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Microwave tomography with phaseless data on the calcaneus by means of artificial neural networks

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Abstract

The aim of this study is to use a multilayer perceptron (MLP) artificial neural network (ANN) for phaseless imaging the human heel (modeled as a bilayer dielectric media: bone and surrounding tissue) and the calcaneus cross-section size and location using a two-dimensional (2D) microwave tomographic array. Computer simulations were performed over 2D dielectric maps inspired by computed tomography (CT) images of human heels for training and testing the MLP. A morphometric analysis was performed to account for the scatterer shape influence on the results. A robustness analysis was also conducted in order to study the MLP performance in noisy conditions. The standard deviations of the relative percentage errors on estimating the dielectric properties of the calcaneus bone were relatively high. Regarding the calcaneus surrounding tissue, the dielectric parameters estimations are better, with relative percentage error standard deviations up to ≈ 15%. The location and size of the calcaneus are always properly estimated with absolute error standard deviations up to ≈ 3 mm.

Microwave tomography of the calcaneus using phaseless data. Simulations were inspired in Computed Tomography images from real heels (above). Inverse problem was solved using Multilayer Perceptron Artificial Neural Network (below).

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Acknowledgments

The authors would like to thank to Dra. Guadalupe Irastorza from Centro Diagnóstico MON, La Plata, Argentina, for the CT images.

Funding

This work was supported by a grant from the “Agencia Nacional de Promoción Científica y Tecnológica de Argentina” (Ref. PICT- 2016–2303) and from the “Universidad Nacional Arturo Jauretche” (Ref. UNAJ Investiga 2017 80020170100019UJ).

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Authors and Affiliations

  1. Instituto de Física de Líquidos y Sistemas Biológicos CONICET - CCT La Plata, La Plata, Argentina

    J. E. Fajardo, F. P. Lotto, F. Vericat, C. M. Carlevaro & R. M. Irastorza

  2. Departamento de Ingeniería Mecánica, UTN - FRLP, Berisso, Argentina

    C. M. Carlevaro

  3. Instituto de Ingeniería y Agronomía, UNAJ. Florencio Varela, Buenos Aires, Argentina

    R. M. Irastorza

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  1. J. E. Fajardo
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  2. F. P. Lotto
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  3. F. Vericat
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  4. C. M. Carlevaro
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  5. R. M. Irastorza
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Correspondence to R. M. Irastorza.

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Fajardo, J.E., Lotto, F.P., Vericat, F. et al. Microwave tomography with phaseless data on the calcaneus by means of artificial neural networks. Med Biol Eng Comput 58, 433–442 (2020). https://doi.org/10.1007/s11517-019-02090-y

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  • DOI: https://doi.org/10.1007/s11517-019-02090-y

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