Original Contribution
Influence of Guided Waves in Tibia on Non-linear Scattering of Contrast Agents

https://doi.org/10.1016/j.ultrasmedbio.2015.10.006Get rights and content

Abstract

The aim of this study was to elucidate the linear and non-linear responses of ultrasound contrast agent (UCA) to frequency-dispersive guided waves from the tibia cortex, particularly two individual modes, S0 (1.23 MHz) and A1 (2.06 MHz). The UCA responses to guided waves were illustrated through the Marmottant model derived from measured guided waves, and then verified by continuous infusion experiments in a vessel–tibia flow phantom. These UCA responses were further evaluated by the enhanced ratio of peak values and the resolutions of UCA backscattered echoes. Because of the individual modes S0 and A1 in the tibia, the peak values of the UCA backscattered echoes were enhanced by 83.57 ± 7.35% (p < 0.05) and 80.77 ± 6.60% (p < 0.01) in the UCA subharmonic frequency and subharmonic imaging, respectively. However, corresponding resolutions were 0.78 ± 0.07 (p < 0.05) and 0.72 ± 0.12 (p < 0.01) times those without guided wave disturbances, respectively. Even though the resolution was partly degenerated, the subharmonic detection sensitivity of UCA was improved by the guided waves. Thus, UCA responses to the double-frequency guided waves should be further explored to benefit the detection of capillary perfusion in tissue layers near the bone cortex, particularly for perfusion imaging in the free flaps and skeletal muscles.

Introduction

Ultrasound contrast agents (UCAs) have been used extensively in contrast-enhanced ultrasonography (CEUS) near the bone cortex, particularly for monitoring free flaps (Chang et al., 2012, Kornmann et al., 2010, Krix et al., 2005, Winter et al., 2001), because UCAs present strong non-linear acoustic responses under insonation (de Jong et al., 2000, Goldberg et al., 2001). On the basis of the non-linear acoustic responses of UCAs, CEUS with second harmonic imaging and pulse inversion harmonic imaging, even subharmonic imaging techniques, has been used to detect dynamic microvascular perfusion, analyze the patency of microvascular anastomoses, and evaluate the microcirculation of flap tissues near the bone cortex (Forsberg et al., 2006, Geis et al., 2012, Kiessling et al., 2011, Lamby et al., 2009, Prantl et al., 2007). The strong backscattered echoes from UCAs can contribute to distinguishing the perfused regions from the biceps, forearm flexor muscles, and tibialis anterior (Krix et al. 2005). The replenishment kinetics of microcirculation near the humerus, ulna, radius, and tibia cortex have also been analyzed using CEUS (Duerschmied et al., 2006, Lamby et al., 2009). To clearly detect capillary perfusion in tissue layers near the bone cortex as mentioned above, CEUS should be applied with high resolution and better contrast-to-tissue ratios (CTRs) (Lamby et al., 2009, Prantl et al., 2007).

Contrast-enhanced ultrasound images near the bone cortex may, however, be affected by guided waves generated from the bone cortex, because the signal-to-noise ratio of acoustic signals is disturbed by guided waves that propagate in the surrounding soft tissue (Moilanen et al., 2006, Ta et al., 2009). These unique guided waves are generated from the bone cortex and leak to surrounding tissues when transmission waves hit the bone (Määttä et al., 2009, Moilanen, 2008, Nicholson et al., 2002, Lee and Kuo, 2006, Protopappas et al., 2006, Ta et al., 2009). They are multimodal and frequency dispersive because of their non-linear propagation (Moilanen, 2008, Nicholson et al., 2002, Protopappas et al., 2006). These guided waves have also been used to detect and trap microdroplets, gas bubbles, and submicron particles in acoustic manipulations (Schmitt et al., 2010, Lindner et al., 2008, Wan et al., 2012). However, such detection is limited to the linear characteristic of guided waves (Zhang et al. 2014), and information on UCA responses to frequency-dispersive guided waves is lacking.

For UCAs in microvessels near the bone cortex, the guided waves can be recognized as “additional transmission waves” from the bone cortex compared with the transmission waves from the imaging scanner. However, to the best of our knowledge, no study has attempted to verify and clarify the additional effects of frequency-dispersive guided waves on the non-linear behaviors of UCAs and on CEUS images. UCAs undoubtedly interact with guided waves when flowing through microvessels near the bone cortex after intravenous injection in CEUS (Kornmann et al., 2010, Winter et al., 2001). Moreover, the non-linear behavior of UCAs is sensitive to the excitation frequency (de Jong et al., 2009, Morgan et al., 2000, Zheng et al., 2005). This non-linear behavior has been reinforced by a multifrequency wave and a chirp excitation wave; the CTRs of CEUS images have also been improved (Novell et al., 2009, Zheng et al., 2005). Therefore, the unknown non-linear behavior of UCAs elicited by guided waves should be investigated, as it may help in the detection of capillary perfusion in tissue layers near the bone cortex (Lamby et al., 2009, Prantl et al., 2007).

