Daniel Rohrbach

Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur

Tissue level structural and mechanical properties are important determinants of bone strength. As an individual ages, microstructural changes occur in bone, e.g., trabeculae and cortex become thinner and porosity increases. However, it is not known how the elastic properties of bone change during aging. Bone tissue may lose its elasticity and become more brittle and prone to fractures as it ages. In the present study the age-dependent variation in the spatial distributions of microstructural and microelastic properties of the human femoral neck and shaft were evaluated by using acoustic microscopy. Although these properties may not be directly measured in vivo, there is a major interest to investigate their relationships with the linear elastic measurements obtained by diagnostic ultrasound at the most severe fracture sites, e.g., the femoral neck. However, before the validity of novel in vivo techniques can be established, it is essential to understand the age-dependent variation in tissue elastic properties and porosity at different skeletal sites. A total of 42 transverse cross-sectional bone samples were obtained from the femoral neck (Fn) and proximal femoral shaft (Ps) of 21 men (mean±SD age 47.1±17.8, range 17-82years). Samples were quantitatively imaged using a scanning acoustic microscope (SAM) equipped with a 50MHz ultrasound transducer. Distributions of the elastic coefficient (c33) of cortical (Ct) and trabecular (Tr) tissues and microstructure of cortex (cortical thickness Ct.Th and porosity Ct.Po) were determined. Variations in c33 were observed with respect to tissue type (c33Trc33(Ct.Fn)=35.3GPa>c33(Tr.Ps)=33.8GPa>c33(Tr.Fn)=31.9GPa), and cadaver age (R(2)=0.28-0.46, p<0.05). Regional variations in porosity were found in the neck (superior 13.1%; inferior 6.1%; anterior 10.1%; posterior 8.6%) and in the shaft (medial 9.5%; lateral 7.7%; anterior 8.6%; posterior 12.0%). In conclusion, significant variations in elastic coefficients were detected between femoral neck and shaft as well as between the quadrants of the cross-sections of neck and shaft. Moreover, an age-related increase in cortical porosity and a stiffening of the bone tissue were observed. These findings may explain in part the increase in susceptibility to suffer low energy fractures during aging and highlight the potential of ultrasound in clinical osteoporosis diagnostics.

Spatial distribution of tissue level properties in a human femoral cortical bone.

The mechanical properties of cortical bone are determined by a combination bone tissue composition, and structure at several hierarchical length scales. In this study the spatial distribution of tissue level properties within a human femoral shaft has been investigated. Cylindrically shaped samples (diameter: 4.4mm, N=56) were prepared from cortical regions along the entire length (20-85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants). The samples were analyzed using scanning acoustic microscopy (SAM) at 50MHz and synchrotron radiation micro computed tomography (SRμCT). For all samples the average cortical porosity (Ct.Po), tissue elastic coefficients (c(ij)) and the average tissue degree of mineralization (DMB) were determined. The smallest coefficient of variation was observed for DMB (1.8%), followed by BV/TV (5.4%), c(ij) (8.2-45.5%), and Ct.Po (47.5%). Different variations with respect to the anatomical position were found for DMB, Ct.Po and c(ij). These data address the anatomical variations in anisotropic elastic properties and link them to tissue mineralization and porosity, which are important input parameters for numerical multi-scale bone models.

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones.

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.

Influence of porosity, pore size, and cortical thickness on the propagation of ultrasonic waves guided through the femoral neck cortex: a simulation study

The femoral neck is a common fracture site in elderly people. The cortical shell is thought to be the major contributor to the mechanical competence of the femoral neck, but its microstructural parameters are not sufficiently accessible under in vivo conditions with current X-ray-based methods. To systematically investigate the influences of pore size, porosity, and thickness of the femoral neck cortex on the propagation of ultrasound, we developed 96 different bone models (combining 6 different pore sizes with 4 different porosities and 4 different thicknesses) and simulated the ultrasound propagation using a finite-difference time-domain algorithm. The simulated singleelement emitter and receiver array consisting of 16 elements (8 inferior and 8 superior) were placed at anterior and posterior sides of the bone, respectively (transverse transmission). From each simulation, we analyzed the waveform collected by each of the inferior receiver elements for the one with the shortest time of flight. The first arriving signal of this waveform, which is associated with the wave traveling through the cortical shell, was then evaluated for its three different waveform characteristics (TOF: time point of the first point of inflection of the received signal, Δt: difference between the time point at which the signal first crosses the zero baseline and TOF, and A: amplitude of the first extreme of the first arriving signal). From the analyses of these waveform characteristics, we were able to develop multivariate models to predict pore size, porosity, and cortical thickness, corresponding to the 96 different bone models, with remaining errors in the range of 50 μm for pore size, 1.5% for porosity, and 0.17 mm for cortical thickness.

