In this chapter, we first review the reasons why conventional ultrasonography fails to image the interior of bones. Next we show our recent work on imaging a cortical bone layer with ultrasound. Revealing the shape of the cortex of a bone, in particular its thickness, is of interest for evaluating bone strength. In addition we describe how the process of reconstructing a truthful image of the bone cortex includes the estimation of ultrasound wave-speed in cortical bone tissue. Cortical bone exhibits elastic anisotropy, which causes anisotropy of ultrasound wave-speed as well. Therefore a faithful and high-quality picture of the bone cortex is obtained if wave-speed anisotropy is taken into account during image reconstruction. Capitalizing on prior knowledge on the elastic anisotropy of cortical bone, a procedure for estimating wave-speed and its anisotropy is described. It is based on the measurement of a head-wave velocity and an autofocus approach. The latter relies on the fact that the reconstructed ultrasound image shows optimal quality if the wave-speed model is correct. In order to achieve real-time imaging of a bone cortex, image reconstruction is performed with a delay-and-sum algorithm. Finally, we report recent advances in the measurement of blood flow in cortical bone.@en

In the above article [1], we mentioned that the superposition of the different symmetric (S) modes in the frequencywavenumber (f-k) domain results in a high-intensity region where its slope corresponds to the longitudinal wave speed in the slab. However, we have recently understood that this highintensity region belongs to the propagation of a wave called lateral wave or head wave [2]-[5]. It is generated if the longitudinal sound speed of the aberrator (i.e., the PVC slab) is larger than that of water and if the incident wavefront is curved. When the incidence angle at the interface between water and PVC is near the critical angle, the refracted wave in PVC reradiates a small part of its energy into the fluid (i.e., the head wave). As discussed in [4], if the thickness of the waveguide is larger than the wavelength, the first arriving signal is the head wave. This is also the case in our study [1] where the ultrasound wavelength of a compressional wave in PVC was close to 1 mm, and a PVC slab with a thickness of 8 mm was used. In this Erratum, numerical simulations (with SimSonic solver [5]) and experimental measurements (with the same PVC slab used in [1]) are conducted to investigate the propagation of the Lamb waves and head wave in detail, for the specific configuration studied in [1]. The pitch and element width of the P4-1 probe were used to assemble the numerical signals [see Fig. 1(a)]. If all the data simulated for the P4-1 probe is used, there indeed is a region with a slope [see Fig. 1(b)], but this has a low intensity, meaning that the head wave has a relatively low amplitude compared to the specular reflections. Once the head wave is isolated, the sound speed can be estimated with a 0.3% error from the f-k domain plot [see Fig. 1(c)]. No significant difference is observed between Fig. 1(b) and (d), in which the head wave is muted. Our experimental results show that if only the head wave (the first arriving signal) is used [see Fig. 2(b)], the slope of the linear fitting in the f-k domain also yields the longitudinal sound speed of the PVC with a 0.3% error. Of note, the signal processing (i.e., linear fitting in the f-k domain) used in our study [1] still works for the head wave and is correct provided that the aberrator is parallel to the probe [6]. Also, in [1, p. 6], it is mentioned that “the curved structure of the skull might lead to other types of modes, such as the torsional modes.” Here, we acknowledge that this sentence is not correct, as torsional modes only exist in cylindrical waveguides or rectangular bars. We would like to mention that Guillaume Renaud is added as a coauthor to acknowledge his contribution to the findings reported in this Erratum.@en

