MOSAIC: A Multiscale Model of Osteogenesis and Sprouting Angiogenesis with Lateral Inhibition of Endothelial Cells
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{"title"=>"MOSAIC: A Multiscale Model of Osteogenesis and Sprouting Angiogenesis with Lateral Inhibition of Endothelial Cells", "type"=>"journal", "authors"=>[{"first_name"=>"Aurélie", "last_name"=>"Carlier", "scopus_author_id"=>"55106871900"}, {"first_name"=>"Liesbet", "last_name"=>"Geris", "scopus_author_id"=>"55901639500"}, {"first_name"=>"Katie", "last_name"=>"Bentley", "scopus_author_id"=>"23007907100"}, {"first_name"=>"Geert", "last_name"=>"Carmeliet", "scopus_author_id"=>"7003279012"}, {"first_name"=>"Peter", "last_name"=>"Carmeliet", "scopus_author_id"=>"7101979069"}, {"first_name"=>"Hans", "last_name"=>"van Oosterwyck", "scopus_author_id"=>"6602135384"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "issn"=>"1553734X", "pui"=>"365953612", "pmid"=>"23071433", "doi"=>"10.1371/journal.pcbi.1002724", "sgr"=>"84868143949", "scopus"=>"2-s2.0-84868143949"}, "id"=>"64f656a1-fd1c-3a3e-bcd7-07c2a87e492b", "abstract"=>"The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel multiscale model of osteogenesis and sprouting angiogenesis, incorporating lateral inhibition of endothelial cells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.", "link"=>"http://www.mendeley.com/research/mosaic-multiscale-model-osteogenesis-sprouting-angiogenesis-lateral-inhibition-endothelial-cells", "reader_count"=>60, "reader_count_by_academic_status"=>{"Unspecified"=>4, "Professor > Associate Professor"=>5, "Researcher"=>16, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>18, "Student > Postgraduate"=>2, "Student > Master"=>7, "Other"=>1, "Student > Bachelor"=>2, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>4, "Professor > Associate Professor"=>5, "Researcher"=>16, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>18, "Student > Postgraduate"=>2, "Student > Master"=>7, "Other"=>1, "Student > Bachelor"=>2, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>24, "Unspecified"=>4, "Biochemistry, Genetics and Molecular Biology"=>2, "Materials Science"=>1, "Agricultural and Biological Sciences"=>19, "Medicine and Dentistry"=>1, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>2, "Chemistry"=>2, "Computer Science"=>4}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>24}, "Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Chemistry"=>{"Chemistry"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>19}, "Computer Science"=>{"Computer Science"=>4}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>2}, "Unspecified"=>{"Unspecified"=>4}}, "reader_count_by_country"=>{"United States"=>3, "Australia"=>2, "Switzerland"=>1, "Portugal"=>2}, "group_count"=>4}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/296741"], "description"=>"<div><p>The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel <u>m</u>ultiscale model of <u>o</u>steogenesis and <u>s</u>prouting <u>a</u>ngiogenesis, incorporating lateral <u>i</u>nhibition of endothelial <u>c</u>ells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.</p> </div>", "links"=>[], "tags"=>["multiscale", "osteogenesis", "sprouting", "angiogenesis", "lateral", "inhibition", "endothelial", "cells"], "article_id"=>118477, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724", "stats"=>{"downloads"=>1, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/MOSAIC_A_Multiscale_Model_of_Osteogenesis_and_Sprouting_Angiogenesis_with_Lateral_Inhibition_of_Endothelial_Cells/118477", "title"=>"MOSAIC: A Multiscale Model of Osteogenesis and Sprouting Angiogenesis with Lateral Inhibition of Endothelial Cells", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-10-11 02:21:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/562945"], "description"=>"<p>Temporal evolution of the bone, cartilage and fibrous tissue fractions (%) in the periosteal, intercortical and endosteal callus as predicted by the MOSAIC model. (full: normal fracture healing; dashed: Dll4 overexpression (δ = 12.64, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi-1002724-g005\" target=\"_blank\">Figure 5A</a>); dotted: VEGF-addition (+ 0.1%, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi-1002724-g007\" target=\"_blank\">Figure 7Bii</a>).</p>", "links"=>[], "tags"=>["silico", "fracture", "healing"], "article_id"=>233438, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g008", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_In_silico_evolution_of_fracture_healing_for_various_conditions_/233438", "title"=>"In silico evolution of fracture healing for various conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/562237"], "description"=>"<p>(left) Geometrical domain deduced from the real callus geometry at postfracture week 3 <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Harrison1\" target=\"_blank\">[35]</a>; 1 periosteal callus; 2 intercortical callus; 3 endosteal callus; 4 cortical bone. (right) Boundary conditions. The mesenchymal stem cells (<i>c<sub>m</sub></i>) and fibroblasts (<i>c<sub>f</sub></i>) are released from the periosteum, the surrounding soft tissues and the bone marrow <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Gerstenfeld1\" target=\"_blank\">[64]</a>. The chondrogenic growth factors (<i>g<sub>c</sub></i>) are released from the degrading bone ends <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Barnes1\" target=\"_blank\">[65]</a> whereas the cortex is modeled to be the source of osteogenic growth factors (<i>g<sub>b</sub></i>) <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Dimitriou1\" target=\"_blank\">[66]</a>. <i>c<sub>v</sub></i> indicates the initial position of the ECs.