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Inverse problem of magneto-acoustic concentration tomography for magnetic nanoparticles with magnetic induction in a saturation magnetization state based on the least squares QR factorization method–trapezoidal method

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Abstract

In order to improve the imaging quality of magneto-acoustic concentration tomography for magnetic nanoparticles (MNPs) with magnetic induction (MACT-MI) and overcome the boundary singularity, this paper built a matrix model which shows the relationship between the partial derivative distribution of MNP concentration and the ultrasound signals, and focused on proposing a concentration reconstruction method based on the least squares QR factorization (LSQR) method–trapezoidal method. Firstly, simulation models with different shapes were established. Secondly, the magnetic and acoustic field simulation data was substituted into the inverse problem method based on LSQR–trapezoidal method for concentration reconstruction. Finally, the reconstructed images were analyzed and the effect of MNP cluster radius on the reconstruction was investigated. Considering the diffusely asymptotic concentration distribution of MNPs in actual biological tissue environment, an asymptotic concentration model was established and the reconstructed images were analyzed. The simulation results show that under the same conditions, compared with the reconstruction method based on the method of moments (MoM), LSQR–trapezoidal method has clearer image boundaries, more stable imaging results, and faster imaging speed. Compared with the uniform concentration model, LSQR–trapezoidal method is more applicable to the asymptotic concentration model. This study provides a basis for further reconstruction of the accuracy of experimental research.

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References

  1. Pu M, Zhao J (2020) Research progress of magnetic iron oxide nanoparticles in biomedical applications. J Huaihai Med 38(04):436–439. https://doi.org/10.14126/j.cnki.1008-7044.2020.04.039

    Article  Google Scholar 

  2. Arriortua OK, Eneko G, Borja H, Maite I, Luis L, Fernando P et al (2016) Antitumor magnetic hyperthermia induced by rgd-functionalized fe3o4 nanoparticles, in an experimental model of colorectal liver metastases. Beilstein J Nanotechnol 7:1532–1542. https://doi.org/10.3762/bjnano.7.147

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Mirza S, Ahmad MS, Shah M, Ateeq M (2020) Magnetic nanoparticles: drug delivery and bioimaging applications. Met Nanopart Drug Delivery Diagn Appl: 189-213. https://doi.org/10.1016/B978-0-12-816960-5.00011-2

  4. He C, Jiang S, Jin H, Chen S, Lin G, Yao H et al (2016) Mitochondrial electron transport chain identified as a novel molecular target of SPIO nanoparticles mediated cancer-specific cytotoxicity. Biomaterials 83:102–114. https://doi.org/10.1016/j.biomaterials.2016.01.010

    Article  CAS  PubMed  Google Scholar 

  5. Ge X , Li M, Deng X et al (2015) Effects of external magnetic field on the transfection rate of spio-shrnadual functional molecular probe into ovarian carcinoma skov3 cells in vitro. Acta Acad Med Sin 37(1): 12–6. http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZYKX201501003.htm

  6. Gleich B, Weizenecker R (2005) Tomographic imaging using the nonlinear response of magnetic particles. Nature 435(7046):1214–1217. https://doi.org/10.1038/nature03808

    Article  CAS  PubMed  Google Scholar 

  7. Han X, Li Y, Liu W, Chen X, Song Z, Wang X et al (2020) The applications of magnetic particle imaging: from cell to body. Diagnostics 10(10):800. https://doi.org/10.3390/diagnostics10100800

    Article  PubMed Central  Google Scholar 

  8. Wei Z, Tay D et al (2019) Pulsed excitation in magnetic particle imaging. IEEE Trans Med Imaging. https://doi.org/10.1109/TMI.2019.2898202

    Article  PubMed  Google Scholar 

  9. Vogel P, Rueckert MA, Kemp SJ et al (2019) Micro-traveling wave magnetic particle imaging—sub-millimeter resolution with optimized tracer LS-008. IEEE Trans Magn 55(10):1–7. https://doi.org/10.1109/TMAG.2019.2924198

    Article  Google Scholar 

  10. Zu W, Ke L, Du Q, Liu Y (2020) Electronically rotated field-free line generation for open bore magnetic particle tomography imaging. Trans China Electrotechn Soc 35(19):4161–4170. https://doi.org/10.19595/j.cnki.1000-6753.tces.191226

    Article  Google Scholar 

  11. Liu Y, Du Q, Ke L et al (2020) Design and analysis of magnetic field-free line in magnetic particle imaging. Trans China Electrotechn Soc 35(10):10. https://doi.org/10.19595/j.cnki.1000-6753.tces.190472

    Article  Google Scholar 

  12. J. Zhong, Z. Jin, C. Wang et al (2021) Advances of research on magnetic particle imaging and its applications in cancer theranostics. Prog Pharm Sci, 45(4):10. http://qikan.cqvip.com/Qikan/Article/Detail?id=7104876674&from=Qikan_Search_Index

  13. Jiang C, Ke L, Du Q et al (2021) Research on the magnetic field-free line system based on ring magnet array. Chin J Sci Inst. https://doi.org/10.19650/j.cnki.cjsi.J2107321

    Article  Google Scholar 

  14. Lu C, Han L, Wang J et al (2021) Engineering of magnetic nanoparticles as magnetic particle imaging tracers. Chem Soc Rev. https://doi.org/10.1039/D0CS00260G

    Article  PubMed  PubMed Central  Google Scholar 

  15. Shi X, Liu G, Yan X, Li Y (2020) Simulation research on magneto-acoustic concentration tomography of magnetic nanoparticles with magnetic induction. Comput Biol Med 119:103653. https://doi.org/10.1016/j.compbiomed.2020.103653

