Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts
Publication Date
September 04, 2013
Journal
PLOS ONE
Authors
Alok Ranjan Nayak, T. K. Shajahan, A. V. Panfilov & Rahul Pandit
Volume
8
Issue
9
Pages
e72950
DOI
https://dx.plos.org/10.1371/journal.pone.0072950
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0072950
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/24023798
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3762734
Europe PMC
http://europepmc.org/abstract/MED/24023798
Web of Science
000324515600056
Scopus
84883350400
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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1190231"], "description"=>"<p>We apply a control pulse of amplitude 30 pA/pF for ms over a square mesh with each block of size mm, i.e., the simulation domain is divided into 4<sup>2</sup> square blocks. Plots in Figs. (a), (b) and (c) are the initial conditions of , i.e., ms, for zero sided coupling with pF, nS, mV and nS, double sided coupling with same fibroblasts parameters as in (a) with and , and double sided coupling with same fibroblasts parameters as in (a) with and , respectively. Figures (b), (e) and (h) are the time evolution of corresponds to Figs. (a), (d), (g), respectively, at ms in absence of any control pulse. However, the spiral-wave is suppressed an application of control pulse as shown in Figs. (c), (f) and (i) at time ms. For the spatiotemporal evolution of these spiral waves see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s013\" target=\"_blank\">Video S12</a>.</p>", "links"=>[], "tags"=>["2d", "fibroblast", "mf", "composite", "inhomogeneity", "mm", "bottom-left", "placed"], "article_id"=>788192, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g015", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spiral_wave_control_in_the_2D_Fibroblast_model_in_the_presence_of_a_square_shape_MF_composite_inhomogeneity_of_size_mm_whose_bottom_left_corner_is_placed_at_56_25_mm_56_25_mm_/788192", "title"=>"Spiral-wave control in the 2D Fibroblast model in the presence of a square shape MF composite inhomogeneity of size mm whose bottom-left corner is placed at (56.25 mm, 56.25 mm).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190185"], "description"=>"<p>(a) The action-potential duration APD versus ; (b) the resting-membrane potential versus ; (c) the maximum upstroke velocity versus ; (d) the maximum value of , during the action potential, versus ; (e) the value of at the position of the notch, i.e., versus ; (f) the maximum value of , in the plateau region of the action potential, i.e., versus ; these figures show plots for the fibroblast resting membrane potential mV (full red triangles), mV (full blue squares), mV (full black circles), mV (full blue diamonds), and mV (full red stars).</p>", "links"=>[], "tags"=>["morphological", "myocyte", "gap-junctional", "conductance", "coupled", "passive", "fibroblast", "capacitance", "pf"], "article_id"=>788149, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g002", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plots_of_various_morphological_features_of_the_myocyte_action_potential_versus_the_gap_junctional_conductance_here_the_myocyte_is_coupled_with_a_passive_fibroblast_with_capacitance_pF_and_conductance_nS_/788149", "title"=>"Plots of various morphological features of the myocyte action potential versus the gap-junctional conductance ; here, the myocyte is coupled with a passive fibroblast with capacitance pF and conductance nS.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190194"], "description"=>"<p> in a square simulation domain of side mm, at time s with nS, mV, with cm<sup>2</sup>/s, and (a) nS (control case, i.e., only myocytes), (b) nS (low coupling), (c) nS (intermediate coupling), and (d) nS (high coupling); the white solid lines show the trajectory of the spiral tip for 2 s s. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s003\" target=\"_blank\">Video S2</a> illustrates the spatiotemporal evolution of these spiral waves. (e) Plot of the rotation period of the spiral wave versus . (f) Plots of the power spectra of the time series of recorded from the representative point ( mm, mm), which is indicated by an asterisk in (a)-(d), for nS (black circles), (b) nS (gray squares), (c) nS (blue diamonds), and (d) nS (red triangles); for these power spectra we use time series with 400000 points.