A Closed-Loop Model of the Respiratory System: Focus on Hypercapnia and Active Expiration
Publication Date
October 10, 2014
Journal
PLOS ONE
Authors
Yaroslav I. Molkov, Natalia A. Shevtsova, Choongseok Park, Alona Ben Tal, et al
Volume
9
Issue
10
Pages
e109894
DOI
https://dx.plos.org/10.1371/journal.pone.0109894
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0109894
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/25302708
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4193835
Europe PMC
http://europepmc.org/abstract/MED/25302708
Web of Science
000343730400091
Scopus
84907855750
Mendeley
http://www.mendeley.com/research/closedloop-model-respiratory-system-focus-hypercapnia-active-expiration
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Mendeley | Further Information

{"title"=>"A closed-loop model of the respiratory system: Focus on hypercapnia and active expiration", "type"=>"journal", "authors"=>[{"first_name"=>"Yaroslav I.", "last_name"=>"Molkov", "scopus_author_id"=>"36519334900"}, {"first_name"=>"Natalia A.", "last_name"=>"Shevtsova", "scopus_author_id"=>"7004326996"}, {"first_name"=>"Choongseok", "last_name"=>"Park", "scopus_author_id"=>"20434539200"}, {"first_name"=>"Alona", "last_name"=>"Ben-Tal", "scopus_author_id"=>"10138847200"}, {"first_name"=>"Jeffrey C.", "last_name"=>"Smith", "scopus_author_id"=>"56255592900"}, {"first_name"=>"Jonathan E.", "last_name"=>"Rubin", "scopus_author_id"=>"7402519157"}, {"first_name"=>"Ilya A.", "last_name"=>"Rybak", "scopus_author_id"=>"57191881039"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84907855750", "issn"=>"19326203", "pui"=>"600125487", "sgr"=>"84907855750", "pmid"=>"25302708", "doi"=>"10.1371/journal.pone.0109894"}, "id"=>"b2b09909-4526-311b-ae20-97cffee6dc48", "abstract"=>"Breathing is a vital process providing the exchange of gases between the lungs and atmosphere. During quiet breathing, pumping air from the lungs is mostly performed by contraction of the diaphragm during inspiration, and muscle contraction during expiration does not play a significant role in ventilation. In contrast, during intense exercise or severe hypercapnia forced or active expiration occurs in which the abdominal \"expiratory\" muscles become actively involved in breathing. The mechanisms of this transition remain unknown. To study these mechanisms, we developed a computational model of the closed-loop respiratory system that describes the brainstem respiratory network controlling the pulmonary subsystem representing lung biomechanics and gas (O2 and CO2) exchange and transport. The lung subsystem provides two types of feedback to the neural subsystem: a mechanical one from pulmonary stretch receptors and a chemical one from central chemoreceptors. The neural component of the model simulates the respiratory network that includes several interacting respiratory neuron types within the Bötzinger and pre-Bötzinger complexes, as well as the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) representing the central chemoreception module targeted by chemical feedback. The RTN/pFRG compartment contains an independent neural generator that is activated at an increased CO2 level and controls the abdominal motor output. The lung volume is controlled by two pumps, a major one driven by the diaphragm and an additional one activated by abdominal muscles and involved in active expiration. The model represents the first attempt to model the transition from quiet breathing to breathing with active expiration. The model suggests that the closed-loop respiratory control system switches to active expiration via a quantal acceleration of expiratory activity, when increases in breathing rate and phrenic amplitude no longer provide sufficient ventilation. The model can be used for simulation of closed-loop control of breathing under different conditions including respiratory disorders.", "link"=>"http://www.mendeley.com/research/closedloop-model-respiratory-system-focus-hypercapnia-active-expiration", "reader_count"=>31, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Librarian"=>2, "Student > Doctoral Student"=>1, "Researcher"=>1, "Student > Ph. D. Student"=>10, "Student > Master"=>5, "Other"=>1, "Student > Bachelor"=>9, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Librarian"=>2, "Student > Doctoral Student"=>1, "Researcher"=>1, "Student > Ph. D. Student"=>10, "Student > Master"=>5, "Other"=>1, "Student > Bachelor"=>9, "Professor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Agricultural and Biological Sciences"=>4, "Arts and Humanities"=>1, "Computer Science"=>2, "Engineering"=>9, "Nursing and Health Professions"=>1, "Mathematics"=>2, "Medicine and Dentistry"=>6, "Design"=>1, "Neuroscience"=>1, "Sports and Recreations"=>1, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Psychology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>6}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Psychology"=>{"Psychology"=>1}, "Mathematics"=>{"Mathematics"=>2}, "Unspecified"=>{"Unspecified"=>1}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Design"=>{"Design"=>1}, "Engineering"=>{"Engineering"=>9}, "Neuroscience"=>{"Neuroscience"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>4}, "Computer Science"=>{"Computer Science"=>2}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}}, "reader_count_by_country"=>{"United States"=>1, "United Kingdom"=>1, "Mexico"=>1}, "group_count"=>3}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1712861"], "description"=>"<p><b>A</b>. General diagram of interactions between the brainstem respiratory neural network and the lungs. <b>B</b>. Model schematic. See text for detailed description. <b><i>Abbreviations</i></b><b>:</b> Abd. – abdominal; AbN – abdominal nerve; aug-E – augmenting expiratory neuron; BötC – Bötzinger complex; CPG – central pattern generator; cVRG – caudal ventral respiratory group; early-I – early-inspiratory neuron; late-E – late-expiratory neuron; Mns – motoneurons; NTS - nucleus of the tractus solitarius; P-cells – Pump cells; P(e) – excitatory pump cells; P(i) – inhibitory pump cells; pFRG – parafacial respiratory group; PN – phrenic nerve; post-I – post-inspiratory neuron; pre-BötC – pre-Bötzinger complex; pre-I/I – pre-inspiratory/inspiratory neuron; PSRs – pulmonary stretch receptors; ramp-I – ramp-inspiratory neuron; RTN – retrotrapezoid nucleus; rVRG – rostral ventral respiratory group; VRC – ventral respiratory column.