- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-06-08 04:26:22+12:00
- Desc:
- Adding model to the workspace for the first time.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/maldonado_borchers_findeisen_allgower_2006/rawfile/44402e8c82fa7e8f2486ce932bdd7311a2fd365f/maldonado_2006.cellml
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<articleinfo>
<title>Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
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<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in both OpenCell and COR to recreate the published results (figure 2). Where parameters were not defined in the paper they were taken from <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/15234198">Lemaire et al. 2004</ulink>. A force of 10N was applied at day 100 and removed at day 130.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Bone is a dynamic living tissue that undergoes continuous adaptation of its mass and structure in response to mechanical and biological environment demands. Studies of bone adaptation have focused on metabolic or mechanical stimulus, but mathematical models of bone adaptation considering both, are not available by now. In this paper, we propose a mathematical model of bone adaptation during a remodeling cycle due to mechanical stimulus with the introduction of osteocytes as mechanotransducers. The model captures qualitatively very well the bone adaptation and cell interactions during the bone remodeling.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
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<title>model diagram</title>
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<caption>Schematic representation of interactions between osteoclasts and osteoblasts included in the model. Thick arrows represent the processes of formation and removal of osteoclasts and osteoblasts. Fine arrows represent the effects of autocrine and paracrine regulators of bone remodeling on the rates of osteoclast and osteoblast formation. TGF-beta, transforming growth factor beta, released and activated by resorbing osteoclasts, directly stimulates formation of osteoclasts and osteoblasts. IGF, insulin-like growth factors, secreted by osteoblasts and released by resorbing osteoclasts, activate osteoblast formation. RANKL, expressed on and released by osteoblasts, activates osteoclastogenesis. OPG, osteoprotegerin, released by osteoblasts, inhibits the actions of RANKL. </caption>
</informalfigure>
<para>
The original paper reference is cited below:
</para>
<para>
Mathematical modeling and analysis of force induced bone growth, Maldonado S, Borchers S, Findeisen R, Allgower F, 2006, <emphasis>Proceedings of the 28th IEEE EMBS Annual International Conference</emphasis>, 1, 3154-3157. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/17947010">PubMed ID: 17947010</ulink>
</para>
</sect1>
</article>
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<variable units="dimensionless" name="pi_c" public_interface="in"/>
<variable units="day" public_interface="in" name="time"/>
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<eq/>
<apply>
<diff/>
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<ci>time</ci>
</bvar>
<ci> xr </ci>
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<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> D_R </ci>
<ci> pi_c </ci>
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<apply>
<times/>
<ci> k_pger </ci>
<ci> x_pge </ci>
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</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> D_B </ci>
<ci> pi_c </ci>
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<ci> xr </ci>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#xb">
<dc:title>xb</dc:title>
<dcterms:alternative>osteoblast population</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="pM" public_interface="out" name="xb" initial_value="7.282e-4"/>
<variable units="first_order_rate_constant" name="k_B" initial_value="0.189"/>
<variable units="pM" public_interface="in" name="xr"/>
<variable units="first_order_rate_constant" public_interface="in" name="D_B"/>
<variable units="dimensionless" name="pi_c" public_interface="in"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> xb </ci>
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<apply>
<minus/>
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<times/>
<apply>
<divide/>
<ci> D_B </ci>
<ci> pi_c </ci>
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<ci> xr </ci>
</apply>
<apply>
<times/>
<ci> k_B </ci>
<ci> xb </ci>
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</apply>
</apply>
</math>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#xc">
<dc:title>xc</dc:title>
<dcterms:alternative>osteoclast population</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="pM" public_interface="out" name="xc" initial_value="9.127e-4"/>
<variable units="flux" name="D_C" initial_value="0.189"/>
<variable units="first_order_rate_constant" name="D_A" initial_value="0.7"/>
<variable units="dimensionless" name="pi_c" public_interface="in"/>
<variable units="dimensionless" name="pi_L" public_interface="in"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<ci> xc </ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> D_C </ci>
<ci> pi_L </ci>
</apply>
<apply>
<times/>
<ci> D_A </ci>
<ci> pi_c </ci>
<ci> xc </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable name="D_B" units="first_order_rate_constant" public_interface="out"/>
<variable name="pi_c" units="dimensionless" public_interface="out"/>
<variable name="pi_p" units="dimensionless" public_interface="out"/>
<variable units="picomole_per_day_picomole_cells" name="K_o_p" public_interface="out" initial_value="2e5"/>
<variable units="flux" name="Io" public_interface="out" initial_value="0.0"/>
<variable name="f0" units="dimensionless" initial_value="0.05"/>
<variable name="dB" units="first_order_rate_constant" initial_value="0.7"/>
<variable name="C_s" units="pM" initial_value="5e-3"/>
<variable name="P" units="pM"/>
<variable name="P_0" units="pM"/>
<variable name="P_s" units="pM"/>
<variable name="SP" units="flux" initial_value="250"/>
<variable name="k5" units="second_order_rate_constant" initial_value="0.02"/>
<variable name="k6" units="first_order_rate_constant" initial_value="3"/>
<variable name="IP" units="flux" initial_value="0"/>
<variable name="kP" units="first_order_rate_constant" initial_value="86"/>
<variable name="xc" units="pM" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>D_B</ci>
<apply>
<times/>
<ci>f0</ci>
<ci>dB</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>pi_c</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>xc</ci>
<apply>
<times/>
<ci>f0</ci>
<ci>C_s</ci>
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</apply>
<apply>
<plus/>
<ci>xc</ci>
<ci>C_s</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pi_p</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>P</ci>
<ci>P_0</ci>
</apply>
<apply>
<plus/>
<ci>P</ci>
<ci>P_s</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P</ci>
