Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue
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{"title"=>"Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue", "type"=>"journal", "authors"=>[{"first_name"=>"Rupamanjari", "last_name"=>"Majumder", "scopus_author_id"=>"37072922000"}, {"first_name"=>"Alok Ranjan", "last_name"=>"Nayak", "scopus_author_id"=>"26421359300"}, {"first_name"=>"Rahul", "last_name"=>"Pandit", "scopus_author_id"=>"56261443900"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"365821734", "issn"=>"19326203", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "doi"=>"10.1371/journal.pone.0045040", "scopus"=>"2-s2.0-84867324822", "pmid"=>"23071505", "sgr"=>"84867324822"}, "id"=>"35f4aac0-5df7-319a-8948-772b3956094a", "abstract"=>"We present a comprehensive numerical study of spiral- and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to N(f) fibroblasts via a gap-junctional conductance G(gap), reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage P(f) of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.", "link"=>"http://www.mendeley.com/research/nonequilibrium-arrhythmic-states-transitions-mathematical-model-diffuse-fibrosis-human-cardiac-tissu", "reader_count"=>25, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>4, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>6, "Student > Master"=>3, "Student > Bachelor"=>1, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>4, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>6, "Student > Master"=>3, "Student > Bachelor"=>1, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Engineering"=>6, "Unspecified"=>3, "Biochemistry, Genetics and Molecular Biology"=>2, "Mathematics"=>2, "Medicine and Dentistry"=>1, "Agricultural and Biological Sciences"=>2, "Physics and Astronomy"=>8, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>6}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Computer Science"=>{"Computer Science"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}, "Mathematics"=>{"Mathematics"=>2}, "Unspecified"=>{"Unspecified"=>3}}, "reader_count_by_country"=>{"South Korea"=>1, "Israel"=>1, "India"=>1, "Spain"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["http://files.figshare.com/563751/Figure_18.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["illustrating", "isosurface", "membrane", "myocytes", "simulation", "plots", "3d", "mural", "scroll-wave"], "title"=>"<p>Pseudocolor isosurface plots of the local membrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e456&amp;representation=PNG\"> illustrating scroll-wave dynamics in a mural slice of our 3D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Pseudocolor_isosurface_plots_of_the_local_membrane_potential_illustrating_scroll_wave_dynamics_in_a_mural_slice_of_our_3D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/234239", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g018"], "published_date"=>"2012-10-08 01:10:39", "article_id"=>234239, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>We obtain three qualitatively different behaviors, namely, <b>SRS</b> (Single Rotating Scroll), <b>MRSP</b> (Multiple Rotating Scrolls), and <b>SA</b> (Scroll Absorption). Illustrative pseudocolor plots with isosurface slicing of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e457&amp;representation=PNG\"> show the time evolution of a scroll wave for (a.1)–(a.3) <b>SRS</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e458&amp;representation=PNG\">, (b.1)–(b.3) <b>MRS</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e459&amp;representation=PNG\">, and (c.1)–(c.5) <b>SA</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e460&amp;representation=PNG\">. (For full spatiotemporal evolutions see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.s006\" target=\"_blank\">Video S6</a>.).</p>"}
  • {"files"=>["http://files.figshare.com/562084/Figure_4.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["transmembrane", "recorded", "mf"], "title"=>"<p>Representative time series of the transmembrane potential recorded from an MF composite.</p>", "figshare_url"=>"http://figshare.com/articles/_Representative_time_series_of_the_transmembrane_potential_recorded_from_an_MF_composite_/232578", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g004"], "published_date"=>"2012-10-08 00:42:58", "article_id"=>232578, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Plots of the transmembrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e228&amp;representation=PNG\"> of the myocyte in the myocyte-fibroblast (MF) composite versus time <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e229&amp;representation=PNG\"> for the strong-coupling case <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e230&amp;representation=PNG\"> nS showing the following: responses of type <b>R1</b> for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e231&amp;representation=PNG\">, <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e232&amp;representation=PNG\"> mV, and (a.1) epicardial myocytes, (a.2) mid-myocardial myocytes, and (a.3) endocardial myocytes; responses of type <b>R2</b> for (b.1) epicardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e233&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e234&amp;representation=PNG\"> mV, (b.2) mid-myocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e235&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e236&amp;representation=PNG\"> mV, and (b.3) endocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e237&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e238&amp;representation=PNG\"> mV; autorhythmic responses of type <b>R3</b> for (c.1) epicardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e239&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e240&amp;representation=PNG\"> mV, (c.2) mid-myocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e241&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e242&amp;representation=PNG\"> mV, and (c.3) endocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e243&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e244&amp;representation=PNG\"> mV; oscillatory responses of type <b>R4</b> for (d.1) epicardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e245&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e246&amp;representation=PNG\"> mV, (d.2) mid-myocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e247&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e248&amp;representation=PNG\"> mV, and (d.3) endocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e249&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e250&amp;representation=PNG\"> mV; responses of type <b>R5</b> for (e.1) epicardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e251&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e252&amp;representation=PNG\"> mV, (e.2) mid-myocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e253&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e254&amp;representation=PNG\"> mV, and (e.3) endocardial myocytes and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e255&amp;representation=PNG\">, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e256&amp;representation=PNG\"> mV.</p>"}
  • {"files"=>["http://files.figshare.com/561738/Figure_1.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "spiral", "3d", "scroll", "configurations", "waves", "simulations"], "title"=>"<p>The initial configurations for the spiral and scroll waves in our 2D and 3D simulations (see text).</p>", "figshare_url"=>"http://figshare.com/articles/_The_initial_configurations_for_the_spiral_and_scroll_waves_in_our_2D_and_3D_simulations_see_text_/232219", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g001"], "published_date"=>"2012-10-08 00:36:59", "article_id"=>232219, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>The initial configurations for the spiral and scroll waves in our 2D and 3D simulations (see text).</p>"}
  • {"files"=>["http://files.figshare.com/1566021/Video_S1", "http://files.figshare.com/1566022/Video_S2", "http://files.figshare.com/1566023/Video_S3", "http://files.figshare.com/1566024/Video_S4", "http://files.figshare.com/1566025/Video_S5", "http://files.figshare.com/1566027/Video_S6"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>14, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["arrhythmic", "mathematical", "states", "cardiac", "transitions", "diffuse", "fibrosis"], "title"=>"<p>Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue</p>", "figshare_url"=>"http://figshare.com/articles/_Nonequilibrium_Arrhythmic_States_and_Transitions_in_a_Mathematical_Model_for_Diffuse_Fibrosis_in_Human_Cardiac_Tissue_/1083669", "defined_type"=>4, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.s001", "http://dx.doi.org/10.1371/journal.pone.0045040.s002", "http://dx.doi.org/10.1371/journal.pone.0045040.s003", "http://dx.doi.org/10.1371/journal.pone.0045040.s004", "http://dx.doi.org/10.1371/journal.pone.0045040.s005", "http://dx.doi.org/10.1371/journal.pone.0045040.s006"], "published_date"=>"2012-10-08 09:28:43", "article_id"=>1083669, "categories"=>["Biophysics", "Biological Sciences", "Physics"], "description"=>"<div><p>We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e001&amp;representation=PNG\"> fibroblasts via a gap-junctional conductance <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e002&amp;representation=PNG\">, reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e003&amp;representation=PNG\"> of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.</p> </div>"}
  • {"files"=>["http://files.figshare.com/563276/Figure_14.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "spiral-wave", "membrane", "myocytes", "simulation", "plots", "mural"], "title"=>"<p>Pseudocolor plots of the local membrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e374&amp;representation=PNG\"> illustrating spiral-wave dynamics in a mural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Pseudocolor_plots_of_the_local_membrane_potential_illustrating_spiral_wave_dynamics_in_a_mural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/233766", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g014"], "published_date"=>"2012-10-08 01:02:46", "article_id"=>233766, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>We obtain six qualitatively different behaviors, namely, <b>SRSP</b> (Single Rotating Spiral Periodic), <b>SRSQ</b> (Single Rotating Spiral Quasiperiodic), <b>MRSP</b> (Multiple Rotating Spirals Periodic), <b>MRSQ</b> (Multiple