The Role of the Frank–Starling Law in the Transduction of Cellular Work to Whole Organ Pump Function: A Computational Modeling Analysis
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{"title"=>"The Role of the Frank-Starling Law in the Transduction of Cellular Work to Whole Organ Pump Function: A Computational Modeling Analysis", "type"=>"journal", "authors"=>[{"first_name"=>"Steven A.", "last_name"=>"Niederer", "scopus_author_id"=>"6507804465"}, {"first_name"=>"Nicolas P.", "last_name"=>"Smith", "scopus_author_id"=>"55613241183"}], "year"=>2009, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"66249100946", "scopus"=>"2-s2.0-66249100946", "doi"=>"10.1371/journal.pcbi.1000371", "isbn"=>"1553-7358 (Electronic)", "pui"=>"354658166", "issn"=>"1553734X", "pmid"=>"19390615"}, "id"=>"302c4bdd-00d8-32f2-994a-d9d10b9764f7", "abstract"=>"We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca(2+) sensitivity of tension (Ca(50)), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca(2+) to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca(50) and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca(50) was caused by an inversion in the regional distribution of strain.", "link"=>"http://www.mendeley.com/research/role-frankstarling-law-transduction-cellular-work-whole-organ-pump-function-computational-modeling-a", "reader_count"=>58, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>4, "Student > Doctoral Student"=>3, "Researcher"=>19, "Student > Ph. D. Student"=>10, "Student > Postgraduate"=>4, "Student > Master"=>7, "Other"=>3, "Student > Bachelor"=>4, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>4, "Student > Doctoral Student"=>3, "Researcher"=>19, "Student > Ph. D. Student"=>10, "Student > Postgraduate"=>4, "Student > Master"=>7, "Other"=>3, "Student > Bachelor"=>4, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>21, "Unspecified"=>4, "Biochemistry, Genetics and Molecular Biology"=>2, "Mathematics"=>8, "Medicine and Dentistry"=>10, "Agricultural and Biological Sciences"=>9, "Physics and Astronomy"=>3, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>21}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>10}, "Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>9}, "Computer Science"=>{"Computer Science"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}, "Mathematics"=>{"Mathematics"=>8}, "Unspecified"=>{"Unspecified"=>4}}, "reader_count_by_country"=>{"United States"=>1, "United Kingdom"=>5, "France"=>1, "Germany"=>1}, "group_count"=>4}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/900261"], "description"=>"<p>Transmural variation in Cauchy active tension at the base, mid and apex from simulations in the absence of length dependent filament overlap plots (A), (B), and (C), respectively and length dependent Ca<sub>50</sub> plots (D), (E), and (F), respectively from the epicardium (epi), midwall circumferential fibers (circ) and endocardium (endo). The extension ratio normalised to end diastolic strain at base, mid and apex from simulations in the absence of length dependent filament overlap plots (G), (H), and (I), respectively, and length dependent Ca<sub>50</sub> plots (J), (K) and (L), respectively, from the epicardium (epi), midwall circumferential fibers (circ) and endocardium (endo). The gray vertical dashed lines correspond to the transitions in boundary conditions. In the absence of length dependent Ca<sub>50</sub> the model does not reach diastole, this reduces the number of vertical gray dashed lines.</p>", "links"=>[], "tags"=>["simulations", "performed", "filament", "overlap"], "article_id"=>570721, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g008", "stats"=>{"downloads"=>4, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Regional_variation_in_stress_and_fiber_extension_ratio_for_simulations_performed_in_the_absence_of_length_dependent_filament_overlap_or_length_dependent_Ca_50_/570721", "title"=>"Regional variation in stress and fiber extension ratio for simulations performed in the absence of length dependent filament overlap or length dependent Ca<sub>50</sub>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:08:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/900549"], "description"=>"<p>Boundary conditions defined with respect to global co-ordinate system and derivatives with respect to local ξ co-ordinates, where u<sub>i</sub> is the displacement in the i<sup>ith</sup> direction.</p>", "links"=>[], "tags"=>["conditions", "defined", "co-ordinate", "derivatives", "displacement"], "article_id"=>571010, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.t002", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Boundary_conditions_defined_with_respect_to_global_co_ordinate_system_and_derivatives_with_respect_to_local_co_ordinates_where_u_i_is_the_displacement_in_the_i_ith_direction_/571010", "title"=>"Boundary conditions defined with respect to global co-ordinate system and derivatives with respect to local ξ co-ordinates, where u<sub>i</sub> is the displacement in the i<sup>ith</sup> direction.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 06:10:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/899824"], "description"=>"<p>Plots of (A) volume, (B) pressure and (C) P-V curve for the left ventricle model. Panels (D) to (I) show the ventricle model at (D) end diastole (0 ms), (E) end IVC (43 ms), (F) end ejection (222 ms), (G) end IVR (1050 ms), (H) end recoil (1240 ms) and (I) end diastases (1667 ms). The orientation and size of the cones embedded within the mesh indicate the direction and magnitude of principal strain, respectively. Blue and red cones represent states of compression and tension, respectively. Gold stream lines indicate the fiber orientation. The 3 coloured spheres assist in visualizing the rotation of the ellipsoid.</p>", "links"=>[], "tags"=>["contraction"], "article_id"=>570299, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g003", "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Normal_model_contraction_cycle_/570299", "title"=>"Normal model contraction cycle.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:06:46"}
