# Performance Study of a Torsional Wave Sensor and Cervical Tissue Characterization

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure of the Sensor

#### 2.2. Simplified Analytical Model

#### 2.3. Experimental Setup

#### 2.4. Specimens and Experimental Protocols

#### 2.4.1. Sensitivity Study

#### 2.4.2. Cervical Tissue Characterization

#### 2.5. Time of Flight—Signal Processing

- To normalize the signal with the first maximum (in absolute value) and to calculate the start from this maximum, using a reference value (typically 5% or 0.05).
- To normalize the signal with the first maximum (in absolute value) and to calculate the start from the crossing of the horizontal axis with the tangent on the linear zone of the first sinusoidal section of the curve.
- To calculate the frequency using the first two maximum and minimum and to extend a quarter of a cycle from the first function extremum.
- To generate a parameter-dependent reference signal that simulates the expected signal. By means of an inverse problem (a combination of genetic algorithms and quasi-Newton type optimization algorithms), to perform and to adjust the experimental and the reference signal minimizing a residue from weight functions.

#### 2.6. Shear Speed from Time of Flight

#### 2.7. Rheological Models

#### 2.8. Rheometry Experiments

#### 2.9. Viscoelastic Parameters Reconstruction

## 3. Results

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

SE | Static elastography |

DE | Dynamic elastography |

TWE | Torsional wave elastography |

3DMMRE | 3D multifrequency MR elastography |

FEM | Finite Element Models |

FEAP | Finite Element Analysis Program |

M | Maxwell rheological model |

GM | Generalized Maxwell rheological model |

KV | Kelvin–Voigt rheological model |

KVFD | Kelvin–Voigt Fractional Derivative rheological model |

Z | Zener rheological model |

ERDF | The European Regional Development Fund |

## References

- Berghella, V. Post-term pregnancy. In Obstetric Evidence Based Guidelines; Informa: Philadelphia, PA, USA, 2007; p. 183. [Google Scholar]
- Bercoff, J.; Tanter, M.; Fink, M. Supersonic shear imaging: A new technique for soft tissue elasticity mapping. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2004**, 51, 396–409. [Google Scholar] [CrossRef] [PubMed] - Fruscalzo, A.; Londero, A.; Schmitz, R. Quantitative cervical elastography during pregnancy: Influence of setting features on strain calculation. J. Med. Ultrason.
**2015**, 42, 1–8. [Google Scholar] [CrossRef] [PubMed] - Feltovich, H.; Hall, T. Quantitative imaging of the cervix: Setting the bar. Ultrasound Obstet. Gynecol.
**2013**, 41, 121–128. [Google Scholar] [CrossRef] [PubMed] - Maurer, M.; Badir, S.; Pensalfini, M.; Bajka, M.; Abitabile, P.; Zimmermann, R.; Mazza, E. Challenging the in-vivo assessment of biomechanical properties of the uterine cervix: A critical analysis of ultrasound based quasi-static procedures. J. Biomech.
**2015**, 48, 1541–1548. [Google Scholar] [CrossRef] [PubMed] - Fruscalzo, A.; Schmitz, R. Quantitative cervical elastography in pregnancy. Ultrasound Obstet. Gynecol.
