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

Improving Transcranial Acoustic Targeting: The Limits of CT-Based Velocity Estimates and the Role of MR

Transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) enables the noninvasive treatment of the deep brain. This capacity relies on the ability to focus acoustic energy through the in-tact skull, a feat that requires accurate estimates of the acoustic velocity in individual patient skulls. In current practice, these estimates are generated using a pretreatment computed tomography (CT) scan and then registered to a magnetic resonance (MR) dataset on the day of the treatment. Treatment safety and efficacy can be improved by eliminating the need to register the CT data to the MR images and by improving the accuracy of acoustic velocity measurements. In this study, we examine the capacity of MR to supplement or replace CT as a means of estimating velocity in the skull. We find that MR can predict velocity with less but comparable accuracy to CT. We then use micro-CT imaging to better understand the limitations of Hounsfield unit (HU)-based estimates of velocity, demonstrating that the macrostructure of pores in the skull contributes to the acoustic velocity of the bone. We find evidence that detailed T2 measurements provide information about pore macrostructure similar to the information obtained with micro-CT, offering a potential clinical mechanism for improving patient-specific estimates of acoustic velocity in the human skull.

Estimation of Cortical Bone Microstructure From Ultrasound Backscatter

Multichannel pulse-echo ultrasound using linear arrays and single-channel data acquisition systems opens new perspectives for the evaluation of cortical bone. In combination with spectral backscatter analysis, it can provide quantitative information about cortical microstructural properties. We present a numerical study, based on the finite-difference time-domain method, to estimate the backscatter cross section of randomly distributed circular pores in a bone matrix. A model that predicts the backscatter coefficient using arbitrary pore diameter distributions was derived. In an ex vivo study on 19 human tibia bones (six males, 13 females, 83.7 ± 8.4 years), multidirectional ultrasound backscatter measurements were performed using an ultrasound scanner equipped with a 6-MHz 128-element linear array with sweep motor control. A normalized depth-dependent spectral analysis was performed to derive backscatter and attenuation coefficients. Site-matched reference values of tissue acoustic impedance Z , cortical thickness (Ct.Th), pore density (Ct.Po.Dn), porosity (Ct.Po), and characteristic parameters of the pore diameter (Ct.Po.Dm) distribution were obtained from 100-MHz scanning-acoustic microscopy images. Proximal femur areal bone mineral density (aBMD), stiffness S , and ultimate force Fu from the same donors were available from a previous study. All pore structure and material properties could be predicted using linear combinations of backscatter parameters with a median to high accuracy (0.28 ≤ adjusted R² ≤ 0.59). The combination of cortical thickness and backscatter parameter provided similar or better prediction accuracies than aBMD. For the first time, a method for the noninvasive assessment of the pore diameter distribution in cortical bone by ultrasound is proposed. The combined assessment of cortical thickness, sound velocity, and pore size distribution in a mobile, nonionizing measurement system could have a major impact on preventing osteoporotic fractures.

Numerical evaluation of the mechanical environment of a fractured long bone for osteoporotic and non-osteoporotic subjects

Competent fracture healing monitoring requires an extensive knowledge of the evolution of the mechanical environment of the healing bone during daily-life activities such as walking. Fractures are caused due to a traumatic incidence, while low trauma or fragility fractures can also occur due to osteoporosis. It is expected that the mechanical behavior of healing bones differs among osteoporotic and non-osteoporotic subjects. This work presents finite element simulations of gait analysis considering a fractured long bone at the hematoma stage. The aim is to investigate the evolution of the mechanical environment of the femur for an osteoporotic and a non-osteoporotic subject. This is the first computational study providing quantitative information for the impact of osteoporosis on the mechanical environment of the femur. It was shown, that higher deformation and equivalent stress values are calculated for osteoporotic bones during a gait cycle, while the highest values were observed in the femoral head.

Autoregressive Signal Processing Applied to High-Frequency Acoustic Microscopy of Soft Tissues

Quantitative acoustic microscopy (QAM) at frequencies exceeding 100 MHz has become an established imaging tool to depict acoustical and mechanical properties of soft biological tissues at microscopic resolutions. In this study, we investigate a novel autoregressive (AR) model to improve signal processing and parameter estimation and to test its applicability to QAM. The performance of the AR model for estimating acoustical parameters of soft tissues (i.e., acoustic impedance, speed of sound, and attenuation) was compared to the performance of the Hozumi model using simulated ultrasonic QAM signals and using experimentally measured signals from thin (i.e., 12 and ) sections of human lymph-node and pig-cornea tissue specimens. Results showed that the AR and Hozumi methods performed equally well (i.e., produced an estimation error of 0) in signals with low, linear attenuation in the tissue and high impedance contrast between the tissue and the coupling medium. However, the AR model outperformed the Hozumi model in estimation accuracy and stability (i.e., parameter error variation and number of outliers) in cases of 1) thin tissue-sample thickness and high tissue-sample speed of sound, 2) small impedance contrast between the tissue sample and the coupling medium, 3) high attenuation in the tissue sample, and 4) nonlinear attenuation in the tissue sample. Furthermore, the AR model allows estimating the exponent of nonlinear attenuation. The results of this study suggest that the AR model approach can improve current QAM by providing more reliable, quantitative, tissue-property estimates and also provides additional values of parameters related to nonlinear attenuation.

