MOVING DIPOLE LOCALIZATION USING LINEAR LEAST SQUARE ESTIMATION: A REVIEW
Keywords:
Electrodes number and interspacing, Forward and inverse problem, Heart models, Least squares estimation, and Moving dipole
Abstract
In this review study we will shed some light on the equivalent source generators in electrocardiography and specially the moving dipole (MVD) and the characteristics of biomedical models used with this type of equivalent source generator. The mathematical derivation of the equations used in localizing this MVD is presented with the clarification of the reasons of inaccuracies due to; non-uniqueness, instability (ill-posedness) of the solution, and how a linear least square estimator method may improve the uniqueness of the solution. In addition, its experimental check in different inhomogeneity situations is also stated, the effect of blood mass on the moment and direction of the dipole throughout the ECG course is discussed too. The contribution and/or the progress of different groups of researchers in the clinical validation of MVD is concisely mentioned, furthermore some modern applications of the MVD are also presented.
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References
Armoundas, A. A., Feldman, A. B., Mukkamala, R., & Cohen, R. J. (2003). A single equivalent moving dipole model: An efficient approach for localizing sites of origin of ventricular electrical activation. Annals of Biomedical Engineering, 31(5), 564–576. https://doi.org/10.1114/1.1567281
Armoundas, A. A., Feldman, A. B., Mukkamala, R., He, B., Mullen, T. J., Belk, P. A., Lee, Y. Z., & Cohen, R. J. (2003). Statistical Accuracy of a Moving Equivalent Dipole Method to Identify Sites of Origin of Cardiac Electrical Activation. IEEE Transactions on Biomedical Engineering, 50(12), 1360–1370. https://doi.org/10.1109/TBME.2003.819849
Armoundas, A. A., Feldman, A. B., Sherman, D. A., & Cohen, R. J. (2001). Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source. Medical and Biological Engineering and Computing, 39(5), 562–570. https://doi.org/10.1007/BF02345147
Barnard, A. C. L., Duck, I. M., Lynn, M. S., & Timlake, W. P. (1967). The Application of Electromagnetic Theory to Electrocardiology: II. Numerical Solution of the Integral Equations. Biophysical Journal, 7(5), 463–491. https://doi.org/10.1016/S0006-3495(67)86599-8
Barr, R. C., Spach, M. S., & Herman-giddens, G. S. (1971). Measuring Locations. IEEE Transactions on Biomedical Engineering, BME-18(2), 125–138.
Bort, R., Mascarell, L., Rodrigo, M., Climent, A. M., Liberos, A., Hernández-romero, I., Arenal, A., Bermejo, J., Fernández-avilés, F., Atienza, F., & Guillem, M. S. (2017). This paper must be cited as : Solving inaccuracies in anatomical models for electrocardiographic inverse problem resolution by using electrical information. 37(3), 733–740.
Brody, D. A., Warr, O. S., Wennemark, J. R., Cox, J. W., Keller, F. W., & Terry, F. H. (1971). Studies of the equivalent cardiac generator behavior of isolated turtle hearts. Circulation Research, 29(5), 512–524. https://doi.org/10.1161/01.RES.29.5.512
Brody, D. A., & Wennemark, J. R. (1974). Dipole ranging in isolated rabbit hearts before and after right bundle branch block’. In Cardiovascular Research (Vol. 8).
Bystricky, W. (2012). MODELING THE ELECTRICAL ACTIVITY OF THE HEART BY A SINGLE DIPOLE, CONCURRENTLY ESTMLATING SUBJECT AND MEASUREMENT RELATED CONDITIONS.
