Rendering of the source text

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<article>
  <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>
</articleinfo>
<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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    <imagedata fileref="maldonado_2006.png"/>
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<caption>Schematic representation of the basic structure of the model.</caption>
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							<objectinfo>
								<title>model diagram</title>
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							<imagedata fileref="lemaire_2004_new.png"/>
						</imageobject>
					</mediaobject>
					<caption>Schematic diagram of the Lemaire et al. 2004 model of which the current model is an extension.</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>
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            <ci>time</ci>
          </bvar> 
          <ci> xr </ci> 
        </apply>
        <apply>
          <minus/>
		  <apply>
            <plus/>
			<apply>
              <times/>
			  <ci> D_R </ci>
			  <ci> pi_c </ci>
			</apply>
			<apply>
              <times/>
			  <ci> k_pger </ci>
			  <ci> x_pge </ci>
			</apply>
		  </apply>
		  <apply>
            <times/>
		    <apply>
              <divide/>
			  <ci> D_B </ci>
			  <ci> pi_c </ci>
			</apply>
			<ci> xr </ci>
	      </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="xb" name="xb">
      
    <variable cmeta:id="xb_xb" initial_value="7.282e-4" name="xb" public_interface="out" units="pM"/>
    
    <variable initial_value="0.189" name="k_B" units="first_order_rate_constant"/>
   
	<variable name="xr" public_interface="in" units="pM"/>
	<variable name="D_B" public_interface="in" units="first_order_rate_constant"/>
	<variable name="pi_c" public_interface="in" units="dimensionless"/>
	<variable name="time" public_interface="in" units="day"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> xb </ci> 
        </apply>
        <apply>
          <minus/>
		  <apply>
            <times/>
			<apply>
              <divide/>
			  <ci> D_B </ci>
			  <ci> pi_c </ci>
			</apply>
			<ci> xr </ci>
	      </apply>
	      <apply>
            <times/>
		    <ci> k_B </ci>
			<ci> xb </ci>
	      </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="xc" name="xc">
      
    <variable cmeta:id="xc_xc" initial_value="9.127e-4" name="xc" public_interface="out" units="pM"/>
    
    <variable initial_value="0.189" name="D_C" units="flux"/>
	<variable initial_value="0.7" name="D_A" units="first_order_rate_constant"/>
	
	<variable name="pi_c" public_interface="in" units="dimensionless"/>
	<variable name="pi_L" public_interface="in" units="dimensionless"/>
	<variable name="time" public_interface="in" units="day"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> xc </ci> 
        </apply>
        <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" public_interface="out" units="first_order_rate_constant"/>
      <variable name="pi_c" public_interface="out" units="dimensionless"/>
      <variable name="pi_p" public_interface="out" units="dimensionless"/>
      <variable initial_value="2e5" name="K_o_p" public_interface="out" units="picomole_per_day_picomole_cells"/>
	  <variable initial_value="0.0" name="Io" public_interface="out" units="flux"/>
	  
	  <variable initial_value="0.05" name="f0" units="dimensionless"/>
      <variable initial_value="0.7" name="dB" units="first_order_rate_constant"/>
      <variable initial_value="5e-3" name="C_s" units="pM"/>
      <variable name="P" units="pM"/>
      <variable name="P_0" units="pM"/>
      <variable name="P_s" units="pM"/>
      <variable initial_value="250" name="SP" units="flux"/>
      <variable initial_value="0.02" name="k5" units="second_order_rate_constant"/>
      <variable initial_value="3" name="k6" units="first_order_rate_constant"/>
      <variable initial_value="0" name="IP" units="flux"/>
      <variable initial_value="86" name="kP" units="first_order_rate_constant"/>
      
	  <variable name="xc" public_interface="in" units="pM"/>
      
	  <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>
                  </apply>
               </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>

  
  <connection>
    <map_components component_1="r_B" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="xy" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="F_s" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="x_no" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="x_pge" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="x_opg" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="x_kl" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="xr" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="xb" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="xc" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="r_B" component_2="A_B"/>
    <map_variables variable_1="r_B" variable_2="r_B"/>
  </connection>

  <connection>
    <map_components component_1="xc" component_2="r_B"/>
    <map_variables variable_1="xc" variable_2="xc"/>
  </connection>
  