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.

Effect of porosity, tissue density, and mechanical properties on radial sound speed in human cortical bone

PURPOSE

The purpose of this study was to investigate the effect of simultaneous changes in cortical porosity, tissue mineral density, and elastic properties on radial speed of sound (SOS) in cortical bone. The authors applied quantitative pulse-echo (PE) ultrasound techniques that hold much potential especially for screening of osteoporosis at primary healthcare facilities. Currently, most PE measurements of cortical thickness, a well-known indicator of fracture risk, use a predefined estimate for SOS in bone to calculate thickness. Due to variation of cortical bone porosity, the use of a constant SOS value propagates to an unknown error in cortical thickness assessment by PE ultrasound.

METHODS

The authors conducted 2.25 and 5.00 MHz focused PE ultrasound time of flight measurements on femoral diaphyses of 18 cadavers in vitro. Cortical porosities of the samples were determined using microcomputed tomography and related to SOS in the samples. Additionally, the effect of cortical bone porosity and mechanical properties of the calcified matrix on SOS was investigated using numerical finite difference time domain simulations.

RESULTS

Both experimental measurements and simulations demonstrated significant negative correlation between radial SOS and cortical porosity (R(2) ≥ 0.493, p < 0.01 and R(2) ≥ 0.989, p < 0.01, respectively). When a constant SOS was assumed for cortical bone, the error due to variation of cortical bone porosity (4.9%-16.4%) was about 6% in the cortical thickness assessment in vitro.

CONCLUSIONS

Use of a predefined, constant value for radial SOS in cortical bone, i.e., neglecting the effect of measured variation in cortical porosity, propagated to an error of 6% in cortical thickness. This error can be critical as characteristic cortical thinning of 1.10% ± 1.06% per yr decreases bending strength of the distal radius and results in increased fragility in postmenopausal women. Provided that the cortical porosity can be estimated in vivo, the relationship between radial SOS and cortical porosity can be utilized and a porosity based radial SOS estimate could be implemented to determine cortical thickness. This would constitute a step toward individualized quantitative ultrasound diagnostics of osteoporosis.

Porosity predicted from ultrasound backscatter using multivariate analysis can improve accuracy of cortical bone thickness assessment

A rapidly growing area of interest in quantitative ultrasound assessment of bone is to determine cortical bone porosity from ultrasound backscatter. Current backscatter analyses are based on numerical simulations, while there are no published reports of successful experimental measurements. In this study, multivariate analysis is applied to ultrasound reflections and backscatter to predict cortical bone porosity. The porosity is then applied to estimate cortical bone radial speed of sound (SOS) and thickness using ultrasound backscatter signals obtained at 2.25 and 5 MHz center frequencies from cortical bone samples (n = 43) extracted from femoral diaphyses. The study shows that the partial least squares regression technique could be employed to successfully predict (R²= 0.71-0.73) cortical porosity. It is found that this multivariate approach can reduce uncertainty in pulse-echo assessment of cortical bone thickness from 0.220 to 0.045 mm when porosity based radial SOS was applied, instead of a constant value from literature. Upon further validation, accurate estimation of cortical bone porosity and thickness may be applied as a financially viable option for fracture risk assessment of individuals.

Ultrasonic bone localization algorithm based on time-series cumulative kurtosis

The design and optimization of protective equipment and devices such as exoskeletons and prosthetics have the potential to be enhanced by the ability of accurately measure the positions of the bones during movement. Existing technologies allow a quite precise measurement of motion-mainly by using coordinate video-cameras and skin-mounted markers-but fail in directly measuring the bone position. Alternative approaches, as fluoroscopy, are too invasive and not usable during extended lapses of time, either for cost or radiation exposure. An approach to solve the problem is to combine the skin-glued markers with ultrasound technology in order to obtain the bone position by measuring at the same time the marker coordinates in 3D space and the depth of the echo from the bone. Given the complex structure of the bones and the tissues, the echoes from the ultrasound transducer show a quite complex structure as well. To reach a good accuracy in determining the depth of the bones, it is of paramount importance the ability to measure the time-of-flight (TOF) of the pulse with a high level of confidence. In this paper, the performance of several methods for determining the TOF of the ultrasound pulse has been evaluated when they are applied to the problem of measuring the bone depth. Experiments have been made using both simple setups used for calibration purposes and in real human tissues to test the performance of the algorithms. The results show that the method used to process the data to evaluate the time-of-flight of the echo signal can significantly affect the value of the depth measurement, especially in the cases when the verticality of the sensor with respect to the surface causing the main echo cannot be guaranteed. Finally, after testing several methods and processing algorithms for both accuracy and repeatability, the proposed cumulative kurtosis algorithm was found to be the most appropriate in the case of measuring bone depths in vivo with ultrasound sensors at frequencies around 5MHz.

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.

