Transcranial Ultrasound Estimation of Viscoelasticity and Fluidity of the Soft Matter

Jianjun Yu, Hao Guo, Meng Han, Fan Wang, Ayache Bouakaz, Hongmei Zhang, and Mingxi Wan

Phys. Rev. Applied 17, 024001 – Published 1 February 2022

Abstract

In the fields of geology, materials and biomedical engineering, the noninvasive and accurate estimation of the dynamic mechanical properties of the soft matter enclosed in a rigid shell induced by a low-frequency vibration is worthy of exploration. The addition of fluidity on the basis of viscoelasticity to describe the properties of the soft matter, especially when containing a large amount of water, may be of great value in the detection of crustal movement, material structure, and early cerebral diseases. In the biomedical field, since the influence of the skull on ultrasound is unknown for viewing the propagation of the transcranial shear wave, it is challenging to obtain the mechanical properties of the brain tissue with the skull using the transcranial ultrasound. In this study, the propagations of the transcranial shear wave within the brain tissue induced by an external low-frequency vibration are presented by finite-element-method simulation. This experiment achieved a transcranial ultrasound estimation and differentiation of viscoelasticity and fluidity of brain phantoms enclosed in the skull using the low-frequency vibration and Kelvin-Voigt fractional derivative modeling, and the estimation results are consistent with the nontranscranial ones. These results represent a great potential in the estimation of viscoelasticity and fluidity of the soft matter under different boundary constraints in various areas.

Received 23 June 2021
Revised 12 November 2021
Accepted 24 December 2021

DOI:https://doi.org/10.1103/PhysRevApplied.17.024001

Physics Subject Headings (PhySH)

Elasticity Mechanical & acoustical properties Ultrasonics

Brain Tissues

Viscosity

Finite-element method Ultrasonography

Physics of Living SystemsPolymers & Soft Matter

Authors & Affiliations

Jianjun Yu ¹, Hao Guo ¹, Meng Han¹, Fan Wang¹, Ayache Bouakaz², Hongmei Zhang^1,*, and Mingxi Wan ^1,†

¹The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Department of Biomedical Engineering, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, China
²UMR 1253, iBrain, Université de Tours, Inserm, Tours 37000, France

^*Corresponding author. claramei@mail.xjtu.edu.cn
^†Corresponding author. mxwan@xjtu.edu.cn

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Vol. 17, Iss. 2 — February 2022

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Images

Figure 1
Simulation of the shear-wave propagation within the brain tissue induced by the LF vibration. The color bar represents the amplitude of the displacement. The simulation models are, respectively, the brain tissue with free boundary (top row) and with the skull (bottom row). (a),(d) Details of the simulation setup. The yellow curved surface represents the film. The film is subjected to a sinusoidal force, and the frequency of the force is from 100–300 Hz in the 50-Hz steps. $f (Hz)$ represents the frequency of the force. (b),(c) Shear wave propagating in an arc along the positive $X$ axis at 6 and 12 ms after film vibration, respectively. (e) At 6 ms after the film vibration, the propagation of the transcranial shear wave is similar to that in (b). (f) The propagation of the shear waves from two directions ( $X$ and $Z$ axis) is clearly observed at 12 ms after film vibration.
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Figure 2
Experimental system of the transcranial ultrasonic shear-wave imaging. The excitation is a continuous LF sine wave. $f$ ( $Hz$ ) represents the frequency of the continuous LF sine wave. The tube and the probe are kept at the same height in the $Z$ axis. $L$ ( $m$ ) represents the length of the tube. The details of the tube’s nozzle are shown in the red circle, and the yellow curved surface represents the film. The displacement maps are retrieved through the correlation of the subsequent transcranial ultrafast plane-wave images.
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Figure 3
(a) $X$ -axis displacement induced by the LF transcranial vibration at 100 Hz. The multilayer blue and red stripes at the depth of 80–100 mm are caused by multiple reflections of the ultrasound passing through the cubic skull model. The color bar represents the amplitude of the displacement. The red and black arrows show the directions of the shear-wave propagation. Propagating transcranial shear wave at three time steps (18, 46, and 48 ms). (b) Phase delay of shear wave along the $Z$ axis at the depth of 10 mm. (c) Phase delay of shear wave along the $Z$ axis at the depth of 50 mm. The green dotted line represents the linear curve of the shift phase.
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Figure 4
Shear-wave speeds within gelatin phantoms (4%, 6%, and 8%) along the $Z$ axis at different frequencies are fitted by the KVFD model. The dots represent the experimental shear-wave speeds that actually represent the average speeds, with the maximum deviation indicated by the error bars. The dotted lines represent the curve fitting by the KVFD model, with 95% confidence interval.
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Figure 5
Comparisons of the elasticity $μ_{0}$ ( $Pa$ ), the viscosity $μ_{α}$ ( $Pa s^{α}$ ), and the fluidity $α$ for the 4%, 6%, and 8% gelatin brain-phantom groups. Results are expressed as mean $\pm$ standard error of the mean. $* * p < 0.01; * * * p < 0.001$ .
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Figure 6
$X$ -axis displacement induced by the LF transcranial vibration at 100 Hz in the three time periods (64, 66, and 68 ms). The shear waves within the 6% gelatin brain phantom in the whole skull model are shown. The waves propagated along the $Z$ axis, which is the direction indicated by the black arrow.
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