Xiran Cai

Cortical bone elasticity measured by resonant ultrasound spectroscopy is not altered by defatting and synchrotron X-ray imaging

In the study of mechanical properties of human bone, specimens may be defatted before experiments to prevent contamination and the risk of infections. High energy synchrotron radiation micro-computed tomography (SR-μCT) is a popular technique to study bone microstructure. However, little is known about the effects of defatting or irradiation during SR-μCT imaging on different elastic coefficients including shear and longitudinal moduli in different anatomical directions. In this work, these effects are evaluated on a set of 24 samples using resonant ultrasound spectroscopy (RUS), which allows one to accurately measure the complete set of elastic coefficients of cortical bone non destructively. The results show that defatting with diethylether and methanol and irradiation up to 2.5kGy has no detectable effect on any of the elastic coefficients of human cortical bone.

A critical assessment of the in-vitro measurement of cortical bone stiffness with ultrasound

HIGHLIGHTSStandardizing ultrasonic bulk wave velocity measurements on cortical bone is needed.Effects of multiple factors on the resulting stiffness are investigated.A methodology is recommended to comply a protocol for measuring bone stiffness. ABSTRACT Elasticity assessment based on bulk wave velocity (BWV) measurements is the most popular technique to characterize the anisotropic stiffness tensor in cortical bone. Typically, a cuboid bone specimen is cut with its sides along the different anatomical directions. Then, the velocity of shear and longitudinal waves propagating along different directions are assessed, from which stiffness coefficients are calculated. Despite the importance of obtaining accurate elasticity values for bone research, there is no generally accepted protocol to measure BWV and the precision of the technique has been seldom investigated. The purpose of this work is to critically assess the method to measure BWV on cuboid specimens in terms of ultrasound frequency, specimen size and signal processing technique. In this study, we measured polycarbonate specimens of different dimensions and 55 human bone specimens with different transducers using frequencies ranging from 2.25 to 10 MHz and 1–5 MHz for longitudinal and shear waves, respectively. We compared four signal processing methods to detect the wave arrival time. The main results are that, (1) the measurement of shear waves is more complex than that of longitudinal wave, being less precise and more sensitive to sample size; (2) the estimated stiffness depends on the signal processing technique used (up to 10% variation for shear coefficients of bone); and (3) bone stiffness assessed from BWV using the first arrival of the signal to determine the time‐of‐flight is not different from stiffness assessed using resonant ultrasound spectroscopy (RUS). These results evidence that the measurement method can have an effect on the stiffness values estimates and hence, a well‐defined protocol is needed to accurately measure bone stiffness coefficients based on BWV.

Assessment of trabecular bone tissue elasticity with resonant ultrasound spectroscopy

The material properties of the trabeculae (tissue-level properties), together with the trabecular architecture and the bone volume fraction determine the apparent millimetre-scale bone mechanical properties. We present a novel method to measure trabecular tissue elastic modulus Et using resonant ultrasound spectroscopy (RUS). The first mechanical resonance frequency fe of a freestanding cuboid specimen is measured and used to back-calculate Et. The steps of the back-calculation are (1) the apparent stiffness tensors C(Et˜) is computed using micro-finite elements for a set of trial values of tissue Youngs modulus Et˜ based on the computed tomography image of the specimen; (2) the modeled free-vibration resonance frequencies fm(Et˜) of the specimen is calculated with the Rayleigh-Ritz method using C(Et˜); (3) finally, Et is obtained by interpolation using fe and fm(Et˜). Four bovine bone specimens were tested (nominal size 5×6 ×6mm3). Average (standard deviation) of Et was 13.12 (1.06)GPa. The measurement of a single resonance frequency enabled an estimation of tissue elasticity in line with available data. RUS is a non destructive technique relatively easy to implement compared to traditional mechanical testing. The novel method could contribute to a better documentation of bone tissue elasticity which is an important parameter of micro-finite element analyses for the clinical assessment of bone strength.

The elastic properties of human cortical bone measured by resonant ultrasound spectroscopy at multiple skeletal sites

Human cortical bone is an anisotropic material, although isotropic stiffness is generally assumed in most finite element analysis. Detailed information about the anisotropic stiffness at a mesoscopic (mm) scale would improve our understanding of bones macroscopic mechanical properties. In this work, we report on the anisotropic stiffness of human cortical bone from different sites, and the variation in anisotropy seen.