Inter-individual changes in cortical bone three-dimensional microstructure and elastic coefficient have opposite effects on radial sound speed

Knowledge about simultaneous contributions of tissue microstructure and elastic properties on ultrasound speed in cortical bone is limited. In a previous study, porosities and elastic coefficients of cortical bone in human femurs were shown to change with age. In the present study, influences of inter-individual and site-dependent variation in cortical bone microstructure and elastic properties on radial speed of sound (SOS; at 4, 6, and 8 MHz) were investigated using three-dimensional (3D) finite difference time domain modeling. Models with fixed (nominal model) and sample-specific (sample-specific model) values of radial elastic coefficients were compared. Elastic coefficients and microstructure for samples (n = 24) of human femoral shafts (n = 6) were derived using scanning acoustic microscopy and micro-computed tomography images, respectively. Porosity-related SOS varied more extensively in nominal models than in sample-specific models. Linear correlation between pore separation and SOS was similar (R = 0.8, p < 0.01, for 4 MHz) for both models. The determination coefficient (R(2)= 0.75, p < 0.05) between porosity and radial SOS, especially at 4 MHz, was highest in the posterior quadrant. The determination coefficient was lower for models with sample-specific values of radial elastic coefficient implemented (R(2) < 0.33, p < 0.05), than for nominal models (0.48 < R(2)< 0.63, p < 0.05). This information could be useful in in vivo pulse-echo cortical thickness measurements applying constant SOS.

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.

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

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 C(Micro) 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 C(Meso) 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 ≤ R(2) ≤ 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.

Cortical bone histomorphometry in male femoral neck: the investigation of age-association and regional differences

Low bone volume and changes in bone quality or microarchitecture may predispose individuals to fragility fractures. As the dominant component of the human skeleton, cortical bone plays a key role in protecting bones from fracture. However, histological investigations of the underlying structural changes, which might predispose to fracture, have been largely limited to the cancellous bone. The aim of this study was to investigate the age-association and regional differences of histomorphometric properties in the femoral neck cortical bone. Undecalcified histological sections of the femoral neck (n = 20, aged 18-82 years, males) were cut (15 μm) and stained using modified Masson-Goldner stain. Complete femoral neck images were scanned, and cortical bone boundaries were defined using our previously established method. Cortical bone histomorphometry was performed with low (×50) and high magnification (×100). Most parameters related to cortical width (Mean Ct.Wi, Inferior Ct.Wi, Superior Ct.Wi) were negatively associated with age both before and after adjustment for height. The inferior cortex was the thickest (P < 0.001) and the superior cortex was the thinnest (P < 0.008) of all cortical regions. Both osteonal size and pores area were negatively associated with age. Osteonal area and number were higher in the antero-inferior area (P < 0.002) and infero-posterior area (P = 0.002) compared to the postero-superior area. The Haversian canal area was higher in the infero-posterior area compared to the postero-superior area (P = 0.002). Moreover, porosity was higher in the antero-superior area (P < 0.002), supero-anterior area (P < 0.002) and supero-posterior area (P < 0.002) compared to the infero-anterior area. Eroded endocortical perimeter (E.Pm/Ec.Pm) correlated positively with superior cortical width. This study describes the changes in cortical bone during ageing in healthy males. Further studies are needed to investigate whether these changes explain the increased susceptibility to femoral neck fractures.

Computational study of the influence of callus porosity on ultrasound propagation in healing bones

In the process of fracture healing, several phases of recovery are observed as the mechanical stability, continuity and normal load carrying capacity are gradually restored. The ultrasonic monitoring and discrimination of different healing stages is a complex process due to the significant microstructure and porous nature of osseous and callus tissues. In this study, we investigate the influence of the callus pores' size and concentration on ultrasound propagation in a long bone at a late healing stage. Different excitation frequencies are applied in the range of 300 kHz-1 MHz. A 2D geometry is developed and axial transmission calculations are performed based on a Finite Element Method. The velocity of the first arriving signal (FAS) and the propagation of guided waves are used as the estimated parameters. It was shown that the FAS velocity can reflect callus porosity changes, while the propagation of guided waves is sensitive to pores' distribution for higher frequencies.

Ultrasound to assess bone quality

Bone quality is determined by a variety of compositional, micro- and ultrastructural properties of the mineralized tissue matrix. In contrast to X-ray-based methods, the interaction of acoustic waves with bone tissue carries information about elastic and structural properties of the tissue. Quantitative ultrasound (QUS) methods represent powerful alternatives to ionizing x-ray based assessment of fracture risk. New in vivo applicable methods permit measurements of fracture-relevant properties, [eg, cortical thickness and stiffness at fragile anatomic regions (eg, the distal radius and the proximal femur)]. Experimentally, resonance ultrasound spectroscopy and acoustic microscopy can be used to assess the mesoscale stiffness tensor and elastic maps of the tissue matrix at microscale resolution, respectively. QUS methods, thus, currently represent the most promising approach for noninvasive assessment of components of fragility beyond bone mass and bone microstructure providing prospects for improved assessment of fracture risk.

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.