{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T06:25:38Z","timestamp":1778826338612,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T00:00:00Z","timestamp":1630022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51607029"],"award-info":[{"award-number":["51607029"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61836011"],"award-info":[{"award-number":["61836011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2020GFZD008"],"award-info":[{"award-number":["2020GFZD008"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2020GFYD011"],"award-info":[{"award-number":["2020GFYD011"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013314","name":"111 Project","doi-asserted-by":"publisher","award":["B16009"],"award-info":[{"award-number":["B16009"]}],"id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Arterial stenosis will reduce the blood flow to various organs or tissues, causing cardiovascular diseases. Although there are mature diagnostic techniques in clinical practice, they are not suitable for early cardiovascular disease prediction and monitoring due to their high cost and complex operation. In this paper, we studied the electromagnetic effect of arterial blood flow and proposed a method based on the deep neural network for arterial blood flow profile reconstruction. The potential difference and weight matrix are used as inputs to the method, and its output is an estimate of the internal blood flow velocity distribution for arterial blood flow profile reconstruction. Firstly, the weight matrix is input into the convolutional auto-encode (CAE) network to extract its features. Then, the weight matrix features and potential difference are combined to obtain the features of the blood velocity distribution. Finally, the velocity features are reconstructed into blood flow velocity distribution by a convolution neural network (CNN). All data sets are obtained from a model of the carotid artery with different rates of stenosis in a uniform magnetic field by COMSOL. The results show that the average root mean square error of the reconstruction results obtained by the proposed method is 0.0333, and the average correlation coefficient is 0.9721, which is better than the corresponding indicators of the Tikhonov, back propagation (BP) and CNN methods. The simulation results show that the proposed method can achieve high accuracy in blood flow profile reconstruction and is of great significance for the early diagnosis of arterial stenosis and other vessel diseases.<\/jats:p>","DOI":"10.3390\/e23091114","type":"journal-article","created":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T09:53:23Z","timestamp":1630058003000},"page":"1114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Deep Neural Network Method for Arterial Blood Flow Profile Reconstruction"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9790-0851","authenticated-orcid":false,"given":"Dan","family":"Yang","sequence":"first","affiliation":[{"name":"School of Information Science & Engineering, Northeastern University, Shenyang 110819, China"},{"name":"Key Laboratory of Infrared Optoelectric Materials and Micro-Nano Devices Liaoning Province, Northeastern University, Shenyang 110819, China"},{"name":"Key Laboratory of Data Analytics and Optimization for Smart Industry, Ministry of Education, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuchen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science & Engineering, Northeastern University, Shenyang 110819, China"},{"name":"Key Laboratory of Infrared Optoelectric Materials and Micro-Nano Devices Liaoning Province, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110169, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science & Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanjun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information Science & Engineering, Northeastern University, Shenyang 110819, China"},{"name":"Key Laboratory of Infrared Optoelectric Materials and Micro-Nano Devices Liaoning Province, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tonglei","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Information Science & Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,27]]},"reference":[{"key":"ref_1","unstructured":"(2020, June 22). World Health Organization. Available online: http:\/\/www.who.int\/mediacentre\/factsheets\/fs310\/en\/."