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In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

Author

Listed:
  • Ali Farajpour

    (Adelaide Medical School, University of Adelaide, The Queen Elizabeth Hospital, Woodville South, SA 5011, Australia
    Robinson Research Institute, University of Adelaide, Adelaide, SA 5006, Australia)

  • Wendy V. Ingman

    (Adelaide Medical School, University of Adelaide, The Queen Elizabeth Hospital, Woodville South, SA 5011, Australia
    Robinson Research Institute, University of Adelaide, Adelaide, SA 5006, Australia)

Abstract

The wave propagation characteristics of biological tissues are of high importance in improving healthcare technologies and can be used as an early clinical indicator of many diseases. However, the current mathematical models that describe the mechanical properties of biological tissues do not account for the difference in softening and hardening observed at different scales and this limits their utility in biomedical imaging. In this paper, a higher-order nonlocal model is developed to study in-plane wave propagation in healthy, benign, and cancerous breast tissues. To verify the mathematical approach, finite element simulations are conducted. Furthermore, a sequential deep neural network model of feedforward type with multiple hidden layers is developed to understand the intrinsic in-plane wave characteristics of breast tissues. The deep learning algorithm shows potential in accurately extracting the frequencies and phase velocities of breast lesions under in-plane waves even when there is a limited number of clinical samples. Using the higher-order nonlocal model, significant differences between healthy fibroglandular tissue and early breast cancer in the form of ductal carcinoma in situ have been found. The combination of nonlocal and strain gradient parameters allows for the concurrent incorporation of stiffness hardening and softening, solving the rigid-tumour–soft-cell paradox of cancer biomechanics.

Suggested Citation

  • Ali Farajpour & Wendy V. Ingman, 2023. "In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning," Mathematics, MDPI, vol. 11(23), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4804-:d:1289614
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    References listed on IDEAS

    as
    1. Emad E. Ghandourah & Ahmed Amine Daikh & Samir Khatir & Abdulsalam M. Alhawsawi & Essam M. Banoqitah & Mohamed A. Eltaher, 2023. "A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium," Mathematics, MDPI, vol. 11(10), pages 1-26, May.
    2. Civalek, Ömer & Demir, Cigdem, 2016. "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 335-352.
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