**2012**, 40, 612–613. [Google Scholar] [CrossRef] [PubMed] - Bamber, J.; Cosgrove, D.; Dietrich, C.; Fromageau, J.; Bojunga, J.; Calliada, F.; Cantisani, V.; Correas, J.; D’Onofrio, M.; Drakonaki, E.; et al. EFSUMB Guidelines and Recommendations on the Clinical Use of Ultrasound Elastography. Part 1: Basic Principles and Technology. Ultraschall Med.
**2013**, 34, 169–184. [Google Scholar] [CrossRef] [PubMed] - Booi, R.; Carson, P.; O’Donnell, M.; Roubidoux, M.; Hall, A.; Rubin, J. Characterization of cysts using differential correlation coefficient values from two dimensional breast elastography: Preliminary study. Ultrasound Med. Biol.
**2008**, 34, 12–21. [Google Scholar] [CrossRef] [PubMed] - Muller, M.; Gennisson, J.; Deffieux, T.; Tanter, M.; Fink, M. Quantitative viscoelasticity mapping of human liver using supersonic shear imaging: Preliminary in vivo feasibility study. Ultrasound Med. Biol.
**2009**, 35, 219–229. [Google Scholar] [CrossRef] [PubMed] - Peralta, L.M. Feasibility of Using Ultrasonic Shear Waves to Assess Cervical Remodelling during the Gestation Period. Ph.D. Thesis, Civil Engineering, Universidad de Granada, Granada, Spain, May 2015. [Google Scholar]
- Fahey, B.; Palmeri, M.; Trahey, G. Frame rate considerations for real-time abdominal acoustic radiation force transient imaging. Ultrason. Imaging
**2006**, 28, 193–210. [Google Scholar] [CrossRef] [PubMed] - Palmeri, M.; Nightingale, K. On the thermal effects associated with radiation force imaging of soft tissue. Ultraschall Med.
**2007**, 51, 551–565. [Google Scholar] [CrossRef] - Walden, A.; Howarth, T. Torsional Shear Wave Transducer. U.S. Patent 5,321,333 A, 14 June 1994. [Google Scholar]
- Ouared, A.; Montagnon, E.; Cloutier, G. Generation of remote adaptive torsional shear waves with an octagonal phased array to enhance displacements and reduce variability of shear wave speeds: Comparison with quasi-plane shear wavefronts. Phys. Med. Biol.
**2015**, 60, 8161–8185. [Google Scholar] [CrossRef] [PubMed] - Melchor, J.; Rus, G. Torsional ultrasonic transducer computational design optimization. Ultrasonics
**2014**, 54, 1950–1962. [Google Scholar] [CrossRef] [PubMed] - Peralta, L.; Molina, F.; Melchor, J.; Gómez, L.F.; Massó, P.; Florido, J.; Rus, G. Transient elastography to assess the cervical ripening during pregnancy: A preliminary study. Ultraschall Med. Eur. J. Ultrasound
**2017**, 38, 395–402. [Google Scholar] [CrossRef] [PubMed] - Catheline, S.; Gennisson, J.; Delon, G.; Fink, M.; Sinkus, R.; Abouelkaram, S.; Culioli, J. Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: An inverse problem approach. J. Acoust. Soc. Am.
**2004**, 116, 3734–3741. [Google Scholar] [CrossRef] [PubMed] - Chen, S.; Urban, W.; Pislaru, C.; Kinnick, R.; Zheng, Y.; Yao, A.; Greenleaf, J. Shear wave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2009**, 56, 55–62. [Google Scholar] [CrossRef] [PubMed] - Vappou, J.; Maleke, C.; Konofagou, E. Quantitative viscoelastic parameters measured by harmonic motion imaging. Phys. Med. Biol.
**2009**, 54, 3579–3594. [Google Scholar] [CrossRef] [PubMed] - Orescanin, M.; Qayyum, M.; Toohey, K.; Insana, M. Complex shear modulus of thermally-damaged liver. In Proceedings of the 2009 IEEE International Ultrasonics Symposium (IUS), Rome, Italy, 20–23 September 2009; pp. 127–130. [Google Scholar]
- Zhang, M.; Castaneda, B.; Wu, Z.; Nigwekar, P.; Joseph, J.; Rubens, D.; Parker, K. Congruence of imaging estimators and mechanical measurements of viscoelatic properties of soft tissues. Ultrasound Med. Biol.
