This study presented a novel approach for the precise ablation of breast tumors using focused ultrasound (FUS), leveraging a physics-informed neural network (PINN) integrated with a realistic breast model. FUS has shown significant promise in treating breast tumors by effectively targeting and ablating cancerous tissue. This technique employs concentrated ultrasonic waves to generate intense heat, effectively destroying cancerous tissue. In previous finite element method (FEM) models, the computational demands of handling extensive datasets, multiple dimensions, and discretization posed significant challenges. Our PINN-based solution operated efficiently in a mesh-free domain, achieving remarkable accuracy with significantly reduced computational demands, compared to conventional FEM techniques. Additionally, employing PINN for estimating partial differential equations (PDE) solutions can notably decrease the enormous number of discretized elements needed. The model employed a bowl-shaped acoustic transducer to focus ultrasound waves accurately on the tumor location. The simulation results offered detailed insights into each step of the FUS treatment process, including the generation of acoustic waves, the targeting of the tumor, and the subsequent heating and ablation of cancerous tissue. By applying a 3.8 nm displacement amplitude of transducer input pulse at a frequency of 1.1 MHz for 1 second, the temperature at the focal point elevated to 38.4 ℃, followed by another 90 seconds of cooling time, which resulted in significant necrosis of the tumor tissues. Validation of the PINN model's accuracy was conducted through FEM analysis, aligning closely with real-world FUS therapy scenarios. This innovative model provided physicians with a predictive tool to estimate the necrosis of tumor tissue, facilitating the customization of FUS treatment strategies for individual breast cancer patients.
Citation: Salman Lari, Hossein Rajabzadeh, Mohammad Kohandel, Hyock Ju Kwon. A holistic physics-informed neural network solution for precise destruction of breast tumors using focused ultrasound on a realistic breast model[J]. Mathematical Biosciences and Engineering, 2024, 21(10): 7337-7372. doi: 10.3934/mbe.2024323
This study presented a novel approach for the precise ablation of breast tumors using focused ultrasound (FUS), leveraging a physics-informed neural network (PINN) integrated with a realistic breast model. FUS has shown significant promise in treating breast tumors by effectively targeting and ablating cancerous tissue. This technique employs concentrated ultrasonic waves to generate intense heat, effectively destroying cancerous tissue. In previous finite element method (FEM) models, the computational demands of handling extensive datasets, multiple dimensions, and discretization posed significant challenges. Our PINN-based solution operated efficiently in a mesh-free domain, achieving remarkable accuracy with significantly reduced computational demands, compared to conventional FEM techniques. Additionally, employing PINN for estimating partial differential equations (PDE) solutions can notably decrease the enormous number of discretized elements needed. The model employed a bowl-shaped acoustic transducer to focus ultrasound waves accurately on the tumor location. The simulation results offered detailed insights into each step of the FUS treatment process, including the generation of acoustic waves, the targeting of the tumor, and the subsequent heating and ablation of cancerous tissue. By applying a 3.8 nm displacement amplitude of transducer input pulse at a frequency of 1.1 MHz for 1 second, the temperature at the focal point elevated to 38.4 ℃, followed by another 90 seconds of cooling time, which resulted in significant necrosis of the tumor tissues. Validation of the PINN model's accuracy was conducted through FEM analysis, aligning closely with real-world FUS therapy scenarios. This innovative model provided physicians with a predictive tool to estimate the necrosis of tumor tissue, facilitating the customization of FUS treatment strategies for individual breast cancer patients.
