Evaluation of Bipolar, Tripolar, and Quadripolar Laplacian Estimates of Electrocardiogram via Concentric Ring Electrodes

[EN] Surface Laplacian estimates via concentric ring electrodes (CREs) have proven to enhance spatial resolution compared to conventional disc electrodes, which is of great importance for P-wave analysis. In this study, Laplacian estimates for traditional bipolar configuration (BC), two tripolar configurations with linearly decreasing and increasing inter-ring distances (TCLDIRD and TCLIIRD, respectively), and quadripolar configuration (QC) were obtained from cardiac recordings with pentapolar CREs placed at CMV1 and CMV2 positions. Normalized P-wave amplitude (NAP) was computed to assess the contrast to study atrial activity. Signals were of good quality (20-30 dB). Atrial activity was more emphasized at CMV1 (NAP similar or equal to 0.19-0.24) compared to CMV2 (NAP similar or equal to 0.08-0.10). Enhanced spatial resolution of TCLIIRD and QC resulted in higher NAP values than BC and TCLDIRD. Comparison with simultaneous standard 12-lead ECG proved that Laplacian estimates at CMV1 outperformed all the limb and chest standard leads in the contrast to study P-waves. Clinical recordings with CRE at this position could allow more detailed observation of atrial activity and facilitate the diagnosis of associated pathologies. Furthermore, such recordings would not require additional electrodes on limbs and could be performed wirelessly, so it should also be suitable for ambulatory monitoring, for example, using cardiac Holter monitors.This research was funded by the National Science Foundation (NSF) Division of Human Resource Development (HRD) Tribal Colleges and Universities Program (TCUP), grants number 1622481 and 1914787 to O.M.Garcia-Casado, J.; Ye Lin, Y.; Prats-Boluda, G.; Makeyev, O. (2019). Evaluation of Bipolar, Tripolar, and Quadripolar Laplacian Estimates of Electrocardiogram via Concentric Ring Electrodes. Sensors. 19(17):1-11. https://doi.org/10.3390/s19173780S1111917Roth, G. A., Johnson, C., Abajobir, A., Abd-Allah, F., Abera, S. F., Abyu, G., … Alam, K. (2017). Global, Regional, and National Burden of Cardiovascular Diseases for 10 Causes, 1990 to 2015. Journal of the American College of Cardiology, 70(1), 1-25. doi:10.1016/j.jacc.2017.04.052Lopez, A. D., Mathers, C. D., Ezzati, M., Jamison, D. T., & Murray, C. J. (2006). Global and regional burden of disease and risk factors, 2001: systematic analysis of population health data. The Lancet, 367(9524), 1747-1757. doi:10.1016/s0140-6736(06)68770-9Bhatnagar, P., Wickramasinghe, K., Wilkins, E., & Townsend, N. (2016). Trends in the epidemiology of cardiovascular disease in the UK. Heart, 102(24), 1945-1952. doi:10.1136/heartjnl-2016-309573https://healthmetrics.heart.org/cardiovascular-disease-a-costly-burden/Leal, J., Luengo-Fernández, R., Gray, A., Petersen, S., & Rayner, M. (2006). Economic burden of cardiovascular diseases in the enlarged European Union. European Heart Journal, 27(13), 1610-1619. doi:10.1093/eurheartj/ehi733Wang, Y., Cuculich, P. S., Zhang, J., Desouza, K. A., Vijayakumar, R., Chen, J., … Rudy, Y. (2011). Noninvasive Electroanatomic Mapping of Human Ventricular Arrhythmias with Electrocardiographic Imaging. Science Translational Medicine, 3(98), 98ra84-98ra84. doi:10.1126/scitranslmed.3002152SippensGroenewegen, A., Peeters, H. A. P., Jessurun, E. R., Linnenbank, A. C., Robles de Medina, E. O., Lesh, M. D., & van Hemel, N. M. (1998). Body Surface Mapping During Pacing at Multiple Sites in the Human Atrium. Circulation, 97(4), 369-380. doi:10.1161/01.cir.97.4.369Kornreich, F., MacLeod, R. S., & Lux, R. L. (2008). Supplemented standard 12-lead electrocardiogram for optimal diagnosis and reconstruction of significant body surface map patterns. Journal of Electrocardiology, 41(3), 251-256. doi:10.1016/j.jelectrocard.2008.02.011Fereniec, M., Stix, G., Kania, M., Mroczka, T., & Maniewski, R. (2013). An