relation between bone gain and drug dose (as known from experiments); doubling the dose from 80 µg/kg/day to 160 µg/kg/day induced a 1.3-fold increase of the bone volume-to-total volume ratio. Furthermore, the model presented in this paper confirmed that bone modelling represents an essential mechanism of the anabolic response of bone to PTH(1-34) administration in rat models, and that the large amount of bone formation observed in such models cannot be explained via remodelling alone.