# Viscoelastic Biomarkers of Ex Vivo Liver Samples via Torsional Wave Elastography

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hydrogel Phantoms and Ex Vivo Samples

#### 2.2. Torsional Wave Elastography

#### Time of Flight (TOF)- Signal Processing

#### 2.3. Shear Wave Elastography

#### 2.3.1. Dispersion Velocity Calculation from Shear Wave Elastography Imaging (SWEI)

#### 2.3.2. Tissue Motion Estimation

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

TWE | Torsional Wave Elastography |

SWEI | Shear Wave Elastography Imaging |

DE | Dynamic Elastography |

ARFI | Acoustic Radiation Force Impulse |

MRE | Magmatic Resonance Elastography |

SWE | Shear Wave Elastography |

KV | Kelvin–Voigt |

M | Maxwell |

PIP | Probabilistic Inverse Problem |

FDTD | Finite Difference Time Domain |

TOF | Time of Flight |

ROI | Region of Interest |

US | Ultrasonics |

IQ | In-phase and Quadrature Data |

CNC | Computer Numerical Control |

SWV | Shear Wave Velocity |

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**Figure 1.**Flow chart showing the steps for scans performed with both techniques, Torsional Wave Elastography (TWE) and Shear Wave Elastography Imaging (SWEI).

**Figure 2.**Three ex vivo liver samples, phantom ingredients, and one of the phantoms subjected to shear wave elastography imaging.

**Figure 3.**Set-up for measurements using TWE technique. The picture was taken during the measurements at the Ultrasonics Lab at the University of Granada. The figure on the left is a computer numerical control (CNC) system for positioning and pressure-control of the TWE probe. The right figure shows a cross-section of the TWE probe.

**Figure 4.**Example of an output of the analyzer software used to analyze the signals obtained from the TWE technique. The upper left sub-figure shows the stiffness obtained at each measurement frame. The lower-right sub-figure shows the theoretical signal start.

**Figure 5.**Set-up for measurements using SWEI. The picture was taken during the measurements at the Ultrasonics Lab at the University of Granada. In the left image, the ex vivo liver sample is measured while one of the hydrogel phantoms is shown in the right image.

**Figure 6.**Procedure for tissue motion estimation using Shear Wave Elastography Imaging (SWEI) technique.

**Figure 7.**Dispersion curve for the two types of samples measured, square/circle marks are the values of shear wave velocity versus frequency via shear wave elastography imaging (SWEI) and torsional wave elastography (TWE) for ex vivo chicken liver samples (

**top**) and hydrogel phantoms (

**bottom**). Kelvin–Voigt (KV) fit is shown with solid lines in black color for SWEI and in red for TWE, and 95% confidence intervals are displayed with dashed lines.

**Figure 8.**Pearson’s correlation between shear wave velocities via SWEI and TWE for both ex vivo liver samples (

**top**) and hydrogel phantoms (

**bottom**) at a frequency range from 200 to 800 Hz. Pearson correlation coefficients are $0.99767$ for liver samples and $0.99838$ for hydrogel phantoms.

**Figure 9.**The power spectrum of the shear wave tracked by the 7.8Mhz ($L11-5v$) transducer for the ex vivo liver sample using a Verasonics vantage system.

**Figure 10.**Experimental particle displacement versus time profiles at the focal depth resulting from the ARFI excitation. The ARFI moves the tissue in the axial and lateral position. In this figure, each displacement trace indicates a lateral position starting nearby the ARFI push focus to 24 lateral positions. Each individual color curve indicates the lateral position of a displacement trace for ex vivo liver sample II (

**left**) and hydrogel phantom II (

**right**). The curves show that, at farther distances (few milliseconds after the push), the particle displacement is reduced, since the shear wave dissipates.

**Figure 11.**A sequence of displacement map (displacements are in meters) of ex vivo liver sample I due to ARFI excitation. The box represents the ROI (Region of Interest) chosen. The sequence from

**A**to

**D**show the push start (

**A**) and the shear wave propagation in different frames (

**A**–

**D**) till its dissipation.

**Table 1.**Torsional wave elastography (TWE) technique acquisition parameters for both ex vivo liver samples and hydrogel phantoms.