  • {"files"=>["https://ndownloader.figshare.com/files/900449"], "description"=>"<p>With row one ((A), (D), and (G)) representing end IVC, row two ((B), (E), and (H)), representing end ejection and row three ((C), (F), and (I)) representing mid relaxation (400 ms from end diastole). Red regions are elongating, blue shortening and green are static.</p>", "links"=>[], "tags"=>["maps", "axis", "filament", "overlap"], "article_id"=>570917, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g009", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Velocity_maps_for_heart_long_axis_for_the_normal_heart_A_C_in_the_absence_of_filament_overlap_D_F_and_in_the_absence_of_Ca_50_G_8211_I_/570917", "title"=>"Velocity maps for heart long axis for the normal heart (A–C), in the absence of filament overlap (D–F) and in the absence of Ca<sub>50</sub> (G–I).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:10:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/900587"], "description"=>"<p>Comparison of normal model with end diastolic volume (EDV), end diastolic pressure (EDP), end systolic volume (ESV), end systolic pressure (EDP), endocardium radius (R<sub>endo</sub>), epicardium radius (R<sub>epi</sub>), and end diastolic (ED) and end systolic (ES) wall thickness (WT).</p>", "links"=>[], "tags"=>["diastolic", "systolic", "endocardium", "radius", "epicardium", "thickness"], "article_id"=>571046, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.t003", "stats"=>{"downloads"=>1, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_normal_model_with_end_diastolic_volume_EDV_end_diastolic_pressure_EDP_end_systolic_volume_ESV_end_systolic_pressure_EDP_endocardium_radius_R_endo_epicardium_radius_R_epi_and_end_diastolic_ED_and_end_systolic_ES_wall_thickness_WT_/571046", "title"=>"Comparison of normal model with end diastolic volume (EDV), end diastolic pressure (EDP), end systolic volume (ESV), end systolic pressure (EDP), endocardium radius (R<sub>endo</sub>), epicardium radius (R<sub>epi</sub>), and end diastolic (ED) and end systolic (ES) wall thickness (WT).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 06:10:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/899940"], "description"=>"<p>Transmural variation in Cauchy active tension at (A) base, (B) mid and (C) apex and extension ratio normalised to end diastolic strain at (D) base, (E) mid and (F) apex from epicardium (epi), midwall circumferential fibers (circ) and endocardium (endo). The gray vertical dashed lines correspond to the transitions in boundary conditions.</p>", "links"=>[], "tags"=>["biophysics/theory and simulation", "computational biology/systems biology"], "article_id"=>570407, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g004", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Regional_variation_in_stress_and_fiber_extension_ratio_in_the_normal_model_/570407", "title"=>"Regional variation in stress and fiber extension ratio in the normal model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:07:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/899657"], "description"=>"<p>(A) Left ventricle geometry, boundary conditions are applied to the highlighted nodes as described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000371#pcbi-1000371-t002\" target=\"_blank\">Table 2</a>. Gray spheres are mid/inner nodes, green spheres are outer base nodes and orange spheres are the apex nodes. (B) Fiber and sheet orientation across the heart wall.</p>", "links"=>[], "tags"=>["conditions"], "article_id"=>570121, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g001", "stats"=>{"downloads"=>3, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_geometry_boundary_conditions_and_fiber_orientation_/570121", "title"=>"Model geometry, boundary conditions and fiber orientation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:05:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/900525"], "description"=>"<p>Perturbations to heart model used to determine the sensitivity of metrics to model parameters and boundary conditions.</p>", "links"=>[], "tags"=>["metrics", "parameters"], "article_id"=>570986, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.t004", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Perturbations_to_heart_model_used_to_determine_the_sensitivity_of_metrics_to_model_parameters_and_boundary_conditions_/570986", "title"=>"Perturbations to heart model used to determine the sensitivity of metrics to model parameters and boundary conditions.