- Author:
- Dewan Sarwar <dsar941@UoA.auckland.ac.nz>
- Date:
- 2019-11-18 23:20:03+13:00
- Desc:
- replace ':' with '='
- Permanent Source URI:
- https://models.cellml.org/workspace/267/rawfile/661b0b502cd840a9e3c0cb580652ba25d98e8963/Holmes_2006.cellml
<?xml version="1.0" encoding="UTF-8"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:semsim="http://www.bhi.washington.edu/SemSim#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="holmes_2006" cmeta:id="holmes_2006">
<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="mNpermmsq">
<unit exponent="-2.0" prefix="milli" units="metre" />
<unit prefix="milli" units="newton" />
</units>
<units name="pms">
<unit exponent="-1.0" prefix="milli" units="second" />
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second" />
</component>
<component name="contraction">
<variable cmeta:id="contraction.a" name="a" units="mNpermmsq" />
<variable cmeta:id="contraction.P" name="P" units="mNpermmsq" />
<variable cmeta:id="contraction.L" name="L" units="dimensionless" />
<variable cmeta:id="contraction_L_ce" name="L_ce" units="dimensionless" />
<variable cmeta:id="contraction_L_se" name="L_se" units="dimensionless" />
<variable cmeta:id="contraction.Po" name="Po" units="mNpermmsq" />
<variable cmeta:id="contraction.L_se_o" name="L_se_o" units="dimensionless" />
<variable cmeta:id="contraction.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="contraction.v" name="v" units="pms" />
<variable cmeta:id="contraction.alpha" name="alpha" units="mNpermmsq" />
<variable cmeta:id="contraction.b" name="b" units="pms" />
<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:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns="http://www.cellml.org/metadata/simulation/1.0#" xmlns:ro="http://www.obofoundry.org/ro/ro.owl#" xmlns:opb="http://bhi.washington.edu/OPB#">
<rdf:Description rdf:about="#contraction.L">
<dcterms:description>Fraction of muscle length</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.P">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_0">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_0">
<semsim:hasPhysicalDefinition rdf:resource="http://purl.obolibrary.org/obo/FMA_14069" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01097" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Steady-state force</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#environment_time">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01023" />
<dcterms:description>Time Domain</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction_L_se">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_2">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#entity_3">
<ro:part_of>
<rdf:Description rdf:about="#entity_2">
<semsim:hasPhysicalDefinition rdf:resource="http://purl.obolibrary.org/obo/FMA_67905" />
</rdf:Description>
</ro:part_of>
<semsim:hasPhysicalDefinition rdf:resource="http://purl.obolibrary.org/obo/FMA_20113" />
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01064" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Contribution of muscle elastic elements to fraction of muscle length</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.L_se_o">
<dcterms:description>Initial contribution of muscle elastic elements to fraction of muscle length</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.a">
<dcterms:description>Slope of the relationship between the change in muscle length and excess heat.</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.time">
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01023" />
<dcterms:description>Time Domain</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#Holmes_2006" semsim:modelId="holmes_2006" semsim:modelName="holmes_2006">
<semsim:AnnotatorName>Chris Thompson</semsim:AnnotatorName>
</rdf:Description>
<rdf:Description rdf:about="#contraction.v">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_3">
<semsim:physicalPropertyOf>
<rdf:Description rdf:about="#process_0">
<semsim:hasSinkParticipant>
<rdf:Description rdf:about="#sink_0" semsim:hasMultiplier="1.0">
<semsim:hasPhysicalEntityReference rdf:resource="#entity_3" />
</rdf:Description>
</semsim:hasSinkParticipant>
<semsim:hasSourceParticipant>
<rdf:Description rdf:about="#source_0" semsim:hasMultiplier="1.0">
<semsim:hasPhysicalEntityReference>
<rdf:Description rdf:about="#entity_1">
<ro:part_of rdf:resource="#entity_2" />
<semsim:hasPhysicalDefinition rdf:resource="http://purl.obolibrary.org/obo/FMA_260657" />
</rdf:Description>
</semsim:hasPhysicalEntityReference>
</rdf:Description>
</semsim:hasSourceParticipant>
<dcterms:description>Contraction of skeletal muscle</dcterms:description>
<semsim:name>Skeletal muscle contraction</semsim:name>
</rdf:Description>
</semsim:physicalPropertyOf>
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01658" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Shortening velocity</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.Po">
<dcterms:description>Maximal isometric tetanic force</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.alpha">
<dcterms:description>Spring constant for series elastic element</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction.b">
<dcterms:description>Slope excess energy rate and steady-state force relationship</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#contraction_L_ce">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_1">
<semsim:physicalPropertyOf rdf:resource="#entity_1" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01064" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Contribution of muscle contractile elements to fraction of muscle length</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#holmes_2006">
<simulation rdf:parseType="Resource">
<boundIntervals rdf:parseType="Resource">
<rdf:first rdf:parseType="Resource">
<maximumStepSize xml:lang="en">0.1</maximumStepSize>
<endingValue xml:lang="en">10</endingValue>
</rdf:first>
<rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#" />
</boundIntervals>
</simulation>
</rdf:Description>
<rdf:Description rdf:about="#Holmes_2006" semsim:modelName="Holmes_2006" semsim:unknown="Holmes_2006">
<ro:modelOf rdf:resource="http://purl.obolibrary.org/obo/CL_0000187" />
<ro:compartmentOf rdf:resource="http://purl.obolibrary.org/obo/FMA_67328" />
<ro:located_in rdf:resource="http://purl.obolibrary.org/obo/FMA_67328" />
<ro:compartmentOf rdf:resource="http://purl.obolibrary.org/obo/FMA_84669" />
<ro:located_in rdf:resource="http://purl.obolibrary.org/obo/FMA_84669" />
</rdf:Description>
</rdf:RDF>
</model>
