TY - GEN

T1 - A time-domain fractional calculus model for shear wave parameter estimation

AU - McGough, Robert J.

AU - Urban, Matthew W.

N1 - Funding Information:
ACKNOWLEGMENTS Support from NIH grants R01 EB012079 and R01 DK092255 is gratefully acknowledged. The authors would also like to thank John Nolan for providing the STABLE toolbox.
Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - A fractional calculus model that describes the effects of propagation and attenuation is introduced for shear wave parameter estimation. This fractional calculus model describes propagation with integer-order derivatives and power law atten-uation with a time-fractional derivative. This model is initially evaluated for the power law exponent y=2, which describes frequency-squared attenuation. Alignment between measured shear wave particle velocity in pig liver within the focal plane and the frequency-squared attenuation model are assessed in the time-domain, where the lack of agreement suggests that some other power law exponent is required for this pig liver data. The power law exponent y = 0.9 is then evaluated within the fractional calculus model, which is evaluated with Riemann-Liouville fractional derivative. The results show that the fractional calculus model evaluated with Riemann-Liouville fractional derivative is unable to achieve alignment with the measured pig liver data, where the source of this problem is the singularity in the phase speed that is caused by the Riemann-Liouville fractional derivative. The problem is solved when the fractional derivative is instead evaluated with the Zolotarev fractional derivative, which enables excellent agreement between the measured shear wave data and the optimized waveform obtained with the proposed fractional calculus model.

AB - A fractional calculus model that describes the effects of propagation and attenuation is introduced for shear wave parameter estimation. This fractional calculus model describes propagation with integer-order derivatives and power law atten-uation with a time-fractional derivative. This model is initially evaluated for the power law exponent y=2, which describes frequency-squared attenuation. Alignment between measured shear wave particle velocity in pig liver within the focal plane and the frequency-squared attenuation model are assessed in the time-domain, where the lack of agreement suggests that some other power law exponent is required for this pig liver data. The power law exponent y = 0.9 is then evaluated within the fractional calculus model, which is evaluated with Riemann-Liouville fractional derivative. The results show that the fractional calculus model evaluated with Riemann-Liouville fractional derivative is unable to achieve alignment with the measured pig liver data, where the source of this problem is the singularity in the phase speed that is caused by the Riemann-Liouville fractional derivative. The problem is solved when the fractional derivative is instead evaluated with the Zolotarev fractional derivative, which enables excellent agreement between the measured shear wave data and the optimized waveform obtained with the proposed fractional calculus model.

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U2 - 10.1109/IUS54386.2022.9957950

DO - 10.1109/IUS54386.2022.9957950

M3 - Conference contribution

AN - SCOPUS:85143842761

T3 - IEEE International Ultrasonics Symposium, IUS

BT - IUS 2022 - IEEE International Ultrasonics Symposium

PB - IEEE Computer Society

T2 - 2022 IEEE International Ultrasonics Symposium, IUS 2022

Y2 - 10 October 2022 through 13 October 2022

ER -