<?xml version="1.0"?>
<model xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" name="holmes_2006" cmeta:id="holmes_2006" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Teaching from classic papers: Hill's model of muscle contraction</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in both PCEnv and COR to reproduce the published results. The units have been checked and they are consistent.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: A. V. Hill's 1938 paper "The heat of shortening and the dynamic constants of muscle" is an enduring classic, presenting detailed methods, meticulous experiments, and the model of muscle contraction that now bears Hill's name. Pairing a simulation based on Hill's model with a reading of his paper allows students to follow his thought process to discover key principles of muscle physiology and gain insight into how to develop quantitative models of physiological processes. In this article, the experience of the author using this approach in a graduate biomedical engineering course is outlined, along with suggestions for adapting this approach to other audiences.
</para>
<para>
Teaching from classic papers: Hill's model of muscle contraction, J.W. Holmes, 2006,
<emphasis>Advances in Physiology Education</emphasis>, 30, 67-72. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/16709736">PubMed ID: 16709736</ulink>
</para>
<informalfigure float="0" id="diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram</title>
</objectinfo>
<imagedata fileref="holmes_2006.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the two component muscle model. Force in the muscle = F_SE = F_CE. By specifying Lm, Fm is calculated from the force velocity properties of CE and the force-length relationship of SE.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<units name="mNpermmsq">
<unit prefix="milli" units="newton"/>
<unit exponent="-2" prefix="milli" units="metre"/>
</units>
<units name="pms">
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="contraction">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="37.24" name="a" units="mNpermmsq"/>
<variable initial_value="0.325" name="b" units="pms"/>
<variable initial_value="144.9" name="Po" units="mNpermmsq"/>
<variable initial_value="1449.027" name="alpha" units="mNpermmsq"/>
<variable initial_value="0.3" name="L_se_o" units="dimensionless"/>
<variable name="L" units="dimensionless"/>
<variable name="v" units="pms"/>
<variable name="L_se" units="dimensionless"/>
<variable initial_value="0.7" name="L_ce" units="dimensionless"/>
<variable name="P" units="mNpermmsq"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>b</ci>
</apply>
<apply>
<minus/>
<ci>Po</ci>
<ci>P</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>P</ci>
<ci>a</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>L_se</ci>
<apply>
<minus/>
<ci>L</ci>
<ci>L_ce</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>L</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<leq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">1</cn>
</apply>
</piece>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.92</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">1</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">5</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.9</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>L_ce</ci>
</apply>
<ci>v</ci>
</apply>
<apply>
<eq/>
<ci>P</ci>
<apply>
<times/>
<ci>alpha</ci>
<apply>
<minus/>
<ci>L_se</ci>
<ci>L_se_o</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="contraction"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:nodeID="n1">
<rdf:first>
<rdf:Description rdf:nodeID="n2"/>
</rdf:first>
<rdf:rest>
<rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
</rdf:rest>
</rdf:Description>
<rdf:Description rdf:about="#holmes_2006">
<simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:nodeID="n3"/>
</simulation>
</rdf:Description>
<rdf:Description rdf:nodeID="n2">
<maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">0.1</maximumStepSize>
<endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">10</endingValue>
</rdf:Description>
<rdf:Description rdf:nodeID="n3">
<boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:nodeID="n1"/>
</boundIntervals>
</rdf:Description>
</rdf:RDF>
<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>Harrington</vCard:Family>
<vCard:Given>Paul</vCard:Given>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>paul.harrington@auckland@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>
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2009-12-09</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#holmes_2006">
<!-- Keyword(s) -->
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>mechanical constitutive laws</rdf:li>
<rdf:li>neuromuscular</rdf:li>
<rdf:li>muscular skeletal</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>16709736</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Holmes</vCard:Family>
<vCard:Given>J</vCard:Given>
<vCard:Other>W</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
Teaching from classic papers: Hill's model of muscle contraction
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>2006-06</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Advances in Physiology Education</dc:title>
</bqs:Journal>
<bqs:volume>30</bqs:volume>
<bqs:first_page>67</bqs:first_page>
<bqs:last_page>72</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
</model>