Bystricky, W. (2018). Identification of Strict Left Bundle Branch Block, Using a Moving Dipole Model. Computing in Cardiology, 2018-Septe. https://doi.org/10.22489/CinC.2018.216
Claydon, F. J., Milligan, K. L., Gray, T. E., & Mirvis, D. M. (1992). An equivalent generator representation of measured intracavitary potentials. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, 2, 582–583. https://doi.org/10.1109/IEMBS.1992.5761120
Dawoud, F., Wagner, G. S., Moody, G., & Horáček, B. M. (2008). Using inverse electrocardiography to image myocardial infarction-reflecting on the 2007 PhysioNet/Computers in Cardiology Challenge. Journal of Electrocardiology, 41(6), 630–635. https://doi.org/10.1016/j.jelectrocard.2008.07.022
Gabor, D., & Nelson, C. V. (1954). Determination of the resultant dipole of the heart from measurements on the body surface. Journal of Applied Physics, 25(4), 413–416. https://doi.org/10.1063/1.1721655
Geselowitz, D. B. (1964). Dipole theory in electrocardiography. The American Journal of Cardiology, 14(3), 301–306. https://doi.org/10.1016/0002-9149(64)90072-4
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Gulrajani, R. M. (1998). The forward and inverse problems of electrocardiography: Gaining a better qualitative and quantitative understanding of the heart’s electrical activity. IEEE Engineering in Medicine and Biology Magazine, 17(5). https://doi.org/10.1109/51.715491
Horáček, B. M. (1971). The Effect on Electrocardiographic Lead Vectors of Conductivity Inhomogeneities in the Human Torso. Dalhousie University.
Horan, L. G., Flowers, N. C., & Miller, C. B. (1972). A rapid assay of dipolar and extradipolar content in the human electrocardiogram. Journal of Electrocardiology, 5(3), 211–223. https://doi.org/10.1016/S0022-0736(72)80001-3
Houari, K. El, Kachenoura, A., Albera, L., Bensaid, S., Karfoul, A., Boichon-Grivot, C., Rochette, M., & Hernández, A. (2018). A fast model for solving the ECG forward problem based on an evolutionary algorithm. 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017, 2017-December(June 2018), 1–5. https://doi.org/10.1109/CAMSAP.2017.8313083
Ideker, R. E., Bandura, J. P., Larsen, R. A., Cox, J. W., Keller, F. W., & Brody, D. A. (1975). Localization of Heart Vectors Produced by Epicardial Burns and Ectopic Stimuli VALIDATION OF A DIPOLE RANGING METHOD. http://ahajournals.org
Kabanikhin, S. I. (2008). Definitions and examples of inverse and ill-posed problems Survey paper. J. Inv. Ill-Posed Problems, 16, 317–357. https://doi.org/10.1515/JIIP.2008.069
Kay, C. F. Schwan, H. P. (1956). Specific resistance of body tissues. Circulation Research, 4(6), 664–670. https://doi.org/10.1161/01.res.4.6.664
LBBB Initiative of the ISCE meeting. (2018). http://www.thew-project.org/LBBB_Initiative.htm
Lux, R. L., Smith, C. R., Wyatt, R. F., & Abildskov, J. A. (1978). Limited Lead Selection for Estimation of Body Surface Potential Maps in Electrocardiography. IEEE Transactions on Biomedical Engineering, BME-25(3), 270–276. https://doi.org/10.1109/TBME.1978.326332
Lv, W., Lee, K., Arai, T., Barrett, C. D., Hasan, M. M., Hayward, A. M., Marini, R. P., Barley, M. E., Galea, A., Hirschman, G., Armoundas, A. A., & Cohen, R. J. (2020). Accuracy of cardiac ablation catheter guidance by means of a single equivalent moving dipole inverse algorithm to identify sites of origin of cardiac electrical activation. In Journal of Interventional Cardiac Electrophysiology (Vol. 58, Issue 3). https://doi.org/10.1007/s10840-019-00605-z
Lynn, M. S., & Timlake, W. P. (1968). The Use of Multiple Deflations in the Numerical Solution of Singular Systems of Equations, with Applications to Potential Theory. SIAM Journal on Numerical Analysis, 5(2), 303–322. https://doi.org/10.1137/0705027
Macfarlane, P. W., Van Oosterom, A., Pahlm, O., Kligfield, P., Janse, M., & Camm, J. (2010). Comprehensive electrocardiology. (Second Edi). Springer Science & Business Media. https://doi.org/10.1007/978-1-84882-046-3
Malmivuo, J., & Plonsey, R. (1995). Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780195058239.001.0001
Martin Arthur’s, R., Geselowitz, D. B., Briller, S. A., & Trost, R. F. (1971). The Path of the Electrical Center of the Human Heart Determined from Surface Electrocardiograms*. In J. ELECTROCARDIOLOGY (Vol. 4, Issue 1).