**2007**, 33, 1617–1631. [Google Scholar] [CrossRef] [PubMed] - Sack, I.; Beierbach, B.; Wuerfel, J.; Klatt, D.; Hamhaber, U.; Papazoglou, S.; Martus, P.; Braun, J. The impact of aging and gender on brain viscoelasticity. NeuroImage
**2009**, 46, 652–657. [Google Scholar] [CrossRef] [PubMed] - Balocco, S.; Basset, O.; Courbebaisse, G.; Boni, E.; Frangi, A.; Tortoli, P.; Cachard, C. Estimation of the viscoelastic properties of vessel walls using a computational model Doppler ultrasound. Phys. Med. Biol.
**2010**, 55, 3557–3575. [Google Scholar] [CrossRef] [PubMed] - Orescanin, M.; Insana, F. Shear modulus estimation with vibrating needle stimulation. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2010**, 57, 1358–1367. [Google Scholar] [CrossRef] [PubMed] - Gennisson, J.; Muller, M.; Ami, O.; Kohl, V.; Gabor, P.; Musset, D.; Tanter, M. Shear wave elastography in obstetrics: Quantification of cervix elasticity and uterine contraction. In Proceedings of the 2011 IEEE International Ultrasonics Symposium (IUS), Orlando, FL, USA, 18–21 October 2011; pp. 2094–2097. [Google Scholar]
- Peralta, L.; Mourier, E.; Richard, C.; Charpigny, G.; Larcher, T.; Ait-Belkacem, D.; Balla, N.; Brasselet, S.; Tanter, M.; Muller, M.; et al. In Vivo Evaluation of Cervical Stiffness Evolution during Induced Ripening Using Shear Wave Elastography, Histology and 2 Photon Excitation Microscopy: Insight from an Animal Model. PLoS ONE
**2015**, 10, e0133377. [Google Scholar] [CrossRef] [PubMed] - Kiss, M.; Hobson, M.; Varghese, T.; Harter, J.; Kliewer, M.; Hartenbach, E.; Zagzebski, J. Frequency-dependent complex modulus of the uterus: Preliminary results. Phys. Med. Biol.
**2006**, 51, 3683–3695. [Google Scholar] [CrossRef] [PubMed] - Jiang, X.; Asbach, P.; Streitberger, K.; Thomas, A.; Hamm, B.; Braun, J.; Sack, I.; Guo, J. In vivo high-resolution magnetic resonance elastography of the uterine corpus and cervix. Eur. Soc. Radiol.
**2014**, 24, 3025–3033. [Google Scholar] [CrossRef] [PubMed] - Rus, G.; Munoz, R.; Melchor, J.; Molina, R.; Callejas, A.; Riveiro, M.; Massó, P.; Torres, J.; Moreu, G.; Molina, F.; et al. Torsion ultrasonic sensor for tissue mechanical characterization. In Proceedings of the IEEE International 2016 Ultrasonic Symposium (IUS), Tours, France, 18–21 September 2016. [Google Scholar]
- Melchor, J.; Muñoz, R.; Rus, C. Torsional ultrasound sensor optimization for soft tissue characterization. Sensors
**2017**, 17, 1402. [Google Scholar] [CrossRef] [PubMed] - Taylor, R. FEAP-Ein Finite Element Analysis Program; Ing.-Gemeinschaft Klee & Wrigges: Laatzen, Germany, 1987. [Google Scholar]
- Kim, J.; Kwon, O. Vibration characteristics of piezoelectric torsional transducers. J. Sound Vibr.