Fine-resolution maps of acoustic properties at 250 MHz of unstained fixed murine retinal layers

Ex vivo assessment of microscale tissue biomechanical properties of the mammalian retina could offer insights into diseases such as keratoconus, and macular degeneration. A 250-MHz scanning acoustic microscope (7-μm resolution) has been constructed to derive two-dimensional quantitative maps of attenuation (α), speed of sound (c), acoustic impedance (Z), bulk modulus (B), and mass density ( ρ). The two-dimensional maps were compared to coregistered hematoxylin-and-eosin stained sections. This study is the first to quantitatively assess  α, c, Z, B, and ρ of individual retinal layers of mammalian animals at high ultrasound frequencies. Significant differences in these parameters between the layers were demonstrated.

Modelling elastic wave propagation using the k-Wave MATLAB Toolbox

A new model for simulating elastic wave propagation using the open-source k-Wave MATLAB Toolbox is described. The model is based on two coupled first-order equations describing the stress and particle velocity within an isotropic medium. For absorbing media, the Kelvin-Voigt model of viscoelasticity is used. The equations are discretised in 2D and 3D using an efficient time-stepping pseudospectral scheme. This uses the Fourier collocation spectral method to compute spatial derivatives and a leapfrog finite-difference scheme to integrate forwards in time. A multi-axial perfectly matched layer (M-PML) is implemented to allow free-field simulations using a finite-sized computational grid. Acceleration using a graphics processing unit (GPU) is supported via the MATLAB Parallel Computing Toolbox. An overview of the simulation functions and their theoretical and numerical foundations is described.

Modeling of Femoral Neck Cortical Bone for the Numerical Simulation of Ultrasound Propagation

Quantitative ultrasound assessment of the cortical compartment of the femur neck (FN) is investigated with the goal of achieving enhanced fracture risk prediction. Measurements at the FN are influenced by bone size, shape and material properties. The work described here was aimed at determining which FN material properties have a significant impact on ultrasound propagation around 0.5 MHz and assessing the relevancy of different models. A methodology for the modeling of ultrasound propagation in the FN, with a focus on the modeling of bone elastic properties based on scanning acoustic microscopy data, is introduced. It is found that the first-arriving ultrasound signal measured in through-transmission at the FN is not influenced by trabecular bone properties or by the heterogeneities of the cortical bone mineralized matrix. In contrast, the signal is sensitive to variations in cortical porosity, which can, to a certain extent, be accounted for by effective properties calculated with the Mori-Tanaka method.

Histogram feature-based classification improves differentiability of early bone healing stages from micro-computed tomographic data.

Objective Contrast between not fully mineralized tissues is weak and limits conventional computed tomography (CT). An automated grayscale histogram-based analysis features could improve the sensitivity to tissue alterations during early bone healing. Materials and Methods Tissue formation in a rat osteotomy model was analyzed using in vivo micro-CT and classified histologically (mineralized, cartilage, and connective tissues). A conventional threshold-based method including manual contouring was compared to a novel moment-based method: after removing the background peak, the histograms of each slice were characterized by their moments and analyzed as a function of the position along the long bone axis. Results The threshold-based method could differentiate between the mineralized and connective tissue (R2 = 0.73). The moment-based approach yielded a clear distinction between all 3 groups with a classification accuracy up to R2 = 0.93. Conclusions The moment-based evaluation outperforms the conventional threshold-based CT analysis in sensitivity to the healing stage, user independence, and time consumption.

Distribution of mesoscale elastic properties and mass density in the human femoral shaft

Abstract Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study, the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor CMicro of cylindrical-shaped samples (diameter: 4.4 mm, N = 56) were obtained from cortical regions between 20 and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation µCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM). Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor CMeso were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c33 measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft. Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1–21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R2 ≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. These data were suitable inputs for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

Two-dimensional simulations of wave propagation in healing long bones based on scanning acoustic microscopy images

Ultrasonic evaluation of bone fracture healing has been recognized as an important assessment method which reflects material, mechanical and structural properties. The objective of the present study is to examine the monitoring role of quantitative ultrasound by conducting axial transmission measurements of the propagation velocity of the first arriving signal (FAS) for two dimensional numerical models and various excitation frequencies (0.1-1 MHz). The models were derived from scanning acoustic microscopy (SAM). Although this is a preliminary study, the observed interaction between the FAS and the change in the material properties was quantified and the results give rise to the investigation of guided wave propagation, as well.