Nonlinear Medical Ultrasound Tomography: 3D Modeling of Sound Wave Propagation in Human Tissues
Abstract
:1. Introducion
2. Governing Equations and the Numerical Method
3. Numerical Experiments
4. Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Strutt, J.W. The Theory of Sound; Cambridge University Press: Cambridge, UK, 2011; Volume 1. [Google Scholar]
- Strutt, J.W. The Theory of Sound; Cambridge University Press: Cambridge, UK, 2011; Volume 2. [Google Scholar]
- Li, S.; Jackowski, M.; Dione, D.P.; Varslot, T.; Staib, L.H.; Mueller, K. Refraction corrected transmission ultrasound computed tomography for application in breast imaging. Med. Phys. 2010, 37, 2233–2246. [Google Scholar] [CrossRef] [PubMed]
- Huthwaite, P.; Simonetti, F. High-resolution imaging without iteration: A fast and robust method for breast ultrasound tomography. J. Acoust. Soc. Am. 2011, 130, 1721–1734. [Google Scholar] [CrossRef] [PubMed]
- Duric, N.; Littrup, P.; Li, C.; Roy, O.; Schmidt, S.; Janer, R.; Cheng, X.; Goll, J.; Rama, O.; Bey-Knight, L.; et al. Breast ultrasound tomography: Bridging the gap to clinical practice. Proc. SPIE 2012, 8320, 832000. [Google Scholar]
- Jirik, R.; Peterlik, I.; Ruiter, N.; Fousek, J.; Dapp, R.; Zapf, M.; Jan, J. Sound-speed image reconstruction in sparse-aperture 3D ultrasound transmission tomography. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2012, 59, 254–264. [Google Scholar] [CrossRef] [PubMed]
- Marmot, M.G.; Altman, D.G.; Cameron, D.A.; Dewar, J.A.; Thompson, S.G.; Wilcox, M. The benefits and harms of breast cancer screening: An independent review. Br. J. Cancer 2013, 108, 2205–2240. [Google Scholar] [CrossRef] [PubMed]
- Birk, M.; Dapp, R.; Ruiter, N.V.; Becker, J. GPU-based iterative transmission reconstruction in 3D ultrasound computer tomography. J. Parallel Distrib. Comput. 2014, 74, 1730–1743. [Google Scholar] [CrossRef]
- Burov, V.A.; Zotov, D.I.; Rumyantseva, O.D. Reconstruction of the sound velocity and absorption spatial distributions in soft biological tissue phantoms from experimental ultrasound tomography data. Acoust. Phys. 2015, 61, 231–248. [Google Scholar] [CrossRef]
- Sandhu, G.Y.; Li, C.; Roy, O.; Schmidt, S.; Duric, N. Frequency domain ultrasound waveform tomography: Breast imaging using a ring transducer. Phys. Med. Biol. 2015, 60, 5381–5398. [Google Scholar] [CrossRef]
- Liu, H.; Uhlmann, G. Determining both sound speed and internal source in thermo- and photo-acoustic tomography. Inverse Probl. 2015, 31, 105005. [Google Scholar] [CrossRef]
- Huang, L.; Shin, J.; Chen, T.; Lin, Y.; Gao, K.; Intrator, M.; Hanson, K. Breast ultrasound tomography with two parallel transducer arrays. In Medical Imaging 2016: Physics of Medical Imaging (International Society for Optics and Photonics); SPIE: Bellingham, WA, USA, 2016; Volume 9783, p. 97830C. [Google Scholar]
- Matthews, T.P.; Wang, K.; Li, C.; Duric, N.; Anastasio, M.A. Regularized dual averaging image reconstruction for full-wave ultrasound computed tomography. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2017, 64, 811–825. [Google Scholar] [CrossRef]
- Opieliński, K.J.; Pruchnicki, P.; Szymanowski, P.; Szepieniec, W.K.; Szweda, H.; Świś, E.; Jóźwik, M.; Tenderenda, M.; Bułkowski, M. Multimodal ultrasound computer-assisted tomography: An approach to the recognition of breast lesions. Comput. Med. Imaging Graph. 2018, 65, 102–114. [Google Scholar] [CrossRef]