    Article  CAS  PubMed  Google Scholar 

  16. Xia R, Li X, He B (2009) Reconstruction of vectorial acoustic sources in time-domain tomography. IEEE Trans Med Imaging 28(5):669–675. https://doi.org/10.1109/TMI.2008.2008972

    Article  PubMed  PubMed Central  Google Scholar 

  17. Li Y, Ma Q, Zhang D, Xia R (2011) Acoustic dipole radiation model for magnetoacoustic tomography with magnetic induction. Chin Phys B 20(8):263–270. https://doi.org/10.1088/1674-1056/20/8/084302

    Article  Google Scholar 

  18. Jing C, Liu G, Hui X (2013) Conductivity reconstruction for magnetoacoustic tomography based on the system matrix. Modern Sci Instruments. http://qikan.cqvip.com/Qikan/Article/Detail?id=45856363

  19. Guo G, Ding H, Dai S, Ma Q (2017) Boundary normal pressure-based electrical conductivity reconstruction for magneto–acoustic tomography with magnetic induction[J]. Chin Phys B 26(08):197–204. https://doi.org/10.1088/1674-1056/26/8/084301

    Article  Google Scholar 

  20. Ren MA, Yang M, Zhang S, Zhou X, Yin T, Liu Z (2019) Magneto-acoustic tomography with magnetic induction reconstruction algorithm based on singular value decomposition method. J Biomed Eng Res. https://doi.org/10.19529/j.cnki.1672-6278.2019.02.01

    Article  Google Scholar 

  21. Yan X, Xu Z, Chen W, Pan Y (2021) Implementation method for magneto-acoustic concentration tomography with magnetic induction (MACT-MI) based on the method of moments. Comput Biol Med 128:104105. https://doi.org/10.1016/j.compbiomed.2020.104105

    Article  CAS  PubMed  Google Scholar 

  22. Yan X, Hu Y, Guang S, Chen W (2021) Simulation research on magneto-acoustic concentration tomography of magnetic nanoparticles based on truncated singular value decomposition (TSVD). Med Biol Eng Comput 59(11–12):2383–2396. https://doi.org/10.1007/s11517-021-02450-7

    Article  PubMed  Google Scholar 

  23. Bong-Ki K, Jeong-Guon I (1996) On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method. J Acoust Soc Am DOI 10(1121/1):417112

    Google Scholar 

  24. He Z, He Y, Wang M (2007) Study of physical problems related to the application of near-field acoustic holography. Acta Acust. http://www.cnki.com.cn/Article/CJFDTotal-XIBA200702007.htm

  25. Paige C, Sanders MA (1982) LSQR: an algorithm for sparse linear equation and sparse least squares. ACM Trans Math Softw 8:43–71. https://doi.org/10.1145/355984.355989

    Article  Google Scholar 

  26. M Chillarón, Vidal V, G Verdú (2020) Evaluation of image filters for their integration with LSQR computerized tomography reconstruction method[J]. PLoS one:15. https://doi.org/10.1371/journal.pone.0229113

  27. Fan W, Wang H (2011) An image reconstruction algorithm based on preconditioned LSQR for 3D EIT. IEEE Instrum Meas Technol Conf :1–6. https://doi.org/10.1109/IMTC.2011.5944178

  28. Yang F, Dai F, Yao D, Kou X, Dong M, He W (2016) Reconstruction method and application of magnetic field reconstruction of grounding network based on least squares QR factorization algorithm. Trans China Electrotechn Soc 31(05):184–191. http://qikan.cqvip.com/Qikan/Article/Detail?id=68717483504849544853485051&from=Qikan_Search_Index

  29. X. Feng, F. Gao and Y. Zheng (2015) Modulatable magnetically mediated thermoacoustic imaging with magnetic nanoparticles. Appl Phys Lett 106(15). https://doi.org/10.1088/1361-6463/abc27c

  30. Yan X, Pan Y, Chen W, Xu Z, Li Z (2020) Simulation research on forward problem of magnetoacoustic concentration tomography of magnetic nanoparticles with magnetic induction in saturation magnetization state. J Phys D: Appl Phys: 54(7). https://doi.org/10.1088/1361-6463/abc27c

  31. Zhao Z, Torres-Díaz I, Vélez C, Arnold D, Rinaldi C (2017) Brownian dynamics simulations of magnetic nanoparticles captured in strong magnetic field gradients. J Phys Chem C 121(1):801–810. https://doi.org/10.1021/acs.jpcc.6b09409

    Article  CAS  Google Scholar 

  32. Sun T, Zeng X, Hao PH, Chin CT, Chen M et al (2020) Optimization of multi-angle magneto-acousto-electrical tomography (MAET) based on a numerical method. Math Biosci Eng 30;17(4):2864–2880. http://www.aimspress.com/article/doi/10.3934/mbe.2020161

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Funding

This research was supported by the Natural Science Foundation of Liaoning Province (No. 2019-ZD-0039), the Basic Research Project of the Liaoning Provincial Department of Education (No. LJ2020JCL003), and the National Science Fund for Youth (No. 52207008).

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  1. Faculty of Electrical and Control Engineering, Liaoning Technical University, Huludao Liaoning, 125105, China

    Xiaoheng Yan, Hong Xu, Jun Li, Weihua Chen & Yu Hu

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  1. Xiaoheng Yan
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  2. Hong Xu
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  3. Jun Li
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Correspondence to Hong Xu.

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Yan, X., Xu, H., Li, J. et al. Inverse problem of magneto-acoustic concentration tomography for magnetic nanoparticles with magnetic induction in a saturation magnetization state based on the least squares QR factorization method–trapezoidal method. Med Biol Eng Comput 60, 3295–3309 (2022). https://doi.org/10.1007/s11517-022-02668-z

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