Full waveform inversion for arterial viscoelasticity

Abstract

Objective. Arterial viscosity is emerging as an important biomarker, in addition to the widely used arterial elasticity. This paper presents an approach to estimate arterial viscoelasticity using shear wave elastography (SWE).Approach. While dispersion characteristics are often used to estimate elasticity from SWE data, they are not sufficiently sensitive to viscosity. Driven by this, we develop a full waveform inversion (FWI) methodology, based on directly matching predicted and measured wall velocity in space and time, to simultaneously estimate both elasticity and viscosity. Specifically, we propose to minimize an objective function capturing the correlation between measured and predicted responses of the anterior wall of the artery.Results. The objective function is shown to be well-behaving (generally convex), leading us to effectively use gradient optimization to invert for both elasticity and viscosity. The resulting methodology is verified with synthetic data polluted with noise, leading to the conclusion that the proposed FWI is effective in estimating arterial viscoelasticity.Significance. Accurate estimation of arterial viscoelasticity, not just elasticity, provides a more precise characterization of arterial mechanical properties, potentially leading to a better indicator of arterial health.

Keywords: arterial stiffness; cross-correlation; guided waves; semi-analytical finite element method; shear wave elastography.

Figure 1

Geometry of the immersed axis-symmetric tube which mimics a healthy human carotid artery.

Figure 2

Variation of the applied excitation force in time (a), in the axial direction (b), and the circumferential direction (c). The axial position range here shows a typical transducer array length.

Figure 3

Generated full wave data at the top wall with the considered excitation force, geometry, and material models: (a) Voigt model; (b) spring-pot model.

Figure 4

Noise-laden synthetic data with Voigt model: (a) medium noise level; (b) higher noise level. SNR stands for signal-to-noise ratio.

Figure 5

Objective function variation for Voigt viscoelastic model for synthetic data: (a) with medium noise; (b) with higher noise (b). The white asterisk is the point of the minimum objective function value.

Figure 6

Iteration history of the gradient optimization for Voigt viscoelastic model for synthetic data with (a) medium noise and (b) higher noise.

Figure 7

Noise-laden Synthetic data with spring-pot model: (a): medium noise level; (b): higher noise level. SNR stands for signal-to-noise ratio.

Figure 8

Objective function variation for the spring-pot viscoelastic model for synthetic data: (a) with medium noise; (b) with higher noise. The white asterisk is the point of the minimum objective function value.

Figure 9

Iteration history of the gradient optimization for spring-pot viscoelastic model for synthetic data with medium noise (a) and higher noise (b).