  <connection>
    <map_components component_1="xb" component_2="r_B"/>
    <map_variables variable_1="xb" variable_2="xb"/>
  </connection>
  
  <connection>
    <map_components component_1="xy" component_2="r_B"/>
    <map_variables variable_1="xy" variable_2="xy"/>
  </connection>
  
  <connection>
    <map_components component_1="xb" component_2="xy"/>
    <map_variables variable_1="xb" variable_2="xb"/>
  </connection>
  
  <connection>
    <map_components component_1="xy" component_2="F_sti"/>
    <map_variables variable_1="xy" variable_2="xy"/>
  </connection>
  
  <connection>
    <map_components component_1="F_s" component_2="F_sti"/>
    <map_variables variable_1="F_s" variable_2="F_s"/>
  </connection>
  
  <connection>
    <map_components component_1="A_B" component_2="F_s"/>
    <map_variables variable_1="A_B" variable_2="A_B"/>
  </connection>
  
  <connection>
    <map_components component_1="F_sti" component_2="x_no"/>
    <map_variables variable_1="F_sti" variable_2="F_sti"/>
  </connection>
  
  <connection>
    <map_components component_1="F_sti" component_2="x_pge"/>
    <map_variables variable_1="F_sti" variable_2="F_sti"/>
  </connection>
  
  <connection>
    <map_components component_1="x_no" component_2="x_pge"/>
    <map_variables variable_1="x_no" variable_2="x_no"/>
  </connection>
  
  <connection>
    <map_components component_1="x_no" component_2="x_opg"/>
    <map_variables variable_1="x_no" variable_2="x_no"/>
  </connection>
  
  <connection>
    <map_components component_1="xr" component_2="x_opg"/>
    <map_variables variable_1="xr" variable_2="xr"/>
  </connection>
  
  <connection>
    <map_components component_1="model_parameters" component_2="x_opg"/>
    <map_variables variable_1="K_o_p" variable_2="K_o_p"/>
    <map_variables variable_1="pi_c" variable_2="pi_c"/>
	<map_variables variable_1="Io" variable_2="Io"/>
  </connection>
  
  <connection>
    <map_components component_1="x_no" component_2="x_kl"/>
    <map_variables variable_1="x_no" variable_2="x_no"/>
  </connection>
  
  <connection>
    <map_components component_1="x_opg" component_2="x_kl"/>
    <map_variables variable_1="x_opg" variable_2="x_opg"/>
  </connection>
  
  <connection>
    <map_components component_1="xb" component_2="x_kl"/>
    <map_variables variable_1="xb" variable_2="xb"/>
  </connection>
  
  <connection>
    <map_components component_1="xr" component_2="x_kl"/>
    <map_variables variable_1="xr" variable_2="xr"/>
  </connection>
  
  <connection>
    <map_components component_1="model_parameters" component_2="x_kl"/>
    <map_variables variable_1="K_o_p" variable_2="K_o_p"/>
    <map_variables variable_1="pi_p" variable_2="pi_p"/>
	<map_variables variable_1="Io" variable_2="Io"/>
  </connection>
  
  <connection>
    <map_components component_1="x_pge" component_2="xr"/>
    <map_variables variable_1="x_pge" variable_2="x_pge"/>
  </connection>
  
  <connection>
    <map_components component_1="model_parameters" component_2="xr"/>
    <map_variables variable_1="D_B" variable_2="D_B"/>
    <map_variables variable_1="pi_c" variable_2="pi_c"/>
  </connection>
  
  <connection>
    <map_components component_1="xr" component_2="xb"/>
    <map_variables variable_1="xr" variable_2="xr"/>
  </connection>
  
  <connection>
    <map_components component_1="model_parameters" component_2="xb"/>
    <map_variables variable_1="D_B" variable_2="D_B"/>
    <map_variables variable_1="pi_c" variable_2="pi_c"/>
  </connection>
  
  <connection>
    <map_components component_1="x_kl" component_2="xc"/>
    <map_variables variable_1="pi_L" variable_2="pi_L"/>
  </connection>
  
  <connection>
    <map_components component_1="model_parameters" component_2="xc"/>
    <map_variables variable_1="pi_c" variable_2="pi_c"/>
	<map_variables variable_1="xc" variable_2="xc"/>
  </connection>
  
