6 papers
Finite element discretization of nonlinear models of ultrasound heating
Julio Careaga, Benjamin Dörich, Vanja Nikolić
Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In…
Combined DG-CG finite element method for the Westervelt equation
Sergio Gómez, Vanja Nikolić
We propose and analyze a space-time finite element method for Westervelt's quasilinear model of ultrasound waves in second-order formulation. The method combines conforming finite…
Mathematical models for nonlinear ultrasound contrast imaging with microbubbles
Vanja Nikolić, Teresa Rauscher
Ultrasound contrast imaging is a specialized imaging technique that applies microbubble contrast agents to traditional medical sonography, providing real-time visualization of bloo…
Application of the thin-film equations in modelling of Marangoni flow patterns amongst surfactant source and drain locations
Julio Careaga, Peter A. Korevaar, Vanja Nikolić +1
Surfactants that are deposited at aqueous liquid films have the ability to generate surface tension gradients at the air-water interface, and thereby induce Marangoni flow. Combine…
Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue
Ben Cox, Barbara Kaltenbacher, Vanja Nikolić +1
We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solve…
blow-up in the Jordan-Moore-Gibson-Thompson equation
Vanja Nikolić, Michael Winkler
The Jordan-Moore-Gibson-Thompson equation \[ τu_{ttt} + αu_{tt} = βΔu_t + γΔu + (f(u))_{tt} \] is considered in a smoothly bounded domain with , whe…