A Few New (?) Facts About Infinite Elements

Demkowicz, Leszek; Shen, Jie

doi:10.21236/ada437980

“…The near-field scattering was typically modeled using finite elements while other techniques were used to find the far-field scattering. Most of these studies concentrated on scattering from rigid objects (Hunt et al, 1975;Demkowicz et al, 2006).…”

Section: Discussionmentioning

confidence: 99%

Modelling high frequency ultrasound scattering from cells and ultrasound contrast agents

Falou¹

2021

Preprint

0

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High frequency ultrasound has been shown to detect structural and physical changes in cell ensembles during apoptosis and hence has the potential of monitoring cancer treatment. Ultrasound contrast agents have also been shown to enhance contrast between blood and the surrounding tissue and hence may be used to distinguish between treated and untreated tumours. Theoretical models of high frequency ultrasound scattering from individual cells and ultrasound contrast agents (UCAs) are needed in order to develop methods for using high frequency ultrasound to classify tumours, quantify their responses to treatment, and eventually provide a better cancer detection and treatment monitoring techniques. This work introduces a new technique for measuring the ultrasound backscatter from individual micron-sized objects by combining a microinjection system with a co-registered optical microscope and an ultrasound imaging device. The system was calibrated by measuring the backscatter response from polystyrene microspheres and comparing it to theoretical predictions of an elastic sphere. The backscatter responses from single sea urchin oocytes and acute myloid leukemia cells were also investigated. It was found that such responses are best modelled using the fluid sphere model. A finite element model was also introduced to study scattering from microspheres and UCAs. The Helmholtz equation was used to describe the propagation of sound waves in the fluid domains whereas the constitutive equation was used to describe the stress-strain relationship in the solid domains. Studies on polystyrene microspheres and UCAs revealed the existence of a systematic relationship between the resonance frequencies and the microsphere surface modes. No such a relationship was found for the UCAs of interest. Instead, these agents exhibited a collection of complex oscillations which appear to be a combination of various surface modes. Increasing the UCA's shell thickness and its shear modulus produced a shift in the resonance frequencies to higher values. A decrease in UCA diameter produced similar effects. The importance of these findings towards the understanding of the UCA behaviour at high frequencies and the generation of harmonics are discussed. Future work includes the measurement of the backscatter response from individual UCAs and cells at various apoptotic stages.

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“…The near-field scattering was typically modeled using finite elements while other techniques were used to find the far-field scattering. Most of these studies concentrated on scattering from rigid objects (Hunt et al, 1975;Demkowicz et al, 2006).…”

Section: Discussionmentioning

confidence: 99%

Modelling high frequency ultrasound scattering from cells and ultrasound contrast agents

Falou¹

2021

Preprint

0

View full text Add to dashboard Cite

High frequency ultrasound has been shown to detect structural and physical changes in cell ensembles during apoptosis and hence has the potential of monitoring cancer treatment. Ultrasound contrast agents have also been shown to enhance contrast between blood and the surrounding tissue and hence may be used to distinguish between treated and untreated tumours. Theoretical models of high frequency ultrasound scattering from individual cells and ultrasound contrast agents (UCAs) are needed in order to develop methods for using high frequency ultrasound to classify tumours, quantify their responses to treatment, and eventually provide a better cancer detection and treatment monitoring techniques. This work introduces a new technique for measuring the ultrasound backscatter from individual micron-sized objects by combining a microinjection system with a co-registered optical microscope and an ultrasound imaging device. The system was calibrated by measuring the backscatter response from polystyrene microspheres and comparing it to theoretical predictions of an elastic sphere. The backscatter responses from single sea urchin oocytes and acute myloid leukemia cells were also investigated. It was found that such responses are best modelled using the fluid sphere model. A finite element model was also introduced to study scattering from microspheres and UCAs. The Helmholtz equation was used to describe the propagation of sound waves in the fluid domains whereas the constitutive equation was used to describe the stress-strain relationship in the solid domains. Studies on polystyrene microspheres and UCAs revealed the existence of a systematic relationship between the resonance frequencies and the microsphere surface modes. No such a relationship was found for the UCAs of interest. Instead, these agents exhibited a collection of complex oscillations which appear to be a combination of various surface modes. Increasing the UCA's shell thickness and its shear modulus produced a shift in the resonance frequencies to higher values. A decrease in UCA diameter produced similar effects. The importance of these findings towards the understanding of the UCA behaviour at high frequencies and the generation of harmonics are discussed. Future work includes the measurement of the backscatter response from individual UCAs and cells at various apoptotic stages.

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“…By specifying an appropriate absorbing boundary condition (ABC) which mimics the wave absorption properties of the unbounded exterior, all computations can be performed on the bounded interior and the truncated exterior. The most popular ABCs are induced by infinite elements [26,27], exact non-reflecting boundary conditions [28], rational ABCs and continued-fraction ABCs [29][30][31][32][33], and PMLs [34].…”

Section: Introductionmentioning

confidence: 99%

On perfectly matched layers for discontinuous Petrov–Galerkin methods

Astaneh

¹

,

Keith

²

,

Demkowicz

³

2018

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In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered in these derivations. Unlike with classical formulations used by Bubnov-Galerkin methods, with so-called ultraweak variational formulations, these two strategies in fact deliver different formulations in the PML region. One of the strategies, which is argued to be more physically natural, is employed for numerically solving two-and three-dimensional time-harmonic acoustic, elastic, and electromagnetic wave propagation problems, defined in unbounded domains. Through these numerical experiments, efficacy of the new DPG methods with PMLs is verified.

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A Few New (?) Facts About Infinite Elements

Cited by 5 publications

References 3 publications

Modelling high frequency ultrasound scattering from cells and ultrasound contrast agents

Modelling high frequency ultrasound scattering from cells and ultrasound contrast agents

Modelling high frequency ultrasound scattering from cells and ultrasound contrast agents

On perfectly matched layers for discontinuous Petrov–Galerkin methods

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