Analysis of the U-Wave and Its Relation to the T-Wave in Body Surface Potential Maps for Healthy Subjects and MI Patients. Annals of Noninvasive Electrocardiology, 19(2), 145-156. doi:10.1111/anec.12110Lian, J., Li, G., Cheng, J., Avitall, B., & He, B. (2002). Body surface Laplacian mapping of atrial depolarization in healthy human subjects. Medical & Biological Engineering & Computing, 40(6), 650-659. doi:10.1007/bf02345304Wu, D., Tsai, H. C., & He, B. (1999). On the Estimation of the Laplacian Electrocardiogram during Ventricular Activation. Annals of Biomedical Engineering, 27(6), 731-745. doi:10.1114/1.224He, B., & Cohen, R. J. (1992). Body surface Laplacian mapping of cardiac electrical activity. The American Journal of Cardiology, 70(20), 1617-1620. doi:10.1016/0002-9149(92)90471-aHe, B., & Cohen, R. J. (1992). Body surface Laplacian ECG mapping. IEEE Transactions on Biomedical Engineering, 39(11), 1179-1191. doi:10.1109/10.168684He, B., & Cohen, R. J. (1995). Body Surface Laplacian Electrocardiographic Mapping−A Review. Critical Reviews in Biomedical Engineering, 23(5-6), 475-510. doi:10.1615/critrevbiomedeng.v23.i5-6.30UMETANI, K., OKAMOTO, Y., MASHIMA, S., ONO, K., HOSAKA, H., & HE, B. (1998). Body Surface Laplacian Mapping in Patients with Left or Right Ventricular Bundle Branch Block. Pacing and Clinical Electrophysiology, 21(11), 2043-2054. doi:10.1111/j.1540-8159.1998.tb01122.xBin He, Guanglin Li, & Jie Lian. (2002). A spline Laplacian ECG estimator in a realistic geometry volume conductor. IEEE Transactions on Biomedical Engineering, 49(2), 110-117. doi:10.1109/10.979350Besio, G., Koka, K., Aakula, R., & Weizhong Dai. (2006). Tri-polar concentric ring electrode development for Laplacian electroencephalography. IEEE Transactions on Biomedical Engineering, 53(5), 926-933. doi:10.1109/tbme.2005.863887Besio, W., Aakula, R., Koka, K., & Dai, W. (2006). Development of a Tri-polar Concentric Ring Electrode for Acquiring Accurate Laplacian Body Surface Potentials. Annals of Biomedical Engineering, 34(3), 426-435. doi:10.1007/s10439-005-9054-8Besio, W., & Chen, T. (2007). Tripolar Laplacian electrocardiogram and moment of activation isochronal mapping. Physiological Measurement, 28(5), 515-529. doi:10.1088/0967-3334/28/5/006Prats-Boluda, G., Garcia-Casado, J., Martinez-de-Juan, J. L., & Ye-Lin, Y. (2011). Active concentric ring electrode for non-invasive detection of intestinal myoelectric signals. Medical Engineering & Physics, 33(4), 446-455. doi:10.1016/j.medengphy.2010.11.009Prats-Boluda, G., Ye-Lin, Y., Bueno-Barrachina, J., Rodriguez de Sanabria, R., & Garcia-Casado, J. (2016). Towards the clinical use of concentric electrodes in ECG recordings: influence of ring dimensions and electrode position. Measurement Science and Technology, 27(2), 025705. doi:10.1088/0957-0233/27/2/025705Zena-Giménez, V., Garcia-Casado, J., Ye-Lin, Y., Garcia-Breijo, E., & Prats-Boluda, G. (2018). A Flexible Multiring Concentric Electrode for Non-Invasive Identification of Intestinal Slow Waves. Sensors, 18(2), 396. doi:10.3390/s18020396Ye-Lin, Y., Alberola-Rubio, J., Prats-boluda, G., Perales, A., Desantes, D., & Garcia-Casado, J. (2014). Feasibility and Analysis of Bipolar Concentric Recording of Electrohysterogram with Flexible Active Electrode. Annals of Biomedical Engineering, 43(4), 968-976. doi:10.1007/s10439-014-1130-5Wang, K., Parekh, U., Pailla, T., Garudadri, H., Gilja, V., & Ng, T. N. (2017). Stretchable Dry Electrodes with Concentric Ring Geometry for Enhancing Spatial Resolution in Electrophysiology. Advanced Healthcare Materials, 6(19), 1700552. doi:10.1002/adhm.201700552Lidón-Roger, J., Prats-Boluda, G., Ye-Lin, Y., Garcia-Casado, J., & Garcia-Breijo, E. (2018). Textile Concentric Ring Electrodes for ECG Recording Based on Screen-Printing Technology. Sensors, 18(1), 300. doi:10.3390/s18010300Makeyev, O., Ding, Q., & Besio, W. G. (2016). Improving the accuracy of Laplacian estimation with novel multipolar concentric ring electrodes. Measurement, 80, 44-52. doi:10.1016/j.measurement.2015.11.017Makeyev, O., & Besio, W. (2016). Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes. Sensors, 16(6), 858. doi:10.3390/s16060858Makeyev, O. (2018). Solving the general inter-ring distances optimization problem for concentric ring electrodes to improve Laplacian estimation. BioMedical Engineering OnLine, 17(1). doi:10.1186/s12938-018-0549-6Ye-Lin, Y., Bueno-Barrachina, J. M., Prats-boluda, G., Rodriguez de Sanabria, R., & Garcia-Casado, J. (2017). Wireless sensor node for non-invasive high precision electrocardiographic signal acquisition based on a multi-ring electrode. Measurement, 97, 195-202. doi:10.1016/j.measurement.2016.11.009Prats-Boluda, G., Ye-Lin, Y., Pradas-Novella, F., Garcia-Breijo, E., & Garcia-Casado, J. (2018). Textile Concentric Ring Electrodes: Influence of Position and Electrode Size on Cardiac Activity Monitoring. Journal of Sensors, 2018, 1-9. doi:10.1155/2018/7290867Huiskamp, G. (1991). Difference formulas for the surface Laplacian on a triangulated surface. Journal of Computational Physics, 95(2), 477-496. doi:10.1016/0021-9991(91)90286-tHamilton, P. S., & Tompkins, W. J. (1986). Quantitative Investigation of QRS Detection Rules Using the MIT/BIH Arrhythmia Database. IEEE Transactions on Biomedical Engineering, BME-33(12), 1157-1165. doi:10.1109/tbme.1986.325695Koka, K., & Besio, W. G. (2007). Improvement of spatial selectivity and decrease of mutual information of tri-polar concentric ring electrodes. Journal of Neuroscience Methods, 165(2), 216-222. doi:10.1016/j.jneumeth.2007.06.007Prats-Boluda, G., Ye-Lin, Y., Bueno Barrachina, J. M., Senent, E., Rodriguez de Sanabria, R., & Garcia-Casado, J. (2015). Development of a portable wireless system for bipolar concentric ECG recording. Measurement Science and Technology, 26(7), 075102. doi:10.1088/0957-0233/26/7/07510

Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs

[EN] Currently, the management of water networks is key to increase their sustainability. This fact implies that water managers have to develop tools that ease the decision-making process in order to improve the efficiency of irrigation networks, as well as their exploitation costs. The present research proposes a mathematical programming model to optimize the selection of the water sources and the volume over time in water networks, minimizing the operation costs as a function of the water demand and the reservoir capacity. The model, which is based on fuzzy methods, improves the evaluation performed by water managers when they have to decide about the acquisition of the water resources under uncertain costs. Different fuzzy solution approaches have been applied and assessed in terms of model complexity and computational efficiency, showing the solution accomplished for each one. A comparison between different methods was applied in a real water network, reaching a 20% total cost reduction for the best solution.Sanchis, R.; Díaz-Madroñero Boluda, FM.; López Jiménez, PA.; Pérez-Sánchez, M. (2019). Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs. Water. 11(12):1-22. https://doi.org/10.3390/w11122432S1221112Biswas, A. K. (2004). Integrated Water Resources Management: A Reassessment. Water International, 29(2), 248-256. doi:10.1080/02508060408691775Pahl-Wostl, C. (2006). Transitions towards adaptive management of water facing climate and global change. Water Resources Management, 21(1), 49-62. doi:10.1007/s11269-006-9040-4Wu, K., & Zhang, L. (2014). Progress in the Development of Environmental Risk Assessment as a Tool for the Decision-Making Process. Journal of Service Science and Management, 07(02), 131-143. doi:10.4236/jssm.2014.72011Hernández-Bedolla, J., Solera, A., Paredes-Arquiola, J., Pedro-Monzonís, M., Andreu, J., & Sánchez-Quispe, S. (2017). The