Measurements Acquisition Parameters | Value |
---|---|

Sampling frequency | 80 Hz (Decimated 10 × after 800 Hz) |

Ring-disc radius | 3 mm |

Frequency | 200–800 Hz |

Averaging | 10 × |

Excitation power | 20 V |

Property | Value |
---|---|

Number of Elements | 128 |

Pitch (mm) | 0.3 |

Elevation focus (mm) | 18 |

Sensitivity (dB) | −52 ± 3 |

Parameter | Value for the $\mathit{L}11-5\mathit{v}$ Transducer |
---|---|

Push frequency (MHz) | 4.8 |

Track frequency (MHz) | 7.81 |

Push duration (cycles) | 1000 |

Pulse repetition interval $\left(\mathsf{\mu}s\right)$ | 100 |

Impulse duration (cycles/$\left(\mathsf{\mu}s\right)$) | 1000, 128 |

Impulse focus (mm) | 16 for ex vivo liver and 12 for hydrogel phantoms |

Beam focus configuration | Plane wave, fully open |

IQ data beam forming sampling frequency | 0.25$\lambda $ |

Excitation voltage (V) | 40 for ex vivo liver and 28 for hydrogel phantoms |

Sampling frequency(Hz) | 3000 |

Number of transmission channels | 128 |

Number of reception channels | 128 |

**Table 4.**Shear moduli in kPa for both ex vivo liver samples and hydrogel phantoms obtained from torsional wave elastography (TWE) and shear wave elastography imaging (SWEI) techniques.

Elastic Parameter: Shear Moduli in kPa | ||||
---|---|---|---|---|

Ex Vivo Liver Samples | Hydrogel Phantoms | |||

Frequency (Hz) | ${\mathbf{\mu}}_{\mathit{TWE}}$ | ${\mathbf{\mu}}_{\mathit{SWEI}}$ | ${\mathbf{\mu}}_{\mathit{TWE}}$ | ${\mathbf{\mu}}_{\mathit{SWEI}}$ |

200 | $1.69\pm 0.78$ | $1.32$ | $0.62\pm 0.04$ | $0.58$ |

400 | $2.66\pm 0.23$ | $2.82$ | $0.68\pm 0.05$ | $0.74$ |

600 | $2.69\pm 0.47$ | $3.69$ | $0.78\pm 0.065$ | $0.85$ |

800 | $4.00\pm 0.42$ | $4.84$ | $0.86\pm 0.055$ | $1.16$ |

**Table 5.**Viscoelastic parameters for ex vivo liver samples and hydrogel phantoms obtained from torsional wave elastography (TWE) and shear wave elastography imaging (SWEI) techniques.

Sample | Fit | Viscous Parameters | The Goodness of Fit R-square | ||||
---|---|---|---|---|---|---|---|

TWE | SWEI | TWE | SWEI | ||||

Ex vivo liver | Kelvin–Voigt (KV) | $\mu \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1.512$ kPa | $\eta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.536$ Pa·s | $\mu \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1.019$ kPa | $\eta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.628$ Pa·s | 0.9198 | 0.9572 |

Maxwell (M) | ${\mu}_{1}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}5.773$ kPa | ${\mu}_{2}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}4.316$ Pa·s | ${\mu}_{1}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}13.720$ kPa | ${\mu}_{2}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}3.712$ Pa·s | 0.835 | 0.9861 | |

Hydrogel phantom | Kelvin–Voigt (KV) | $\mu \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.615$ kPa | $\eta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.093$ Pa·s | $\mu \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.532$ kPa | $\eta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.148$ Pa·s | 0.9926 | 0.9764 |

Maxwell (M) | ${\mu}_{1}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.827$ kPa | ${\mu}_{2}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}2.897$ Pa·s | ${\mu}_{1}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1.267$ kPa | ${\mu}_{2}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}1.663$ Pa·s | 0.7879 | 0.8237 |

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**MDPI and ACS Style**

Faris, I.H.; Melchor, J.; Callejas, A.; Torres, J.; Rus, G.
Viscoelastic Biomarkers of Ex Vivo Liver Samples via Torsional Wave Elastography. *Diagnostics* **2020**, *10*, 111.
https://doi.org/10.3390/diagnostics10020111

**AMA Style**

Faris IH, Melchor J, Callejas A, Torres J, Rus G.
Viscoelastic Biomarkers of Ex Vivo Liver Samples via Torsional Wave Elastography. *Diagnostics*. 2020; 10(2):111.
https://doi.org/10.3390/diagnostics10020111

**Chicago/Turabian Style**

Faris, Inas H., Juan Melchor, Antonio Callejas, Jorge Torres, and Guillermo Rus.
2020. "Viscoelastic Biomarkers of Ex Vivo Liver Samples via Torsional Wave Elastography" *Diagnostics* 10, no. 2: 111.
https://doi.org/10.3390/diagnostics10020111