Decreased thickness of the bone cortex due to bone loss in the course of ageing and osteoporosis is associated with reduced bone strength. Cortical thickness measurement from ultrasound images was recently demonstrated in young adults. This requires the identification of both the outer (periosteum) and inner (endosteum) surfaces of the bone cortex. However, with bone loss, the cortical porosity and the size of the vascular pores increase resulting in enhanced ultrasound scattering which may prevent the detection of the endosteum. The aim of this work was to study the influence of cortical bone microstructure variables, such as porosity and pore size, on the contrast of the endosteum in ultrasound images. We wanted to estimate the range of these variables for which ultrasound imaging of the endosteum is feasible. We generated synthetic data using a two-dimensional time-domain code to simulate the propagation of elastodynamic waves. A synthetic aperture imaging sequence with an array transducer operating at a center frequency of 2.5 MHz was used. The numerical simulations were conducted for 105 cortical microstructures obtained from high resolution X-ray computed tomography images of ex vivo bone samples with a porosity ranging from 2% to 24 %. Images were reconstructed using a delay-and-sum (DAS) algorithm with optimized f-number, correction of refraction at the periosteum, and sample-specific wave-speed. We observed a range variation of 18 dB of endosteum contrast in our data set depending on the bone microstructure. We found that as porosity increases, speckle intensity inside the bone cortex increases whereas the intensity of the signal from the endosteum decreases. Also, a microstructure with large pores (diameter >250 μm) was associated with poor endosteum visibility, compared with a microstructure with equal porosity but a more narrow distribution of pore sizes. These findings suggest that ultrasound imaging of the bone cortex with a probe operating at a central frequency of 2.5 MHz using refraction-corrected DAS is capable of detecting the endosteum of a cortex with moderate porosity (less than about 10%) if the largest pores remain smaller than about 200 μm.@en

The authors regret that there was a mistake in reporting the mol% of the microbubble coating composition used. For all experiments, the unit in mg/mL was used and the conversion mistake occurred only when converting to mol% to define the ratio between the coating formulation components. The correct molecular weight of PEG-40 stearate is 2046.54 g/mol (Shen et al. 2008; Kilic and Bolukcu 2018), not 328.53 g/mol. On page 1433, the sentence should read “The lipid coating was composed of 84.8 mol% DSPC (P6517, Sigma-Aldrich, Zwijndrecht, Netherlands) or DPPC (850355, Avanti Polar Lipids, Alabaster, AL, USA); 8.2 mol% polyoxyethylene-40-stearate (PEG40 stearate, P3440, Sigma-Aldrich); 5.9 mol% 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[carboxy(polyethylene glycol)2000 (DSPE-PEG2000, 880125, Avanti Polar Lipids); and 1.1 mol% 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[biotinyl(polyethylene glycol)-2000] (DSPE-PEG2000-biotin) (880129, Avanti Polar Lipids).” This correction does not change the conclusions published in this work. The authors apologize for any inconvenience caused.@en

The authors regret that there was a mistake in reporting the mol% of the microbubble coating composition used. For all experiments, the unit in mg/mL was used and the conversion mistake occurred only when converting to mol% to define the ratio between the coating formulation components. The correct molecular weight of PEG-40 stearate is 2046.54 g/mol (Shen et al. 2008; Kilic and Bolukcu 2018), not 328.53 g/mol. On page 1433, the sentence should read “The lipid coating was composed of 84.8 mol% DSPC (P6517, Sigma-Aldrich, Zwijndrecht, Netherlands) or DPPC (850355, Avanti Polar Lipids, Alabaster, AL, USA); 8.2 mol% polyoxyethylene-40-stearate (PEG40 stearate, P3440, Sigma-Aldrich); 5.9 mol% 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[carboxy(polyethylene glycol)2000 (DSPE-PEG2000, 880125, Avanti Polar Lipids); and 1.1 mol% 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[biotinyl(polyethylene glycol)-2000] (DSPE-PEG2000-biotin) (880129, Avanti Polar Lipids).” This correction does not change the conclusions published in this work. The authors apologize for any inconvenience caused.@en

The authors regret that there was a mistake in reporting the mol% of the microbubble coating composition used. For all experiments, the unit in mg/mL was used and the conversion mistake occurred only when converting to mol% to define the ratio between the coating formulation components. The correct molecular weight of PEG-40 stearate is 2046.54 g/mol (Shen et al. 2008; Kilic and Bolukcu 2018), not 328.53 g/mol. On page 1433, the sentence should read “The lipid coating was composed of 84.8 mol% DSPC (P6517, Sigma-Aldrich, Zwijndrecht, Netherlands) or DPPC (850355, Avanti Polar Lipids, Alabaster, AL, USA); 8.2 mol% polyoxyethylene-40-stearate (PEG40 stearate, P3440, Sigma-Aldrich); 5.9 mol% 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[carboxy(polyethylene glycol)2000 (DSPE-PEG2000, 880125, Avanti Polar Lipids); and 1.1 mol% 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[biotinyl(polyethylene glycol)-2000] (DSPE-PEG2000-biotin) (880129, Avanti Polar Lipids).” This correction does not change the conclusions published in this work. The authors apologize for any inconvenience caused.@en

