{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:05:50Z","timestamp":1787029550507,"version":"build-2736575974"},"reference-count":32,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T00:00:00Z","timestamp":1562544000000},"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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a mathematical model of measuring blood flow based on electromagnetic induction for predicting the rate of arterial stenosis. Firstly, an electrode sensor was used to collect the induced potential differences from human skin surface in a uniform magnetic field. Then, the inversion matrix was constructed by the weight function theory and finite element method. Next, the blood flow volume inversion model was constructed by combining the induction potential differences and inversion matrix. Finally, the rate of arterial stenosis was predicted based on mathematical relationship between blood flow and the area of arterial stenosis. To verify the accuracy of the model, a uniform magnetic field distribution of Helmholtz coil and a 3D geometric model of the ulnar artery of the forearm with different rates of stenosis were established in COMSOL, a finite element analysis software. Simulation results showed that the inversion model had high accuracy in the measurement of blood flow and the prediction of rate of stenosis, and is of great significance for the early diagnosis of arterial stenosis and other vessel diseases.<\/jats:p>","DOI":"10.3390\/s19133006","type":"journal-article","created":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T11:02:37Z","timestamp":1562583757000},"page":"3006","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Blood Flow Volume Linear Inversion Model Based on Electromagnetic Sensor for Predicting the Rate of Arterial Stenosis"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9790-0851","authenticated-orcid":false,"given":"Dan","family":"Yang","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"},{"name":"Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University, Shenyang 110819, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan-jun","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun-hui","family":"Duo","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,8]]},"reference":[{"key":"ref_1","unstructured":"(2019, May 19). World Health Organization. Available online: http:\/\/www.who.int\/mediacentre\/factsheets\/fs310\/en\/."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0033-8389(22)00559-0","article-title":"Current Status of Digital Angiography in Vascular Imaging","volume":"33","author":"Katzen","year":"1995","journal-title":"Radiol. Clin. N. Am."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1148\/radiology.207.2.9577502","article-title":"Distal lower extremity arteries: Evaluation with two-dimensional MR digital subtraction angiography","volume":"207","author":"Lee","year":"1998","journal-title":"Radiology"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s00106-003-0982-z","article-title":"Magnetic resonance angiography for the head and neck region","volume":"52","author":"Aschenbach","year":"2004","journal-title":"Hno"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1148\/radiology.220.1.r01jl35179","article-title":"Carotid artery stenosis: Prospective comparison of CT, three-dimensional gadolinium-enhanced MR, and conventional angiography","volume":"220","author":"Randoux","year":"2001","journal-title":"Radiology"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"S421","DOI":"10.2214\/AJR.04.1955","article-title":"Acute and chronic pulmonary emboli: Angiography-CT correlation","volume":"186","author":"Wittram","year":"2006","journal-title":"Am. J. Roentgenol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1148\/radiology.209.1.9769819","article-title":"Takayasu arteritis: Evaluation of the thoracic aorta with CT angiography","volume":"209","author":"Yamada","year":"1998","journal-title":"Radiology"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1007\/s10439-005-9071-7","article-title":"Influence of multiple stenoses on echo-Doppler functional diagnosis of peripheral arterial disease: A numerical and experimental study","volume":"34","author":"Bertolotti","year":"2006","journal-title":"Ann. Biomed. Eng."},{"key":"ref_9","first-page":"405","article-title":"Neural network analysis of internal carotid arterial Doppler signals: Predictions of stenosis and occlusion","volume":"35","author":"Ubeyli","year":"2003","journal-title":"Expert Syst. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/508956","article-title":"Duplex Ultrasound Evaluation of Hemodialysis Access: A Detailed Protocol","volume":"2012","author":"Teodorescu","year":"2012","journal-title":"Int. J. Nephrol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"e1","DOI":"10.1016\/j.jvs.2005.07.014","article-title":"Human factors as a source of error in peak Doppler velocity measurement","volume":"42","author":"Lui","year":"2005","journal-title":"J. Vasc. Surg."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1097\/00004647-200001000-00003","article-title":"Quantitative measurement of local cerebral blood flow in the anesthetized mouse using intraperitoneal [C-14]iodoantipyrine injection and final arterial heart blood sampling","volume":"20","author":"Maeda","year":"2000","journal-title":"J. Cereb. Blood Flow Metab."