- Malik, B.; Terry, R.; Wiskin, J.; Lenox, M. Quantitative transmission ultrasound tomography: Imaging and performance characteristics. Med. Phys. 2018, 45, 3063–3075. [Google Scholar] [CrossRef] [PubMed]
- Guo, R.; Lu, G.; Qin, B.; Fei, B. Ultrasound imaging technologies for breast cancer detection and management: A review. Ultrasound Med. Biol. 2018, 44, 37–70. [Google Scholar] [CrossRef] [PubMed]
- Wiskin, J.; Malik, B.; Natesan, R.; Lenox, M. Quantitative assessment of breast density using transmission ultrasound tomography. Med. Phys. 2019, 46, 2610–2620. [Google Scholar] [CrossRef] [PubMed]
- Sood, R.; Rositch, A.F.; Shakoor, D.; Ambinder, E.; Pool, K.L.; Pollack, E.; Mollura, D.J.; Mullen, L.A.; Harvey, S.C. Ultrasound for breast cancer detection globally: A systematic review and meta-analysis. J. Glob. Oncol. 2019, 5, 1–17. [Google Scholar] [CrossRef] [PubMed]
- Vourtsis, A. Three-dimensional automated breast ultrasound: Technical aspects and first results. Diagn. Intervent. Radiol. 2019, 100, 579–592. [Google Scholar] [CrossRef]
- Park, C.K.S.; **. ar**&author=Zhang,+Y.&publication_year=2023&journal=ar**v" class='google-scholar' target='_blank' rel='noopener noreferrer'>Google Scholar]
- Wiskin, J.; Malik, B.; Klock, J. Low frequency 3D transmission ultrasound tomography: Technical details and clinical implications. Z. Med. Phys. 2023, 33, 427–443. [Google Scholar] [CrossRef]
- Wiskin, J.; Malik, B.; Ruoff, C.; Pirshafiey, N.; Lenox, M.; Klock, J. Whole-Body Imaging Using Low Frequency Transmission Ultrasound. Acad. Radiol. 2023, 30, 2674–2685. [Google Scholar] [CrossRef]
- Lashkin, S.V.; Kozelkov, A.S.; Yalozo, A.V.; Gerasimov, V.Y.; Zelensky, D.K. Efficiency analysis of the parallel implementation of the simple algorithm on multiprocessor computers. J. Appl. Mech. Tech. Phys. 2017, 58, 1242–1259. [Google Scholar] [CrossRef]
- Kozelkov, A.; Tyatyushkina, E.; Kurkin, A.; Kurulin, V.; Kurkina, O.; Kochetkova, O. Fluid flow simulation in a T-connection of square pipes using modern approaches to turbulence modeling. Sib. Electron. Math. Rep. 2023, 20, 25–46. [Google Scholar]
- Kozelkov, A.; Kurkin, A.; Utkin, D.; Tyatyushkina, E.; Kurulin, V.; Strelets, D. Application of Non-Reflective Boundary Conditions in Three-Dimensional Numerical Simulations of Free-Surface Flow Problems. Geosciences 2022, 12, 427. [Google Scholar] [CrossRef]
- Kozelkov, A.S.; Lashkin, S.V.; Efremov, V.R.; Volkov, K.N.; Tsibereva, Y.A.; Tarasova, N.V. An implicit algorithm of solving Navier–Stokes equations to simulate flows in anisotropic porous media. Comput. Fluids 2018, 160, 164–174. [Google Scholar] [CrossRef]
- Chen, Z.J.; Przekwas, A.J. A coupled pressure-based computational method for incompressible/compressible flows. J. Comput. Phys. 2010, 229, 9150–9165. [Google Scholar] [CrossRef]
- Moukalled, F.; Darwish, M. Pressure-Based Algorithms for Multi-Fluid Flow at All Speeds—Part I: Mass Conservation Formulation, Numerical Heat Transfer. Part B Fundam. 2004, 45, 495–522. [Google Scholar] [CrossRef]
- Jasak, H. Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows. Ph.D. Thesis, Department of Mechanical Engineering, Imperial College of Science, London, UK, 1996. [Google Scholar]