Martínez, J. P., Pahlm, O., Ringborn, M., Warren, S., Laguna, P., & Sörnmo, L. (2017). The STAFF III Database: ECGs recorded during acutely induced myocardial ischemia. Computing in Cardiology, 44(September), 1–4. https://doi.org/10.22489/CinC.2017.266-133
McFee, R., & Baule, G. M. (2008). Research in electrocardiography and magnetocardiography. Proceedings of the IEEE, 60(3), 290–321. https://doi.org/10.1109/proc.1972.8621
Moss, A. J., Hall, W. J., Cannom, D. S., Klein, H., Brown, M. W., Daubert, J. P., Estes, N. A. M., Foster, E., Greenberg, H., Higgins, S. L., Pfeffer, M. A., Solomon, S. D., Wilber, D., & Zareba, W. (2009). Cardiac-Resynchronization Therapy for the Prevention of Heart-Failure Events. New England Journal of Medicine, 361(14), 1329–1338. https://doi.org/10.1056/nejmoa0906431
Nakane, T., Ito, T., Matsuura, N., Togo, H., & Hirata, A. (2019). Forward electrocardiogram modeling by small dipoles based on whole-body electric field analysis. IEEE Access, 7, 123463–123472. https://doi.org/10.1109/ACCESS.2019.2938409
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Nelson, C. V., Gastonguay, P. R., Wilkinson, A. F., & Voukydis, P. C. (1971). A lead system for direction and magnitude of the heart vector. Vectorcardiography, 2, 85–97.
Nelson, C. V., Rand, P. W., Angelakos, E. T., & Hugenholtz, P. G. (1972). Effect of intracardiac blood on the spatial vectorcardiogram. I. Results in the dog. In Circulation research (Vol. 31, Issue 1). https://doi.org/10.1161/01.RES.31.1.95
Nelson, C. V, Hodgkin, B. C., & Voukydis, P. C. (1975). Determination of the Locus of the Heart Vector from Body Surface Measurements: Model Experiments. In J. ELECTROCARDIOLOGY (Vol. 8, Issue 2).
Nguyen, M., & Schanze, T. (2017). Spatial resolution of electrical source localization depends on inter-electrode spacing and signal-to-noise ratio. Current Directions in Biomedical Engineering, 3(2), 87–90. https://doi.org/10.1515/cdbme-2017-0019
Odille, F., Liu, S., Van Dam, P., & Felblinger, J. (2017). Statistical variations of heart orientation in healthy adults. Computing in Cardiology, 44, 1–4. https://doi.org/10.22489/CinC.2017.225-058
Plonsey, R., & Barr, R. C. (2007). Bioelectricity A Quantitative Approach (Third Edit). Springer Science & Business Media. https://doi.org/10.1007/978-0-387-48865-3
R Core Team,. (2017). https://www.r-project.org/R System
Rush, S. (1971). An inhomogeneous anisotropic model of the human torso for electrocardiographic studies. Medical and Biological Engineering, 9, 201–211.