Rotating Spirals Quasiperiodic), <b>ST</b> (Spiral Turbulence), and <b>SA</b> (Spiral Absorption). Illustrative pseudocolor plots of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e375&amp;representation=PNG\"> show the time evolution of a spiral wave for (a.1)–(a.5) <b>SRSP</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e376&amp;representation=PNG\">, (b.1)–(b.5) <b>SRSQ</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e377&amp;representation=PNG\">, (c.1)–(c.5) <b>MRSP</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e378&amp;representation=PNG\">, (d.1)–(d.5) <b>MRSQ</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e379&amp;representation=PNG\">, (e.1)–(e.5) <b>ST</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e380&amp;representation=PNG\">, and (f.1)–(f.5) <b>SA</b> with <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e381&amp;representation=PNG\">. (For full spatiotemporal evolutions see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.s005\" target=\"_blank\">Video S5</a>.).</p>"}
  • {"files"=>["http://files.figshare.com/562704/Figure_9.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "plane-wave", "transmural", "membrane", "myocytes", "propagation", "plots", "simulation"], "title"=>"<p>Pseudocolor plots of the local membrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e303&amp;representation=PNG\"> illustrating plane-wave propagation through a transmural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Pseudocolor_plots_of_the_local_membrane_potential_illustrating_plane_wave_propagation_through_a_transmural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/233191", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g009"], "published_date"=>"2012-10-08 00:53:11", "article_id"=>233191, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Here we consider the moderate-coupling case <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e304&amp;representation=PNG\"> cm<sup>2</sup>/ms, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e305&amp;representation=PNG\"> and in (a.1)–(a.5) the percentage of fibroblasts <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e306&amp;representation=PNG\">, in (b.1)–(b.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e307&amp;representation=PNG\">, in (c.1)–(c.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e308&amp;representation=PNG\">, in (d.1)–(d.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e309&amp;representation=PNG\">, in (e.1)–(e.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e310&amp;representation=PNG\">, and in (f.1)–(f.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e311&amp;representation=PNG\">. As <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e312&amp;representation=PNG\"> increases, not only does the distortion of the wavefront increase but the wave also propagates preferentially through the zone that has epicardial myocytes (rather than the zones with mid-myocardial and endocardial myocytes).(For full spatiotemporal evolutions see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.s003\" target=\"_blank\">Video S3</a>.).</p>"}
  • {"files"=>["http://files.figshare.com/563400/Figure_15.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "high-order", "temporal", "propagation", "spiral-wave", "myocytes", "cycles", "mural", "simulation"], "title"=>"<p>Time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e385&amp;representation=PNG\"> illustrating high-order temporal cycles during spiral-wave propagation in a mural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Time_series_of_illustrating_high_order_temporal_cycles_during_spiral_wave_propagation_in_a_mural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/233884", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g015"], "published_date"=>"2012-10-08 01:04:44", "article_id"=>233884, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Plots of the time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e386&amp;representation=PNG\">, from representative points in the simulation domain, and the resulting plots of the interbeat interval IBI versus the beat number <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e387&amp;representation=PNG\"> and the power spectrum <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e388&amp;representation=PNG\"> versus the frequency <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e389&amp;representation=PNG\"> illustrating temporal <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e390&amp;representation=PNG\">-cycles (a.1)–(a.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e391&amp;representation=PNG\">, <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e392&amp;representation=PNG\">-cycles (b.1)–(b.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e393&amp;representation=PNG\">), <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e394&amp;representation=PNG\">-cycles (c.1)–(c.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e395&amp;representation=PNG\">), and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e396&amp;representation=PNG\">-cycles (d.1)–(d.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e397&amp;representation=PNG\">; these cycles show up most clearly in the IBI plots (a.2), (b.2), (c.2), and (d.2); but their presence can also be surmised from the time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e398&amp;representation=PNG\"> (a.1), (b.1), (c.1), and (d.1) and the sharp peaks in the power spectra (a.3), (b.3), (c.3), and (d.3)).</p>"}