</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200289, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g001", "stats"=>{"downloads"=>7, "page_views"=>172, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Closed_loop_respiratory_system_/1200289", "title"=>"Closed-loop respiratory system.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712864"], "description"=>"<p>The top 6 traces in <b>A</b> and <b>B</b> represent output activity (normalized firing rate) of the corresponding neurons. The bottom two traces represent the end capillary blood <i>p<sub>c</sub></i> (<i>p<sub>ce</sub></i>) just before the next heart beat and the RTN drive, respectively. Note that vagotomy (removal of mechanical feedback) prolongs inspiration and expiration, increases the amplitude of ramp-I (and hence PN) activity and lung inflation (maximal lung volume and tidal volume), and slows the respiratory oscillations.</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200292, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g002", "stats"=>{"downloads"=>3, "page_views"=>28, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_performance_in_control_conditions_A_and_after_vagotomy_B_/1200292", "title"=>"Model performance in control conditions (A) and after vagotomy (B).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712866"], "description"=>"<p><b>A</b>. Model performance after vagotomy. <b>B</b>. Model performance after vagotomy and subsequent removal of pontine excitatory drive. Note the apneustic breathing pattern characterized by the significant increase in the duration of inspiration and slowing of the respiratory oscillations. <b>C</b>. Simulations of the effects of brief and continuous stimulation of mechanoreceptor afferents. The first stimulus (bottom trace, 7 ml of lung inflation) applied in the middle of the respiratory phase terminated the current inspiration. The second, reduced stimulus (5 ml) applied at the same phase was unable to terminate inspiration. The third stimulus of the same size as the second one (5 ml) applied later in inspiration terminated the inspiratory phase. Finally, continuous linearly increasing stimulation was applied. This stimulation shortened inspiration and prolonged expiration and then produced expiratory “apnea”, when all inspiratory neurons were inhibited by continuously active expiratory neurons.</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200294, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g003", "stats"=>{"downloads"=>2, "page_views"=>23, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Perturbations_of_respiratory_neural_activity_pattern_by_pontine_removal_and_vagal_stimulations_/1200294", "title"=>"Perturbations of respiratory neural activity pattern by pontine removal and vagal stimulations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712867"], "description"=>"<p><i>f<sub>cm</sub></i> is CO<sub>2</sub> content in the mouth. In both cases, hypercapnia evoked increases in RTN drive (bottom traces in <b>A</b> and <b>B</b>). The applied hypercapnia increased the RTN drive to the late-E neuron evoking late-E discharges with the ratio 1∶3 to the ramp-I discharges in the vagus intact model (late-E trace in <b>A</b>) and the ratio 1∶2 in the vagotomized model (late-E trace in <b>B</b>). Each late-E pulse actuates the abdominal pump, reducing the base level of lung volume (see V<sub>A</sub> traces in <b>A</b> and <b>B</b>).</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200295, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g004", "stats"=>{"downloads"=>2, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effects_of_hypercapnia_maintained_at_f_cm__5_in_the_intact_A_and_vagotomized_B_models_/1200295", "title"=>"Effects of hypercapnia maintained at <i>f<sub>cm</sub></i> = 5% in the intact (A) and vagotomized (B) models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712874"], "description"=>"<p>The continuous increase of hypercapnia (the grey ramp at the bottom) was induced by increasing CO<sub>2</sub> content in the mouth <i>f<sub>cm</sub></i> from 0 to 10%. Active expiration starts with the first appearance of late-E discharges (indicated by the left vertical dot-dashed line at <i>f<sub>cm</sub></i> = 2.6%) and reaches the regime with a 1∶1 ratio of late-E to ramp-I activations at <i>f<sub>cm</sub></i> = 7.2%. As described in the text, each late-E discharge, representing the activity of AbN output, actuates the abdominal pump that reduces the baseline level of lung volume (see in the V<sub>A</sub> trace).