Frequency-wavenumber domain inversion for arterial viscoelasticity

To estimate viscoelastic properties of the arterial wall, this study presents a novel frequency-wavenumber (f-k) domain inversion approach that enhances the sensitivity and robustness of the parameter estimation.

The proposed method leverages the ultrasound-based shear wave elastography data, particularly the spatiotemporal arterial wall motion data which is first transformed into the f-k domain using a two-dimensional Fast Fourier Transform (2D FFT). The viscoelastic properties are then obtained by maximizing the correlation between the resulting (measured) f-k motion with that simulated motion using semi-analytical finite element method.

Through in silico, phantom, and ex vivo experiments incorporating Voigt and spring-pot viscoelastic models, we show that the proposed f-k inversion achieves higher sensitivity, improved fit (lower objective function value), and better convexity (condition number closer to one) in estimating viscoelastic shear moduli compared to existing approaches. The model achieved parameter estimation accuracy within 1.8 % for all in silico cases with superior robustness (normalized minimum: 0.01 % for the Voigt model, and 1.4 % for the spring-pot model) and better conditioning (condition number: 4.13 and 3.42 for the Voigt and spring-pot models) compared to existing x-t (minima: 3.01 % and 7.1 %, condition number: 7.89 and 5.28 for Voigt and spring-pot models) and dispersion-based approaches (condition number: 9.66 and 10.56 for Voigt and spring-pot models). This performance advantage confirmed in phantom and ex vivo experiments.

Through in silico, artery‑mimicking phantom, and ex vivo porcine aorta experiments, we show that the proposed f-k inversion yields accurate and comparatively better‑conditioned estimates of viscoelastic shear moduli than x-t and dispersion‑based approaches under the same modeling assumptions. These results should be interpreted as a methodological step toward in vivo application; extensive validation across specimens and independent mechanical testing of arterial samples are left to future work.