| [1] |
A. Bhowmik, R. Repaka, S. C. Mishra, K. Mitra, Thermal assessment of ablation limit of subsurface tumor during focused ultrasound and laser heating, J. Ther. Sci. Eng. Appl., 8 (2015), 011012. https://doi.org/10.1115/1.4030731 doi: 10.1115/1.4030731
|
| [2] | R. L. Siegel, Cancer statistics, 2020, Ca-Cancer J. Clin., 70 (2020), 7. https://doi.org/10.3322/caac.21601 |
| [3] |
P. Montienthong, P. Rattanadecho, Focused ultrasound ablation for the treatment of patients with localized deformed breast cancer: Computer simulation, J. Heat Transfer, 141 (2019), 101101. https://doi.org/10.1115/1.4044393 doi: 10.1115/1.4044393
|
| [4] |
J. E. Kennedy, High-intensity focused ultrasound in the treatment of solid tumours, Nat. Rev. Cancer, 5 (2005), 321–327. https://doi.org/10.1038/nrc1591 doi: 10.1038/nrc1591
|
| [5] |
G. T. Haar, Ultrasound mediated drug delivery: A 21st century phoenix?, Int. J. Hyperthermia, 28 (2012), 279–281. https://doi.org/10.3109/02656736.2012.678029 doi: 10.3109/02656736.2012.678029
|
| [6] |
R. Deckers, L. G. Merckel, B. D. De Senneville, G. Schubert, K. Gerald, K. Max, et al., Performance analysis of a dedicated breast MR-HIFU system for tumor ablation in breast cancer patients, Phys. Med. Biol., 60 (2015), 5527. https://doi.org/10.1088/0031-9155/60/14/5527 doi: 10.1088/0031-9155/60/14/5527
|
| [7] | M. C. L. Peek, F. Wu, High-intensity focused ultrasound in the treatment of breast tumours, Ecancermedicalscience, 12 (2018). https://doi.org/10.3332%2Fecancer.2018.794 |
| [8] |
L. B. Feril, R. L. Fernan, K. Tachibana, High-intensity focused ultrasound in the treatment of breast cancer, Curr. Med. Chem., 28 (2021), 5179–5188. https://doi.org/10.2174/0929867327666201111143206 doi: 10.2174/0929867327666201111143206
|
| [9] |
K. Yoon, W. Lee, P. Croce, A. Cammalleri, S. Yoo, Multi-resolution simulation of focused ultrasound propagation through ovine skull from a single-element transducer, Phys. Med. Biol., 63 (2018), 105001. https://doi.org/10.1088/1361-6560/aabe37 doi: 10.1088/1361-6560/aabe37
|
| [10] |
P. Gupta, A. Srivastava, Numerical analysis of thermal response of tissues subjected to high intensity focused ultrasound, Int. J. Hyperthermia, 35 (2018), 419–434. https://doi.org/10.1080/02656736.2018.1506166 doi: 10.1080/02656736.2018.1506166
|
| [11] |
M. Rezaeian, A. Sedaghatkish, M. Soltani, Numerical modeling of high-intensity focused ultrasound-mediated intraperitoneal delivery of thermosensitive liposomal doxorubicin for cancer chemotherapy, Drug Delivery, 26 (2019), 898–917. https://doi.org/10.1080/10717544.2019.1660435 doi: 10.1080/10717544.2019.1660435
|
| [12] |
P. Gupta, A. Srivastava, Non-Fourier transient thermal analysis of biological tissue phantoms subjected to high intensity focused ultrasound, Int. J. Heat Mass Transfer, 136 (2019), 1052–1063. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.014 doi: 10.1016/j.ijheatmasstransfer.2019.03.014
|
| [13] |
K. Kaczmarek, T. Hornowski, M. Kubovcikova, M. Timko, M. Koralewski, A. Jozefczak, Heating induced by therapeutic ultrasound in the presence of magnetic nanoparticles, ACS Appl. Mater. Interfaces, 10 (2018), 11554–11564. https://doi.org/10.1021/acsami.8b02496 doi: 10.1021/acsami.8b02496
|
| [14] |
