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We present a novel formulation of the Rayleigh–Plesset equation to describe stable gas bubble dynamics in viscoelastic media, using bubble volume variation, rather than radius, as the primary variable of the resulting nonlinear ordinary differential equation. This formulation incorporates the linear Kelvin–Voigt model as the constitutive relation for the surrounding fluid, capturing both viscous and elastic contributions, to track the oscillations of a gas bubble subjected to an ultrasonic field over time. The proposed model is solved numerically, subjected to a convergence analysis, and validated by comparisons with theoretical and experimental results from the literature. We systematically investigate the nonlinear oscillations of a single spherical gas bubble in various viscoelastic environments, each modeled with varying levels of rheological complexity. The influence of medium properties, specifically shear elasticity and viscosity, is examined in detail across both linear and nonlinear regimes. This work improves our understanding of stable cavitation dynamics by emphasizing key differences from Newtonian fluid behavior, resonance frequency, phase shifts, and oscillation damping. Elasticity has a pronounced effect in low-viscosity media, whereas viscosity emerges as the dominant factor modulating the amplitude of oscillations in both the linear and nonlinear regimes. The model equation developed here provides a robust tool for analyzing how viscoelastic properties affect bubble dynamics, contributing to improved the prediction and control of stable cavitation phenomena in complex media.

Purpose:To assess volume variations in target site due to changes in bladder filling and rectal content including air bubbles during simultaneous-integrated boost intensity-modulated radiotherapy (SIB-IMRT) of patients suffering from squamous cell carcinoma of uterine cervix.Materials and methods:A total of ten patients of squamous cell carcinoma of uterine cervix were enrolled in this analysis. All patients were planned to undergo SIB-IMRT using 10 MV beam. Planning target volume of the tumour (PTVtumour) and PTVnodal were prescribed with 5,040 and 4,500 cGy doses, respectively. During planning, PTVtumour V95%, PTVnodal V95% and organs at risk (OARs) (bladder, rectum, femoral heads and small bowel) volumes were measured from initial CT planning scans taken with full bladder. CT scans were acquired once in a week over a treatment period of 5·5 weeks. Intra-treatment scans with full bladder were then fused with the planning scans to determine variations in the target volume and the OAR volume. Changes in radiation dose to the PTVtumour and the PTVnodal were also assessed by comparing intra-treatment scans with the planning (first) scans.Results:All patients showed intra-treatment bladder volume larger than the planning bladder volume. Difference between planning bladder and intra-treatment bladder volumes ranged from 4·5 to 49%. Rectal volume varied from 17 to 60 cc. A wide variation between planning and intra-treatment air volumes was found in most of the patients. When comparing initial and inter-fraction air volumes, the maximum difference was 366·67%. Due to bladder and rectal volume variations, PTVtumour V95% and PTVnodal V95% doses did not remain constant throughout the treatment. The maximum discrepancy between intra-treatment PTVtumour dose and planning PTVtumour dose was 12·15%. The maximum difference between planning and inter-fraction PTV V95% was 48·28%. PTVnodal dose observed from scan taken in last week of treatment was 12·87% less than planning PTVnodal dose analysed from planning CT scan. Maximum difference in planning and inter-fraction PTVnodal V95% was 57·78%.Conclusion:Inconsistent bladder and rectal volumes had a significant impact on target volume and dosage during an entire course of SIB-IMRT. For radiotherapy of gynaecological malignancies, data on variations in PTV should be acquired on daily basis to target radiation dose to the tumour site with accuracy.

When freshly cut segments of naturally decorticated steles of horizontal roots of the Australian grass tree (Xanthorrhea preissii) are subjected to gentle suction, bubbles of gas sometimes appear, as well as liquid, in capillaries attached to the aspirated ends of the steles. We tested the hypothesis that this gas comes from vessels embolized in the intact xylem stream, and that the gas volume extruded is therefore an effective measure of the extent of this embolism. To do this, twin samples were taken from individual roots of X. preissii in the field, one was fast-frozen intact for subsequent estimation of vessel embolisms in the cryo-scanning electron microscope (CSEM), the other 15-cm segment rapidly assessed for volume of gas aspirated into a standard micropipette tube. The two measures mutually confirmed one another by showing a strong positive correlation between numbers of embolized vessels and extracted gas volume. Similar gas volumes were obtained from replicate root segments excised directly from a root when the ends of the segment were frozen before excision, and aspiration conducted after subsequent thawing of the ends under water. The pattern of changes in embolisms during unstressed conditions in early summer, shown by both CSEM and aspiration, indicated almost no embolisms before dawn, followed by a rapid rise to a peak in mid morning, than a progressive loss of embolisms in late afternoon. It was also shown that the amount of embolism did not change with time after excision of the roots up to at least 30 min. A comparison of changes in leaf transpiration with gas volumes in steles during a 24-h cycle at peak transpiration stress in mid summer showed rapid rates of transpiration in early morning and late afternoon, with an intervening period of low water loss during the rest of the day. Numbers of embolisms rose to an early morning peak, followed by apparent repair of these before noon. There was a second spate of embolisms in late afternoon, followed by complete refilling of all xylem with liquid by an hour or so after dusk. All vessels then remained fully recharged until the following dawn. We believe that aspiration is a direct and reliable technique, which offers a simple, inexpensive means of assessing the relative extent of embolism of vessels in xylem, and a means to test earlier findings by the other direct method of the CSEM. In a broad context, the technique should provide new opportunities for evaluating water relations of the xylem of whole plants.