Assessment of Sustainability Indexes and Climate Change Impacts on Integrated Water Resource Management. Water, 9(3), 213. doi:10.3390/w9030213Hunink, J., Simons, G., Suárez-Almiñana, S., Solera, A., Andreu, J., Giuliani, M., … Bastiaanssen, W. (2019). A Simplified Water Accounting Procedure to Assess Climate Change Impact on Water Resources for Agriculture across Different European River Basins. Water, 11(10), 1976. doi:10.3390/w11101976Pérez-Sánchez, M., Sánchez-Romero, F., Ramos, H., & López-Jiménez, P. (2016). Modeling Irrigation Networks for the Quantification of Potential Energy Recovering: A Case Study. Water, 8(6), 234. doi:10.3390/w8060234Corominas, J. (2010). Agua y energía en el riego, en la época de la sostenibilidad. Ingeniería del agua, 17(3). doi:10.4995/ia.2010.2977Romero, L., Pérez-Sánchez, M., & Amparo López-Jiménez, P. (2017). Improvement of sustainability indicators when traditional water management changes: a case study in Alicante (Spain). AIMS Environmental Science, 4(3), 502-522. doi:10.3934/environsci.2017.3.502Davies, E. G. R., & Simonovic, S. P. (2011). Global water resources modeling with an integrated model of the social–economic–environmental system. Advances in Water Resources, 34(6), 684-700. doi:10.1016/j.advwatres.2011.02.010ALCAMO, J., DÖLL, P., HENRICHS, T., KASPAR, F., LEHNER, B., RÖSCH, T., & SIEBERT, S. (2003). Development and testing of the WaterGAP 2 global model of water use and availability. Hydrological Sciences Journal, 48(3), 317-337. doi:10.1623/hysj.48.3.317.45290Sanchis, R., & Poler, R. (2019). Enterprise Resilience Assessment—A Quantitative Approach. Sustainability, 11(16), 4327. doi:10.3390/su11164327Rahaman, M. M., & Varis, O. (2005). Integrated water resources management: evolution, prospects and future challenges. Sustainability: Science, Practice and Policy, 1(1), 15-21. doi:10.1080/15487733.2005.11907961Markantonis, V., Reynaud, A., Karabulut, A., El Hajj, R., Altinbilek, D., Awad, I. M., … Bidoglio, G. (2019). Can the Implementation of the Water-Energy-Food Nexus Support Economic Growth in the Mediterranean Region? The Current Status and the Way Forward. Frontiers in Environmental Science, 7. doi:10.3389/fenvs.2019.00084Food and Agriculture Organization (FAO)www.fao.orgDirective 2000/60/EC of the European Parliament and of the Councilhttps://eur-lex.europa.eu/eli/dir/2000/60/ojNamany, S., Al-Ansari, T., & Govindan, R. (2019). Sustainable energy, water and food nexus systems: A focused review of decision-making tools for efficient resource management and governance. Journal of Cleaner Production, 225, 610-626. doi:10.1016/j.jclepro.2019.03.304Archibald, T. W., & Marshall, S. E. (2018). Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty. Environmental Modeling & Assessment, 23(6), 753-777. doi:10.1007/s10666-018-9628-0Chen, S., Shao, D., Gu, W., Xu, B., Li, H., & Fang, L. (2017). An interval multistage water allocation model for crop different growth stages under inputs uncertainty. Agricultural Water Management, 186, 86-97. doi:10.1016/j.agwat.2017.03.001Xie, Y. L., Xia, D. H., Huang, G. H., Li, W., & Xu, Y. (2015). A multistage stochastic robust optimization model with fuzzy probability distribution for water supply management under uncertainty. Stochastic Environmental Research and Risk Assessment, 31(1), 125-143. doi:10.1007/s00477-015-1164-8Heumesser, C., Fuss, S., Szolgayová, J., Strauss, F., & Schmid, E. (2012). Investment in Irrigation Systems under Precipitation Uncertainty. Water Resources Management, 26(11), 3113-3137. doi:10.1007/s11269-012-0053-xPereira-Cardenal, S. J., Mo, B., Riegels, N. D., Arnbjerg-Nielsen, K., & Bauer-Gottwein, P. (2015). Optimization of Multipurpose Reservoir Systems Using Power Market Models. Journal of Water Resources Planning and Management, 141(8), 04014100. doi:10.1061/(asce)wr.1943-5452.0000500Kumari, S., & Mujumdar, P. P. (2017). Fuzzy Set–Based