Samann, F., Rausch, A., & Schanze, T. (2019). Electrical Dipole Source Localization using Hybrid Least Squares Method in combination with ICA. Current Directions in Biomedical Engineering, 5(1), 361–363. https://doi.org/10.1515/cdbme-2019-0091
Savard, P., Ackaoui, A., Gulrajani, R. M., Nadeau, R. A., Roberge, F. A., Guardo, R., & Dube, B. (1985). Localization of cardiac ectopic activity in man by a single moving dipole. Comparison f different computation techniques. In Journal of Electrocardiology (Vol. 18, Issue 3). https://doi.org/10.1016/S0022-0736(85)80045-5
Savard, P., Mailloux, G. E., Roberge, F. A., Gulrajani, R. M., & Guardo, R. (1982). A Simulation Study of the Single Moving Dipole Representation of Cardiac Electrical Activity. IEEE Transactions on Biomedical Engineering, BME-29(10), 700–707. https://doi.org/10.1109/TBME.1982.324863
Selvester, R. H., Strauss, D. G., & Wagner, G. S. (2010). Myocardial Infarction BT - Comprehensive Electrocardiology. Springer Verlag. https://doi.org/10.1007/978-1-84882-046-3_16
Starc, V., & Schlegel, T. T. (2020). Moving Dipole Determination from 12-Lead ECGs Can Improve Detection of Acute Myocardial Ischemia. Computing in Cardiology, 2020-September. https://doi.org/10.22489/CinC.2020.115
Starc, V., & Swenne, C. A. (2017). Spatial distribution and orientation of a single moving dipole computed in 12-lead ECGs of a healthy population using a spherically bounded model. Computing in Cardiology, 44, 1–4. https://doi.org/10.22489/CinC.2017.242-277
Strauss, D. G., Selvester, R. H., & Wagner, G. S. (2011). Defining left bundle branch block in the era of cardiac resynchronization therapy. In American Journal of Cardiology (Vol. 107, Issue 6, pp. 927–934). https://doi.org/10.1016/j.amjcard.2010.11.010
Svehlikova, J., Teplan, M., & Tysler, M. (2018). Geometrical constraint of sources in noninvasive localization of premature ventricular contractions. Journal of Electrocardiology, 51(3), 370–377. https://doi.org/10.1016/j.jelectrocard.2018.02.013
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Armoundas, A. A., Feldman, A. B., Mukkamala, R., He, B., Mullen, T. J., Belk, P. A., Lee, Y. Z., & Cohen, R. J. (2003). Statistical Accuracy of a Moving Equivalent Dipole Method to Identify Sites of Origin of Cardiac Electrical Activation. IEEE Transactions on Biomedical Engineering, 50(12), 1360–1370. https://doi.org/10.1109/TBME.2003.819849
Armoundas, A. A., Feldman, A. B., Sherman, D. A., & Cohen, R. J. (2001). Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source. Medical and Biological Engineering and Computing, 39(5), 562–570. https://doi.org/10.1007/BF02345147
Barnard, A. C. L., Duck, I. M., Lynn, M. S., & Timlake, W. P. (1967). The Application of Electromagnetic Theory to Electrocardiology: II. Numerical Solution of the Integral Equations. Biophysical Journal, 7(5), 463–491. https://doi.org/10.1016/S0006-3495(67)86599-8
Barr, R. C., Spach, M. S., & Herman-giddens, G. S. (1971). Measuring Locations. IEEE Transactions on Biomedical Engineering, BME-18(2), 125–138.
Bort, R., Mascarell, L., Rodrigo, M., Climent, A. M., Liberos, A., Hernández-romero, I., Arenal, A., Bermejo, J., Fernández-avilés, F., Atienza, F., & Guillem, M. S. (2017). This paper must be cited as : Solving inaccuracies in anatomical models for electrocardiographic inverse problem resolution by using electrical information. 37(3), 733–740.
Brody, D. A., Warr, O. S., Wennemark, J. R., Cox, J. W., Keller, F. W., & Terry, F. H. (1971). Studies of the equivalent cardiac generator behavior of isolated turtle hearts. Circulation Research, 29(5), 512–524. https://doi.org/10.1161/01.RES.29.5.512
Brody, D. A., & Wennemark, J. R. (1974). Dipole ranging in isolated rabbit hearts before and after right bundle branch block’. In Cardiovascular Research (Vol. 8).