**2003**, 264, 453–473. [Google Scholar] [CrossRef] - Klatt, D.; Hamhaber, U.; Asbach, P.; Braun, J.; Sack, I. Noninvasive assessment of the rheological behaviour of human organs using multifrequency MR elastography: A study of brain and liver viscoelasticity. Phys. Med. Biol.
**2007**, 52, 7281–7294. [Google Scholar] [CrossRef] [PubMed] - Chen, S.; Fatemi, M.; Greenleaf, J. Quantifying elasticity and viscosity from measurement of shear wave speed dispersion. J. Acoust. Soc. Am.
**2004**, 115, 2781–2785. [Google Scholar] [CrossRef] [PubMed] - Macosko, C.; Ronald, L. Rheology: Principles, Measurements and Applications; Wiley-VCH: New York, NY, USA, 1994; 550 p. [Google Scholar]
- Eldred, L.; Baker, W.; Palazotto, A. Kelvin-voigt vs fractional derivative model as constitutive relations for viscoelastic materials. AIAA J.
**1995**, 33, 547–550. [Google Scholar] [CrossRef] - Urban, M.; Nenadic, I.; Mitchell, S.; Chen, S.; Greenleaf, J. Generalized response of a sphere embedded in a viscoelastic medium excited by an ultrasonic radiation force. J. Acoust. Soc. Am.
**2011**, 130, 1133–1141. [Google Scholar] [CrossRef] [PubMed] - Amador, C.; Kinnick, R.; Urban, M.; Fatemi, M.; Greenleaf, J. Viscoelastic tissue mimicking phantom validation study with shear wave elasticity imaging and viscoelastic spectroscopy. In Proceedings of the 2015 IEEE International Ultrasonics Symposium, Taipei, Taiwan, 21–24 October 2015; pp. 1–4. [Google Scholar]
- Carcione, J. Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media; Elsevier Science: Oxford, UK, 2001. [Google Scholar]
- Malkin, A.; Isayev, A.I. Rheology: Concepts, Methods, and Applications; Elsevier: Amsterdam, The Netherlands; ChemTec Publishing: Toronto, ON, Canada, 2011; 528 p. [Google Scholar]
- Chan, R.; Titze, I. Viscoelastic shear properties of human vocal fold mucosa: Measurement methodology and empirical results. J. Acoust. Soc. Am.
**1999**, 106, 2008–2021. [Google Scholar] [CrossRef] [PubMed] - Campos, F.; Bonhome, A.; García, L.; Durán, J.; López, M.; Alaminos, M.; Sánchez, M.; Carriel, V. Ex vivo characterization of a novel tissue-like cross-linked fibrin-agarose hydrogel for tissue engineering applications. Biomed. Mat.
**2016**, 11, 055004. [Google Scholar] [CrossRef] [PubMed] - Rodríguez, I.; López, M.; Oliveira, A.; Sánchez, M.; Campos, A.; Alaminos, M.; Durán, J. Rheological characterization of human fibrin and fibrin-agarose oral mucosa substitutes generated by tissue engineering. J. Tissue Eng. Regen. Med.
**2012**, 6, 636–644. [Google Scholar] - Lin, H.; Shen, Y.; Chen, X.; Zhu, Y.; Zheng, Y.; Zhang, X.; Guo, Y.; Wang, T.; Chen, S. Viscoelastic properties of normal rat liver measured by ultrasound elastography: Comparison with oscillatory rheometry. Biorheology
**2016**, 53, 193–207. [Google Scholar] [CrossRef] [PubMed] - Bernal, M.; Gennisson, J.L.; Flaud, P.; Tanter, M. Correlation between classical rheometry and supersonic shear wave imaging in blood clots. Ultrasound Med. Biol.
**2013**, 39, 2123–2136. [Google Scholar] [CrossRef] [PubMed] - Man, N.; Shiwei, Z.; Jean-Luc, R.; Vijay, S.; Hua, X. Development of oil-in-gelatin phantoms for viscoelasticity measurement in ultrasound shear wave elastography. Ultrasound Med. Biol.
**2013**, 40, 168–176. [Google Scholar]

