Potential of first arriving signal to assess cortical bone geometry at the Hip with QUS: a model based study

Numerical evaluation of the backward propagating acoustic field in healing long bones

The propagation of ultrasound in healing long bones induces complex scattering phenomena due to the interaction of an ultrasonic wave with the composite nature of callus and osseous tissues. This work presents numerical simulations of ultrasonic propagation in healing long bones using the boundary element method aiming to provide insight into the complex scattering mechanisms and better comprehend the state of bone regeneration. Numerical models of healing long bones are established based on scanning acoustic microscopy images from successive postoperative weeks considering the effect of the nonhomogeneous callus structure. More specifically, the scattering amplitude and the acoustic pressure variation are calculated in the backward direction to investigate their potential to serve as quantitative and qualitative indicators for the monitoring of the bone healing process. The role of the excitation frequency is also examined considering frequencies in the range 0.2-1 MHz. The results indicate that the scattering amplitude decreases at later stages of healing compared to earlier stages of healing. Also, the acoustic pressure could provide supplementary qualitative information on the interaction of the scattered energy with bone and callus.

Precursor wave in a layered waveguide

The precursor wave (often called the first arriving signal) in a layered waveguide is investigated. It is known that the velocity of such a signal is close to the velocity of the fastest medium in the waveguide, and it may be bigger than the fastest group velocity given by the dispersion diagram of the waveguide. Usually the precursor pulse decays with the propagation distance. A model layered waveguide is studied in the paper. It is shown that the precursor is associated with the pseudo-branch structure of the dispersion diagram. The velocity of the precursor is determined by the slope of the pseudo-branch. The decay is exponential and it depends on the structure of the pseudo-branch. Three approaches to precursors are described in the paper: the Miklowitz-Randles approach based on analytical continuation of the dispersion diagram, the leaky wave approach, and the approximate technique based on the properties of the real dispersion diagram.

Computational Study of the Effect of Cortical Porosity on Ultrasound Wave Propagation in Healthy and Osteoporotic Long Bones

Computational studies on the evaluation of bone status in cases of pathologies have gained significant interest in recent years. This work presents a parametric and systematic numerical study on ultrasound propagation in cortical bone models to investigate the effect of changes in cortical porosity and the occurrence of large basic multicellular units, simply called non-refilled resorption lacunae (RL), on the velocity of the first arriving signal (FAS). Two-dimensional geometries of cortical bone are established for various microstructural models mimicking normal and pathological tissue states. Emphasis is given on the detection of RL formation which may provoke the thinning of the cortical cortex and the increase of porosity at a later stage of the disease. The central excitation frequencies 0.5 and 1 MHz are examined. The proposed configuration consists of one point source and multiple successive receivers in order to calculate the FAS velocity in small propagation paths (local velocity) and derive a variation profile along the cortical surface. It was shown that: (a) the local FAS velocity can capture porosity changes including the occurrence of RL with different number, size and depth of formation; and (b) the excitation frequency 0.5 MHz is more sensitive for the assessment of cortical microstructure.

A μCT-based investigation of the influence of tissue modulus variation, anisotropy and inhomogeneity on ultrasound propagation in trabecular bone