System Performance Evaluation of an Irrigation Reservoir System. Journal of Irrigation and Drainage Engineering, 143(5), 04017002. doi:10.1061/(asce)ir.1943-4774.0001155Jairaj, P. G., & Vedula, S. (2000). Water Resources Management, 14(6), 457-472. doi:10.1023/a:1011117918943Li, M., Guo, P., Singh, V. P., & Zhao, J. (2016). Irrigation Water Allocation Using an Inexact Two-Stage Quadratic Programming with Fuzzy Input under Climate Change. JAWRA Journal of the American Water Resources Association, 52(3), 667-684. doi:10.1111/1752-1688.12415Bozorg-Haddad, O., Malmir, M., Mohammad-Azari, S., & Loáiciga, H. A. (2016). Estimation of farmers’ willingness to pay for water in the agricultural sector. Agricultural Water Management, 177, 284-290. doi:10.1016/j.agwat.2016.08.011Raju, K. S., & Duckstein, L. (2003). Multiobjective fuzzy linear programming for sustainable irrigation planning: an Indian case study. Soft Computing - A Fusion of Foundations, Methodologies and Applications, 7(6), 412-418. doi:10.1007/s00500-002-0230-6Regulwar, D. G., & Gurav, J. B. (2012). Sustainable Irrigation Planning with Imprecise Parameters under Fuzzy Environment. Water Resources Management, 26(13), 3871-3892. doi:10.1007/s11269-012-0109-yMula, J., Poler, R., & Garcia-Sabater, J. P. (2008). Capacity and material requirement planning modelling by comparing deterministic and fuzzy models. International Journal of Production Research, 46(20), 5589-5606. doi:10.1080/00207540701413912Díaz-Madroñero, M., Mula, J., Jiménez, M., & Peidro, D. (2016). A rolling horizon approach for material requirement planning under fuzzy lead times. International Journal of Production Research, 55(8), 2197-2211. doi:10.1080/00207543.2016.1223382Mula, J., Poler, R., & Garcia, J. P. (2006). MRP with flexible constraints: A fuzzy mathematical programming approach. Fuzzy Sets and Systems, 157(1), 74-97. doi:10.1016/j.fss.2005.05.045Mula, J., Poler, R., & Garcia-Sabater, J. P. (2007). Material Requirement Planning with fuzzy constraints and fuzzy coefficients. Fuzzy Sets and Systems, 158(7), 783-793. doi:10.1016/j.fss.2006.11.003Díaz-Madroñero, M., Mula, J., & Jiménez, M. (2014). Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions. International Journal of Production Research, 52(23), 6971-6988. doi:10.1080/00207543.2014.920115Pérez-Sánchez, M., Díaz-Madroñero, M., Díaz-Madroñero, D.-M., … Josefa, J. (2017). Mathematical Programming Model for Procurement Selection in Water Irrigation Systems. A Case Study. Journal of Engineering Science and Technology Review, 10(6), 154-162. doi:10.25103/jestr.106.19Herrera, F., & Verdegay, J. L. (1995). Three models of fuzzy integer linear programming. European Journal of Operational Research, 83(3), 581-593. doi:10.1016/0377-2217(93)e0338-xHerrera, F., & Verdegay, J. L. (1996). Fuzzy boolean programming problems with fuzzy costs: A general study. Fuzzy Sets and Systems, 81(1), 57-76. doi:10.1016/0165-0114(94)00324-6Alavidoost, M. H., Babazadeh, H., & Sayyari, S. T. (2016). An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem. Applied Soft Computing, 40, 221-235. doi:10.1016/j.asoc.2015.11.025Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193-214. doi:10.1016/j.fss.2007.08.010Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24(2), 143-161. doi:10.1016/0020-0255(81)90017-7Lai, Y.-J., & Hwang, C.-L. (1992). A new approach to some possibilistic linear programming problems. Fuzzy Sets and Systems, 49(2), 121-133. doi:10.1016/0165-0114(92)90318-xZimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55. doi:10.1016/0165-0114(78)90031-3Selim, H., & Ozkarahan, I. (2006). A supply chain distribution network design model: An interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3-4), 401-418. doi:10.1007/s00170-006-0842-6Bellman, R. E., & Zadeh, L. A. (1970). Decision-Making in a Fuzzy Environment. Management Science, 17(4), B-141-B-164. doi:10.1287/mnsc.17.4.b14