Patrik Christen

Bone morphology allows estimation of loading history in a murine model of bone adaptation.

Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.

Challenges in longitudinal measurements with HR-pQCT: Evaluation of a 3D registration method to improve bone microarchitecture and strength measurement reproducibility

Definition of identical regions between repeated computed tomography (CT) scans is a key factor to monitor changes in bone microarchitecture. In longitudinal studies, accurate determination of the volume of interest (VOI), using three dimensional (3D) registration may improve precision. Therefore, the aim of our study was to investigate the short-term reproducibility of bone geometry, density, microstructure and biomechanical parameters assessed by HR-pQCT and micro-finite element (μFE) derived analyses, using the cross-sectional area (CSA) registration method in comparison with the use of 3D registration, to find overlapping regions between scans. Fifteen healthy individuals (aged 21-47 years) underwent 3 separate scans at the distal radius and tibia, within a one-month interval. Reproducibility was assessed after double contouring the cortical compartment and after applying three different methods to determine the common region between repeated scans: (i) the VOI was determined with no registration, i.e., on 110 slices, (ii) the VOI was determined after CSA-based registration, and (iii) the VOI was determined after 3D registration. Both pre- and post-registration short-term reproducibility for each subject was determined. With no registration, CVrms of geometry parameters ranged from 0.5 to 3.7%, showing a slight variation in the CSA between scans. When the CSA registration method was employed, the variability of geometry (CVrms<1.8%) and density parameters (CVrms<1.8%), was better than that obtained without registration. By removing the effect of repositioning, the 3D registration further improved the reproducibility of cortical bone measurements compared to other methods. Indeed, significant improvements were found for cortical geometry and microstructure measurements (CVrms ranged from 0.4% to 10.7% at both sites; p<0.05), whereas the impact on trabecular bone measurements was restricted to its geometry parameter. The repositioning error was significantly reduced, most markedly at the radius compared to the tibia. For μFE measures, the impact of 3D registration on whole bone stiffness was negligible, indicating adequate assessment of longitudinal changes in estimated biomechanical properties, even without registration. In conclusion, we have shown that the 3D registration improved the identification of the common region retained for longitudinal analysis, contributing to improve the reproducibility of cortical bone parameter measurements. We also quantified the minimally detectable bone changes to help designing future studies with HR-pQCT.

Patient-specific bone modelling and remodelling simulation of hypoparathyroidism based on human iliac crest biopsies

We previously developed a load-adaptive bone modelling and remodelling simulation model that can predict changes in the bone micro-architecture as a result of changes in mechanical loading or cell activity. In combination with a novel algorithm to estimate loading conditions, this offers the possibility for patient-specific predictions of bone modelling and remodelling. Based on such models, the underlying mechanisms of bone diseases and/or the effects of certain drugs and their influence on the bone micro-architecture can be investigated. In the present study we test the ability of this approach to predict changes in bone micro-architecture during hypoparathyroidism (HypoPT), as an illustrative example. We hypothesize that, apart from reducing bone turnover, HypoPT must also lead to increased osteocyte mechanosensitivity in order to explain the changes in bone mass seen in patients. Healthy human iliac crest biopsies were used as the starting point for the simulations that mimic HypoPT conditions and the resultant micro-architectures were compared to age-matched clinical HypoPT biopsies. Simulation results were in good agreement with the clinical data when osteocyte mechanosensitivity was increased by 40%. In conclusion, the results confirm our hypothesis, and also demonstrate that patient-specific bone modelling and remodelling simulations are feasible.

Subject-specific bone loading estimation in the human distal radius

High-resolution in vivo bone micro-architecture assessment, as possible now for the distal forearm, in combination with bone remodelling simulation algorithms could, eventually, predict patient-specific bone morphology changes. To simulate load-adaptive bone remodelling, however, physiological loading conditions must be defined. In this paper we test a previously developed algorithm to estimate such physiological loading conditions from the bone micro-architecture. The aims of this study were to investigate if realistic boundary forces and moments are predicted for the scanned distal radius section and how these predicted forces and moments should be distributed to the scanned section in order to obtain a load transfer similar to that in situ. Images at in vivo resolution were generated for the clinically measured section of nine distal radius cadaver bones, converted to micro-finite element models and used for load estimation. Models of the full distal radius were created to analyse tissue loading distributions of the sections in situ. It was found that predicted forces and moments at the boundaries of the scanned region varied considerably but, when translated to equivalent radiocarpal joint forces, agreed well with values reported in the literature. Bone tissue loading distribution was in best agreement with in situ distributions when loading was applied to an extra layer of material at both ends of the clinical scan region. The agreement of the predicted loading to previous studies and the wide range of predicted loading values indicate that subject-specific bone loading estimation is possible and necessary.

Validation of a bone loading estimation algorithm for patient-specific bone remodelling simulations

Patient-specific simulations of bone remodelling could enable predicting how bone micro-structural integrity would be affected by bone diseases, drugs or other factors, and, ultimately could help clinicians to improve their prognoses. To simulate load-adaptive remodelling, however, knowledge about the physiological external loading acting on the bone is required. Assuming that load adaptation leads to homogeneous tissue loading, we previously developed a method to estimate the physiological loading history from bone micro-structural morphology. We were able to reconstruct the loading history of a simple load case that was applied in an animal experiment. However, we found considerable inhomogeneity in tissue loading suggesting that the bones were not fully adapted. Also, we noted differences in bone micro-architecture between animals despite common loading history, possibly due to differences caused by the stochastic nature of the bone remodelling process. In the present study, we aim at validating the load estimation algorithm in a well-controlled environment in which more complicated loading conditions are applied. Specifically, we want to test its accuracy for partially and fully developed bone structures and for differences in bone micro-architectures as they can occur due to stochastic events, even for bones with a common loading history. This was possible by using synthetic micro-architectures obtained from bone remodelling simulations as the basis for our load estimation algorithm. Loading histories based on fully adapted structures were predicted with a maximum error of 4.4% and predictions were not affected by differences in bone micro-architecture. These results show that our load estimation algorithm produces reasonable predictions and might be a suitable tool to define in vivo loading for patient-specific bone remodelling studies.