M. Mohammadpour, B. Firoozabadi, High intensity focused ultrasound (HIFU) ablation of porous liver: Numerical analysis of heat transfer and hemodynamics, Appl. Ther. Eng., 170 (2020), 115014. https://doi.org/10.1016/j.applthermaleng.2020.115014 doi: 10.1016/j.applthermaleng.2020.115014
|
| [15] | M. Almekkawy, J. Chen, M. D. Ellis, D. Haemmerich, D. R. Holmes, C. A. Linte, et al., Therapeutic systems and technologies: State-of-the-art applications, opportunities, and challenges, IEEE Rev. Biomed. Eng., 13 (2019), 325–339. https://doi.org/10.1109%2FRBME.2019.2908940 |
| [16] |
I. A. S. Elhelf, H. Albahar, U. Shah, A. Oto, E. Cressman, M. Almekkawy, High intensity focused ultrasound: the fundamentals, clinical applications and research trends, Diagn. Interventional Imaging, 99 (2018), 349–359. https://doi.org/10.1016/j.diii.2018.03.001 doi: 10.1016/j.diii.2018.03.001
|
| [17] |
J. C. Oliveira, F. S. V. Bazán, Poisson approach for evaluating numerical methods for the two-dimensional wave equation constrained to absorbing boundary conditions, Appl. Math. Comput., 209 (2009), 273–284. https://doi.org/10.1016/j.amc.2008.12.043 doi: 10.1016/j.amc.2008.12.043
|
| [18] |
W. Shen, J. Zhang, F. Yang, Modeling and numerical simulation of bioheat transfer and biomechanics in soft tissue, Math. Comput. Modell., 41 (2005), 1251–1265. https://doi.org/10.1016/j.mcm.2004.09.006 doi: 10.1016/j.mcm.2004.09.006
|
| [19] |
A. Pinkus, Approximation theory of the MLP model in neural networks, Acta Numer., 8 (1999), 143–195. https://doi.org/10.1017/S0962492900002919 doi: 10.1017/S0962492900002919
|
| [20] |
M. Dehghan, M. Sabouri, A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements, Appl. Math. Modell., 36 (2012), 6031–6049. https://doi.org/10.1016/j.apm.2012.01.018 doi: 10.1016/j.apm.2012.01.018
|
| [21] |
C. Beck, E. Weinan, A. Jentzen, Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations, J. Nonlinear Sci., 29 (2019), 1563–1619. https://doi.org/10.1007/s00332-018-9525-3 doi: 10.1007/s00332-018-9525-3
|
| [22] |
M. Raissi, G. E. Karniadakis, Hidden physics models: Machine learning of nonlinear partial differential equations, J. Comput. Phys., 357 (2018), 125–141. https://doi.org/10.1016/j.jcp.2017.11.039 doi: 10.1016/j.jcp.2017.11.039
|
| [23] | A. M. Tartakovsky, C. O. Marrero, P. Perdikaris, G. D. Tartakovsky, D. Barajas-Solano, Learning parameters and constitutive relationships with physics informed deep neural networks, preprint, arXiv: 1808.03398. https://doi.org/10.48550/arXiv.1808.03398 |
| [24] |
L. Lu, X. Meng, Z. Mao, G. E. Karniadakis, DeepXDE: A deep learning library for solving differential equations, SIAM Rev., 63 (2021), 208–228. https://doi.org/10.1137/19M1274067 doi: 10.1137/19M1274067
|
| [25] | UWCEM-Phantom Repository, https://uwcem.ece.wisc.edu/phantomRepository.html, Accessed: 2023-06-06. |
| [26] | E. Zastrow, S. K. Davis, M. Lazebnik, F. Kelcz, B. D. Van Veen, S. C. Hagness, Database of 3D Grid-Based Numerical Breast Phantoms for use in Computational Electromagnetics Simulations, Department of Electrical and Computer Engineering University of Wisconsin-Madison. |
| [27] | S. Thüroff, C. Chaussy, High-Intensity focused ultrasound for prostate cancer, Li-Ming Su, Young Stephen C, editors, Early Dignosis and Treatment of Cancer: Prostate Cancer, (2010), 177–92. |
| [28] | Y. F. Zhou, High intensity focused ultrasound in clinical tumor ablation, World J. Clin. Oncol., 2 (2011), 8. https://doi.org/10.5306%2Fwjco.v2.i1.8 |