  • {"files"=>["http://files.figshare.com/562802/Figure_10.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "plane-wave", "propagation", "diagram", "myocytes", "transmural", "simulation"], "title"=>"<p>Stability diagram in the <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e313&amp;representation=PNG\"> plane for plane-wave propagation through a transmural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Stability_diagram_in_the_plane_for_plane_wave_propagation_through_a_transmural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/233291", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g010"], "published_date"=>"2012-10-08 00:54:51", "article_id"=>233291, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>The stability diagram shows the regions with spatiotemporal behaviors <b>R1&#8211;R5</b> in the strong-coupling case (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e314&amp;representation=PNG\">); the regions <b>R1</b>, <b>R2</b>, <b>R3</b>, <b>R4</b>, and <b>R5</b> are denoted, respectively, by blue diamonds, green triangles, pink pentagrams, black squares, and red circles; the spatiotemporal evolution of plane waves in these regions is described in the text.</p>"}
  • {"files"=>["http://files.figshare.com/563162/Figure_13.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["fibroblasts", "2d", "mid-myocardial", "myocytes", "simulation"], "title"=>"<p>Spiral-wave dynamics in the absence of fibroblasts (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e356&amp;representation=PNG\">) in a 2D simulation domain with myocytes of the mid-myocardial type.</p>", "figshare_url"=>"http://figshare.com/articles/_Spiral_wave_dynamics_in_the_absence_of_fibroblasts_in_a_2D_simulation_domain_with_myocytes_of_the_mid_myocardial_type_/233652", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g013"], "published_date"=>"2012-10-08 01:00:52", "article_id"=>233652, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>(A) Illustrative pseudocolor plot of the transmembrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e357&amp;representation=PNG\"> showing a spiral wave at <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e358&amp;representation=PNG\">. (B) A plot of the time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e359&amp;representation=PNG\"> recorded from the representative point <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e360&amp;representation=PNG\">; (C) a plot versus the frequency <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e361&amp;representation=PNG\"> of the power spectrum <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e362&amp;representation=PNG\"> of this time series; (D) a plot of the inter-beat interval (IBI) versus the beat number <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e363&amp;representation=PNG\"> for this time series (here we have discarded the first <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e364&amp;representation=PNG\"> beats to remove the initial transients.</p>"}
  • {"files"=>["http://files.figshare.com/563560/Figure_16.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "high-order", "temporal", "propagation", "spiral-wave", "myocytes", "cycles", "mural", "simulation"], "title"=>"<p>Time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e399&amp;representation=PNG\"> illustrating high-order temporal cycles during spiral-wave propagation in a mural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Time_series_of_illustrating_high_order_temporal_cycles_during_spiral_wave_propagation_in_a_mural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/234050", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g016"], "published_date"=>"2012-10-08 01:07:30", "article_id"=>234050, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Plots of the time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e400&amp;representation=PNG\">, from the representative point <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e401&amp;representation=PNG\">, and the resulting plots of the interbeat interval IBI versus the beat number <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e402&amp;representation=PNG\"> and the power spectrum <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e403&amp;representation=PNG\"> versus the frequency <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e404&amp;representation=PNG\"> illustrating temporal <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e405&amp;representation=PNG\">-cycles (a.1)–(a.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e406&amp;representation=PNG\">, <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e407&amp;representation=PNG\">-cycles (b.1)–(b.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e408&amp;representation=PNG\">), <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e409&amp;representation=PNG\">-cycles (c.1)–(c.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e410&amp;representation=PNG\">), and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e411&amp;representation=PNG\">-cycles (d.1)–(d.3) for <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e412&amp;representation=PNG\">; these cycles show up most clearly in the IBI plots (a.2), (b.2), (c.2), and (d.2); but their presence can also be surmised from the time series of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e413&amp;representation=PNG\"> (a.1), (b.1), (c.1), and (d.1) and the sharp peaks in the power spectra (a.3), (b.3), (c.3), and (d.3)).</p>"}
