{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T14:53:39Z","timestamp":1768402419095,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T00:00:00Z","timestamp":1629504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000070","name":"National Institute of Biomedical Imaging and Bioengineering","doi-asserted-by":"publisher","award":["R01EB026710"],"award-info":[{"award-number":["R01EB026710"]}],"id":[{"id":"10.13039\/100000070","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bedside imaging of ventilation and perfusion is a leading application of 2-D medical electrical impedance tomography (EIT), in which dynamic cross-sectional images of the torso are created by numerically solving the inverse problem of computing the conductivity from voltage measurements arising on electrodes due to currents applied on electrodes on the surface. Methods of reconstruction may be direct or iterative. Calder\u00f3n\u2019s method is a direct reconstruction method based on complex geometrical optics solutions to Laplace\u2019s equation capable of providing real-time reconstructions in a region of interest. In this paper, the importance of accurate modeling of the electrode location on the body is demonstrated on simulated and experimental data, and a method of including a priori spatial information in dynamic human subject data is presented. The results of accurate electrode modeling and a spatial prior are shown to improve detection of inhomogeneities not included in the prior and to improve the resolution of ventilation and perfusion images in a human subject.<\/jats:p>","DOI":"10.3390\/s21165635","type":"journal-article","created":{"date-parts":[[2021,8,22]],"date-time":"2021-08-22T22:59:27Z","timestamp":1629673167000},"page":"5635","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Calder\u00f3n\u2019s Method with a Spatial Prior for 2-D EIT Imaging of Ventilation and Perfusion"],"prefix":"10.3390","volume":"21","author":[{"given":"Kwancheol","family":"Shin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chungbuk National University, Cheongju 28644, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2583-5771","authenticated-orcid":false,"given":"Jennifer L.","family":"Mueller","sequence":"additional","affiliation":[{"name":"Department of Mathematics and School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vincent, J.L. (2009). Electrical impedance tomography. Intensive Care Medicine, Springer.","DOI":"10.1007\/978-0-387-92278-2"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1088\/0967-3334\/33\/5\/695","article-title":"A review on electrical impedance tomography for pulmonary perfusion imaging","volume":"33","author":"Nguyen","year":"2012","journal-title":"Physiol. Meas."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1088\/0967-3334\/30\/4\/006","article-title":"The detection of pleural effusion using a parametric eit technique","volume":"30","author":"Arad","year":"2009","journal-title":"Physiol. Meas."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.1097\/CCM.0b013e31816a0380","article-title":"Real-time detection of pneumothorax using electrical impedance tomography","volume":"36","author":"Costa","year":"2008","journal-title":"Crit. Care Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1159\/000193994","article-title":"Assessment of changes in distribution of lung perfusion by electrical impedance tomography","volume":"77","author":"Frerichs","year":"2009","journal-title":"Respiration"},{"key":"ref_6","first-page":"1024","article-title":"Regional intratidal gas distribution in acute lung injury and acute respiratory distress syndrome\u2014Assessed by electric impedance tomography","volume":"76","author":"Lowhagen","year":"2010","journal-title":"Minerva Anestesiol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1097\/MCC.0b013e3283390cbf","article-title":"Impedance tomography as a new monitoring technique","volume":"16","author":"Muders","year":"2010","journal-title":"Curr. Opin. Crit. Care"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1111\/aas.12455","article-title":"Real-time ventilation and perfusion distributions by electrical impedance tomography during one-lung ventilation with capnothorax","volume":"59","author":"Reinius","year":"2015","journal-title":"Acta Anaesthesiol. Scand."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1164\/rccm.200301-133OC","article-title":"Imbalances in regional lung ventilation: A validation study on electrical impedance tomography","volume":"169","author":"Victorino","year":"2004","journal-title":"Am. J. Respir. Crit. Care Med."},{"key":"ref_10","unstructured":"Calder\u00f3n, A.P. (1980). On an inverse boundary value problem. Seminar on Numerical Analysis and Its Applications to Continuum Physics, Sociedade Brasileira de Matem\u00e0tica."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1137\/060656930","article-title":"D-Bar method for electrical impedance tomography with discontinuous conductivities","volume":"7","author":"Knudsen","year":"2007","journal-title":"SIAM J. Appl. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"124005","DOI":"10.1088\/1361-6420\/abb014","article-title":"A second order Calder\u00f3n\u2019s method with a correction term and a priori information","volume":"32","author":"Shin","year":"2020","journal-title":"Inverse Probl."},{"key":"ref_13","first-page":"71","article-title":"Global uniqueness of a two-dimensional inverse boundary value problem","volume":"2","author":"Nachman","year":"1966","journal-title":"Ann. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"43","DOI":"10.3934\/ipi.2008.2.43","article-title":"2D EIT reconstructions using Calder\u00f3n\u2019s method","volume":"2","author":"Bikowski","year":"2008","journal-title":"Inverse Probl. Imaging"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1088\/0967-3334\/34\/6\/609","article-title":"Calder\u00f3n\u2019s method on an elliptical domain","volume":"34","author":"Muller","year":"2013","journal-title":"Physiol. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1109\/TMI.2017.2695893","article-title":"Real-Time Implementation of Calder\u00f3n\u2019s Method on Subject-Specific Domains","volume":"36","author":"Muller","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Muller, P.A., and Mueller, J.L. (2018, January 25\u201329). Reconstruction of complex conductivities by calderon\u2019s method on subject-specific domains. Proceedings of the 2018 International Applied Computational Electromagnetics Society Symposium (ACES), Denver, CO, USA.","DOI":"10.23919\/ROPACES.2018.8364157"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1109\/TBME.2006.890139","article-title":"A reconstruction Algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry","volume":"54","author":"Choi","year":"2007","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1109\/TBME.2020.3039197","article-title":"Three dimensional Calder\u00f3n\u2019s method for EIT on the cylindrical geometry","volume":"68","author":"Shin","year":"2021","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1088\/0266-5611\/10\/2\/008","article-title":"An image-enhancement technique for electrical impedance tomography","volume":"10","author":"Dobson","year":"1994","journal-title":"Inverse Probl."