Determination of hip-joint loading patterns of living and extinct mammals using an inverse Wolff’s law approach

It is well known that bone adapts its microstructure in response to loading. Based on this form-follows-function relationship, we previously developed a reverse approach to derive joint loads from bone microstructure as acquired with micro-computed tomography. Here, we challenge this approach by calculating hip-joint loading patterns for human and dog, two species exhibiting different locomotion, and comparing them to in vivo measurements. As a proof of concept to use the approach also for extinct taxa, we applied it to a cave lion fossil bone. Calculations were in close agreement with in vivo measurements during walking for extant species, showing distinguished patterns for bipedalism and quadrupedalism. The cave lion calculations clearly revealed its quadrupedal locomotion and suggested a more diverse behaviour compared to the dog, which is in agreement with extant felids. This indicates that our novel approach is potentially useful for making inferences about locomotion in living as well as extinct mammals and to study evolutionary joint development.

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bones loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 µm and downscaled to 50, 61, 75, 82, 100, 125 and 150 µm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 µm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 µm, but that the dependency increases considerably at voxel sizes bigger than 82 µm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 µm, but that smaller voxel sizes would be advantageous.

In vivo Visualisation and Quantification of Bone Resorption and Bone Formation from Time-Lapse Imaging

Purpose of ReviewMechanoregulation of bone cells was proposed over a century ago, but only now can we visualise and quantify bone resorption and bone formation and its mechanoregulation. In this review, we show how the newest advances in imaging and computational methods paved the way for this breakthrough.Recent FindingsNon-invasive in vivo assessment of bone resorption and bone formation was demonstrated by time-lapse micro-computed tomography in animals, and by high-resolution peripheral quantitative computed tomography in humans. Coupled with micro-finite element analysis, the relationships between sites of bone resorption and bone formation and low and high tissue loading, respectively, were shown.SummaryTime-lapse in vivo imaging and computational methods enabled visualising and quantifying bone resorption and bone formation as well as its mechanoregulation. Future research includes visualising and quantifying mechanoregulation of bone resorption and bone formation from molecular to organ scales, and translating the findings into medicine using personalised bone health prognosis.

Load-adaptive bone remodeling simulations reveal osteoporotic microstructural and mechanical changes in whole human vertebrae

Osteoporosis is a major medical burden and its impact is expected to increase in our aging society. It is associated with low bone density and microstructural deterioration. Treatments are available, but the critical factor is to define individuals at risk from osteoporotic fractures. Computational simulations investigating not only changes in net bone tissue volume, but also changes in its microstructure where osteoporotic deterioration occur might help to better predict the risk of fractures. In this study, bone remodeling simulations with a mechanical feedback loop were used to predict microstructural changes due to osteoporosis and their impact on bone fragility from 50 to 80 years of age. Starting from homeostatic bone remodeling of a group of seven, mixed sex whole vertebrae, five mechanostat models mimicking different biological alterations associated with osteoporosis were developed, leading to imbalanced bone formation and resorption with a total net loss of bone tissue. A model with reduced bone formation rate and cell sensitivity led to the best match of morphometric indices compared to literature data and was chosen to predict postmenopausal osteoporotic bone loss in the whole group. Thirty years of osteoporotic bone loss were predicted with changes in morphometric indices in agreement with experimental measurements, and only showing major deviations in trabecular number and trabecular separation. In particular, although being optimized to match to the morphometric indices alone, the predicted bone loss revealed realistic changes on the organ level and on biomechanical competence. While the osteoporotic bone was able to maintain the mechanical stability to a great extent, higher fragility towards error loads was found for the osteoporotic bones.

Feasibility of rigid 3D image registration of high-resolution peripheral quantitative computed tomography images of healing distal radius fractures

For accurate analysis of bone formation and resorption during fracture healing, correct registration of follow-up onto baseline image is required. A per-fragment approach could improve alignment compared to standard registration based on the whole fractured region. In this exploratory study, we tested the effect of fragment size and displacement on a per-fragment registration, and compared the results of this per-fragment registration to the results of the standard registration in two stable fractures and one unstable fracture. To test the effect of fragment size and displacement, high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of three unfractured radii were divided into subvolumes. Different displacements in x-, y, or z-direction or rotations around each axis were applied, and each subvolume was registered onto the initial volume to realign it. Next, registration of follow-up onto baseline scan was performed in two stable and one unstable fracture. After coarsely aligning the follow-up onto the baseline scan, a more accurate registration was performed of the whole fracture, i.e. the standard registration, and of each fracture fragment separately, i.e. per-fragment registration. Alignment was checked using overlay images showing baseline, follow-up and overlap between these scans, and by comparing correlation coefficients between the standard and per-fragment registration. Generally, subvolumes as small as 300 mm3 that were displaced up to 0.82 mm in x- or y-, or up to 1.64 mm in z-direction could be realigned correctly. For the fragments of all fractures, correlation coefficients were higher after per-fragment registration compared to standard registration. Most improvement was found in the unstable fracture and one fragment of the unstable fracture did not align correctly. This exploratory study showed that image registration of individual subvolumes, such as fracture fragments, is feasible in both stable and unstable fractures, and leads to better alignment of these fragments compared to an approach that is based on registration using the whole fractured region. This result is promising for additional analysis of bone formation and resorption in HR-pQCT studies on fracture healing.