Modeling ultrasound attenuation in porous structures with mono-disperse random pore distributions using the independent scattering approximation: a 2D simulation study

Abstract

Osteoporosis is increasingly prevalent, and the societal impact of age-related bone loss is becoming progressively greater. It is estimated that 4-6 million U.S. women have osteoporosis, and that 13-17 million have osteopenia (Looker et al 1997). The gold standard for the diagnosis of osteoporosis is the measurement of bone mineral density (BMD) using dual-energy x ray absorptiometry (DXA) for trabecular/cancellous bone and high resolution peripheral quantitative computed tomography (HR-pQCT) for cortical bone. However, measuring bone density alone does not reflect the changes in bone microstructure associated with osteopenia. Women with osteopenia account for the highest number of fragility fractures, although they remain untreated because of their relatively high areal BMD (Bala et al 2014). In fact, over half of the patients with insufficiency fractures exhibit normal BMD scores (Schuit et al 2004, Sornay-Rendu et al 2005. For a given solid volume fraction or density, two structures with different micro-architectures can have very different mechanical competences. The information provided by BMD is only part of the picture, because it only reflects changes in overall bone mass, and does not account for changes in the micro-architecture. However, osteoporosis and osteopenia affect the micro-structure of cortical bone, through changes in average pore diameter and pore density (Schaffler and Burr 1988, McCalden et al 1993, Yerramshetty and Akkus 2012, Chen et al 2013. The definition of osteoporosis was updated in 2001, and includes both low bone mass and micro-architectural deterioration of bone tissue (NIH Consensus Development Panel on Osteoporosis Prevention, Diagnosis, and Therapy 2001). Bio-mechanical and morphometry testing have revealed strong correlations between cortical bone material properties and intracortical porosity (Augat and Schorlemmer 2006). The mechanical competence of cortical bone strongly depends on these two parameters (Osterhoff et al 2016). The size and number of pores determine intracortical porosity, which accounts for almost 55% of yield stress and 70% of elastic modulus (Neil Dong and Edward Guo 2004). Fracture toughness also decreases significantly with increasing porosity, possibly by diminishing the net loading area (Yeni et al 1997). All of these results lead to the conclusion that combining micro-structural with bone mass assessment in cortical bone improves the screening for osteoporosis and the prediction of

Investigation of silk as a phantom material for ultrasound and photoacoustic imaging

“…A recent study by Milazzo et al demonstrated with micro-CT and SEM images that silk scaffolds have an irregular sponge shape characterized by alveolar structures and pores of various diameters while also possessing a relatively smooth surface [39] . These pores while making it an ideal tissue engineering scaffold to grow cells, also lead to multiple scattering events [40] , generating echoes similar to ultrasound signatures of tissue. For the 5 MHz transducer, the signal amplitude throughout the 5 mm depth decreased by a ratio of approximately 1.59 which corresponds to an attenuation of 4.02 dB ( Fig.…”

Frequency-dependent analysis of ultrasound apparent absorption coefficient in multiple scattering porous media: application to cortical bone

“…This enables us to study the attenuation behavior in different scattering regimes (kϕ < 0.8: low scattering regime, 0.8 < kϕ < 1: medium scattering regime, 1 < kϕ: high scattering regime). Some scattering models such as the Independent Scattering Approximation are suited for specific scattering regimes and cannot be expected to describe the attenuation in other regimes accurately (Yousefian et al 2019). For each pore diameter-density combination, 16 different simulations are executed to investigate the whole spectroscopy range (1-8 MHz frequency range with 0.5 MHz intervals).…”

“…Second model: Previous works done by the authors Yousefian et al (2019) showed that the Independent Scattering Approximation (ISA) can be used to accurately predict the attenuation in simplified structures of cortical bone for kϕ < 1. Briefly, the ISA predicts the scattering attenuation as follows:…”

“…where σ td is the total scattering cross section of one individual scatterer. The details of the ISA model and how to calculate the total scattering cross section are described in Yousefian et al (2019). In this study, we use the ISA model combined with the relationship proposed in equation ( 5) to model the total attenuation.…”

“…Such a model, which would accurately estimate the total frequency-dependent attenuation as a function of cortical porosity will potentially enable one to solve an inverse problem and get access to micro-structure of cortical bone from measuring attenuation. In another study by our group, the frequency-dependent attenuation due to scattering was modeled in media resembling cortical bone (Yousefian et al 2019), but the effect of absorption on attenuation was not taken into account.…”