Bystricky, W. (2012). MODELING THE ELECTRICAL ACTIVITY OF THE HEART BY A SINGLE DIPOLE, CONCURRENTLY ESTMLATING SUBJECT AND MEASUREMENT RELATED CONDITIONS.
Bystricky, W. (2018). Identification of Strict Left Bundle Branch Block, Using a Moving Dipole Model. Computing in Cardiology, 2018-Septe. https://doi.org/10.22489/CinC.2018.216
Claydon, F. J., Milligan, K. L., Gray, T. E., & Mirvis, D. M. (1992). An equivalent generator representation of measured intracavitary potentials. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, 2, 582–583. https://doi.org/10.1109/IEMBS.1992.5761120
Dawoud, F., Wagner, G. S., Moody, G., & Horáček, B. M. (2008). Using inverse electrocardiography to image myocardial infarction-reflecting on the 2007 PhysioNet/Computers in Cardiology Challenge. Journal of Electrocardiology, 41(6), 630–635. https://doi.org/10.1016/j.jelectrocard.2008.07.022
Gabor, D., & Nelson, C. V. (1954). Determination of the resultant dipole of the heart from measurements on the body surface. Journal of Applied Physics, 25(4), 413–416. https://doi.org/10.1063/1.1721655
Geselowitz, D. B. (1964). Dipole theory in electrocardiography. The American Journal of Cardiology, 14(3), 301–306. https://doi.org/10.1016/0002-9149(64)90072-4
Geselowitz, D. B. (1965). Two Theorems Concerning the Quadrupole Applicable to Electrocardiography. IEEE Transactions on Biomedical Engineering, BME-12(3), 164–168. https://doi.org/10.1109/TBME.1965.4502373
Goldberger, J. J., & Ng, J. (2010). Practical signal and image processing in clinical cardiology. In Practical Signal and Image Processing in Clinical Cardiology. https://doi.org/10.1007/978-1-84882-515-4
Gulrajani, R. M. (1998). The forward and inverse problems of electrocardiography: Gaining a better qualitative and quantitative understanding of the heart’s electrical activity. IEEE Engineering in Medicine and Biology Magazine, 17(5). https://doi.org/10.1109/51.715491
Horáček, B. M. (1971). The Effect on Electrocardiographic Lead Vectors of Conductivity Inhomogeneities in the Human Torso. Dalhousie University.
Horan, L. G., Flowers, N. C., & Miller, C. B. (1972). A rapid assay of dipolar and extradipolar content in the human electrocardiogram. Journal of Electrocardiology, 5(3), 211–223. https://doi.org/10.1016/S0022-0736(72)80001-3
Houari, K. El, Kachenoura, A., Albera, L., Bensaid, S., Karfoul, A., Boichon-Grivot, C., Rochette, M., & Hernández, A. (2018). A fast model for solving the ECG forward problem based on an evolutionary algorithm. 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017, 2017-December(June 2018), 1–5. https://doi.org/10.1109/CAMSAP.2017.8313083
Ideker, R. E., Bandura, J. P., Larsen, R. A., Cox, J. W., Keller, F. W., & Brody, D. A. (1975). Localization of Heart Vectors Produced by Epicardial Burns and Ectopic Stimuli VALIDATION OF A DIPOLE RANGING METHOD. http://ahajournals.org
Kabanikhin, S. I. (2008). Definitions and examples of inverse and ill-posed problems Survey paper. J. Inv. Ill-Posed Problems, 16, 317–357. https://doi.org/10.1515/JIIP.2008.069
Kay, C. F. Schwan, H. P. (1956). Specific resistance of body tissues. Circulation Research, 4(6), 664–670. https://doi.org/10.1161/01.res.4.6.664
LBBB Initiative of the ISCE meeting. (2018). http://www.thew-project.org/LBBB_Initiative.htm