  • {"files"=>["http://files.figshare.com/562186/Figure_5.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["parameter", "diagrams", "mf", "responses"], "title"=>"<p>Stability diagrams in the <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e260&amp;representation=PNG\"> parameter space for the responses of an MF composite.</p>", "figshare_url"=>"http://figshare.com/articles/_Stability_diagrams_in_the_parameter_space_for_the_responses_of_an_MF_composite_/232675", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g005"], "published_date"=>"2012-10-08 00:44:35", "article_id"=>232675, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>The regions in which the MF composite shows responses of types <b>R1&#8211;R5</b> are shown in (a.1), (a.2), (b.1), (b.2), (c.1), and (c.2). For the moderate-coupling case, <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e261&amp;representation=PNG\"> nS, (a.1), (b.1), and (c.1) show the stability diagrams for, respectively, endocardial, mid-myocardial, and epicardial myocytes in the MF composite; their analogs for the strong-coupling case, <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e262&amp;representation=PNG\"> nS, are given in (a.2), (b.2), and (c.2); the régimes <b>R1</b>, <b>R2</b>, <b>R3</b>, <b>R4</b>, and <b>R5</b> are denoted, respectively, by yellow hexagrams, red squares, green circles, pink diamonds, and blue pentagrams.</p>"}
  • {"files"=>["http://files.figshare.com/561972/Figure_3.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["duration", "mf", "composite"], "title"=>"<p>Dependence of action potential duration (APD) of an MF composite on <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e212&amp;representation=PNG\"> and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e213&amp;representation=PNG\">.</p>", "figshare_url"=>"http://figshare.com/articles/_Dependence_of_action_potential_duration_APD_of_an_MF_composite_on_and_/232468", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g003"], "published_date"=>"2012-10-08 00:41:08", "article_id"=>232468, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Illustrative pseudocolor plots of the APD for MFs, with epicardial, mid-myocardial, and endocardial myocytes, as functions of the gap-junctional conductance <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e214&amp;representation=PNG\"> and the resting membrane potential of fibroblasts <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e215&amp;representation=PNG\">, for the number of coupled fibroblasts <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e216&amp;representation=PNG\"> = 1, 2, 3, and 4.</p>"}
  • {"files"=>["http://files.figshare.com/563677/Figure_17.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "3d", "spiral-wave", "states", "diagrams", "transitions", "illustrating", "scroll-wave"], "title"=>"<p>Representative band diagrams of states, in our 2D and in 3D studies, illustrating transitions between different spiral-wave (for 2D) and scroll-wave (for 3D) states as a function of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e430&amp;representation=PNG\">.</p>", "figshare_url"=>"http://figshare.com/articles/_Representative_band_diagrams_of_states_in_our_2D_and_in_3D_studies_illustrating_transitions_between_different_spiral_wave_for_2D_and_scroll_wave_for_3D_states_as_a_function_of_/234163", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g017"], "published_date"=>"2012-10-08 01:09:23", "article_id"=>234163, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Top panel: This band diagram shows the rich sequence of transitions, from one nonequilibrium state to another, that takes us from the state <b>SRSP</b>, which occurs predominantly at low values of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e431&amp;representation=PNG\">, to the state <b>SA</b>, which occurs at large values of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e432&amp;representation=PNG\">; the values of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e433&amp;representation=PNG\"> are given below the band and the six states <b>SRSP</b>- <b>SA</b> are shown by a gray scale. Bottom panel: This band diagram shows the sequence of transitions, from one nonequilibrium state to another, that takes us from the state <b>SRS</b>, which occurs predominantly at low values of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e434&amp;representation=PNG\">, to the state <b>SA</b>, which occurs at predominantly large values of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e435&amp;representation=PNG\">; the values of <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e436&amp;representation=PNG\"> are given below the band and the three states <b>SRS</b>- <b>SA</b> are shown by a gray scale. The fine resolution of the transitions in 2D (top panel) cannot be achieved easily in 3D (bottom panel) without a prohibitive increase in computational costs.</p>"}