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e5370","DOI":"10.1097\/MD.0000000000005370","article-title":"Comparison of extracranial artery stenosis and cerebral blood flow, assessed by quantitative magnetic resonance, using digital subtraction angiography as the reference standard","volume":"95","author":"Cai","year":"2016","journal-title":"Medicine"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"986","DOI":"10.3174\/ajnr.A5113","article-title":"Quantifying Intracranial Internal Carotid Artery Stenosis on MR Angiography","volume":"38","author":"Baradaran","year":"2017","journal-title":"Am. J. Neuroradiol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s13244-018-0622-5","article-title":"Grading of carotid artery stenosis with computed tomography angiography: Whether to use the narrowest diameter or the cross-sectional area","volume":"9","author":"Samarzija","year":"2018","journal-title":"Insights Imaging"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1097\/RUQ.0b013e31818625b6","article-title":"Ultrasound imaging of carotid artery stenosis: Application of the Society of Radiologists in Ultrasound Consensus Criteria to a Single Institution Clinical Practice","volume":"24","author":"Braun","year":"2008","journal-title":"Ultrasound Q."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.watres.2019.02.028","article-title":"Microplastic abundance, characteristics, and removal in wastewater treatment plants in a coastal city of China","volume":"155","author":"Long","year":"2019","journal-title":"Water Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yang, Q.-Y., Jin, N.-D., Zhai, L.-S., Ren, Y.-Y., Yu, C., and Wei, J.-D. (2020). Measurement of Water Velocity in Gas\u2013Water Two-Phase Flow with the Combination of Electromagnetic Flowmeter and Conductance. Sensors, 20.","DOI":"10.3390\/s20113122"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bonnett, B., Mitchell, B., Frampton, M., and Hayes, M. (2019, January 20\u201323). Low-noise instrumentation for electromagnetic groundwater flow measurement. Proceedings of the 2019 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Auckland, New Zealand.","DOI":"10.1109\/I2MTC.2019.8827136"},{"key":"ref_9","unstructured":"Ali, M. (2016). Development of an Electromagnetic Induction Method for Non-Invasive Blood Flow Measurement. [Ph.D. Thesis, Huddersfield University]."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yang, D., Liu, Y.-J., Xu, B., and Duo, Y.-H. (2019). A Blood Flow Volume Linear Inversion Model Based on Electromagnetic Sensor for Predicting the Rate of Arterial Stenosis. Sensors, 19.","DOI":"10.3390\/s19133006"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Marinova, I., and Mateev, V. (2019, January 2\u20134). Noninvasive Blood Flow Sensing from Surface Skin Measurements. Proceedings of the 2019 13th International Conference on Sensing Technology (ICST), Sydney, Australia.","DOI":"10.1109\/ICST46873.2019.9047719"},{"key":"ref_12","first-page":"193","article-title":"Electrical impedance tomography (EIT) and its medical applications: A review","volume":"3","author":"Rajaguru","year":"2013","journal-title":"Int. J. Soft Comp. Eng."},{"key":"ref_13","first-page":"1","article-title":"Application of a class of iterative algorithms and their accelerations to Jacobian-based linearized EIT image reconstruction","volume":"29","author":"Wang","year":"2020","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"17","DOI":"10.2528\/PIER12032403","article-title":"Four dimensional reconstruction using magnetic induction tomography: Experimental study","volume":"129","author":"Wei","year":"2012","journal-title":"Prog. Electromagn. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"136819","DOI":"10.1109\/ACCESS.2020.3009991","article-title":"ART-TV Algorithm for Diffuse Correlation Tomography Blood Flow Imaging","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3049","DOI":"10.1109\/JSEN.2019.2892179","article-title":"An Improved Tikhonov Regularization Method for Lung Cancer Monitoring Using Electrical Impedance Tomography","volume":"19","author":"Sun","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7212","DOI":"10.1038\/s41598-017-07727-2","article-title":"A Post-Processing Method for Three-Dimensional Electrical Impedance Tomography","volume":"7","author":"Martin","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"074002","DOI":"10.1088\/1361-6579\/ab21b2","article-title":"Beltrami-net: Domain-independent deep D-bar learning for absolute imaging with electrical impedance tomography (a-EIT)","volume":"40","author":"Hamilton","year":"2019","journal-title":"Physiol. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4887","DOI":"10.1109\/TIM.2019.2954722","article-title":"A Two-Stage Deep Learning Method for Robust Shape Reconstruction With Electrical Impedance Tomography","volume":"69","author":"Ren","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"185597","DOI":"10.1109\/ACCESS.2019.2960850","article-title":"A Novel Algorithm for High-Resolution Magnetic Induction Tomography Based on Stacked Auto-Encoder for Biological Tissue Imaging","volume":"7","author":"Chen","year":"2019","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"014233121984503","DOI":"10.1177\/0142331219845037","article-title":"A novel deep neural network method for electrical impedance tomography","volume":"41","author":"Li","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1109\/TMI.2019.2936522","article-title":"Deep Learning Diffuse Optical Tomography","volume":"39","author":"Yoo","year":"2020","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"124704","DOI":"10.1063\/5.0025881","article-title":"One-dimensional convolutional neural network (1D-CNN) image reconstruction for electrical impedance tomography","volume":"91","author":"Li","year":"2020","journal-title":"Rev. Sci. Instrum."