</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200302, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g005", "stats"=>{"downloads"=>2, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_of_progressive_hypercapnia_in_the_intact_model_/1200302", "title"=>"Simulation of progressive hypercapnia in the intact model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712879"], "description"=>"<p>The continuous increase of hypercapnia (the grey ramp at the bottom) was induced by increasing CO<sub>2</sub> content in the mouth <i>f<sub>cm</sub></i> from 0 to 10%. Active expiration starts with the first appearance of late-E discharges (indicated by the left vertical dot-dashed line at <i>f<sub>cm</sub></i> = 1.2%) and reaches the regime with the 1∶1 ratio of late-E to ramp-I activations at <i>f<sub>cm</sub></i> = 7%. Again, each late-E discharge, representing the activity of AbN output, actuates the abdominal pump that reduces the baseline level of lung volume (see in the V<sub>A</sub> trace).</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200306, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g006", "stats"=>{"downloads"=>2, "page_views"=>25, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulation_of_progressive_hypercapnia_in_the_vagotomized_model_/1200306", "title"=>"Simulation of progressive hypercapnia in the vagotomized model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712880"], "description"=>"<p>CO2 content in the mouth <i>f<sub>cm</sub></i> was linearly increased from zero to 10%. Changes in three major breathing characteristics (tidal volume, breathing rate, and ventilation) that would occur without active expiration (simulated by setting AbN = 0) are shown by the corresponding dashed lines. The vertical dot-dashed lines bound the development (quantal acceleration) of active expiration.</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200308, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g007", "stats"=>{"downloads"=>1, "page_views"=>34, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Changes_in_tidal_volume_breathing_rate_and_ventilation_relative_to_normocapnia_with_the_development_of_hypercapnia_in_the_intact_panel_A_and_vagotomized_panel_B_models_/1200308", "title"=>"Changes in tidal volume, breathing rate, and ventilation (relative to normocapnia) with the development of hypercapnia in the intact (panel A) and vagotomized (panel B) models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712884"], "description"=>"<p><b>A</b>. Breathing stimulation elicited in conscious adult rat in a flow-through, whole-body plethysmography chamber by photostimulation via channelrodopsin genetically engineered in RTN Phox2b-expressing glutamatergic neurons. The left diagrams were constructed for hyperoxic normocapnia (100% O<sub>2</sub>), and the right diagrams for hypercapnia (8% CO<sub>2</sub>, balance O<sub>2</sub>). Continuous RTN stimulation (23 Hz, 3 ms pulses, 30 s total duration, blue bar at the top) raised tidal volume, V<sub>T</sub>, and breathing frequency, fR. During hyperoxic hypercapnia (right), RTN photostimulation produced a small increase in V<sub>T</sub> but no increase in fR. Adapted from Abbott et al. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0109894#pone.0109894-Abbott1\" target=\"_blank\">[52]</a>, Fig. 1B, with permission. <b>B</b>. The results of our simulations. An additional 30s-duration increase in the blood CO<sub>2</sub> level (Δ<i>p<sub>c</sub></i>  = 30 mmHg, blue bar at the top) was applied in the normocapnic case (left) and on the background of simulated hypercapnia (<i>f<sub>cm</sub></i> = 8%) (right).</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200312, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.g008", "stats"=>{"downloads"=>1, "page_views"=>29, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_model_simulations_with_experimental_data_/1200312", "title"=>"Comparison of model simulations with experimental data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712886"], "description"=>"<p>Note that <i>PSR</i> is the peripheral feedback provided by the lung stretch receptors. In our model, we use , the inspired lung volume (excess of the lung volume above the basal volume, see (25)), as the <i>PSR</i> signal that is multiplied by the <i>e<sub>i</sub>, f<sub>i</sub></i> values indicated in the table.</p><p>Parameters of neural network.</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200314, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.t001", "stats"=>{"downloads"=>3, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameters_of_neural_network_/1200314", "title"=>"Parameters of neural network.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-10-10 02:45:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/1712887"], "description"=>"<p>Parameters of the model.</p>", "links"=>[], "tags"=>["control system switches", "expiratory activity", "quantal acceleration", "CO 2 level", "lung biomechanics", "Respiratory system", "Active Expiration Breathing", "rtn", "chemical feedback", "motor output", "neuron types", "stretch receptors", "phrenic amplitude", "O 2", "expiration", "chemoreception module", "breathing rate", "lung subsystem", "Muscle contraction", "lung volume", "model"], "article_id"=>1200315, "categories"=>["Biological Sciences"], "users"=>["Yaroslav I. Molkov", "Natalia A. Shevtsova", "Choongseok Park", "Alona Ben-Tal", "Jeffrey C. Smith", "Jonathan E. Rubin", "Ilya A. Rybak"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0109894.t002", "stats"=>{"downloads"=>5, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameters_of_the_model_/1200315", "title"=>"Parameters of the model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-10-10 02:45:57"}

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