  • {"files"=>["http://files.figshare.com/562570/Figure_8.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "plane-wave", "propagation", "membrane", "myocytes", "simulation", "plots", "mural"], "title"=>"<p>Pseudocolor plots of the local membrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e290&amp;representation=PNG\"> illustrating plane-wave propagation through a mural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Pseudocolor_plots_of_the_local_membrane_potential_illustrating_plane_wave_propagation_through_a_mural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/233059", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g008"], "published_date"=>"2012-10-08 00:50:59", "article_id"=>233059, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Here we consider the strong-coupling case and different régimes in the stability diagram of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone-0045040-g006\" target=\"_blank\">Fig. 6</a>; (a.1)–(a.4) propagation in régime <b>R1</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e291&amp;representation=PNG\">); (b.1)–(b.4) propagation in régime <b>R2</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e292&amp;representation=PNG\">); (c.1)–(c.4) propagation in régime <b>R3</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e293&amp;representation=PNG\">); (d.1)–(d.4) propagation in régime <b>R4</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e294&amp;representation=PNG\">); (e.1)–(e.4) propagation in régime <b>R5</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e295&amp;representation=PNG\">).(For full spatiotemporal evolutions see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.s002\" target=\"_blank\">Video S2</a>.).</p>"}
  • {"files"=>["http://files.figshare.com/562402/Figure_7.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "plane-wave", "propagation", "membrane", "myocytes", "simulation", "plots", "mural"], "title"=>"<p>Pseudocolor plots of the local membrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e281&amp;representation=PNG\"> illustrating plane-wave propagation through a mural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Pseudocolor_plots_of_the_local_membrane_potential_illustrating_plane_wave_propagation_through_a_mural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/232888", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g007"], "published_date"=>"2012-10-08 00:48:08", "article_id"=>232888, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Here we consider the moderate-coupling case <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e282&amp;representation=PNG\"> cm<sup>2</sup>/ms, and <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e283&amp;representation=PNG\"> and in (a.1)–(a.5) the percentage of fibroblasts <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e284&amp;representation=PNG\">, in (b.1)–(b.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e285&amp;representation=PNG\">, in (c.1)–(c.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e286&amp;representation=PNG\">, in (d.1)–(d.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e287&amp;representation=PNG\">, in (e.1)–(e.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e288&amp;representation=PNG\">, and in (f.1)–(f.5) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e289&amp;representation=PNG\">. (For full spatiotemporal evolutions see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.s001\" target=\"_blank\">Video S1</a>.).</p>"}
  • {"files"=>["http://files.figshare.com/562272/Figure_6.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "plane-wave", "propagation", "diagram", "myocytes", "simulation", "mural"], "title"=>"<p>Stability diagram in the <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e272&amp;representation=PNG\"> plane for plane-wave propagation through a mural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Stability_diagram_in_the_plane_for_plane_wave_propagation_through_a_mural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/232761", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g006"], "published_date"=>"2012-10-08 00:46:01", "article_id"=>232761, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>The stability diagram shows the regions with spatiotemporal behaviors <b>R1&#8211;R5</b> in the strong-coupling case (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e273&amp;representation=PNG\">); the regions <b>R1</b>, <b>R2</b>, <b>R3</b>, <b>R4</b>, and <b>R5</b> are denoted, respectively, by blue diamonds, green triangles, pink pentagrams, black squares, and red circles; the spatiotemporal evolution of plane waves in these regions is described in the text.</p>"}