Bone matrix elastic properties determined by FFT-based inverse homogenization

Cortical bone is an anisotropic material with hierarchical structure whose elastic properties are described at different length scales. At millimeter-scale, the whole set of stiffness tensor can be conveniently measured by resonant ultrasound spectroscopy (RUS). At microscopic-scale, micro-indentation and scanning acoustic microscopy are often used to quantify tissue matrix elastic properties. However, the last two methods do not easily provide the entire tissue stiffness tensor, but rather the elasticity or stiffness along a single direction. To overcome this limitation, we introduce a new approach to retrieving the elastic tensor of the tissue based on a numerical optimization procedure using Fast Fourier Transform (FFT)-based homogenization for the forward computation.

Relationships between cortical bone quality biomarkers: Stiffness, toughness, microstructure, mineralization, cross-links and collagen

Bone quality encompasses bone properties that contribute to fracture risk, such as bone stiffness, microstructure, matrix constituents or tissue material properties. These aspects cannot be quantified in-vivo except for stiffness, a surrogate biomarker of strength, which can be assessed using quantitative ultrasound techniques. To better predict bone fracture risk, investigating the relationships between stiffness and other bone quality factors is important. Toward this goal, our group adapted resonant ultrasound spectroscopy (RUS) to precisely measure the whole set of stiffness coefficients of cortical bone by improving the signal processing and automatizing the inversion procedure based on a Bayesian framework. In this work, we present the relationships between bone quality biomarkers including stiffness, fracture toughness, microstructure, mineralization, cross-links and collagen.

Recent advances in resonant ultrasound spectroscopy to measure bone stiffness tensor

Resonant Ultrasound Spectroscopy (RUS) is a method to measure the elasticity tensor of a material. RUS is particularly advantageous to measure small samples of anisotropic materials. In RUS, resonant frequencies of a sample are measured and computed frequencies of a numerical model of the sample are fitted, yielding the stiffness tensor. RUS was developed in the 1990s, but until recently, it was in practice limited to measure materials with a high quality factor. We have adapted the method to measure bone whose quality factor is about 25. Our strategy combines Bayesian methods to retrieve overlapped resonant peaks in the RUS spectra and to solve the inverse problem using a limited number of resonant frequencies. The method allows a quasi-automated processing of RUS spectra where it is not necessary to know a priori the pairing between measured and computed frequencies. In the last years we have extensively used RUS to document the anisotropic elastic properties of human cortical bone and to investigate th...

Efficient dispersion analysis of guided waves in cortical bone

Guided wave propagation is at the heart of the axial transmission techniques designed to assess bone health status. The method involves matching observed and predicted dispersion characteristics of guided waves. The strength of the technique is that it can infer more than one bone property from the measured ultrasonic data, such as cortical thickness, stiffness, or porosity. The suitability of the model chosen for the inversion has recently been debated and the question has been raised whether the physical model must take the soft tissue coating influence into account as well as perhaps other factors such as bone curvature. We present in this talk a series of experiments conducted on bone-mimicking phantoms (plates or tubes) with or without soft tissue-mimicking coating showing evidence 1/ that the experimental guided wave branches in the range of 0.4-1.6 MHz mainly exhibit sensitivity to the influence of the solid subsystem (bone) and 2/ that a simple non absorbing transverse isotropic free plate model p...

An introduction to measurements of human cortical bone elasticity using Resonant Ultrasound Spectroscopy

To understand the structure-function relationship of bone and to investigate bone fragility, a precise and practical way to measure cortical bone elasticity is important. Resonant Ultrasound Spectroscopy (RUS) has shown its accuracy and convenience in fully characterizing the stiffness coefficients of anisotropic solid materials. However, it was long believed that the method is not applicable to bone, a highly damping material. This paper reviews the basic concepts of RUS measurement and the recent progress of adapting this technique to the measurement of the elasticity tensor of highly damping materials. Meanwhile, a successful implementation of RUS with latest progress to measure the elasticity tensor of a collection of human tibia cortical bone specimens was demonstrated.