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 06:10:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/900622"], "description"=>"<p>Coefficients of Omens material laws. b<sub>0</sub> was fitted using passive inflation data.</p>", "links"=>[], "tags"=>["omens", "was", "fitted", "passive"], "article_id"=>571083, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.t001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Coefficients_of_Omens_material_laws_b_0_was_fitted_using_passive_inflation_data_/571083", "title"=>"Coefficients of Omens material laws. b<sub>0</sub> was fitted using passive inflation data.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 06:10:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/900110"], "description"=>"<p>Plot (A) compares the percentage change in η in the absence of TDF mechanisms when strain is defined from the normal solution. Plot (B) compares the percentage changes in η in the normal model where strain is defined from solutions in the absence of TDF mechanisms.</p>", "links"=>[], "tags"=>["changes", "tdf", "mechanisms"], "article_id"=>570573, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g006", "stats"=>{"downloads"=>3, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dependence_of_changes_in_951_in_the_absence_of_TDF_mechanisms_on_the_strain_and_tension_fields_/570573", "title"=>"Dependence of changes in η in the absence of TDF mechanisms on the strain and tension fields.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:08:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/900176"], "description"=>"<p>Transmural variation in work density at base, mid ventricle and apex from epicardium (epi), midwall circumferential fibers (circ) and endocardium (endo) for (A) the normal model, (B) in the absent of length dependent filament overlap and (C) in the absence of length dependent Ca<sub>50</sub>.</p>", "links"=>[], "tags"=>["simulations", "performed", "filament", "overlap"], "article_id"=>570640, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g007", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_regional_work_in_the_normal_model_with_simulations_performed_in_the_absence_of_length_dependent_filament_overlap_or_length_dependent_Ca_50_/570640", "title"=>"Comparison of regional work in the normal model with simulations performed in the absence of length dependent filament overlap or length dependent Ca<sub>50</sub>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:08:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/899749"], "description"=>"<p>Validation of model (black solid line) passive pressure volume relationship compared with Cingolani et al., <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000371#pcbi.1000371-Cingolani1\" target=\"_blank\">[31]</a> (•), Omens et al., <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000371#pcbi.1000371-Omens1\" target=\"_blank\">[16]</a> (▿) and Herrmann et al., <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000371#pcbi.1000371-Herrmann1\" target=\"_blank\">[32]</a> (□).</p>", "links"=>[], "tags"=>["passive", "compared", "cingolani", "et", "omens", "herrmann"], "article_id"=>570201, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g002", "stats"=>{"downloads"=>2, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Validation_of_model_black_solid_line_passive_pressure_volume_relationship_compared_with_Cingolani_et_al_31__Omens_et_al_16__and_Herrmann_et_al_32__/570201", "title"=>"Validation of model (black solid line) passive pressure volume relationship compared with Cingolani et al., [31] (•), Omens et al., [16] (▿) and Herrmann et al., [32] (□).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:06:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/900031"], "description"=>"<p>Plots (A), (C) and (E) plot the normal values of η, tension variability and stretch variability, respectively. Plots (B), (D) and (F) plot the relative changes in η, tension variability and stretch variability, respectively, to the normal model, in the absence of each TDF mechanism (velocity dependence of tension (▪), filament overlap (×), tension dependent binding of Ca<sup>2+</sup> to TnC (▾) and length dependent Ca<sub>50</sub> (•)) and the maximum and minimum relative sensitivity of each metric to the perturbations listed in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000371#pcbi-1000371-t004\" target=\"_blank\">Table 4</a> (black error bars). η is calculated by integrating the ratio of positive work to the sum of positive and negative work (Eq. 6) over each phase of contraction and is plotted for isovolumetric contraction (IVC), ejection (EJ), isovolumetric relaxation (IVR) and diastolic filling (D). Variability in tension and stretch are calculated at a point in time and are calculated at end diastole (ED), start systole (SS), end systole (ES) and start diastole (SD).</p>", "links"=>[], "tags"=>["homogeneity", "tdf"], "article_id"=>570491, "categories"=>["Medicine", "Biophysics"], "users"=>["Steven A. Niederer", "Nicolas P. Smith"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000371.g005", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Changes_in_951_and_stress_and_strain_homogeneity_in_the_absence_of_TDF_mechanisms_/570491", "title"=>"Changes in η and stress and strain homogeneity in the absence of TDF mechanisms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 06:07:48"}

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