The guided waves generated from the bone cortex have also attracted considerable interest in the quantitative ultrasonic assessment of bone status in the past few years (Barkmann et al., 2008, Moilanen, 2008, Nicholson et al., 2002, Protopappas et al., 2006, Ta et al., 2009). These are known as Lamb waves in a thin free plate model (Lee and Kuo, 2006, Moilanen et al., 2006, Viktorov, 1967). The multifrequency and dispersion of guided waves in bone have been widely studied on the basis of the Rayleigh–Lamb frequency equation (Ta et al., 2009, Viktorov, 1967), because the dispersion of guided waves is a source of diagnostic information on bone (Xu et al. 2012). The second harmonic of guided waves has been observed in experiments and used to evaluate plasticity (Pruell et al., 2007, Zhang et al., 2014). Additionally, many separate detection and experimental methods for individual mode guided waves have also been developed on the basis of dispersion (Alleyne and Cawley, 1991, Balvantín et al., 2012, Lee and Yoon, 2004, Lefebvre et al., 2002, Ta et al., 2006, Xu et al., 2012). The waveforms and velocities of individual mode guided waves have been detected through a plate model mimicking bone (Foiret et al., 2014, Lee and Yoon, 2004, Lefebvre et al., 2002, Moilanen et al., 2007). These individual mode guided waves from the bone cortex and plate surface have been extracted and identified using a smoothed pseudo-Wigner–Ville (SPWV) energy distribution superimposed with theoretical dispersion curves (Balvantín et al., 2012, Protopappas et al., 2006, Xu et al., 2012).

In this study, we used the guided waves from the tibia cortex as an example to elucidate UCA responses to guided waves from bone cortex. Acoustic responses of UCAs include vibration and scattering, which have been comprehensively studied with the oscillating theoretical model, as well as in acoustical and optical experiments (de Jong et al., 2009, Morgan et al., 2000). However, acoustical measurements are more sensitive than optical observations in terms of detecting UCA non-linear behavior (Sijl et al. 2008). Therefore, the mechanism underlying the UCA response to guided waves was illustrated using the Marmottant model derived from measured guided waves (Marmottant et al. 2005), and was then verified in continuous infusion experiments in a vessel–tibia flow phantom. Moreover, the changes in backscattered echo intensities and resolutions of the perfused region attributed to guided waves were also illustrated in this study.

Section snippets

Strategies

As illustrated in Figure 1a, an encapsulated microbubble is in a coupled acoustic field. This microbubble near the tibia cortex is under insonation from both the transmission waves (Pressure, Pe) and the guided waves from the tibia cortex (Pressure, PLi). When the guided waves drove the Marmottant model, we obtained the simulated instantaneous radius and backscattered pressure curves of UCAs with different initial radii. Multimodal guided waves without disturbance by transmission waves are

Reconstructed guided waves

In Figure 2 (a, b) are the pressure waveforms of pure guided waves in the tibia and plate. Corresponding SPWV energy distributions with theoretical dispersion curves are provided in Figure 2 (c, d). Two types of guided waves, defined as symmetric (S) and anti-symmetric (A), modes were then identified. Thus, individual modes S0 and A1 were extracted from the pure guided waves in the tibia. Individual modes A0, S0, A1, and S2 were identified from the guided waves in the plate. Table 3 outlines

Comparison with guided waves from plate

As outlined in Table 3, the attenuation coefficients of guided waves from the tibia were greater than those from the plate because the non-linear elasticity of guided waves from the tibia was smaller, as confirmed by Minonzio et al. (2011) and Zhang et al. (2014). Thus, the non-linear propagation of guided waves in the tibia was weaker than that of guided waves in the plate. In this study, compared with the PNP of guided waves from the plate, the PNP of guided waves from the tibia decreased by

Conclusions

This study elucidated the non-linear responses of UCAs to frequency-dispersive guided waves from the tibia cortex, particularly individual modes S0 and A1. Such responses were illustrated through the Marmottant model, then verified in continuous infusion experiments. These responses were further quantified by the enhanced ratio of peak values and the resolutions of UCA backscattered echoes. For non-linear scattering of UCAs, the peak values of the UCA backscattered echoes were enhanced by the

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 81127901 and 81471671) from Ministry of Science and Technology.

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