Lux, R. L., Smith, C. R., Wyatt, R. F., & Abildskov, J. A. (1978). Limited Lead Selection for Estimation of Body Surface Potential Maps in Electrocardiography. IEEE Transactions on Biomedical Engineering, BME-25(3), 270–276. https://doi.org/10.1109/TBME.1978.326332
Lv, W., Lee, K., Arai, T., Barrett, C. D., Hasan, M. M., Hayward, A. M., Marini, R. P., Barley, M. E., Galea, A., Hirschman, G., Armoundas, A. A., & Cohen, R. J. (2020). Accuracy of cardiac ablation catheter guidance by means of a single equivalent moving dipole inverse algorithm to identify sites of origin of cardiac electrical activation. In Journal of Interventional Cardiac Electrophysiology (Vol. 58, Issue 3). https://doi.org/10.1007/s10840-019-00605-z
Lynn, M. S., & Timlake, W. P. (1968). The Use of Multiple Deflations in the Numerical Solution of Singular Systems of Equations, with Applications to Potential Theory. SIAM Journal on Numerical Analysis, 5(2), 303–322. https://doi.org/10.1137/0705027
Macfarlane, P. W., Van Oosterom, A., Pahlm, O., Kligfield, P., Janse, M., & Camm, J. (2010). Comprehensive electrocardiology. (Second Edi). Springer Science & Business Media. https://doi.org/10.1007/978-1-84882-046-3
Malmivuo, J., & Plonsey, R. (1995). Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780195058239.001.0001
Martin Arthur’s, R., Geselowitz, D. B., Briller, S. A., & Trost, R. F. (1971). The Path of the Electrical Center of the Human Heart Determined from Surface Electrocardiograms*. In J. ELECTROCARDIOLOGY (Vol. 4, Issue 1).
Martínez, J. P., Pahlm, O., Ringborn, M., Warren, S., Laguna, P., & Sörnmo, L. (2017). The STAFF III Database: ECGs recorded during acutely induced myocardial ischemia. Computing in Cardiology, 44(September), 1–4. https://doi.org/10.22489/CinC.2017.266-133
McFee, R., & Baule, G. M. (2008). Research in electrocardiography and magnetocardiography. Proceedings of the IEEE, 60(3), 290–321. https://doi.org/10.1109/proc.1972.8621
Moss, A. J., Hall, W. J., Cannom, D. S., Klein, H., Brown, M. W., Daubert, J. P., Estes, N. A. M., Foster, E., Greenberg, H., Higgins, S. L., Pfeffer, M. A., Solomon, S. D., Wilber, D., & Zareba, W. (2009). Cardiac-Resynchronization Therapy for the Prevention of Heart-Failure Events. New England Journal of Medicine, 361(14), 1329–1338. https://doi.org/10.1056/nejmoa0906431
Nakane, T., Ito, T., Matsuura, N., Togo, H., & Hirata, A. (2019). Forward electrocardiogram modeling by small dipoles based on whole-body electric field analysis. IEEE Access, 7, 123463–123472. https://doi.org/10.1109/ACCESS.2019.2938409
Nakano, Y., Rashed, E. A., Nakane, T., Laakso, I., & Hirata, A. (2021). Ecg localization method based on volume conductor model and kalman filtering. Sensors, 21(13). https://doi.org/10.3390/s21134275
Nelson, C. V., Gastonguay, P. R., Wilkinson, A. F., & Voukydis, P. C. (1971). A lead system for direction and magnitude of the heart vector. Vectorcardiography, 2, 85–97.
Nelson, C. V., Rand, P. W., Angelakos, E. T., & Hugenholtz, P. G. (1972). Effect of intracardiac blood on the spatial vectorcardiogram. I. Results in the dog. In Circulation research (Vol. 31, Issue 1). https://doi.org/10.1161/01.RES.31.1.95
Nelson, C. V, Hodgkin, B. C., & Voukydis, P. C. (1975). Determination of the Locus of the Heart Vector from Body Surface Measurements: Model Experiments. In J. ELECTROCARDIOLOGY (Vol. 8, Issue 2).