Ultrasound propagation is widely used in the diagnosis of osteoporosis by providing information on bone mechanical quality. When it loses calcium, the tissue properties will first decrease. However, limited research about the influence of tissue properties on ultrasound propagation have been done due to the cumbersome experiment. The goal of this study was to explore the relationships between tissue modulus (Es) and speed of sound (SOS) through numerical simulations, and to study the influence of Es on the acoustical behavior in characterizing the local structural anisotropy and inhomogeneity. In this work, three-dimensional finite element (FE) simulations were performed on a cubic high-resolution (15μm) bovine trabecular bone sample (4×4×4mm(3), BV/TV=0.18) mapped from micro-computed tomography. Ultrasound excitations of 50kHz, 500kHz and 2MHz were applied in three orthogonal axes and the first arriving signal (FAS) was collected to quantify wave velocity. In this study, a strong power law relationship between Es and SOS was measured with estimated exponential index β=2.08-3.44 for proximal-distal (PD), anterior-posterior (AP) and medial-lateral (ML), respectively (all R(2)>0.95). For various Es, a positive dispersion of sound speed with respect to sound frequency was observed and the velocity dispersion magnitude (VDM) was measured. Also, with Es=15GPa in three orientations, the SOS in PD axis is 2009±120m/s, faster than that of AP (1762±106m/s) and ML (1798±132m/s) (f=2MHz) directions. Besides, the standard deviation of SOS increases with the sound frequency and the Es in all directions except for that at 50kHz. For the mechanical properties, the apparent modulus with certain Es was highest in the longitudinal direction compared with the transverse directions. It indicates that the tissue modulus combining with anisotropy and inhomogeneity has great influence on ultrasound propagation. Simulation results agree well with theoretical and experimental results.

Ultrasound propagation in cortical bone: Axial transmission and backscattering simulations

Cortical bone is a heterogeneous, composite medium with a porosity from 5-10%. The characterization of cortical bone using ultrasonic techniques is a complicated procedure especially in numerical studies as several assumptions must be made to describe the concentration and size of pores. This study presents numerical simulations of ultrasound propagation in two-dimensional numerical models of cortical bone to investigate the effect of porosity on: a) the propagation of the first arriving signal (FAS) velocity using the axial transmission method, and b) the displacement and scattering amplitude in the backward direction. The excitation frequency 1 MHz was used and different receiving positions were examined to provide a variation profile of the examined parameters along cortical bone. Cortical porosity was simulated using ellipsoid scatterers and the concentrations of 0-10% were examined. The results indicate that the backscattering method is more appropriate for the evaluation of cortical porosity in comparison to the axial transmission method.

A novel ultrasound methodology for estimating spine mineral density

We investigated the possible clinical feasibility and accuracy of an innovative ultrasound (US) method for diagnosis of osteoporosis of the spine. A total of 342 female patients (aged 51-60 y) underwent spinal dual X-ray absorptiometry and abdominal echographic scanning of the lumbar spine. Recruited patients were subdivided into a reference database used for US spectral model construction and a study population for repeatability and accuracy evaluation. US images and radiofrequency signals were analyzed via a new fully automatic algorithm that performed a series of spectral and statistical analyses, providing a novel diagnostic parameter called the osteoporosis score (O.S.). If dual X-ray absorptiometry is assumed to be the gold standard reference, the accuracy of O.S.-based diagnoses was 91.1%, with k = 0.859 (p < 0.0001). Significant correlations were also found between O.S.-estimated bone mineral densities and corresponding dual X-ray absorptiometry values, with r(2) values up to 0.73 and a root mean square error of 6.3%-9.3%. The results obtained suggest that the proposed method has the potential for future routine application in US-based diagnosis of osteoporosis.

A hybrid FDTD-Rayleigh integral computational method for the simulation of the ultrasound measurement of proximal femur

The development of novel quantitative ultrasound (QUS) techniques to measure the hip is critically dependent on the possibility to simulate the ultrasound propagation. One specificity of hip QUS is that ultrasounds propagate through a large thickness of soft tissue, which can be modeled by a homogeneous fluid in a first approach. Finite difference time domain (FDTD) algorithms have been widely used to simulate QUS measurements but they are not adapted to simulate ultrasonic propagation over long distances in homogeneous media. In this paper, an hybrid numerical method is presented to simulate hip QUS measurements. A two-dimensional FDTD simulation in the vicinity of the bone is coupled to the semi-analytic calculation of the Rayleigh integral to compute the wave propagation between the probe and the bone. The method is used to simulate a setup dedicated to the measurement of circumferential guided waves in the cortical compartment of the femoral neck. The proposed approach is validated by comparison with a full FDTD simulation and with an experiment on a bone phantom. For a realistic QUS configuration, the computation time is estimated to be sixty times less with the hybrid method than with a full FDTD approach.