  
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:nodeID="n1"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n2"/></subject></rdf:Description><rdf:Description rdf:nodeID="n3"><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type><rdf:value xml:lang="en">c.lloyd@auckland.ac.nz</rdf:value></rdf:Description><rdf:Description rdf:nodeID="n4"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n5"/></boundIntervals></rdf:Description><rdf:Description rdf:about="#r_B"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">r_B</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">bone radius</alternative></rdf:Description><rdf:Description rdf:nodeID="n6"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n7"/></N></rdf:Description><rdf:Description rdf:nodeID="n8"><N 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xml:lang="en">endocrine</rdf:_4><rdf:_2 xml:lang="en">osteoblast</rdf:_2><rdf:_3 xml:lang="en">bone</rdf:_3><rdf:_1 xml:lang="en">osteoclast</rdf:_1></rdf:Description><rdf:Description rdf:about="#xb"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">xb</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">osteoblast population</alternative></rdf:Description><rdf:Description rdf:about="#x_pge"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">x_pge</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">PGE2 concentration</alternative></rdf:Description><rdf:Description rdf:nodeID="n13"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n6"/></Person></rdf:Description><rdf:Description rdf:nodeID="n7"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">F</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Allgower</Family></rdf:Description><rdf:Description 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rdf:nodeID="n17"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n14"/></N></rdf:Description><rdf:Description rdf:about="#x_no"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">x_no</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">nitric oxide concentration</alternative></rdf:Description><rdf:Description rdf:nodeID="n5"><rdf:first><rdf:Description rdf:nodeID="n18"/></rdf:first><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest></rdf:Description><rdf:Description rdf:about="#x_opg"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">x_opg</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">OPG concentration</alternative></rdf:Description><rdf:Description rdf:about="#A_B"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">A_B</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">circular area of the bone</alternative></rdf:Description><rdf:Description rdf:nodeID="n18"><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">150</endingValue><maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">10</maximumStepSize><pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">100000</pointDensity></rdf:Description><rdf:Description rdf:nodeID="n19"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
            Mathematical modeling and analysis of force induced bone growth
          </title><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n20"/></issued><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">1</volume><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n21"/></Journal><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">3154</first_page><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">3157</last_page><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n22"/></creator></rdf:Description><rdf:Description rdf:nodeID="n21"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Proceedings of the 28th IEEE EMBS Annual International Conference</title></rdf:Description><rdf:Description rdf:nodeID="n23"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n24"/></N></rdf:Description><rdf:Description rdf:nodeID="n2"><rdf:value><rdf:Description rdf:nodeID="n12"/></rdf:value><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n25"/></creator></rdf:Description><rdf:Description rdf:nodeID="n11"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">17947010</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n19"/></JournalArticle></rdf:Description><rdf:Description rdf:about="#xc"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">xc</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">osteoclast population</alternative></rdf:Description><rdf:Description rdf:nodeID="n26"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n23"/></Person></rdf:Description><rdf:Description rdf:about="#x_kl"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">x_kl</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">RANKL concentration</alternative></rdf:Description><rdf:Description rdf:nodeID="n20"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2006</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n22"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type><rdf:_4><rdf:Description rdf:nodeID="n13"/></rdf:_4><rdf:_2><rdf:Description rdf:nodeID="n27"/></rdf:_2><rdf:_3><rdf:Description rdf:nodeID="n10"/></rdf:_3><rdf:_1><rdf:Description rdf:nodeID="n26"/></rdf:_1></rdf:Description><rdf:Description rdf:nodeID="n24"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">S</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Maldonado</Family></rdf:Description><rdf:Description rdf:about="#xr"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">xr</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">responding osteoblast population</alternative></rdf:Description><rdf:Description rdf:about="#xy"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">xy</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">osteocyte population</alternative></rdf:Description><rdf:Description rdf:nodeID="n27"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n17"/></Person></rdf:Description><rdf:Description rdf:nodeID="n9"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">R</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Findeisen</Family></rdf:Description><rdf:Description rdf:nodeID="n25"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n15"/></N><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n3"/></EMAIL><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n16"/></ORG></rdf:Description></rdf:RDF></model>