</p>", "links"=>[], "tags"=>["zero-sided"], "article_id"=>788155, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g007", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pseudocolour_plots_of_with_zero_sided_couplings_/788155", "title"=>"Pseudocolour plots of with zero-sided couplings:", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190207"], "description"=>"<p><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s007\" target=\"_blank\">Video S6</a> illustrates the spatiotemporal evolution of these spiral waves. The plots in (d)-(f) show the time series for , in the interval , which are obtained from a point outside ( for all cases) and inside the fibroblast inhomogeneity ( and for (a), (b), and (c), respectively), represented by black circles and red triangles, respectively; (g), (h), and (i) show plots of the inter-beat intervals (ibis) versus the beat number for the time series of mentioned above; each one of these time series contain data points; the power spectra , which follow from these time series, are given in (j), (k), and (l).</p>", "links"=>[], "tags"=>["transmembrane", "myocyte", "mf", "composite", "zero-sided", "bottom-left", "inhomogeneity", "lines", "figures", "spiral-tip", "trajectories", "recorded", "points"], "article_id"=>788168, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g010", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pseudocolor_plots_of_the_transmembrane_potential_of_the_myocyte_at_time_s_in_the_presence_of_a_square_shape_MF_composite_inhomogeneity_of_side_mm_for_the_case_of_zero_sided_coupling_the_bottom_left_corner_of_the_inhomogeneity_is_fixed_at_a_b_and_c_the_wh/788168", "title"=>"Pseudocolor plots of the transmembrane potential of the myocyte at time, s, in the presence of a square shape MF composite inhomogeneity, of side mm, for the case of zero-sided coupling; the bottom-left corner of the inhomogeneity is fixed at (a) , (b) , and (c) ; the white solid lines in these figures show the spiral-tip trajectories in the time interval and the local time series data are recorded from points that are shown by asterisks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190219"], "description"=>"<p><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s010\" target=\"_blank\">Video S9</a> illustrates the spatiotemporal evolution of these spiral waves. The time series for , with , from a point outside the inhomogeneity () and a point inside it (), both of which are depicted by asterisks in (a)-(c), are plotted in (d), (e), and (f) for , 100, and 200, respectively (data from the points outside and inside the inhomogeneity are represented, respectively, by black circles and red triangles); (g), (h), and (i) show the corresponding plots of the ibi versus the beat number ; and the associated power spectra are depicted in (j), (k), and (l).</p>", "links"=>[], "tags"=>["transmembrane", "myocyte", "mf-composite", "mm", "lower-left-hand", "placed", "doubled-sided", "coupling"], "article_id"=>788180, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g013", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pseudocolor_plots_of_the_transmembrane_potential_of_the_myocyte_at_time_s_in_the_presence_of_a_square_MF_composite_inhomogeneity_of_side_mm_and_with_its_lower_left_hand_corner_placed_at_for_the_case_of_doubled_sided_coupling_with_and_nS_a_b_and_c_/788180", "title"=>"Pseudocolor plots of the transmembrane potential of the myocyte , at time s, in the presence of a square, MF-composite inhomogeneity, of side mm and with its lower-left-hand corner placed at for the case of doubled-sided coupling with and nS: (a) , (b) , and (c) .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190234"], "description"=>"<p>We concentrate on the APD, , and and list the changes, indicated by , in these parameters. , and denote, respectively, the changes in the APD at 70%, 80%, and 90% repolarization. Note that here we have high values (see text) for both (4 nS) and (8 nS).</p>", "links"=>[], "tags"=>["mf", "composite", "ap", "uncoupled"], "article_id"=>788195, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.t002", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_values_of_and_for_a_single_MF_composite_and_the_changes_in_the_AP_morphology_relative_to_that_of_an_uncoupled_myocyte_/788195", "title"=>"The values of , and for a single MF composite and the changes in the AP morphology, relative to that of an uncoupled myocyte.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190184"], "description"=>"<p>The myocyte action potential (full symbols and lines) and the fibroblast action potential (unshaded symbols and dashed lines), with a passive fibroblast of capacitance pF coupled with a myocyte for (a) mV and nS, (b) mV and nS, (c) mV and nS, (d) mV and nS, (e) mV, and nS, (f) mV and nS, (g) mV and nS, (h) mV and nS, and (i) mV and nS; red squares (full or unshaded) indicate nS; blue diamonds (full or unshaded) indicate nS; gray triangles (full or unshaded) indicate nS; black squares (full or unshaded) indicate an uncoupled myocyte.