| [29] |
G. T. Haar, HIFU tissue ablation: concept and devices, Therapeutic Ultrasound, (2016), 3–20. https://doi.org/10.1007/978-3-319-22536-4_1 doi: 10.1007/978-3-319-22536-4_1
|
| [30] |
J. Huang, R. G. Holt, R. O. Cleveland, R. A. Roy, Experimental validation of a tractable numerical model for focused ultrasound heating in flow-through tissue phantoms, J. Acoust. Soc. Am., 116 (2004), 2451–2458. https://doi.org/10.1121/1.1787124 doi: 10.1121/1.1787124
|
| [31] |
H. H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol., 1 (1948), 93–122. https://doi.org/10.1152/jappl.1948.1.2.93 doi: 10.1152/jappl.1948.1.2.93
|
| [32] | M. F. Hamilton, D. T. Blackstock, Nonlinear Acoustics, Academic press San Diego, 237 (1998). |
| [33] | J. S. Kim, Architectural Acoustics, Sejin Co, 2014. |
| [34] | K. J. Laidler, The development of the Arrhenius equation, J. Chem. Educ., 61 (1984). https://doi.org/10.1021/ed061p494 |
| [35] |
H. Wang, J. Wu, Z. Zhuo, J. Tang, A three-dimensional model and numerical simulation regarding thermoseed mediated magnetic induction therapy conformal hyperthermia, Technol. Health Care, 24 (2016), S827–S839. https://doi.org/10.3233/thc-161211 doi: 10.3233/thc-161211
|
| [36] | S. Matlab, Matlab, The MathWorks, Natick, MA, (2012). |
| [37] | American College of Radiology, Illustrated Breast Imaging Reporting and Data System (BI-RADS), (2003). https://doi.org/10.3804/jjabcs.13.258 |
| [38] | D. Systemes, Solidworks 2019, Dessault Systemes: Vélizy-Villacoublay, France, 2011. |
| [39] |
J. Koh, M. J. Kim, Introduction of a new staging system of breast cancer for radiologists: an emphasis on the prognostic stage, Korean J. Radiol., 20 (2019), 69–82. https://doi.org/10.3348/kjr.2018.0231 doi: 10.3348/kjr.2018.0231
|
| [40] |
M. A. Diaz, M. A. Solovchuk, T. W. H. Sheu, A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media, J. Comput. Phys., 363 (2018), 200–230. https://doi.org/10.1016/j.jcp.2018.02.005 doi: 10.1016/j.jcp.2018.02.005
|
| [41] | J. J. Valencia, P. N. Quested, Thermophysical properties, Model. Cast. Solidif. Process., 189 (2001). https://doi.org/10.31399/asm.hb.v22b.a0005523 |
| [42] | R. Rahpeima, M. Soltani, F. M. Kashkooli, Numerical study of microwave induced thermoacoustic imaging for initial detection of cancer of breast on anatomically realistic breast phantom, Comput. Methods Programs Biomed., 196 (2020). https://doi.org/10.1016/j.cmpb.2020.105606 |
| [43] | M. Soltani, R. Rahpeima, F. M. Kashkooli, Breast cancer diagnosis with a microwave thermoacoustic imaging technique—a numerical approach, Med. Biol. Eng. Comput., 57 (2019). https://doi.org/10.1007/s11517-019-01961-8 |
| [44] |
A. Miaskowski, B. Sawicki, Magnetic fluid hyperthermia modeling based on phantom measurements and realistic breast model, IEEE Trans. Biomed. Eng., 60 (2013), 1806–1813. https://doi.org/10.1109/tbme.2013.2242071 doi: 10.1109/tbme.2013.2242071
|
| [45] |
M. O. Culjat, D. Goldenberg, P. Tewari, R. S. Singh, A review of tissue substitutes for ultrasound imaging, Ultrasound Med. Biol., 36 (2010), 861–873. https://doi.org/10.1016/j.ultrasmedbio.2010.02.012 doi: 10.1016/j.ultrasmedbio.2010.02.012
|
| [46] |
