Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials

Drug-Loaded Microbubbles Combined with Ultrasound for Thrombolysis and Malignant Tumor Therapy

Cardiac-cerebral thrombosis and malignant tumor endanger the safety of human life seriously. Traditional chemotherapy drugs have side effects which restrict their applications. Drug-loaded microbubbles can be destroyed by ultrasound irradiation at the focus position and be used for thrombolysis and tumor therapy. Compared with traditional drug treatment, the drug-loaded microbubbles can be excited by ultrasound and release drugs to lesion sites, increasing the local drug concentration and the exposure dose to nonfocal regions, thus reducing the cytotoxicity and side effects of drugs. This article reviews the applications of drug-loaded microbubbles combined with ultrasound for thrombolysis and tumor therapy. We focus on highlighting the advantages of using this new technique for disease treatment and concluding with recommendations for future efforts on the applications of this technology.

Model and experimental analysis of oblique incident ultrasound in a tissue layer using doublet mechanics theory

The fundamental framework of doublet mechanics (DM) is used to analyze high-frequency ultrasound wave propagation in materials with discrete microstructure. Ultrasonic reflection coefficients were measured from a thin layer of tissue embedded between two glass substrates at oblique incidence. Theoretical calculations for the reflection coefficients of a multi-layered system at oblique angles are performed using both DM theory and the classical continuum mechanics theory (CCM). For example, at the frequency of 10 MHz at incident angle 8° in sample with 30 μm thickness, the discrepancy in the magnitude of the reflection coefficient between experimental results and theoretical prediction is 15.8% for DM but 79.0% for CCM; similar results at other frequencies and incident angle in the samples with 30 and 60 μm thickness have also been obtained, which demonstrates that the DM theory can better describe the wave propagation in tissue. The influence of the incident angles and tissue thickness are also discussed in this paper.

Fractal ladder models and power law wave equations

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers-Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters.

Theoretical study in applications of doublet mechanics to detect tissue pathological changes in elastic properties using high frequency ultrasound

The mathematical framework of a new elastic theory-doublet mechanics (DM)-was reviewed. The fundamental difference between DM and classical continuum mechanics (CCM) is that the former has taken the discrete nature of tissue on the cellular level into account and the latter assumes tissue is uniform and continuous. Theoretical calculations based on DM were performed for reflection coefficients of a substrate-tissue layer-substrate assembly. Results of computer simulations have shown that ultrasound reflection coefficients in the range of 15-30 MHz are sensitive to changes in cell size and elastic moduli of tissue according to DM but not to CCM. Potential experimental applications of this technique to tissue characterization are discussed.