</p>", "links"=>[], "tags"=>[], "article_id"=>788148, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g001", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plots_of_action_potentials_/788148", "title"=>"Plots of action potentials:", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190201"], "description"=>"<p>Pseudocolor plots of at time s in a simulation domain with cm, an MF composite at every site, with a myocyte M coupled via nS with one fibroblast F ( pF, nS, and mV) for (a) control case with only myocytes and no fibroblasts, (b) zero-sided coupling, (c) single-sided coupling with , and (d) double-sided coupling with and ; the white solid lines in plots (a), (b), (c), and (d) show the trajectories of the spiral tip for . <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s006\" target=\"_blank\">Video S5</a> illustrates the spatiotemporal evolution of these spiral waves. (e) Time series data for are recorded at the point , shown by an asterisk, for . (f) Plot of the inter-beat interval (ibi) versus the beat number , and (g) the power spectrum (of ) versus the frequency for the control case (black circles), zero-sided coupling (gray squares), single-sided coupling (blue diamonds), and double-sided coupling (red triangles); these plots of ibi and are obtained from a time series of , with 400000 data points separated by 0.02 ms.</p>", "links"=>[], "tags"=>["waves", "two-sided"], "article_id"=>788162, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g009", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spiral_waves_with_zero_one_and_two_sided_couplings_/788162", "title"=>"Spiral waves with zero-, one-, and two-sided couplings:", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190215"], "description"=>"<p> Pseudocolor plots of the transmembrane potential of the myocyte at time, s, in the presence of three square MF-composite inhomogeneities with sides (a) , (b) , and (c) , for the case of zero-sided coupling; the bottom-left corner of these squares is fixed at ; the white solid lines in these figures show the spiral-tip trajectories in the time interval and the local time series data are recorded from points that are shown by asterisks. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s008\" target=\"_blank\">Video S7</a> illustrates the spatiotemporal evolution of these spiral waves. The plots in (d)-(f) show the time series for , in the interval , which are obtained from the point outside the inhomogeneity and a point inside it , represented by black filled circles and red filled triangles, respectively; (g), (h), and (i) show plots of the inter-beat intervals (ibis) versus the beat number for the time series of mentioned above; each one of these time series contain data points; the power spectra , which follow from these time series, are given in (j), (k), and (l).</p>", "links"=>[], "tags"=>["mf-composite"], "article_id"=>788176, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g011", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pseudocolor_plots_of_with_MF_composite_inhomogeneities_/788176", "title"=>"Pseudocolor plots of with MF-composite inhomogeneities:", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190227"], "description"=>"<p>Plots in (a), (d) and (g) are the initial conditions of , i.e., ms, for the control case, i.e., nS, zero sided coupling with pF, nS, mV and nS, and double-sided coupling with the same fibroblasts parameters as in (d) and with and , respectively; (b), (e) and (h) show the pseudocolor plots of at ms in the absence of any control pulse. However, the spiral-wave is suppressed by an application of the control pulse as shown (c), (f) and (i) at time ms. The <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s012\" target=\"_blank\">Video S11</a>, which comprises six animations of pseudocolor plots of , shows the spatiotemporal evolution of these spiral waves for these cases, with and without control pulses.</p>", "links"=>[], "tags"=>["2d", "m-f", "composite", "amplitude", "30", "ms", "mesh", "simulation", "divided"], "article_id"=>788188, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g014", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spiral_wave_control_in_our_2D_M_F_composite_model_by_the_application_of_a_control_pulse_of_amplitude_30_pA_pF_for_ms_over_a_square_mesh_with_each_block_of_side_mm_i_e_the_simulation_domain_is_divided_into_4_2_square_blocks_/788188", "title"=>"Spiral-wave control in our 2D M-F composite model, by the application of a control pulse of amplitude 30 pA/pF for ms over a square mesh with each block of side mm, i.e., the simulation domain is divided into 4<sup>2</sup> square blocks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190189"], "description"=>"<p>Plots of versus for (g) zero-sided coupling, (h) single-sided coupling with (blue circles), (black squares), and (red triangles), and (i) double-sided coupling with and . For double-sided coupling, conduction failure can occur for low and intermediate values of , e.g., 0.5 nS and 2.0 nS, as shown in (d).