},{"key":"ref_21","unstructured":"Camargo, E.D.L.B. (2013). Development of an Absolute Electrical Impedance Imaging Algorithm for Clinical Use, University of S\u00e3o Paulo."},{"key":"ref_22","first-page":"3000","article-title":"Toward Morphological Thoracic EIT: Major Signal Sources Correspond to Respective Organ Locations in CT","volume":"59","author":"Ferrario","year":"2012","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Flores-Tapia, D., and Pistorius, S. (September, January 31). Electrical impedance tomography reconstruction using a monotonicity approach based on a priori knowledge. Proceedings of the 2010 Annual International Conference of the IEEE, Buenos Aires, Argentina.","DOI":"10.1109\/IEMBS.2010.5627204"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1088\/0967-3334\/20\/1\/007","article-title":"Incorporating a priori anatomical information into image reconstruction in electrical impedance tomography","volume":"20","author":"Dehghani","year":"1999","journal-title":"Physiol. Meas."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1088\/0266-5611\/15\/3\/306","article-title":"Inverse problems with structural prior information","volume":"15","author":"Kaipio","year":"1999","journal-title":"Inverse Probl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/42.700740","article-title":"Tikhonov regularization and prior information in electrical impedance tomography","volume":"17","author":"Vauhkonen","year":"1998","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"A111","DOI":"10.1088\/0967-3334\/16\/3A\/011","article-title":"Incorporating a priori information into the Sheffield filtered backprojection algorithm","volume":"16","author":"Avis","year":"1995","journal-title":"Physiol. Meas."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1475-925X-5-8","article-title":"Electrical impedance tomography imaging using a priori ultrasound data","volume":"5","author":"Soleimani","year":"2006","journal-title":"BioMed. Eng. Online"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3589","DOI":"10.1088\/0031-9155\/43\/12\/015","article-title":"Use of a priori information in estimating tissue resistivities\u2014A simulation study","volume":"43","author":"Baysal","year":"1998","journal-title":"Phys. Med. Biol."},{"key":"ref_30","unstructured":"Alsaker, M. (2016). Computational Advancements in the D-Bar Reconstruction Method for 2-D Electrical Impedance Tomography. [Ph.D. Dissertation, Colorado State University]."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"427","DOI":"10.3934\/ipi.2017020","article-title":"A direct D-bar method for partial boundary data electrical impedance tomography with a prior information","volume":"11","author":"Alsaker","year":"2017","journal-title":"Inverse Probl. Imaging"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1137\/15M1020137","article-title":"A D-bar algorithm with a priori information for 2 dimensional electrical impedance tomography","volume":"9","author":"Alsaker","year":"2016","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"883","DOI":"10.3934\/ipi.2018037","article-title":"Use of an optimized spatial prior in D-bar reconstructions of EIT tank data","volume":"12","author":"Alsaker","year":"2018","journal-title":"Inverse Probl. Imaging"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4085","DOI":"10.1109\/TMI.2020.3012428","article-title":"Introduction of sample based prior into the D-Bar method through a Schur complement property","volume":"39","author":"Santos","year":"2020","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.cam.2018.07.039","article-title":"Dynamic optimized priors for D-bar reconstructions of human ventilation using electrical impedance tomography","volume":"362","author":"Alsaker","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2400","DOI":"10.1109\/TMI.2019.2900031","article-title":"A Statistical Shape-Constrained Reconstruction Framework for Electrical Impedance Tomography","volume":"38","author":"Ren","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1109\/TMI.2020.3030024","article-title":"Shape-Driven EIT Reconstruction Using Fourier Representations","volume":"40","author":"Liu","year":"2021","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1109\/TMI.2019.2961938","article-title":"B-Spline Level Set Method for Shape Reconstruction in Electrical Impedance Tomography","volume":"39","author":"Liu","year":"2020","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2937","DOI":"10.1109\/TMI.2019.2918566","article-title":"A Moving Morphable Components Based Shape Reconstruction Framework for Electrical Impedance Tomography","volume":"38","author":"Liu","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Evans, L.C. (2010). Partial Differential Equations, American Mathematical Society.","DOI":"10.1090\/gsm\/019"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1109\/TIM.2018.2874127","article-title":"The ACE1 Electrical Impedance Tomography System for Thoracic Imaging","volume":"68","author":"Mellenthin","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Mellenthin, M.M., Meuller, J.L., de Camargo, E.D.L.B., Moura, F.S.D., Himilton, S.J., and Lima, R.G. (2015, January 25\u201329). The ACE1 thoracic Electrical Impedance Tomography system for ventilation and perfusion. Proceedings of the 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milan, Italy.","DOI":"10.1109\/EMBC.2015.7319289"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"113591","DOI":"10.1016\/j.cam.2021.113591","article-title":"Complementary use of priors for pulmonary imaging with electrical impedance and ultrasound computed tomography","volume":"395","author":"Alsaker","year":"2021","journal-title":"J. Comput. Appl. Math."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1109\/TMI.2012.2237389","article-title":"Direct EIT reconstructions of complex admittivities on a chest-shaped domain in 2-D","volume":"32","author":"Hamilton","year":"2013","journal-title":"IEEE Trans. Med. Imaging"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5635\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:48:37Z","timestamp":1760165317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5635"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,21]]},"references-count":44,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["s21165635"],"URL":"https:\/\/doi.org\/10.3390\/s21165635","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,21]]}}}