Micro Air-Pulse Spatial Deformation Spreading Characterizes Degree of Anisotropy in Tissues

Abstract

In optical coherence elastography (OCE), air-pulse stimulation has been widely used to produce propagation of mechanical waves for elastic characterization of tissues. In this paper, we propose the use of spatial deformation spreading (SDS) on the surface of samples produced by air-pulse stimulation for the OCE of transverse isotropic tissues. Experiments in isotropic tissue-mimicking phantoms and anisotropic chicken tibialis muscle were conducted using a spectral-domain optical coherence tomography system synchronized with a confocal air-pulse stimulation. SDS measurements were compared with wave speeds values calculated at different propagation angles. We found an approximately linear relationship between shear wave speed and SDS in isotropic phantoms, which was confirmed with predictions made by the numerical integration of a wave propagation model. Experimental measurements in chicken muscle show a good agreement between SDS and surface wave speed taken along and across the axis of symmetry of the tissues, also called degree of anisotropy. In summary, these results demonstrated the capabilities of SDS produced by the air-pulse technique in measuring the shear elastic anisotropy of transverse isotropic tissues.

Keywords: Air-pulse; OCE; anisotropy; chicken tibialis muscle; particle velocity; phantoms; transverse isotropic material; wave propagation.

Fig. 1.

Spatio-temporal characteristics of air-pulse excitation in elastic media using a cylindrical shear wave propagation model (Eq. (3)). (a) Cylindrical and Cartesian coordinate system definition, location of air-pulse source and temporal profile of air-release. (b) Normalized particle velocity (NPV) temporal profile depicting the loading and propagation regimes for 3 cases of shear wave speed. (c) SDS plots in 4 cases of shear wave speed. Half-width α-maximun estimations for each plot are conducted at αNPV_max for α = {0.1, 0.2, 0.3}. (d) Half-width α-maximun of SDS plots versus shear wave speed for three cases of α = {0.1, 0.2, 0.3} (correlation quality R² > 0.998).

Fig. 2.

Schematic of the air-pulse OCE system combining a SD-OCT system and a focused air-pulse device. SLD – superluminescent light diode; CCD – line-scan camera; DAC – Digital-to-analog converter.

Fig. 3.

Elastic and isotropic phantom studies. (a) Particle velocity (PV) snapshot obtained at the surface of the phantom at time t₀ = 10 ms. (b) Spatio-temporal map along the x-axis of (a) for y₀ = 3.5 mm. Color bar represents particle velocity in mm/s. (c) Particle velocity temporal profiles obtained at the excitation source center (x₀ = y₀ = 3.5 mm) for different agar phantom concentrations. (d) SDS plots obtained at different PV levels comparing phantoms with shear wave speeds {c₁ c₂, c₃} m/s when PV_max = 1.77 mm/s, and {c₃, c₄, c₅} m/s when PV_max = 1.19 mm/s. (e) Half-width α-maximum values obtained from (d) at different αPV_max levels versus shear wave speed for PV_max = 1.77 mm/s (correlation quality R² > 0.994), and PV_max = 1.19 mm/s (correlation quality R² > 0.996).

Fig. 4.

2D SDS maps of a chicken tibialis muscle sample when the sample is rotated with fibers (AoS) oriented at φ = 0 rad with respect to the x-axis (a, d); φ = π/6 rad (b, e), and φ = π/2 rad (e, f). (a–c) Structural en face intensity plots of the surface of the muscle indicating the fiber distribution for each angle φ case. (d–e) Particle velocity snapshot obtained at the surface of the phantom at time t₀ = 9 ms corresponding to the loading regime. Color bar represents particle velocity in arbitrary units.

Fig. 5.

Spatio-temporal rt-maps of a chicken muscle sample obtained at angles θ = 0 rad (a), θ = π/4 rad (b), and θ = π/2 rad relative to the muscle fiber orientation. Color bar represents particle velocity in arbitrary units. Three temporal instants {t₁ = 10, t₂ = 9, t₃ = 9} ms within the loading regime were selected to evaluate SDS profiles in each angle case θ = 0 rad (d), θ = π/4 rad (e), and θ = π/2 rad (f). The propagation regime was used to calculate shear wave speed in each angle for further comparison.

Fig. 6.

SDS profiles obtained in chicken muscle rearranged from Fig. 5 in three set of plots when times t₁ = 10 ms (a), t₂ = 9 ms (b), and t₃ = 8 ms (c) were chosen in the rt-map within the loading regime. The half-width α-maximun (HWαM) of each SDS plot was evaluated at different αPV_max levels in order to produce comparable measurements of equivalent size and displayed in the polar plot of (d). The degree of shear elastic anisotropy (b/a) was computed for each case, and an average b/a = 1.96 ± 0.07 was obtained. (e) Shear wave speed polar plot showing b/a = 1.91 ± 0.06. SE: standard error, CI: confidence interval. Radial scale in polar plot (d) represents HWαM of SDS in mm. Radial scale in polar plot (e) represents shear wave speed in m/s.

Fig. 7.

SDS (a, c, e) and shear wave speed (b, d, f) polar plots for the remaining three chicken muscle samples. The average accuracy error (N = 4 samples) of SDS results (considering shear wave speed as the ground truth parameter) was 3.91% for the anisotropy level b/a. Radial scale in polar plots (a, c, e) represents HWαM of SDS in mm. Radial scale in polar plots (b, d, f) represents shear wave speed in m/s. SE: standard error, CI: confidence interval.