</p>", "links"=>[], "tags"=>["genetics and genomics", "physiology", "Computational biology", "biotechnology"], "article_id"=>232726, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g003", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Geometrical_domain_and_boundary_conditions_/232726", "title"=>"Geometrical domain and boundary conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:45:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/563149"], "description"=>"<p>(A) standard condition; (B) addition of 2% VEGF.</p>", "links"=>[], "tags"=>["vegfr-2", "receptors", "endothelial"], "article_id"=>233645, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g009", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Amount_of_VEGFR_2_receptors_on_every_endothelial_cell_/233645", "title"=>"Amount of VEGFR-2 receptors on every endothelial cell.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 01:00:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/561992"], "description"=>"<p>(A) Scale separation map indicating schematically the modeled processes at different spatial and temporal scales. Intracellular variables are further explained in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi-1002724-t001\" target=\"_blank\">Table 1</a> and govern endothelial cell (EC) behavior. Cell types that are considered at the tissue scale (MSCs: mesenchymal stem cells, CHs: chondrocytes, OBs: osteoblasts, FBs: fibroblasts) can migrate (only MSCs and FBs), proliferate (circular arrows), differentiate (vertical arrows) and produce growth factors (<i>gb</i>: osteogenic growth factor concentration, <i>gc</i>: chondrogenic growth factor concentration, <i>gv</i>: angiogenic growth factor concentration) and extracellular matrix (<i>mf</i>: fibrous tissue density, <i>mb</i>: bone density, <i>mc</i>: cartilage density, <i>m</i>: total tissue density). Blood vessels serve as an oxygen source (<i>n</i>: oxygen concentration). Variables next to an arrow indicate their mediating role for a certain tissue level process. (B) Flowchart of the numerical implementation of the MOSAIC model (: vector of the continuous variables, <i>t</i>: time, <i>δt</i>: time step of the inner loop, <i>Δt</i>: time step of the outer loop, <i>c<sub>v</sub></i>: endothelial cells).</p>", "links"=>[], "tags"=>["overview", "multiscale", "flowchart", "numerical"], "article_id"=>232481, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g001", "stats"=>{"downloads"=>4, "page_views"=>68, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_overview_of_the_multiscale_model_and_a_flowchart_of_its_numerical_implementation_/232481", "title"=>"Schematic overview of the multiscale model and a flowchart of its numerical implementation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:41:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/562639"], "description"=>"<p>Evolution of the average VEGFR-2 concentration (day 0 corresponds to the time of fracture). The threshold line represents the first requirement that needs to be fulfilled to obtain the tip cell phenotype, i.e. V>V<sub>max</sub>/2. Remark that in very high VEGF concentrations (+10%) the average receptor concentration is far below the threshold.</p>", "links"=>[], "tags"=>["vegfr-2", "ecs", "callus", "levels", "vegf"], "article_id"=>233127, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g006", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Temporal_evolution_of_the_average_amount_of_VEGFR_2_on_ECs_in_the_callus_for_different_levels_of_VEGF_addition_corresponding_to_Figure_7B_/233127", "title"=>"Temporal evolution of the average amount of VEGFR-2 on ECs in the callus for different levels of VEGF addition (corresponding to <b>Figure 7B</b>).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:52:07"}
  • {"files"=>["https://ndownloader.figshare.com/files/562132"], "description"=>"<p>The dark grey ECs represent the original branch whereas Ti and Si are part of a newly formed sprout (T = tip cell, S = stalk cell). The amount of Dll4 was arbitrarily chosen, a maximal amount of 25 000 ligands per EC (for an EC with a length of 25 µm) was calculated by Bentley et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Bentley1\" target=\"_blank\">[3]</a>, estimated from Liu et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Liu2\" target=\"_blank\">[63]</a>.</p>", "links"=>[], "tags"=>["dll4", "membranes", "endothelial"], "article_id"=>232623, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g002", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Conceptual_representation_of_the_Dll4_distribution_across_the_cell_membranes_of_endothelial_cells_/232623", "title"=>"Conceptual representation of the Dll4 distribution across the cell membranes of endothelial cells.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:43:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/562557"], "description"=>"<p>The figure is focused on the periosteal callus (area 1 in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi-1002724-g003\" target=\"_blank\">Figure 3</a>). Remark that the tip cells have a lot of VEGFR-2 (dark brown) whereas the following stalk cells are inhibited, giving rise to a low number of VEGFR-2 (dark blue). (A) Influence of Dll4 levels. (B) Influence of Notch1 activity levels. Left: heterozygous knockout, middle: standard condition, right: overexpression.</p>", "links"=>[], "tags"=>["vegfr-2", "ec", "dll4", "notch", "levels", "fracture"], "article_id"=>233040, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g005", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Image_of_the_amount_of_VEGFR_2_per_EC_for_different_Dll4_expression_and_Notch_activity_levels_at_post_fracture_day_19_/233040", "title"=>"Image of the amount of VEGFR-2 per EC for different Dll4 expression and Notch activity levels at post fracture day 19.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:50:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/563306"], "description"=>"<p>Initial values of EC state variables.</p>", "links"=>[], "tags"=>["ec"], "article_id"=>233803, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.t002", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Initial_values_of_EC_state_variables_/233803", "title"=>"Initial values of EC state variables.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-10-11 01:03:23"}
