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      Estimating uterine source current during contractions using magnetomyography measurements

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          Abstract

          Understanding the uterine source of the electrophysiological activity of contractions during pregnancy is of scientific interest and potential clinical applications. In this work, we propose a method to estimate uterine source currents from magnetomyography (MMG) temporal course measurements on the abdominal surface. In particular, we develop a linear forward model, based on the quasistatic Maxwell’s equations and a realistic four-compartment volume conductor, relating the magnetic fields to the source currents on the uterine surface through a lead-field matrix. To compute the lead-field matrix, we use a finite element method that considers the anisotropic property of the myometrium. We estimate the source currents by minimizing a constrained least-squares problem to solve the non-uniqueness issue of the inverse problem. Because we lack the ground truth of the source current, we propose to predict the intrauterine pressure from our estimated source currents by using an absolute-value-based method and compare the result with real abdominal deflection recorded during contractile activity. We test the feasibility of the lead-field matrix by displaying the lead fields that are generated by putative source currents at different locations in the myometrium: cervix and fundus, left and right, front and back. We then illustrate our method by using three synthetic MMG data sets, which are generated using our previously developed multiscale model of uterine contractions, and three real MMG data sets, one of which has simultaneous real abdominal deflection measurements. The numerical results demonstrate the ability of our method to capture the local contractile activity of human uterus during pregnancy. Moreover, the predicted intrauterine pressure is in fair agreement with the real abdominal deflection with respect to the timing of uterine contractions.

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          Most cited references36

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          Interpreting magnetic fields of the brain: minimum norm estimates

          The authors have applied estimation theory to the problem of determining primary current distributions from measured neuromagnetic fields. In this procedure, essentially nothing is assumed about the source currents, except that they are spatially restricted to a certain region. Simulation experiments show that the results can describe the structure of the current flow fairly well. By increasing the number of measurements, the estimate can be made more localised. The current distributions may be also used as an interpolation and an extrapolation for the measured field patterns.
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            Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem

            J Sarvas (1987)
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              Visualization of magnetoencephalographic data using minimum current estimates.

              The locations of active brain areas can be estimated from the magnetic field the neural current sources produce. In this work we study a visualization method of magnetoencephalographic data that is based on minimum[symbol: see text] (1)-norm estimates. The method can represent several local or distributed sources and does not need explicit a priori information. We evaluated the performance of the method using simulation studies. In a situation resembling typical magnetoencephalographic measurement, the mean estimated source strength exceeded baseline level up to 2 cm from the simulated point-like source. The method can also visualize several sources, activated simultaneously or in a sequence, which we demonstrated by analyzing magnetic responses associated with sensory stimulation and a picture naming task. Copyright 1999 Academic Press.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: InvestigationRole: MethodologyRole: ValidationRole: Writing – review & editing
                Role: Data curationRole: Funding acquisitionRole: InvestigationRole: Project administrationRole: ResourcesRole: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: ResourcesRole: SupervisionRole: Writing – original draftRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2018
                23 August 2018
                : 13
                : 8
                : e0202184
                Affiliations
                [1 ] Preston M. Green Department of Electrical and Systems Engineering, Washington University in Saint Louis, Saint Louis, Missouri, United States of America
                [2 ] Geospatial Analytics, Global IT Analytics, Monsanto Company, Saint Louis, Missouri, United States of America
                [3 ] Department of Obstetrics and Gynecology, University of Arkansas for Medical Sciences, Little Rock, Arkansas, United States of America
                PreTel, UNITED STATES
                Author notes

                Competing Interests: We have the following interests: Patricio S. La Rosa is employed by Monsanto Company. There are no patents, products in development or marketed products to declare. This does not alter our adherence to all the PLOS ONE policies on sharing data and materials, as detailed online in the guide for authors.

                Author information
                http://orcid.org/0000-0002-9055-9865
                Article
                PONE-D-17-39718
                10.1371/journal.pone.0202184
                6121809
                30138376
                eb234b86-5355-48f3-bb37-b5b3636b5327
                © 2018 Zhang et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 8 November 2017
                : 29 May 2018
                Page count
                Figures: 19, Tables: 2, Pages: 29
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/100000070, National Institute of Biomedical Imaging and Bioengineering;
                Award ID: R01EB016567
                Award Recipient :
                This study was funded by National Institute of Biomedical Imaging and Bioengineering ( https://www.nibib.nih.gov/) grant R01EB016567. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Monsanto Company provided support in the form of salaries for author PSL, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific role of this author is articulated in the ‘author contributions’ section.
                Categories
                Research Article
                Biology and Life Sciences
                Anatomy
                Reproductive System
                Uterus
                Medicine and Health Sciences
                Anatomy
                Reproductive System
                Uterus
                Physical Sciences
                Physics
                Condensed Matter Physics
                Magnetism
                Magnetic Fields
                Biology and Life Sciences
                Anatomy
                Reproductive System
                Uterus
                Myometrium
                Medicine and Health Sciences
                Anatomy
                Reproductive System
                Uterus
                Myometrium
                Biology and Life Sciences
                Anatomy
                Abdomen
                Medicine and Health Sciences
                Anatomy
                Abdomen
                Medicine and Health Sciences
                Women's Health
                Maternal Health
                Pregnancy
                Medicine and Health Sciences
                Women's Health
                Obstetrics and Gynecology
                Pregnancy
                Physical Sciences
                Materials Science
                Materials by Attribute
                Conductors
                Biology and Life Sciences
                Anatomy
                Reproductive System
                Genital Anatomy
                Cervix
                Medicine and Health Sciences
                Anatomy
                Reproductive System
                Genital Anatomy
                Cervix
                Biology and Life Sciences
                Physiology
                Electrophysiology
                Membrane Potential
                Action Potentials
                Medicine and Health Sciences
                Physiology
                Electrophysiology
                Membrane Potential
                Action Potentials
                Biology and Life Sciences
                Physiology
                Electrophysiology
                Neurophysiology
                Action Potentials
                Medicine and Health Sciences
                Physiology
                Electrophysiology
                Neurophysiology
                Action Potentials
                Biology and Life Sciences
                Neuroscience
                Neurophysiology
                Action Potentials
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                All relevant data are within the paper and its Supporting Information files.

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