},{"key":"ref_24","unstructured":"Chen, Z., Yuan, Q., Song, X., Chen, C., Zhang, D., Xiang, Y., Liu, R., and Xuan, Q. (2021). Mitnet: Gan enhanced magnetic induction tomography based on complex cnn. arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1109\/JSEN.2020.3019309","article-title":"Image Reconstruction for Electrical Impedance Tomography Using Radial Basis Function Neural Network Based on Hybrid Particle Swarm Optimization Algorithm","volume":"21","author":"Wang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"195402","DOI":"10.1088\/1361-6463\/ab7325","article-title":"Numerical model and finite element simulation of arterial blood flow profile reconstruction in a uniform magnetic field","volume":"53","author":"Liu","year":"2020","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Masci, J., Meier, U., Cire\u015fan, D., and Schmidhuber, J. (2011, January 14\u201317). Stacked convolutional auto-encoders for hierarchical feature extraction. Proceedings of the International Conference on Artificial Neural Networks, Espoo, Finland.","DOI":"10.1007\/978-3-642-21735-7_7"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"108803","DOI":"10.1016\/j.oceaneng.2021.108803","article-title":"An unsupervised learning method with convolutional auto-encoder for vessel trajectory similarity computation","volume":"225","author":"Liang","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"9277","DOI":"10.1109\/JSEN.2021.3050845","article-title":"Shape Reconstruction With Multiphase Conductivity for Electrical Impedance Tomography Using Improved Convolutional Neural Network Method","volume":"21","author":"Wu","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_30","unstructured":"(2021, March 22). Cross Section of Neck Fascial Layers. Available online: https:\/\/www.sohu.com\/a\/150672306_777477."},{"key":"ref_31","unstructured":"Ma, H. (2016). The Research of Characteristics of Electrode-Skin Interface and the Suppression of its Influence in EIS. [Master\u2019s Thesis, School of Biomedical Engineering, Fourth Military Medical University]."},{"key":"ref_32","unstructured":"Shen, H. (2020). Hemodynamic Modeling and Analysis of the Conductivity and Electrical Impedance of Arterial Blood Flows. [Ph.D. Thesis, Dalian University of Technology]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1088\/0967-3334\/25\/3\/009","article-title":"Carotid flow rates and flow division at the bifurcation in healthy volunteers","volume":"25","author":"Marshall","year":"2004","journal-title":"Physiol. Meas."},{"key":"ref_34","first-page":"295","article-title":"Study on the hemodynamics of carotid artery stenosis","volume":"22","author":"Wu","year":"2016","journal-title":"J. Tianjin Med. Univ."},{"key":"ref_35","unstructured":"Li, Y. (2008). A Study for the Stenosis of Arteria and Its Effect on the Blood Flow. [Master\u2019s Thesis, Tsinghua University]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1088\/0967-3334\/34\/7\/823","article-title":"A novel combined regularization algorithm of total variation and Tikhonov regularization for open electrical impedance tomography","volume":"34","author":"Liu","year":"2013","journal-title":"Physiol. Meas."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"David, O.E., and Nathan, S.N. (2016). Deeppainter: Painter classification using deep convolutional autoencoders. International Conference on Artificial Neural Networks, Springer.","DOI":"10.1007\/978-3-319-44781-0_3"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Parashar, K.N., Oveneke, M.C., Rykunov, M., Sahli, H., and Bourdoux, A. (2017, January 8\u201312). Micro-Doppler feature extraction using convolutional auto-encoders for low latency target classification. Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944488"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1016\/j.neucom.2015.10.035","article-title":"An efficient and effective convolutional auto-encoder extreme learning machine network for 3d feature learning","volume":"174","author":"Wang","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3671","DOI":"10.1109\/LRA.2019.2927950","article-title":"Convolutional autoencoder for feature extraction in tactile sensing","volume":"4","author":"Polic","year":"2019","journal-title":"IEEE Robot. Autom. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/9\/1114\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:53:33Z","timestamp":1760165613000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/9\/1114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,27]]},"references-count":40,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["e23091114"],"URL":"https:\/\/doi.org\/10.3390\/e23091114","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,27]]}}}