Transcranial ultrasound imaging (TUI) is a diagnostic modality with numerous applications, but unfortunately, it is hindered by phase aberration caused by the skull. In this article, we propose to reconstruct a transcranial B-mode image with a refraction-corrected synthetic aperture imaging (SAI) scheme. First, the compressional sound velocity of the aberrator (i.e., the skull) is estimated using the bidirectional headwave technique. The medium is described with four layers (i.e., lens, water, skull, and water), and a fast marching method calculates the travel times between individual array elements and image pixels. Finally, a delay-and-sum algorithm is used for image reconstruction with coherent compounding. The point spread function (PSF) in a wire phantom image and reconstructed with the conventional technique (using a constant sound speed throughout the medium), and the proposed method was quantified with numerical synthetic data and experiments with a bone-mimicking plate and a human skull, compared with the PSF achieved in a ground truth image of the medium without the aberrator (i.e., the bone plate or skull). A phased-array transducer (P4-1, ATL/Philips, 2.5 MHz, 96 elements, pitch $=$ 0.295 mm) was used for the experiments. The results with the synthetic signals, the bone-mimicking plate, and the skull indicated that the proposed method reconstructs the scatterers with an average lateral/axial localization error of 0.06/0.14 mm, 0.11/0.13 mm, and 1.0/0.32 mm, respectively. With the human skull, an average contrast ratio (CR) and full-width-half-maximum (FWHM) of 37.1 dB and 1.75 mm were obtained with the proposed approach, respectively. This corresponds to an improvement of CR and FWHM by 7.1 dB and 36% compared with the conventional method, respectively. These numbers were 12.7 dB and 41% with the bone-mimicking plate.@en

Intraosseous blood circulation is thought to have a critical role in bone growth and remodeling, fracture healing, and bone disorders. However, it is rarely considered in clinical practice because of the absence of a suitable noninvasive in vivo measurement technique. In this work, we assessed blood perfusion in tibial cortical bone simultaneously with blood flow in the superficial femoral artery with ultrasound imaging in five healthy volunteers. After suppression of stationary signal with singular-value-decomposition, pulsatile blood flow in cortical bone tissue is revealed, following the heart rate measured in the femoral artery. Using a method combining transverse oscillations and phase-based motion estimation, 2D vector flow was obtained in the cortex of the tibia. After spatial averaging over the cortex, the peak blood velocity along the long axis of the tibia was measured at four times larger than the peak blood velocity across the bone cortex. This suggests that blood flow in central (Haversian) canals is larger than in perforating (Volkmann's) canals, as expected from the intracortical vascular organization in humans. The peak blood velocity indicates a flow from the endosteum to the periosteum and from the heart to the foot for all subjects. Because aging and the development of bone disorders are thought to modify the direction and velocity of intracortical blood flow, their quantification is crucial. This work reports for the first time an in vivo quantification of the direction and velocity of blood flow in human cortical bone.@en

Transcranial ultrasound imaging is a suitable technology for diagnosis of strokes as it is safe, portable, relatively inexpensive and available in emergency medicine services, however it currently offers poor image quality due to the phase aberration caused by the human skull. In this work, we evaluate an approach for two-dimensional transcranial ultrasound imaging through the temporal window of a sagittally-cut human skull using the commercial P4-1 phased-array probe, where the position and true geometry of the bone layer is estimated for accurate phase aberration correction. The medium is described with four layers (probe lens, soft tissue, skull, soft tissue). A synthetic aperture imaging scheme is used as the transmission of spherical wave-fronts facilitates the modeling of refraction. First, the bidirectional headwave method estimates the compressional wave-speed in the temporal bone. Next, a fast marching method calculates the travel times between individual array elements and image pixels to be used with delay-and-sum reconstruction algorithm. Sound speed maps are generated with adaptive beamforming including the successive segmentation of the near and far surfaces of the cortical bone layer. The proposed method reconstructs the scatterers with an average lateral and axial localization error of about 1.25 mm and 0.37 mm, compared to the ground truth, respectively. In average, it improves the contrast ratio and lateral resolution by 7 dB and 36%, compared to the conventional method, respectively.@en