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1148\/radiol.2232010428","article-title":"Breast cancer: Regional blood flow and blood volume measured with magnetic susceptibility-based MR imaging\u2013Initial results","volume":"223","author":"Delille","year":"2002","journal-title":"Radiology"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/13873954.2013.763831","article-title":"Calculation of arterial characteristic impedance: A comparison using different blood flow models","volume":"19","author":"Hametner","year":"2013","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1053\/ajkd.1998.v31.pm9506688","article-title":"Accuracy of dilution techniques for access flow measurement during hemodialysis","volume":"31","author":"Krivitski","year":"1998","journal-title":"Am. J. Kidney Dis."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"417","DOI":"10.12693\/APhysPolA.124.417","article-title":"The Application of Ultrasonic Methods to Flow Measurement and Detection of Microembolus in Heart Prostheses","volume":"124","author":"Gawlikowski","year":"2013","journal-title":"Acta Phys. Pol. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1007\/s10877-016-9953-2","article-title":"A feasability study of color flow doppler vectorization for automated blood flow monitoring","volume":"31","author":"Schorer","year":"2017","journal-title":"J. Clin. Monit. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1177\/0954411918771098","article-title":"Magnetic resonance conditional paramagnetic choke for suppression of imaging artifacts during magnetic resonance imaging","volume":"232","author":"Wu","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part h J. Eng. Med."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1148\/radiology.208.2.9680569","article-title":"Multisection cerebral blood flow MR imaging with continuous arterial spin labeling","volume":"208","author":"Alsop","year":"1998","journal-title":"Radiology"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.flowmeasinst.2018.10.024","article-title":"Fast imaging of the velocity profile of the conducting continuous phase in multiphase flows using an electromagnetic flowmeter","volume":"64","author":"Webilor","year":"2018","journal-title":"Flow Meas. Instrum."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"055301","DOI":"10.1088\/0957-0233\/26\/5\/055301","article-title":"Reconstruction of velocity profiles in axisymmetric and asymmetric flows using an electromagnetic flow meter","volume":"26","author":"Kollar","year":"2015","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","first-page":"59","article-title":"A Novel Numerical Approach for Solving Weight Function of Electromagnetic Flow Meter","volume":"30","author":"Li","year":"2019","journal-title":"Mapan-J. Metrol. Soc. India"},{"key":"ref_23","unstructured":"Wahhab, H.A.A., Aziz, A.R.A., and Al-Kayiem, H.H. (2017, January 22\u201323). Application of Electromagnetic Induction Technique to Measure the Void Fraction in Oil\/Gas Two Phase Flow. Proceedings of the 3rd International Conference on Mechanical, Manufacturing and Process Plant Engineering (ICMMPE), Penang, Malaysia."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1119\/1.2180283","article-title":"Teaching Faraday\u2019s law of electromagnetic induction in an introductory physics course","volume":"74","author":"Galili","year":"2006","journal-title":"Am. J. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF02791256","article-title":"Theorems of unicity for the tridimensional Navier-Stokes system","volume":"77","author":"Chemin","year":"1999","journal-title":"J. D Anal. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1002\/eej.22953","article-title":"Unified Theory of Electromagnetic Induction and Magnetic Resonant Coupling","volume":"199","author":"Imura","year":"2017","journal-title":"Electr. Eng. Jpn"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1088\/0143-0807\/31\/5\/010","article-title":"Current density and continuity in discretized models","volume":"31","author":"Boykin","year":"2010","journal-title":"Eur. J. Phys."},{"key":"ref_28","unstructured":"Shercliff, J.A. (1962). The Theory of Electromagnetic Flow-Measurement, Cambridge University Press."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"577590","DOI":"10.1017\/S0022112070002586","article-title":"The theory of induced voltage electromagnetic flowmeters","volume":"43","author":"Bevir","year":"1970","journal-title":"J. Fluid Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1119\/1.19421","article-title":"Virtual probability current associated with the spin","volume":"68","author":"Mita","year":"2000","journal-title":"Am. J. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s10439-014-1075-8","article-title":"Geometric and Flow Features of Type B Aortic Dissection: Initial Findings and Comparison of Medically Treated and Stented Cases","volume":"43","author":"Cheng","year":"2015","journal-title":"Ann. Biomed. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1063\/1.3458908","article-title":"Electrical properties with relaxation through human blood","volume":"4","author":"Abdalla","year":"2010","journal-title":"Biomicrofluidics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/13\/3006\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:03:34Z","timestamp":1760187814000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/13\/3006"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,8]]},"references-count":32,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["s19133006"],"URL":"https:\/\/doi.org\/10.3390\/s19133006","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,8]]}}}