ArticleUltrasonics sonochemistry2022
Weakly nonlinear propagation of focused ultrasound in bubbly liquids with a thermal effect: Derivation of two cases of Khokolov-Zabolotskaya-Kuznetsoz equations.
Article in Ultrasonics sonochemistry, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
6 citing papers in PubMed.
- Simulation Study on the Effect of HIFU Irradiation Frequency and Duty Cycle Combination Parameter Optimization on Thermal Lesion of Biological Tissue.Journal of biomedical physics & engineering · 2025Article
- Study on the Effect of Lesion Volume and Focal Temperature Caused by HIFU Combined with Different Concentrations and Volumes of Ethanol on Porcine Liver.Journal of biomedical physics & engineering · 2025Article
- Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles.Ultrasonics sonochemistry · 2023Article
- Probing the pressure dependence of sound speed and attenuation in bubbly media: Experimental observations, a theoretical model and numerical calculations.Ultrasonics sonochemistry · 2023Article
- Numerical investigation of the translational motion of bubbles: The comparison of capabilities of the time-resolved and the time-averaged methods.Ultrasonics sonochemistry · 2023Article
- Production and dispersion of free radicals from transient cavitation Bubbles: An integrated numerical scheme and applications.Ultrasonics sonochemistry · 2022Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
A physico-mathematical model composed of a single equation that consistently describes nonlinear focused ultrasound, bubble oscillations, and temperature fluctuations is theoretically proposed for microbubble-enhanced medical applications. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation that has been widely used as a simplified model for nonlinear propagation of focused ultrasound in pure liquid is extended to that in liquid containing many spherical microbubbles, by applying the method of multiple scales to the volumetric averaged basic equations for bubbly liquids. As a result, for two-dimensional and three-dimensional cases, KZK equations composed of the linear combination of nonlinear, dissipation, dispersion, and focusing terms are derived. Especially, the dissipation term depends on three factors, i.e., interfacial liquid viscosity, liquid compressibility, and thermal conductivity of gas inside bubbles; the thermal conduction is evaluated by using four types of temperature gradient models. Finally, we numerically solve the derived KZK equation and show a moderate temperature rise appropriate to medical applications.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.