  • {"files"=>["https://ndownloader.figshare.com/files/562818"], "description"=>"<p>(A) Variation in the amount of the decoy receptor VEGFR-1 (i: <i>V<sub>sink</sub></i> = 100% (standard condition), ii: <i>V<sub>sink</sub></i> = 45%, iii: <i>V<sub>sink</sub></i> = 9%, iv: <i>V<sub>sink</sub></i> = 0.9%); (B) Variation in the amount of VEGF addition in the multiscale model with the standard tip cell selection criterion (based on V; <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724.e017\" target=\"_blank\">Equation 6</a>) (i: 0% (standard condition), ii: 0.1%, iii: 2%, iv: 10%); (C) Variation in the amount of VEGF addition in the multiscale model with an altered tip cell selection criterion (based on V′) (i: 0%, ii: 0.1%, iii: 2%, iv: 10%); (D) Variation in the amount of VEGF addition in the hybrid model (i: 0%, ii: 0.1%, iii: 2%, iv: 10%).</p>", "links"=>[], "tags"=>["35", "days", "fracture"], "article_id"=>233308, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g007", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Vasculature_at_35_days_post_fracture_for_different_conditions_/233308", "title"=>"Vasculature at 35 days post fracture for different conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:55:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/563344"], "description"=>"<p>The vascular density is measured at three time points post fracture (7, 21 and 35 days). In the standard condition the parameter values are <i>σ</i> = 47.4, <i>δ</i> = 6.32, <i>V<sub>sink</sub></i> = 0.275, <i>V′*</i> = 200, <i>A<sub>0</sub></i> = 5000, <i>D<sub>0</sub></i> = 0, which can also be found in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi-1002724-t001\" target=\"_blank\">Tables 1</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi-1002724-t002\" target=\"_blank\">2</a>.</p>", "links"=>[], "tags"=>["genetics and genomics", "physiology", "Computational biology", "biotechnology"], "article_id"=>233834, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.t003", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Overview_of_the_results_of_the_sensitivity_analysis_/233834", "title"=>"Overview of the results of the sensitivity analysis.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-10-11 01:03:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/562331"], "description"=>"<p>Temporal evolution of the bone, cartilage and fibrous tissue fractions (%) in the periosteal, intercortical and endosteal callus as predicted using the hybrid model of Peiffer et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Peiffer1\" target=\"_blank\">[18]</a> and the newly developed multiscale model and as measured by Harrison et al. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724-Harrison1\" target=\"_blank\">[35]</a>.</p>", "links"=>[], "tags"=>["silico", "fracture"], "article_id"=>232822, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g004", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_In_silico_and_in_vivo_evolution_of_normal_fracture_healing_/232822", "title"=>"<i>In silico and in vivo</i> evolution of normal fracture healing.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 00:47:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/563375"], "description"=>"<p>Parameter values of EC state variables.</p>", "links"=>[], "tags"=>["ec"], "article_id"=>233871, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.t001", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameter_values_of_EC_state_variables_/233871", "title"=>"Parameter values of EC state variables.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-10-11 01:04:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/563240"], "description"=>"<p>Remark that although the VEGFR-2 receptor is down-regulated, the VEGF concentration is high enough to compensate for this effect resulting in high <i>V′</i> levels (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002724#pcbi.1002724.e002\" target=\"_blank\">Equation 1</a>).</p>", "links"=>[], "tags"=>["dll4-notch", "pathway", "vegf", "environments"], "article_id"=>233729, "categories"=>["Biotechnology", "Biological Sciences", "Physiology", "Genetics"], "users"=>["Aurélie Carlier", "Liesbet Geris", "Katie Bentley", "Geert Carmeliet", "Peter Carmeliet", "Hans Van Oosterwyck"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002724.g010", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_representation_of_the_Dll4_Notch_pathway_in_high_VEGF_environments_for_two_neighboring_ECs_/233729", "title"=>"Schematic representation of the Dll4-Notch pathway in high VEGF environments for two neighboring ECs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-11 01:02:09"}

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Relative Metric

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