Experimental observation of cumulative second-harmonic generation of lamb waves propagating in long bones

The experimental observation of cumulative second-harmonic generation of fundamental Lamb waves in long bones is reported. Based on the modal expansion approach to waveguide excitation and the dispersion characteristics of Lamb waves in long bones, the mechanism underlying the generation and accumulation of second harmonics by propagation of the fundamental Lamb waves was investigated. An experimental setup was established to detect the second-harmonic signals of Lamb wave propagation in long bones in vitro. Through analysis of the group velocities of the received signals, the appropriate fundamental Lamb wave modes and the duration of the second-harmonic signals could be identified. The integrated amplitude of the time-domain second-harmonic signal was introduced and used to characterize the efficiency of second-harmonic generation by fundamental Lamb wave propagation. The results indicate that the second-harmonic signal generated by fundamental Lamb waves propagating in long bones can be observed clearly, and the effect was cumulative with propagation distance when the fundamental Lamb wave mode and the double-frequency Lamb wave mode had the same phase velocities. The present results may be important in the development of a new method to evaluate the status of long bones using the cumulative second harmonic of ultrasonic Lamb waves.

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.

Circumferential guided wave measurements of a cylindrical fluid-filled bone-mimicking phantom

In the context of hip fracture risk prediction, measurement of guided waves could improve the assessment of cortical femoral neck properties. The decomposition of the time reversal operator (DORT) method was previously shown to be efficient to measure circumferential guided modes in an empty cortical bone-mimicking tube of circular cross section. In this study, an adaptation of the DORT method is proposed to probe the same bone-mimicking tube but filled with a marrow-mimicking fluid. The contributions to the backscattered field of waves multiply reflected in the cavity of the tube interfere with those of circumferential guided waves. The former contributions are eliminated in the backpropagation image using ad hoc criterion determined with simulation. Eight portions of different guided modes were observed from experimental and simulated data. They were identified by comparison with theoretical predictions. This work confirms the feasibility of measuring guided waves in a fluid-filled tube of bone-mimicking material with the DORT method.

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 single-element 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.

Quantitative ultrasound of cortical bone in the femoral neck predicts femur strength: results of a pilot study

A significant risk of femoral neck (FN) fracture exists for men and women with an areal bone mineral density (aBMD) higher than the osteoporotic range, as measured with dual-energy X-ray absorptiometry (DXA). Separately measuring the cortical and trabecular FN compartments and combining the results would likely be a critical aspect of enhancing the diagnostic capabilities of a new technique. Because the cortical shell determines a large part of FN strength a novel quantitative ultrasound (QUS) technique that probes the FN cortical compartment was implemented. The sensitivity of the method to variations of FN cortical properties and FN strength was tested. Nine femurs (women, mean age 83 years) were subjected to QUS to measure the through transmission time-of-flight (TOF) at the FN and mechanical tests to assess strength. Quantitative computed tomography (QCT) scans were performed to enable analysis of the dependence of TOF on bone parameters. DXA was also performed for reference. An ultrasound wave propagating circumferentially in the cortical shell was measured in all specimens. Its TOF was not influenced by the properties of the trabecular compartment. Averaged TOF for nine FN measurement positions/orientations was significantly correlated to strength (R2  = 0.79) and FN cortical QCT variables: total BMD (R(2)  = 0.54); regional BMD in the inferoanterior (R2  = 0.90) and superoanterior (R2  = 0.57) quadrants; and moment of inertia (R2  = 0.71). The results of this study demonstrate that QUS can perform a targeted measurement of the FN cortical compartment. Because the method involves mechanical guided waves, the QUS variable is related to the geometric and material properties of the cortical shell (cortical thickness, tissue elasticity, and porosity). This work opens the way to a multimodal QUS assessment of the proximal femur, combining our approach targeting the cortical shell with the existing modality sensitive to the trabecular compartment. In vivo feasibility of our approach has to be confirmed with experimental data in patients.

Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.