**Figure 1.**Schematic view of the sensor elements. (

**a**) the receiver; (

**b**) the emitter; (

**c**) contact sensor–phantom.

**Figure 3.**A counterweight device to control the applied pressure (phantom positioned on a balance) and the angle of incidence phantom-sensor. (

**a**) angle of incidence 0${}^{\circ}$; (

**b**) angle of incidence 7.5${}^{\circ}$.

**Figure 4.**(

**a**) measurement with the torsional wave sensor of a cervical tissue sample; (

**b**) cervical tissue sample.

**Figure 5.**Rheological models. (

**a**) the Kelvin–Voigt model; (

**b**) the Kelvin–Voigt Fractional Derivative model; (

**c**) the Maxwell model; (

**d**) the Zener model.

**Figure 6.**(

**a**) A controlled-rate magnetorheometer MCR 300 Physica-Anton Paar, Graz, Austria. Pink matter corresponds to the cervical tissue sample. (

**b**) schematic view of the rheometer.

**Figure 7.**Shear wave signals at different pressures’ phantom–sensors (from 4.81 to 24.06 kPa), frequency: 300 Hz; gelatin concentration: 10%.

**Figure 8.**Box and whisker plots of shear wave speed measurements at different applied pressures phantom-sensor. Mean (lines within boxes), interquartile range (IQR, boxes) and extreme values (whiskers) are shown. (

**a**) 8% gelatin; (

**b**) 10% gelatin.

**Figure 9.**Measurement of shear wave speed at different angles of incidence sensor–phantom; frequency: 300 Hz. (

**a**) 8% gelatin; (

**b**) 10% gelatin.

**Figure 10.**Box and whisker plots of shear wave speed measurements at different angles of incidence phantom–sensor. Mean (lines within boxes), interquartile range (IQR, boxes) and extreme values (whiskers) are shown; frequency: 300 Hz. (

**a**) 8% gelatin; (

**b**) 10% gelatin.

**Figure 12.**Fitted curves using data from rheometry, from elastography and using the combined data from the rheometry and elastography for each model. The circles are the mean values over the three cervix and the horizontal bars are the standard deviations. The curves for the Kelvin–Voigt (solid red line), Kelvin–Voigt Fractional Derivative (solid yellow line), Maxwell (solid purple line) and Zener model (solid green line) are shown. (

**a**) data from rheometry; (

**b**) data from elastography; (

**c**) data from rheometry and elastography.

Disc Frequency [Hz] | 2.80 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{4}$ |

Ring Frequency [Hz] | 2.82 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{4}$ |

FEM Frequency [Hz] | 2.82 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{4}$ |

Error 1 (%) | 0.68 |

Error 2 (%) | 0.04 |

**Table 2.**Viscoelastic parameters using the data from rheometry, TWE, and a combination of the two methods for the Kelvin–Voigt model.

Cervix Number | Elasticity $\mathit{\mu}$ (kPa) | Viscosity $\mathit{\eta}$ (Pa·s) | ||||
---|---|---|---|---|---|---|

Rheometry | TWE | R + TWE | Rheometry | TWE | R + TWE | |

1 | 1.69 | 2.13 | 1.82 | 5.31 | 4.32 | 4.21 |

2 | 1.83 | 2.52 | 2.10 | 6.52 | 4.55 | 4.64 |

3 | 1.85 | 2.64 | 1.84 | 7.19 | 4.9 | 4.65 |

Mean | 1.79 | 2.43 | 1.92 | 6.34 | 4.59 | 4.5 |

Standard Deviation | 0.08 | 0.26 | 0.15 | 0.95 | 0.29 | 0.25 |

**Table 3.**Viscoelastic parameters using the data from rheometry, TWE, and a combination of the two methods for the Kelvin–Voigt Fractional Derivative model.

Cervix Number | Elasticity $\mathit{\mu}$ (kPa) | Viscosity $\mathit{\eta}$ (Pa·s) | Fract. Deriv. Power $\mathit{\alpha}$ | ||||||
---|---|---|---|---|---|---|---|---|---|

Rheometry | TWE | R + TWE | Rheometry | TWE | R + TWE | Rheometry | TWE | R + TWE | |

1 | 1.10 | 2.13 | 2.07 | 12 | 4.02 | 4.54 | 0.42 | 0.98 | 0.99 |

2 | 0.80 | 1.93 | 2.22 | 31 | 4.21 | 4.73 | 0.13 | 0.99 | 0.96 |

3 | 0.86 | 2.12 | 1.74 | 26 | 4.46 | 4.65 | 0.20 | 0.94 | 0.99 |

Mean | 0.92 | 2.06 | 2.01 | 23 | 4.23 | 4.64 | 0.25 | 0.97 | 0.98 |

Standard Deviation | 0.15 | 0.11 | 0.24 | 9.84 | 0.22 | 0.09 | 0.15 | 0.02 | 0.01 |

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## Share and Cite

**MDPI and ACS Style**

Callejas, A.; Gomez, A.; Melchor, J.; Riveiro, M.; Massó, P.; Torres, J.; López-López, M.T.; Rus, G.
Performance Study of a Torsional Wave Sensor and Cervical Tissue Characterization. *Sensors* **2017**, *17*, 2078.
https://doi.org/10.3390/s17092078

**AMA Style**

Callejas A, Gomez A, Melchor J, Riveiro M, Massó P, Torres J, López-López MT, Rus G.
Performance Study of a Torsional Wave Sensor and Cervical Tissue Characterization. *Sensors*. 2017; 17(9):2078.
https://doi.org/10.3390/s17092078

**Chicago/Turabian Style**

Callejas, Antonio, Antonio Gomez, Juan Melchor, Miguel Riveiro, Paloma Massó, Jorge Torres, Modesto T. López-López, and Guillermo Rus.
2017. "Performance Study of a Torsional Wave Sensor and Cervical Tissue Characterization" *Sensors* 17, no. 9: 2078.
https://doi.org/10.3390/s17092078