While transcranial ultrasound imaging is a promising diagnostic modality, it is still hindered due to phase aberration and multiple scattering caused by the skull. In this paper, we compare near-field phase-screen modeling (PS) to a geometry-based phase aberration correction technique (GB) when an ultrafast imaging sequence (five plane waves tilted from −15 to +15 degrees in the cutaneous tissue layer) is used for data acquisition. With simulation data, the aberration profile (AP) of two aberrator models (flat and realistic temporal bone) was estimated in five isoplanatic patches, while the wave-speed of the brain tissue surrounding the point targets was either modeled homogeneously (ideal) or slightly heterogeneously to generate speckle (for mimicking a more realistic brain tissue). For the experiment, a phased array P4-1 transducer was used to image a wire phantom; a 4.2-mm-thick bone-mimicking plate was placed in front of the probe. The AP of the plate was estimated in three isoplanatic patches. The numerical results indicate that, while all the scatterers are detectable in the image reconstructed by the GB method, many scatterers are not detected with the PS method when the dataset used for AP estimation is generated with a realistic bone model and heterogeneous brain tissue. The experimental results show that the GB method increases the signal-to-clutter ratio (SCR) by 7.5 dB and 6.5 dB compared to the PS and conventional reconstruction methods, respectively. The GB method reduces the axial/lateral localization error by 1.97/0.66 mm and 2.08/0.7 mm compared to the PS method and conventional reconstruction, respectively. The lateral spatial resolution (full-width-half-maximum) is also improved by 0.1 mm and 1.06 mm compared to the PS method and conventional reconstruction, respectively. Our comparison study suggests that GB aberration correction outperforms the PS method when an ultrafast multi-angle plane wave sequence is used for transcranial imaging with a single transducer. @en

We present a technique called photoacoustic vector-flow (PAVF) to quantify the speed and direction of flowing optical absorbers at each pixel from acoustic-resolution PA images. By varying the receiving angle at each pixel in post-processing, we obtain multiple estimates of the phase difference between consecutive frames. These are used to solve the overdetermined photoacoustic Doppler equation with a least-squares approach to estimate a velocity vector at each pixel. This technique is tested in bench-top experiments and compared to simultaneous pulse-echo ultrasound vector-flow (USVF) on whole rat blood at speeds on the order of 1 mm/s. Unlike USVF, PAVF can detect flow without stationary clutter filtering in this experiment, although the velocity estimates are highly underestimated. When applying spatio-temporal singular value decomposition clutter filtering, the flow speed can be accurately estimated with an error of 16.8% for USVF and −8.9% for PAVF for an average flow speed of 2.5 mm/s.@en

Ultrasound (US) contrast agents consist of microbubbles ranging from 1 to 10 μm in size. The acoustical response of individual microbubbles can be studied with high-frame-rate optics or an "acoustical camera"(AC). The AC measures the relative microbubble oscillation while the optical camera measures the absolute oscillation. In this article, the capabilities of the AC are extended to measure the absolute oscillations. In the AC setup, microbubbles are insonified with a high- (25 MHz) and low-frequency US wave (1-2.5 MHz). Other than the amplitude modulation (AM) from the relative size change of the microbubble (employed in Renaud, Bosch, van der Steen, and de Jong (2012a). "An 'acoustical camera' for in vitro characterization of contrast agent microbubble vibrations,"Appl. Phys. Lett. 100(10), 101911, the high-frequency response from individual vibrating microbubbles contains a phase modulation (PM) from the microbubble wall displacement, which is the extension described here. The ratio of PM and AM is used to determine the absolute radius, R0. To test this sizing, the size distributions of two monodisperse microbubble populations (R 0 = 2.1 and 3.5 μm) acquired with the AC were matched to the distribution acquired with a Coulter counter. As a result of measuring the absolute size of the microbubbles, this "extended AC"can capture the full radial dynamics of single freely floating microbubbles with a throughput of hundreds of microbubbles per hour. @en

By changing the ultrasonic receiving angle in post-processing, we can obtain flow vectors from a photoacoustic experiment on a blood vessel phantom by solving the photoacoustic Doppler equation using a least-squares optimisation approach.@en