</p>", "links"=>[], "tags"=>["waves", "pseudocolor", "ms", "2d", "simulation", "ns", "illustrates", "spatiotemporal"], "article_id"=>788153, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g006", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plane_waves_shown_via_pseudocolor_plots_of_at_ms_in_a_2D_square_simulation_domain_of_side_mm_for_a_the_control_case_with_only_myocytes_b_zero_sided_coupling_c_single_sided_coupling_with_d_double_sided_coupling_with_and_nS_e_double_sided_coupling_with_and/788153", "title"=>"Plane waves shown via pseudocolor plots of at ms in a 2D square simulation domain of side mm: for (a) the control case with only myocytes, (b) <i>zero-sided coupling</i>, (c) <i>single-sided coupling</i> with , (d) <i>double-sided coupling</i> with , , and nS, (e) <i>double-sided coupling</i> with , , and nS, and (f) <i>double-sided coupling</i> with , , and nS (Video S1 illustrates the spatiotemporal evolution of these plane waves).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190255", "https://ndownloader.figshare.com/files/1190256", "https://ndownloader.figshare.com/files/1190257", "https://ndownloader.figshare.com/files/1190258", "https://ndownloader.figshare.com/files/1190259", "https://ndownloader.figshare.com/files/1190260", "https://ndownloader.figshare.com/files/1190261", "https://ndownloader.figshare.com/files/1190262", "https://ndownloader.figshare.com/files/1190263", "https://ndownloader.figshare.com/files/1190264", "https://ndownloader.figshare.com/files/1190265", "https://ndownloader.figshare.com/files/1190266", "https://ndownloader.figshare.com/files/1190267"], "description"=>"<div><p>Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.</p></div>", "links"=>[], "tags"=>["mathematical", "ventricular", "myocytes"], "article_id"=>788213, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0072950.s001", "https://dx.doi.org/10.1371/journal.pone.0072950.s002", "https://dx.doi.org/10.1371/journal.pone.0072950.s003", "https://dx.doi.org/10.1371/journal.pone.0072950.s004", "https://dx.doi.org/10.1371/journal.pone.0072950.s005", "https://dx.doi.org/10.1371/journal.pone.0072950.s006", "https://dx.doi.org/10.1371/journal.pone.0072950.s007", "https://dx.doi.org/10.1371/journal.pone.0072950.s008", "https://dx.doi.org/10.1371/journal.pone.0072950.s009", "https://dx.doi.org/10.1371/journal.pone.0072950.s010", "https://dx.doi.org/10.1371/journal.pone.0072950.s011", "https://dx.doi.org/10.1371/journal.pone.0072950.s012", "https://dx.doi.org/10.1371/journal.pone.0072950.s013"], "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spiral_Wave_Dynamics_in_a_Mathematical_Model_of_Human_Ventricular_Tissue_with_Myocytes_and_Fibroblasts_/788213", "title"=>"Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190187"], "description"=>"<p>(a) the fast inward current, ; (b) the L-type slow inward current, ; (c) the transient outward current, ; (d) the slow delayed rectifier current, ; (e) the rapid delayed rectifier current, ; (f) the inward rectifier current, ; (g) the exchanger current, ; (h) the pump current, ; (i) the plateau current, ; (j) the plateau current, ; (k) the background current, ; (l) the background current, .</p>", "links"=>[], "tags"=>["ionic", "myocyte", "mf", "composite", "fibroblast", "pf", "coupled", "circles", "shows", "uncoupled", "filled", "squares", "triangles", "mv"], "article_id"=>788151, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g004", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plots_of_ionic_current_of_the_myocyte_versus_time_of_an_MF_composite_with_the_fibroblast_parameters_are_pF_and_nS_and_it_coupled_with_a_myocyte_with_nS_the_full_black_curve_with_circles_shows_for_an_uncoupled_myocyte_the_blue_filled_squares_and_the_red_t/788151", "title"=>"Plots of ionic current, , of the myocyte versus time of an MF composite with ; the fibroblast parameters are pF and nS, and it coupled with a myocyte with nS; the full black curve with circles shows for an uncoupled myocyte; the blue filled squares and the red triangles are, respectively, for mV and mV.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190188"], "description"=>"<p>for , i.e., no fibroblasts (black circles), (red squares), (blue diamonds), and (gray triangles) for the illustrative parameter values pF, nS, mV, and a low value of , namely, 0.3 nS (plots in the left panel (a), (d), and (g)), an intermediate value of , namely, 1.0 nS (plots in the middle panel(b),(e), and (h)), and a high value of , namely, 8.0 nS (plots in the right panel (c), (f), and (i)).