T. Hopp, N. V. Ruiter, N. Duric, Breast tissue characterization by sound speed: correlation with mammograms using a 2D/3D image registration, 2012 IEEE Int. Ultrason. Symp., (2012), 1–4. https://doi.org/10.1109/ULTSYM.2012.0234 doi: 10.1109/ULTSYM.2012.0234
|
| [47] | P. A. Hasgall, F. D. Gennaro, C. Baumgartner, E. Neufeld, B. Lloyd, M. C. Gosselin, et al., IT'IS Database for thermal and electromagnetic parameters of biological tissues, Version 4.0, IT'IS, 2018. |
| [48] |
R. Rahpeima, C. A. Lin, Numerical study of magnetic hyperthermia ablation of breast tumor on an anatomically realistic breast phantom, Plos One, 17 (2022), e0274801. https://doi.org/10.1371/journal.pone.0274801 doi: 10.1371/journal.pone.0274801
|
| [49] |
C. Boutelier, L. Bougues, J. Timbal, Experimental study of convective heat transfer coefficient for the human body in water, J. Appl. Physiol., 42 (1977), 93–100. https://doi.org/10.1152/jappl.1977.42.1.93 doi: 10.1152/jappl.1977.42.1.93
|
| [50] |
M. Charlton, S. A. Stanley, Z. Whitman, V. Wenn, T. J. Coats, M. Sims, et al, The effect of constitutive pigmentation on the measured emissivity of human skin, Plos One, 15 (2020), e0241843. https://doi.org/10.1371/journal.pone.0241843 doi: 10.1371/journal.pone.0241843
|
| [51] |
J. Han, A. Jentzen, E. Weinan, Solving high-dimensional partial differential equations using deep learning, Proc. Nat. Acad. Sci., 115 (2018), 8505–8510. https://doi.org/10.1073/pnas.1718942115 doi: 10.1073/pnas.1718942115
|
| [52] | M. S. Maslakowski, S. J. Ilham, T. Hall, T. Subramanian, M. Kiani, M. Almekkawy, The characterization and assembly of an efficient, cost effective focused ultrasound transducer, in 2020 IEEE 14th Dallas Circuits and Systems Conference (DCAS), (2020), 1–6. https://doi.org/10.1109/DCAS51144.2020.9330669 |
| [53] | M. Almekkawy, E. S. Ebbini, The optimization of transcostal phased array refocusing using the semidefinite relaxation method, IEEE Trans. Ultrason., Ferroelectr. Freq Control, 67 (2019), 318–328. https://doi.org/10.1109%2FTUFFC.2019.2944434 |
| [54] |
L. S. Goldstein, M. W. Dewhirst, M. Repacholi, L. Kheifets, Summary, conclusions and recommendations: adverse temperature levels in the human body, Int. J. Hyperthermia, 19 (2003), 373–384. https://doi.org/10.1080/0265673031000090701 doi: 10.1080/0265673031000090701
|
| [55] |
M. Singh, Modified Pennes bioheat equation with heterogeneous blood perfusion: A newer perspective, Int. Commun. Heat Mass Transfer, 218 (2024), 124698. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124698 doi: 10.1016/j.ijheatmasstransfer.2023.124698
|
| [56] |
M. Singh, Incorporating vascular-stasis based blood perfusion to evaluate the thermal signatures of cell-death using modified Arrhenius equation with regeneration of living tissues during nanoparticle-assisted thermal therapy, Int. Commun. Heat Mass Transfer, 135 (2022), 106046. https://doi.org/10.1016/j.icheatmasstransfer.2022.106046 doi: 10.1016/j.icheatmasstransfer.2022.106046
|
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Salman Lari, Hossein Rajabzadeh, Mohammad Kohandel, Hyock Ju Kwon. A holistic physics-informed neural network solution for precise destruction of breast tumors using focused ultrasound on a realistic breast model[J]. Mathematical Biosciences and Engineering, 2024, 21(10): 7337-7372. doi: 10.3934/mbe.2024323
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