Nguyen, M., & Schanze, T. (2017). Spatial resolution of electrical source localization depends on inter-electrode spacing and signal-to-noise ratio. Current Directions in Biomedical Engineering, 3(2), 87–90. https://doi.org/10.1515/cdbme-2017-0019
Odille, F., Liu, S., Van Dam, P., & Felblinger, J. (2017). Statistical variations of heart orientation in healthy adults. Computing in Cardiology, 44, 1–4. https://doi.org/10.22489/CinC.2017.225-058
Plonsey, R., & Barr, R. C. (2007). Bioelectricity A Quantitative Approach (Third Edit). Springer Science & Business Media. https://doi.org/10.1007/978-0-387-48865-3
R Core Team,. (2017). https://www.r-project.org/R System
Rush, S. (1971). An inhomogeneous anisotropic model of the human torso for electrocardiographic studies. Medical and Biological Engineering, 9, 201–211.
Samann, F., Rausch, A., & Schanze, T. (2019). Electrical Dipole Source Localization using Hybrid Least Squares Method in combination with ICA. Current Directions in Biomedical Engineering, 5(1), 361–363. https://doi.org/10.1515/cdbme-2019-0091
Savard, P., Ackaoui, A., Gulrajani, R. M., Nadeau, R. A., Roberge, F. A., Guardo, R., & Dube, B. (1985). Localization of cardiac ectopic activity in man by a single moving dipole. Comparison f different computation techniques. In Journal of Electrocardiology (Vol. 18, Issue 3). https://doi.org/10.1016/S0022-0736(85)80045-5
Savard, P., Mailloux, G. E., Roberge, F. A., Gulrajani, R. M., & Guardo, R. (1982). A Simulation Study of the Single Moving Dipole Representation of Cardiac Electrical Activity. IEEE Transactions on Biomedical Engineering, BME-29(10), 700–707. https://doi.org/10.1109/TBME.1982.324863
Selvester, R. H., Strauss, D. G., & Wagner, G. S. (2010). Myocardial Infarction BT - Comprehensive Electrocardiology. Springer Verlag. https://doi.org/10.1007/978-1-84882-046-3_16
Starc, V., & Schlegel, T. T. (2020). Moving Dipole Determination from 12-Lead ECGs Can Improve Detection of Acute Myocardial Ischemia. Computing in Cardiology, 2020-September. https://doi.org/10.22489/CinC.2020.115
Starc, V., & Swenne, C. A. (2017). Spatial distribution and orientation of a single moving dipole computed in 12-lead ECGs of a healthy population using a spherically bounded model. Computing in Cardiology, 44, 1–4. https://doi.org/10.22489/CinC.2017.242-277
Strauss, D. G., Selvester, R. H., & Wagner, G. S. (2011). Defining left bundle branch block in the era of cardiac resynchronization therapy. In American Journal of Cardiology (Vol. 107, Issue 6, pp. 927–934). https://doi.org/10.1016/j.amjcard.2010.11.010
Svehlikova, J., Teplan, M., & Tysler, M. (2018). Geometrical constraint of sources in noninvasive localization of premature ventricular contractions. Journal of Electrocardiology, 51(3), 370–377. https://doi.org/10.1016/j.jelectrocard.2018.02.013
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Published
2023-12-24
How to Cite
DAWOD, I. A., SCHANZE, T., & ATROSHEY, S. M. S. (2023). MOVING DIPOLE LOCALIZATION USING LINEAR LEAST SQUARE ESTIMATION: A REVIEW. Journal of Duhok University, 26(2), 754 - 771. https://doi.org/10.26682/csjuod.2023.26.2.67
Section
Pure and Engineering Sciences
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