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Finite Element Resonant Ultrasound Spectroscopy to Characterize Maturation of Cortical Bone Elastic Properties

Periodic Reporting for period 1 - FE-RUS-Blast (Finite Element Resonant Ultrasound Spectroscopy to Characterize Maturation of Cortical Bone Elastic Properties)

Reporting period: 2015-04-01 to 2017-03-31

In the European Union, osteoporosis is a leading cause of mortality and morbidity in the elderly and a key factor in the high cost of medical care. The multiple factors implicated in osteoporosis, its obscure pathogenesis, make the need for further experimentation to gain insights into the biomechanical competence of bone and to investigate factors implicated in the determination of the strength or fragility of bones.
It is believed that the bone adapts to changes in the matrix strain to optimize bone mass and architecture so that bone is sufficiently strong to bear the loads it experiences. Therefore detailed knowledge of bone stiffness is highly relevant to gain insight into these mechanisms.
Animal models have provided outstanding information on bone diseases and are essential for the development of new drugs for osteoporosis. A large variety of animal species, including rodents, rabbits, dogs, and primates, have been used as animal models in osteoporosis research. New Zealand White rabbits were selected because they achieve skeletal maturity shortly after reaching complete sexual development at approximately 6 months, and they show significant intracortical remodeling.
The focus of the project is accurate measurement of bone stiffness (elasticity) and its anisotropy in a rabbit model.

There is an increasing awareness about osteoporosis, because of the consequences of fractures on morbidity, quality of life and mortality. In western countries, and particularly in Europe, approximately one in two women and up to one in four men age 50 and older will break a bone due to osteoporosis. Approximately 3.5 million new fragility fractures occur annually in the EU. In 2010 alone, fragility fractures resulted in costs of €37 billion.
Bone mineral density measured using X-ray densitometric techniques forms a cornerstone for the general management of osteoporosis, being used for diagnosis, risk prediction, the selection of patients for treatment and monitoring of patients on treatment. Nevertheless, the pathogenesis of osteoporosis is not fully elucidated yet and bone mineral density does not identify all individuals at risk. Half of elderly women who present with non-vertebral fractures would not be classified as osteoporotic from X-ray densitometry. This lack of correlation between BMD and fractures opens the possibility that other factors, the so-called bone ‘quality factors’, including microstructure and material properties, affect bone propensity to fracture.
Among these properties, it has been hypothesized that testing of stiffness is a substitute to strength, a quantity which cannot be measured in vivo. Fracture risk assessment could be improved by the concurrent consideration of stiffness (as a fracture risk factor) that operates independently of BMD. Furthermore, elucidating the relationships of bone stiffness to microstructure and chemical composition can result in identification of new therapeutic targets. Ultimately, the study may lead to better patient management, which may reduce the socio-economic burden of osteoporosis.

The state-of-art approach to determine bone elasticity is the conventional ultrasonic pulse method by measuring acoustic velocities along various directions of a specimen with a major drawback of sample size limitation, typically larger than 5 mm and specimen preparation as a regularly shaped specimen. However, studies on bone metabolism greatly relies on small animal models, e.g. rabbit, rat, and mouse, with smaller bones compared with the human bones and the cortical thicknesses are close to or even smaller than 1 mm. Resonant ultrasound spectroscopy (RUS) has been well established to measure the anisotropic elasticity of small metallic samples. However, it was known to be not applicable to high-damping materials like bone, due to the complicated extraction of resonant frequencies from the overlapping resonant peaks. Recently, such a limitation has been overcome in the host lab, which allows the measurement of the high-damping cortical bone materials. However, current RUS method still can only be used to measure regularly-shaped (e.g. cylinders, parallelepiped) specimens of cortical bone. An alternative approach, with a combination of the finite element (FE) method and RUS (FE-RUS) has already been proposed, which theoretically relaxes the restriction of the specimen geometry preparation, but has not really been used due to the lack of practical application. In the project, we propose to introduce the FE-RUS principle to improve our previous method towards developing a truly practical technology for a complete elasticity determination of small animal irregularly-shaped bone specimens.
Specific objectives of the project include:
1. To develop and to validate FE-RUS method for testing small animal cortical bone elasticity.
2. Measure cortical bone elasticity variations in aging rabbits as a first application of FE-RUS method.
3. Investigate the biomechanical and microstructural determinants of not only the Young’s modulus (precisely assessed by RUS) but also the other elastic coefficients derived from the elastic tensor (shear coefficients, anisotropy ratios, Poisson ratios), and statistically analyze the relationship between the cortical bone strength and elasticity.
Currently, all methodology developments planned in the Grant Agreement have been fulfilled. Some experiments of rabbit model validation are still undergoing. According to the objectives proposed in the Grant Agreement, the following results have been achieved,
1. To overcome the material limitation of bone attenuation, a new strategy using a Bayesian-based reversible jump Markov chain Monte Carlo (RJ-MCMC) technique has been developed to automatically estimate multiple parameters, including frequency, damping factor, sinusoid amplitude, and noise magnitude, from multiple spectra measured on a cortical bone specimen.
2. The FE method (FEM) has been applied to analyze the free-vibration frequencies of the irregularly-shaped sample. The forward problem, i.e. computation of the natural frequencies using FEM, has been validated using an aluminum specimen prepared by a computer numerical control milling machine.
3. A Monte Carlo Markov Chain sampling strategy is used to solve the inverse problem of FE-RUS based elasticity coefficients determination in a Bayesian framework. The results illustrate the feasibility of applying FE-RUS method to evaluate the elasticity of the irregular-shaped small animal cortical bone.
During the project, many methodology challenges of the FE-RUS technique towards the application have been overcome. We proposed a novel advanced FE-RUS methodology for measuring the complete set of anisotropic elastic constants of small-scale specimen with irregular geometry and high-attenuating material properties. Our results will be submitted to peer-reviewed journals this year and will be presented at the European Symposium on Ultrasonic Characterization of Bone (ESUCB) 2017. Patents will be considered.
We believe that the project will be very helpful for building a new research community in the field of RUS-based cortical bone elasticity measurement. In addition, the devices developed in the host lab will attract more talents and technology on the topics of cortical bone millimeter-scale elasticity determination with great potentials of collaboration.