Exact viscoelastic Green's functions of the Voigt-model-based Navier's equation

Acoustic radiation force based ultrasound shear wave elastography (SWE) is a non-invasive tool for extracting quantitative tissue viscoelasticity information. Often, the first line of evaluation of an ultrasound SWE reconstruction technique is its performance on homogenous phantoms, either physical or numerical, with various viscoelastic properties. Here we address the numerical aspect by solving a governing equation of tissue response to force, the Navier's equation with viscoelastic Voigt model. Following a Lamé's theorem approach, we have derived two exact Green's functions, one being a function of position and temporal frequency and the other of spatial frequency and time. The first Green's function can serve as a gold standard for evaluating other Green's functions at specific positions while the second allows for fast 3-D or 4-D (space and time) simulations on acoustic radiation force induced shear wave generation and propagation over an extended region. These Green's functions can help optimize shear wave induction and develop SWE reconstruction algorithms to achieve more accurate estimate of shear modulus and viscosity for clinical diagnosis.