# Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia

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## Abstract

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## Featured Application

**Generation of low phase velocity nearly non-dispersive propagating guided wave modes in tibial diaphysis using shear actuation**.

## Abstract

## 1. Introduction

## 2. Methods

#### 2.1. Experimental Setup

_{p}= 2πf/k so that the results can be overlaid onto the dispersion curves.

#### 2.2. Numerical Modeling

## 3. Results

#### 3.1. Experimental Results

#### 3.2. Numerical Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An omni-directional shear transducer located at the center of an isotropic plate generates circular-crested shear-horizontal waves that are axisymmetric. An example wave vector and the associated particle displacement are marked.

**Figure 2.**The experimental setup comprises a synthetic tibia, an omni-directional shear transducer, and reflective tape for laser Doppler vibrometer (LDV) reception.

**Figure 3.**The cross-section at the mid-diaphyseal region of a human tibia showing the finite element mesh used to determine dispersion curves.

**Figure 4.**LDV results measured on a synthetic tibia: (

**a**) measurement points on the reflective tape; (

**b**) A-scans recorded at points 1, 4, 7, and 10; (

**c**) phase velocity spectrum obtained from 2D-FFT of data recorded at 10 points overlaid on dispersion curves obtained from finite element simulation.

**Figure 5.**Finite element simulation of wave propagation in a human tibia provided displacement waveforms at the analogous point where LDV measurements were made on the synthetic bone. (

**a**) Relative position of normal at the reception region, (

**b**) the displacement components v and w, and (

**c**) the displacement component normal to the surface and the Hilbert envelope used to identify peaks.

**Figure 6.**Contour maps of the in-plane displacement magnitude $\sqrt{{v}^{2}+{w}^{2}}$, at different times obtained from finite element simulation of human tibia. The black line at the medial facet is tangent to the surface at the position on the synthetic tibia where LDV measurements were made.

**Figure 7.**2D wave structures from SAFE analysis for the eigenvalues corresponding to the dispersion curve region for the extracted phase velocities are shown. The wave structures are expressed as displacement magnitude distribution corresponding to the in-plane displacement components v and w combined as $\sqrt{{v}^{2}+{w}^{2}}$.

Properties | Values | |
---|---|---|

Young’s moduli (GPa) | {E_{x}, E_{y}, E_{z}} | {16.0, 6.3, 6.3} |

Shear moduli (GPa) | {G_{xy}, G_{yz}, G_{xz}} | {3.3, 3.6, 3.3} |

Poisson’s ratio | {ν_{xy}, _{yz}, ν_{xz}} | {0.30, 0.45, 0.30} |

Density (kg/m^{3}) | ρ | 1930 |

Rayleigh damping coefficients | {α, β} | {0, 79.6 ns} |

Mid-Span Cross-Section | Synthetic Bone | Simulation (From Ct-Scan) |
---|---|---|

Antero-posterior diameter, D_{AP} | 22.41 | 21.95 |

Medio-lateral diameter, D_{ML} | 32.97 | 31.12 |

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**MDPI and ACS Style**

Guha, A.; Aynardi, M.; Shokouhi, P.; Lissenden, C.J.
Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia. *Appl. Sci.* **2020**, *10*, 8397.
https://doi.org/10.3390/app10238397

**AMA Style**

Guha A, Aynardi M, Shokouhi P, Lissenden CJ.
Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia. *Applied Sciences*. 2020; 10(23):8397.
https://doi.org/10.3390/app10238397

**Chicago/Turabian Style**

Guha, Anurup, Michael Aynardi, Parisa Shokouhi, and Cliff J. Lissenden.
2020. "Shear-Actuation and Vibrometer Reception of Penetrating Ultrasonic Guided Wave Modes in Human Tibia" *Applied Sciences* 10, no. 23: 8397.
https://doi.org/10.3390/app10238397