  • {"files"=>["http://files.figshare.com/561820/Figure_2.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["fibroblasts", "myocytes", "simulation", "distributions"], "title"=>"<p>Spatial distributions of myocytes and fibroblasts in our simulation domain.</p>", "figshare_url"=>"http://figshare.com/articles/_Spatial_distributions_of_myocytes_and_fibroblasts_in_our_simulation_domain_/232315", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g002"], "published_date"=>"2012-10-08 00:38:35", "article_id"=>232315, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Illustrative plots of the distributions of fibroblasts and myocytes, on a representative <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e140&amp;representation=PNG\"> part of our simulation domain in two dimensions (2D). Fibroblasts (filled black squares) and myocytes (unfilled white squares) are distributed randomly in our simulation domain so that a given grid point contains either a myocyte or a fibroblast, but not both; the percentage of fibroblasts <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e141&amp;representation=PNG\"> is (A) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e142&amp;representation=PNG\">, (B) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e143&amp;representation=PNG\">, (C) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e144&amp;representation=PNG\">, (D) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e145&amp;representation=PNG\">, and (E) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e146&amp;representation=PNG\">. In (F) we show an illustrative arrangement of myocytes (pink circles) and fibroblasts (blue ellipses); for such an arrangement the diffusion terms are as given in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.e156\" target=\"_blank\">Eqs. 6</a>–<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.e158\" target=\"_blank\">8</a>.</p>"}
  • {"files"=>["http://files.figshare.com/562947/Figure_11.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["2d", "illustrating", "plane-wave", "transmural", "membrane", "myocytes", "propagation", "plots", "simulation"], "title"=>"<p>Pseudocolor plots of the local membrane potential <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e315&amp;representation=PNG\"> illustrating plane-wave propagation through a transmural slice of our 2D simulation domain with a random distribution of myocytes and fibroblasts.</p>", "figshare_url"=>"http://figshare.com/articles/_Pseudocolor_plots_of_the_local_membrane_potential_illustrating_plane_wave_propagation_through_a_transmural_slice_of_our_2D_simulation_domain_with_a_random_distribution_of_myocytes_and_fibroblasts_/233436", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g011"], "published_date"=>"2012-10-08 00:57:16", "article_id"=>233436, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Here we consider the strong-coupling case and different régimes in the stability diagram of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone-0045040-g010\" target=\"_blank\">Fig. 10</a>; (a.1)–(a.4) propagation in régime <b>R1</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e316&amp;representation=PNG\">); (b.1)–(b.4) propagation in régime <b>R2</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e317&amp;representation=PNG\">); (c.1)–(c.4) propagation in régime <b>R3</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e318&amp;representation=PNG\">); (d.1)–(d.4) propagation in régime <b>R4</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e319&amp;representation=PNG\">); (e.1)–(e.4) propagation in régime <b>R5</b> (<img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e320&amp;representation=PNG\">). (For full spatiotemporal evolutions see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045040#pone.0045040.s004\" target=\"_blank\">Video S4</a>.).</p>"}
  • {"files"=>["http://files.figshare.com/563074/Figure_12.tif"], "pos_in_sequence"=>0, "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "users"=>["Rupamanjari Majumder", "Alok Ranjan Nayak", "Rahul Pandit"], "links"=>[], "tags"=>["conduction", "plane-wave", "velocity", "wavelength", "dependence", "fibrosis"], "title"=>"<p>The dependence of the plane-wave conduction velocity <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e338&amp;representation=PNG\"> and wavelength <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e339&amp;representation=PNG\"> on the percentage of fibrosis <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e340&amp;representation=PNG\">.</p>", "figshare_url"=>"http://figshare.com/articles/_The_dependence_of_the_plane_wave_conduction_velocity_and_wavelength_on_the_percentage_of_fibrosis_/233567", "defined_type"=>1, "doi"=>["http://dx.doi.org/10.1371/journal.pone.0045040.g012"], "published_date"=>"2012-10-08 00:59:27", "article_id"=>233567, "categories"=>["Biophysics", "Physics", "Biological Sciences", "Information And Computing Sciences"], "description"=>"<p>Plots of (a) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e341&amp;representation=PNG\"> and (b) <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e342&amp;representation=PNG\"> versus <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e343&amp;representation=PNG\"> for the moderate-coupling case (solid black line with filled black circles), i.e., <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e344&amp;representation=PNG\"> cm<sup>2</sup>/ms, and the strong-coupling case (solid blue line with unfilled blue circles), i.e., <img src=\"http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0045040.e345&amp;representation=PNG\"> cm<sup>2</sup>/ms.</p>"}

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