</p>", "links"=>[], "tags"=>[], "article_id"=>788152, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g005", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plots_versus_of_and_/788152", "title"=>"Plots versus of , and :", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190195"], "description"=>"<p> Spiral-wave tip trajectories for the time intervals (a) 2 s s, (b) 4 s s, and (c) 6 s s, with zero-sided coupling, and for the control case with ns (black circles), ns (gray squares), ns (blue diamonds), and ns (red triangles), and all other parameter values as in Fig. 7. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s003\" target=\"_blank\">Videos S2</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s004\" target=\"_blank\">S3</a>, and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s005\" target=\"_blank\">S4</a> illustrate the spatiotemporal evolution of these spiral-tip trajectories.</p>", "links"=>[], "tags"=>["spiral-wave-tip", "trajectories", "zero-sided"], "article_id"=>788156, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g008", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plots_of_spiral_wave_tip_trajectories_with_zero_sided_couplings_/788156", "title"=>"Plots of spiral-wave-tip trajectories with zero-sided couplings:", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190186"], "description"=>"<p>(a) Plots versus time of the transmembrane potentials (full curves with filled symbols), for a myocyte, and (dashed curves with open symbols), for a passive fibroblast coupled with a myocyte cell; here pF, nS, nS and mV (blue squares) and mV (red triangles); the full black curve with circles shows for an uncoupled myocyte. (b) Plots versus of the gap-junctional current with parameters and symbols as in (b). Plots versus , for the first 2 ms after the application of a stimulus of −52 pA/pF, of (c) , (d) , (e) the myocyte sodium current , and (f) the total activation (full lines with filled symbols) and total inactivation (dashed lines with open symbols) gates; the parameters and symbols here are as in (a).</p>", "links"=>[], "tags"=>["transmembrane", "potentials", "currents", "mf"], "article_id"=>788150, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plots_of_transmembrane_potentials_and_currents_for_an_MF_composite_/788150", "title"=>"Plots of transmembrane potentials and currents for an MF composite:", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/1190218"], "description"=>"<p><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072950#pone.0072950.s009\" target=\"_blank\">Video S8</a> illustrates the spatiotemporal evolution of these spiral waves for (a), (d), (f) and (h). The smallest MF-composite inhomogeneity that can anchor a spiral wave has ; (i) shows a plot of the rotation period of such an anchored spiral wave.</p>", "links"=>[], "tags"=>["transmembrane", "myocyte", "mf-composite", "placed", "lower-left"], "article_id"=>788179, "categories"=>["Biological Sciences"], "users"=>["Alok Ranjan Nayak", "T. K. Shajahan", "A. V. Panfilov", "Rahul Pandit"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0072950.g012", "stats"=>{"downloads"=>0, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pseudocolor_plots_of_the_transmembrane_potential_of_the_myocyte_at_time_s_when_a_square_MF_composite_inhomogeneity_with_and_is_placed_with_its_lower_left_corner_at_the_square_has_a_side_of_length_a_i_e_no_inhomogeneity_b_c_d_e_f_g_and_h_/788179", "title"=>"Pseudocolor plots of the transmembrane potential of the myocyte at time, s, when a square MF-composite inhomogeneity, with and , is placed with its lower-left corner at ; the square has a side of length (a) , i.e., no inhomogeneity, (b) , (c) , (d) , (e) , (f) , (g) , and (h) .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-09-04 01:56:41"}
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PMC Usage Stats | Further Information

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Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Anatomy", "average_usage"=>[248, 440, 562, 666, 765, 856, 944, 1028, 1112, 1198, 1282, 1362, 1430]}, {"subject_area"=>"/Biology and life sciences/Physiology", "average_usage"=>[256, 449, 572, 676, 775, 866, 955, 1041, 1127, 1213, 1290, 1370, 1437]}, {"subject_area"=>"/Medicine and health sciences/Anatomy", "average_usage"=>[248, 441, 564, 668, 769, 859, 948, 1034, 1117, 1202, 1290, 1368, 1437]}, {"subject_area"=>"/Medicine and health sciences/Physiology", "average_usage"=>[258, 449, 572, 679, 775, 866, 956, 1041, 1124, 1211, 1291, 1371, 1437]}, {"subject_area"=>"/Physical sciences", "average_usage"=>[254, 431, 547, 651, 748, 842, 932, 1017, 1098, 1178, 1259, 1336, 1404]}, {"subject_area"=>"/Physical sciences/Physics", "average_usage"=>[254, 421, 527, 626, 720, 813, 900, 983, 1063, 1136, 1210, 1283, 1342]}]}
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