<apply>
<divide/>
<ci>IP</ci>
<ci>kP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_0</ci>
<apply>
<divide/>
<ci>SP</ci>
<ci>kP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_s</ci>
<apply>
<divide/>
<ci>k6</ci>
<ci>k5</ci>
</apply>
</apply>
</math>
</component>
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<map_components component_2="environment" component_1="r_B"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="xy"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="F_s"/>
<map_variables variable_2="time" variable_1="time"/>
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<connection>
<map_components component_2="environment" component_1="x_no"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="x_pge"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="x_opg"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="x_kl"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="xr"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="xb"/>
<map_variables variable_2="time" variable_1="time"/>
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<connection>
<map_components component_2="environment" component_1="xc"/>
<map_variables variable_2="time" variable_1="time"/>
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<connection>
<map_components component_2="A_B" component_1="r_B"/>
<map_variables variable_2="r_B" variable_1="r_B"/>
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<connection>
<map_components component_2="r_B" component_1="xc"/>
<map_variables variable_2="xc" variable_1="xc"/>
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<connection>
<map_components component_2="r_B" component_1="xb"/>
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<map_components component_2="r_B" component_1="xy"/>
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<map_components component_2="xy" component_1="xb"/>
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<map_components component_2="F_sti" component_1="F_s"/>
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<map_components component_2="F_s" component_1="A_B"/>
<map_variables variable_2="A_B" variable_1="A_B"/>
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<map_components component_2="x_no" component_1="F_sti"/>
<map_variables variable_2="F_sti" variable_1="F_sti"/>
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<map_components component_2="x_pge" component_1="F_sti"/>
<map_variables variable_2="F_sti" variable_1="F_sti"/>
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<map_components component_2="x_pge" component_1="x_no"/>
<map_variables variable_2="x_no" variable_1="x_no"/>
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<map_components component_2="x_opg" component_1="x_no"/>
<map_variables variable_2="x_no" variable_1="x_no"/>
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<map_components component_2="x_opg" component_1="xr"/>
<map_variables variable_2="xr" variable_1="xr"/>
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<connection>
<map_components component_2="x_opg" component_1="model_parameters"/>
<map_variables variable_2="K_o_p" variable_1="K_o_p"/>
<map_variables variable_2="pi_c" variable_1="pi_c"/>
<map_variables variable_2="Io" variable_1="Io"/>
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<map_components component_2="x_kl" component_1="x_no"/>
<map_variables variable_2="x_no" variable_1="x_no"/>
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<map_components component_2="x_kl" component_1="x_opg"/>
<map_variables variable_2="x_opg" variable_1="x_opg"/>
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<map_components component_2="x_kl" component_1="xb"/>
<map_variables variable_2="xb" variable_1="xb"/>
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<connection>
<map_components component_2="x_kl" component_1="xr"/>
<map_variables variable_2="xr" variable_1="xr"/>
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<connection>
<map_components component_2="x_kl" component_1="model_parameters"/>
<map_variables variable_2="K_o_p" variable_1="K_o_p"/>
<map_variables variable_2="pi_p" variable_1="pi_p"/>
<map_variables variable_2="Io" variable_1="Io"/>
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<connection>
<map_components component_2="xr" component_1="x_pge"/>
<map_variables variable_2="x_pge" variable_1="x_pge"/>
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<connection>
<map_components component_2="xr" component_1="model_parameters"/>
<map_variables variable_2="D_B" variable_1="D_B"/>
<map_variables variable_2="pi_c" variable_1="pi_c"/>
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<connection>
<map_components component_2="xb" component_1="xr"/>
<map_variables variable_2="xr" variable_1="xr"/>
</connection>
<connection>
<map_components component_2="xb" component_1="model_parameters"/>
<map_variables variable_2="D_B" variable_1="D_B"/>
<map_variables variable_2="pi_c" variable_1="pi_c"/>
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<connection>
<map_components component_2="xc" component_1="x_kl"/>
<map_variables variable_2="pi_L" variable_1="pi_L"/>
</connection>
<connection>
<map_components component_2="xc" component_1="model_parameters"/>
<map_variables variable_2="pi_c" variable_1="pi_c"/>
<map_variables variable_2="xc" variable_1="xc"/>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description rdf:about="">
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
</rdf:Description>
<rdf:Description rdf:about="#maldonado_2006">
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<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:li>osteoclast</rdf:li>
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<rdf:li>endocrine</rdf:li>
</rdf:Bag>
</rdf:value>
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</bqs:reference>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>17947010</bqs:Pubmed_id>
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<vCard:Family>Maldonado</vCard:Family>
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</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Borchers</vCard:Family>
<vCard:Given>S</vCard:Given>
</vCard:N>
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</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Findeisen</vCard:Family>
<vCard:Given>R</vCard:Given>
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</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Allgower</vCard:Family>
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</dc:creator>
<dc:title>
Mathematical modeling and analysis of force induced bone growth
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<dcterms:W3CDTF>2006</dcterms:W3CDTF>
</dcterms:issued>
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<dc:title>Proceedings of the 28th IEEE EMBS Annual International Conference</dc:title>
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<bqs:volume>1</bqs:volume>
<bqs:first_page>3154</bqs:first_page>
<bqs:last_page>3157</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
</model>