- Jasak, H.; Weller, H.G.; Gosman, A.D. High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int. J. Numer. Methods Fluids 1999, 31, 431–449. [Google Scholar] [CrossRef]
- Leonard, B.P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech./Eng. 1979, 19, 59–98. [Google Scholar] [CrossRef]
- Gaskell, P.H. Curvature-compensated convective-transport—SMART, A new boundedness-preserving transport algorithm. Int. J. Numer. Methods Fluids 1988, 8, 617–641. [Google Scholar] [CrossRef]
- Goss, S.A.; Johnston, R.L.; Dunn, F. Comprehensive compilation of empirical ultrasonic properties of mammalian tissues. J. Acoust. Soc. Am. 1978, 64, 423–457. [Google Scholar] [CrossRef]
- Mast, T.D. Empirical relationships between acoustic parameters in human soft tissues. Acoust. Res. Lett. 2000, 1, 37–42. [Google Scholar] [CrossRef]
- Klyuchinskiy, D.; Novikov, N.; Shishlenin, M. A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations. Computation 2020, 8, 73. [Google Scholar] [CrossRef]
- Shishlenin, M.A.; Savchenko, N.A.; Novikov, N.S.; Klyuchinskiy, D.V. On the reconstruction of the absorption coefficient for the 2D acoustic system. Sib. Electron. Math. Rep. 2023, 20, 1474–1489. [Google Scholar]
- Klyuchinskiy, D.V.; Novikov, N.S.; Shishlenin, M.A. CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach. J. Comput. Phys. 2021, 439, 110374. [Google Scholar] [CrossRef]
- Jenaliyev, M.T.; Bektemesov, M.A.; Yergaliyev, M.G. On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition. J. Inverse Ill-Posed Probl. 2023, 31, 611–624. [Google Scholar] [CrossRef]
- Wang, Z.; Dulikravich, G. A numerical Method for Solving Cascade Inverse Problems Using Navier-Stokes Equations. 33rd Aerospace Sciences Meeting and Exhibit. 1995. Published Online: 22 August 2012. Available online: https://arc.aiaa.org/doi/abs/10.2514/6.1995-304 (accessed on 20 November 2023).
- Arridge, S.; Maass, P.; Öktem, O.; Schönlieb, C. Solving inverse problems using data-driven models. Acta Numer. 2019, 28, 1–174. [Google Scholar] [CrossRef]
- Basurto-Hurtado, J.A.; Cruz-Albarran, I.A.; Toledano-Ayala, M.; Ibarra-Manzano, M.A.; Morales-Hernandez, L.A.; Perez-Ramirez, C.A. Diagnostic Strategies for Breast Cancer Detection: From Image Generation to Classification Strategies Using Artificial Intelligence Algorithms. Cancers 2022, 14, 3442. [Google Scholar] [CrossRef]
- Fan, Y.; Wang, H.; Gemmeke, H.; Hopp, T.; Hesser, J. Model-data-driven image reconstruction with neural networks for ultrasound computed tomography breast imaging. Neurocomputing 2022, 467, 10–21. [Google Scholar] [CrossRef]
Speed of Sound, m/s | Density, kg/m3 | |
---|---|---|
Muscular tissue | 1550 | 994 |
Adipose tissue | 1460 | 904 |
Liver | 1570 | 1083 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Shishlenin, M.; Kozelkov, A.; Novikov, N. Nonlinear Medical Ultrasound Tomography: 3D Modeling of Sound Wave Propagation in Human Tissues. Mathematics 2024, 12, 212. https://doi.org/10.3390/math12020212
Shishlenin M, Kozelkov A, Novikov N. Nonlinear Medical Ultrasound Tomography: 3D Modeling of Sound Wave Propagation in Human Tissues. Mathematics. 2024; 12(2):212. https://doi.org/10.3390/math12020212
Chicago/Turabian StyleShishlenin, Maxim, Andrey Kozelkov, and Nikita Novikov. 2024. "Nonlinear Medical Ultrasound Tomography: 3D Modeling of Sound Wave Propagation in Human Tissues" Mathematics 12, no. 2: 212. https://doi.org/10.3390/math12020212